News <2007>

December 2007

Dec 31, 2007

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(2·10¹⁶⁶+7)/9 = (2)₁₆₅3_<166> = 3² · 13 · 19 · 2203 · 92591638837_<11> · C148

C148 = P62 · P87

P62 = 10579117484643669985321526488483937482639067300717328050482541_<62>

P87 = 463246679702034732206614919683068341832261226156838899536755186335885948793861377955651_<87>

Number: n
N=4900741048938921529386312376049753422014062526470395527666102273448608728036064841441443726000645540939103525055300397035584580148478781490647789191
  ( 148 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Dec 31 10:05:46 2007  prp62 factor: 10579117484643669985321526488483937482639067300717328050482541
Mon Dec 31 10:05:46 2007  prp87 factor: 463246679702034732206614919683068341832261226156838899536755186335885948793861377955651
Mon Dec 31 10:05:46 2007  elapsed time 01:19:50 (Msieve 1.32)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 48.46 hours.
Scaled time: 63.48 units (timescale=1.310).
Factorization parameters were as follows:
name: KA_2_165_3
n: 4900741048938921529386312376049753422014062526470395527666102273448608728036064841441443726000645540939103525055300397035584580148478781490647789191
skew: 0.81
deg: 5
c5: 20
c0: 7
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2200000)
Primes: RFBsize:230209, AFBsize:229397, largePrimes:7279611 encountered
Relations: rels:6773272, finalFF:518245
Max relations in full relation-set: 28
Initial matrix: 459672 x 518245 with sparse part having weight 38557490.
Pruned matrix : 415223 x 417585 with weight 27293794.
Total sieving time: 45.28 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 48.46 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁵⁴-9 = 6(9)₁₅₃1_<155> = 24187568437147_<14> · 357505542381274647193_<21> · C121

C121 = P35 · P86

P35 = 87307807817705591131142443529365687_<35>

P86 = 92719261960991305708767306625668063796197431975684064005420378748486361040936361668683_<86>

7·10¹⁶⁵-9 = 6(9)₁₆₄1_<166> = 449 · 96293 · 193732283 · C150

C150 = P60 · P91

P60 = 119720935477183205712026361015748167111027951799849560997421_<60>

P91 = 6980473515066820668028752248342210383473908035017528053560574089914810233581451339796380341_<91>

Number: n
N=835708819297501087161209256684919312616575197394475766671782482860339428847159691345411763978143923133144396640238950619922829764501373132545436100561
  ( 150 digits)
SNFS difficulty: 165 digits.
Divisors found:

Mon Dec 31 23:17:09 2007  prp60 factor: 119720935477183205712026361015748167111027951799849560997421
Mon Dec 31 23:17:09 2007  prp91 factor: 6980473515066820668028752248342210383473908035017528053560574089914810233581451339796380341
Mon Dec 31 23:17:09 2007  elapsed time 02:16:22 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 58.35 hours.
Scaled time: 102.75 units (timescale=1.761).
Factorization parameters were as follows:
name: KA_6_9_164_1
n: 835708819297501087161209256684919312616575197394475766671782482860339428847159691345411763978143923133144396640238950619922829764501373132545436100561
type: snfs
skew: 1.05
deg: 5
c5: 7
c0: -9
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2800001)
Primes: RFBsize:230209, AFBsize:230717, largePrimes:7456900 encountered
Relations: rels:6921697, finalFF:489538
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 58.10 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 58.35 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(7·10¹⁶⁴-61)/9 = (7)₁₆₃1_<164> = 67 · 16943 · 608743 · 4855817 · 723493411 · 103466618887166809_<18> · C120

C120 = P39 · P40 · P43

P39 = 200987859740178940829671987628842189511_<39>

P40 = 1524315768672965057529391990531835488823_<40>

P43 = 1010681974438265260089808346426272470700763_<43>

Tue Jan 01 00:33:37 2008  
Tue Jan 01 00:33:37 2008  
Tue Jan 01 00:33:37 2008  Msieve v. 1.32
Tue Jan 01 00:33:37 2008  random seeds: 670f8060 b722816b
Tue Jan 01 00:33:37 2008  factoring 203134806920325175654885525513483664774580080235041609363980893235812401418296893 (81 digits)
Tue Jan 01 00:33:37 2008  searching for 15-digit factors
Tue Jan 01 00:33:38 2008  commencing quadratic sieve (80-digit input)
Tue Jan 01 00:33:38 2008  using multiplier of 5
Tue Jan 01 00:33:38 2008  using 64kb Opteron sieve core
Tue Jan 01 00:33:38 2008  sieve interval: 6 blocks of size 65536
Tue Jan 01 00:33:38 2008  processing polynomials in batches of 17
Tue Jan 01 00:33:38 2008  using a sieve bound of 1305691 (50294 primes)
Tue Jan 01 00:33:38 2008  using large prime bound of 129263409 (26 bits)
Tue Jan 01 00:33:38 2008  using trial factoring cutoff of 27 bits
Tue Jan 01 00:33:38 2008  polynomial 'A' values have 10 factors
Tue Jan 01 00:51:33 2008  50454 relations (25765 full + 24689 combined from 273397 partial), need 50390
Tue Jan 01 00:51:34 2008  begin with 299162 relations
Tue Jan 01 00:51:34 2008  reduce to 72049 relations in 2 passes
Tue Jan 01 00:51:34 2008  attempting to read 72049 relations
Tue Jan 01 00:51:35 2008  recovered 72049 relations
Tue Jan 01 00:51:35 2008  recovered 62785 polynomials
Tue Jan 01 00:51:35 2008  attempting to build 50454 cycles
Tue Jan 01 00:51:35 2008  found 50454 cycles in 1 passes
Tue Jan 01 00:51:35 2008  distribution of cycle lengths:
Tue Jan 01 00:51:35 2008     length 1 : 25765
Tue Jan 01 00:51:35 2008     length 2 : 24689
Tue Jan 01 00:51:35 2008  largest cycle: 2 relations
Tue Jan 01 00:51:35 2008  matrix is 50294 x 50454 with weight 1538986 (avg 30.50/col)
Tue Jan 01 00:51:35 2008  filtering completed in 4 passes
Tue Jan 01 00:51:35 2008  matrix is 42992 x 43056 with weight 1286275 (avg 29.87/col)
Tue Jan 01 00:51:35 2008  saving the first 48 matrix rows for later
Tue Jan 01 00:51:35 2008  matrix is 42944 x 43056 with weight 1002106 (avg 23.27/col)
Tue Jan 01 00:51:35 2008  matrix includes 64 packed rows
Tue Jan 01 00:51:35 2008  commencing Lanczos iteration
Tue Jan 01 00:52:18 2008  lanczos halted after 680 iterations (dim = 42920)
Tue Jan 01 00:52:18 2008  recovered 6 nontrivial dependencies
Tue Jan 01 00:52:18 2008  prp39 factor: 200987859740178940829671987628842189511
Tue Jan 01 00:52:18 2008  prp43 factor: 1010681974438265260089808346426272470700763
Tue Jan 01 00:52:18 2008  elapsed time 00:18:41

Dec 30, 2007 (2nd)

By Sinkiti Sibata / PFGW

(2·10²⁴⁴²+7)/9 is prime.

Dec 30, 2007

By Robert Backstrom / GGNFS, Msieve

(28·10¹⁶³+17)/9 = 3(1)₁₆₂3_<164> = 3 · 11 · 113 · 5227723 · 5474506657_<10> · C144

C144 = P54 · P90

P54 = 568254104215421080733918790780653788490645701320935561_<54>

P90 = 513006657969163357232705769402175646798527021065255936378677850134407454699737691808031507_<90>

Number: n
N=291518138880813831877316139677912045506082513260025572748734915030214053671271873482644565087545343430540161717571420952814494855357103004720427
  ( 144 digits)
SNFS difficulty: 164 digits.
Divisors found:

Sun Dec 30 22:22:57 2007  prp54 factor: 568254104215421080733918790780653788490645701320935561
Sun Dec 30 22:22:57 2007  prp90 factor: 513006657969163357232705769402175646798527021065255936378677850134407454699737691808031507
Sun Dec 30 22:22:57 2007  elapsed time 00:55:31 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.78 hours.
Scaled time: 54.81 units (timescale=1.532).
Factorization parameters were as follows:
name: KA_3_1_162_3
n: 291518138880813831877316139677912045506082513260025572748734915030214053671271873482644565087545343430540161717571420952814494855357103004720427
skew: 0.45
deg: 5
c5: 875
c0: 17
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2600000)
Primes: RFBsize:216816, AFBsize:216531, largePrimes:7351213 encountered
Relations: rels:6806772, finalFF:496921
Max relations in full relation-set: 28
Initial matrix: 433413 x 496921 with sparse part having weight 48938966.
Pruned matrix : 
Total sieving time: 35.60 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 35.78 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(89·10¹⁶¹+1)/9 = 9(8)₁₆₀9_<162> = 11 · 151 · 54497 · 4734857424467_<13> · 29333719355391524558753_<23> · C119

C119 = P50 · P70

P50 = 24068764486818214538179925119843116225195355366201_<50>

P70 = 3267965275130364758731306727795381662655553549388276194815369559709367_<70>

Number: n
N=78655886558212839023556857120942142003924560409165078599494695301264178096244478079634342453626033940099746525414904767
  ( 119 digits)
SNFS difficulty: 162 digits.
Divisors found:

Sun Dec 30 22:54:11 2007  prp50 factor: 24068764486818214538179925119843116225195355366201
Sun Dec 30 22:54:11 2007  prp70 factor: 3267965275130364758731306727795381662655553549388276194815369559709367
Sun Dec 30 22:54:11 2007  elapsed time 01:13:42 (Msieve 1.32)

Version: GGNFS-0.77.1-20050930-k8
Total time: 37.56 hours.
Scaled time: 31.47 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_9_8_160_9
n: 78655886558212839023556857120942142003924560409165078599494695301264178096244478079634342453626033940099746525414904767
type: snfs
deg: 5
c5: 890
c0: 1
skew: 0.22
m: 100000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3600001)
Primes: RFBsize:216816, AFBsize:217061, largePrimes:5646354 encountered
Relations: rels:5529662, finalFF:441875
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 37.45 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 37.56 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

Dec 29, 2007 (2nd)

By Robert Backstrom / GMP-ECM

2·10¹⁶³+3 = 2(0)₁₆₂3_<164> = 166140237444137244767_<21> · C144

C144 = P39 · P105

P39 = 190635692847477990579123632346869310511_<39>

P105 = 631467424737264651495425260061946168071504561817690296672097889180937084893277408137330615731353547645619_<105>

7·10¹⁵³-9 = 6(9)₁₅₂1_<154> = 137945979054044323691_<21> · C134

C134 = P33 · P101

P33 = 772167558584103691869638283989203_<33>

P101 = 65716956589780721844302884925214520835046088468765165698360498247128407329527151604691722545317100967_<101>

Dec 29, 2007

By Jo Yeong Uk / GGNFS

7·10¹⁴⁸-9 = 6(9)₁₄₇1_<149> = 7354479179_<10> · 18371504286793171_<17> · C123

C123 = P55 · P69

P55 = 2814258676699625279171724231993155814622006129842908123_<55>

P69 = 184093046599172102452699913165893938014185229449403497478166109476613_<69>

Number: 69991_148
N=518085453711788532865190630641573477595982123762441212022596337954685562506751479459950679549038087281476496982221376227399
  ( 123 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=2814258676699625279171724231993155814622006129842908123 (pp55)
 r2=184093046599172102452699913165893938014185229449403497478166109476613 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 15.54 hours.
Scaled time: 33.21 units (timescale=2.137).
Factorization parameters were as follows:
n: 518085453711788532865190630641573477595982123762441212022596337954685562506751479459950679549038087281476496982221376227399
m: 1000000000000000000000000000000
c5: 7
c0: -900
skew: 2.64
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2200001)
Primes: RFBsize:176302, AFBsize:175703, largePrimes:5573819 encountered
Relations: rels:5511681, finalFF:495649
Max relations in full relation-set: 28
Initial matrix: 352073 x 495649 with sparse part having weight 44562981.
Pruned matrix : 293821 x 295645 with weight 24414844.
Total sieving time: 15.02 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.40 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 15.54 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

Dec 28, 2007 (4th)

By Sinkiti Sibata / GGNFS

3·10¹⁷¹+1 = 3(0)₁₇₀1_<172> = 59 · 2421821 · 1600388452377973_<16> · 19226964394318121967711782431_<29> · C120

C120 = P42 · P79

P42 = 454231567465961238949597490091615349190531_<42>

P79 = 1502151578223577638654775137097332901436078950967469661170957656557872845681903_<79>

Number: 30001_171
N=682324665947963157631469728271325158696221411931460030747532541936673539403173263878033566456941819939868757489765660493
  ( 120 digits)
Divisors found:
 r1=454231567465961238949597490091615349190531 (pp42)
 r2=1502151578223577638654775137097332901436078950967469661170957656557872845681903 (pp79)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 72.45 hours.
Scaled time: 143.38 units (timescale=1.979).
Factorization parameters were as follows:
name: 30001_171
n: 682324665947963157631469728271325158696221411931460030747532541936673539403173263878033566456941819939868757489765660493
skew: 44071.04
# norm 1.16e+16
c5: 49080
c4: -8193826874
c3: -490521821772937
c2: 13679562189223828075
c1: 268407340291989159886011
c0: -3575626527912292763955712170
# alpha -5.23
Y1: 1376995663549
Y0: -106811371197497656583221
# Murphy_E 2.89e-10
# M 516601066594921290271387127147345628955044795772215321251305996854853784465683210678704718808492261730386730080006420124
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4350001)
Primes: RFBsize:315948, AFBsize:316211, largePrimes:7704182 encountered
Relations: rels:7780725, finalFF:757685
Max relations in full relation-set: 32
Initial matrix: 632244 x 757685 with sparse part having weight 71595438.
Pruned matrix : 531677 x 534902 with weight 46827802.
Total sieving time: 67.50 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 4.05 hours.
Time per square root: 0.47 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 72.45 hours.
 --------- CPU info (if available) ----------

Dec 28, 2007 (3rd)

By Jo Yeong Uk / GGNFS

7·10¹⁴⁰-9 = 6(9)₁₃₉1_<141> = 26003 · 49967046113187701_<17> · C120

C120 = P49 · P72

P49 = 3072384756632832193294930209979933326902287322161_<49>

P72 = 175353850256855514724412620180648233024414774451978568104314670271200777_<72>

Number: 70009_140
N=538754496546039129594575511841279608916142932610183608764794445522735349555460282454684421134028742368503726717312519097
  ( 120 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=3072384756632832193294930209979933326902287322161 (pp49)
 r2=175353850256855514724412620180648233024414774451978568104314670271200777 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.12 hours.
Scaled time: 13.11 units (timescale=2.144).
Factorization parameters were as follows:
n: 538754496546039129594575511841279608916142932610183608764794445522735349555460282454684421134028742368503726717312519097
m: 10000000000000000000000000000
c5: 7
c0: -9
skew: 1.05
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:113992, largePrimes:3368951 encountered
Relations: rels:3483950, finalFF:405792
Max relations in full relation-set: 28
Initial matrix: 228213 x 405792 with sparse part having weight 35387880.
Pruned matrix : 168806 x 170011 with weight 13391873.
Total sieving time: 5.95 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.12 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

7·10¹⁴⁴-9 = 6(9)₁₄₃1_<145> = 1487 · 3084617 · 6753139867_<10> · C126

C126 = P55 · P72

P55 = 2066420873807475272508154570496764559275489805725499291_<55>

P72 = 109360704402145490620976185805347880615820804660378980898198273592328057_<72>

Number: 69991_144
N=225985242350882492390817091181539241057870132922821577330562232474083020570409647436082746217322496695164359587616913392907587
  ( 126 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=2066420873807475272508154570496764559275489805725499291 (pp55)
 r2=109360704402145490620976185805347880615820804660378980898198273592328057 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.14 hours.
Scaled time: 21.75 units (timescale=2.144).
Factorization parameters were as follows:
n: 225985242350882492390817091181539241057870132922821577330562232474083020570409647436082746217322496695164359587616913392907587
m: 100000000000000000000000000000
c5: 7
c0: -90
skew: 1.67
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1450001)
Primes: RFBsize:114155, AFBsize:114352, largePrimes:3482197 encountered
Relations: rels:3539168, finalFF:329576
Max relations in full relation-set: 28
Initial matrix: 228573 x 329576 with sparse part having weight 32251907.
Pruned matrix : 200812 x 202018 with weight 16980012.
Total sieving time: 9.89 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 10.14 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

Dec 28, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

7·10¹⁸⁶-9 = 6(9)₁₈₅1_<187> = 1882873212211_<13> · 5833979226117373_<16> · 47533639674475314086029_<23> · 22494947546032604356359491_<26> · C111

C111 = P43 · P69

P43 = 2515472027805282686708792675704535850836383_<43>

P69 = 236922626264959098658721156310440198919184175106191358028227502394681_<69>

Number: n
N=595972239123669791995895721145326920898097780541200339694452957278131466762170631342974085756411616949220478823
  ( 111 digits)
Divisors found:
 r1=2515472027805282686708792675704535850836383 (pp43)
 r2=236922626264959098658721156310440198919184175106191358028227502394681 (pp69)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.07 hours.
Scaled time: 33.44 units (timescale=1.753).
Factorization parameters were as follows:
name: KA_6_9_185_1
n: 595972239123669791995895721145326920898097780541200339694452957278131466762170631342974085756411616949220478823
skew: 7691.60
# norm 7.39e+14
c5: 65280
c4: -3707517143
c3: -59981266406565
c2: 195444948138712791
c1: 464656384627185252258
c0: -666305598531814435117600
# alpha -4.72
Y1: 299854219969
Y0: -1556288568485250579843
# Murphy_E 8.93e-10
# M 261347015577692975215738963466108609772390237867217698520093975466862424241959027489401092781747038850578899133
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 100000)
Primes: RFBsize:230209, AFBsize:229965, largePrimes:7449706 encountered
Relations: rels:7280948, finalFF:562779
Max relations in full relation-set: 28
Initial matrix: 460254 x 562779 with sparse part having weight 47426767.
Pruned matrix : 375082 x 377447 with weight 27995113.
Total sieving time: 16.82 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.45 hours.
Total square root time: 0.65 hours, sqrts: 4.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 19.07 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁵⁸-9 = 6(9)₁₅₇1_<159> = 665507 · 4787893769_<10> · C144

C144 = P34 · P110

P34 = 4551229532797823713440523924237357_<34>

P110 = 48269429654485286004700435874371392955763120608188765913835335149678303496468383067863156974558912669025897961_<110>

5·10¹⁶⁷+3 = 5(0)₁₆₆3_<168> = 7 · 773 · 8329 · C161

C161 = P68 · P93

P68 = 66986389608208370945649030468786635518218514529828739674619854324867_<68>

P93 = 165620097981775245286549676152338224696848100622028775546996783901831190108848495803829997811_<93>

Number: n
N=11094292410356841480689529799258319926065860290596351278048063092974674681508936485819419666883219858321891974475405828661656232743521548965580379379979492866137
  ( 161 digits)
SNFS difficulty: 167 digits.
Divisors found:

Fri Dec 28 08:58:01 2007  prp68 factor: 66986389608208370945649030468786635518218514529828739674619854324867
Fri Dec 28 08:58:01 2007  prp93 factor: 165620097981775245286549676152338224696848100622028775546996783901831190108848495803829997811
Fri Dec 28 08:58:01 2007  elapsed time 01:10:29 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 46.34 hours.
Scaled time: 84.62 units (timescale=1.826).
Factorization parameters were as follows:
name: KA_5_0_166_3
n: 11094292410356841480689529799258319926065860290596351278048063092974674681508936485819419666883219858321891974475405828661656232743521548965580379379979492866137
skew: 0.36
deg: 5
c5: 500
c0: 3
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3200000)
Primes: RFBsize:250150, AFBsize:249916, largePrimes:7647488 encountered
Relations: rels:7156043, finalFF:585019
Max relations in full relation-set: 28
Initial matrix: 500132 x 585019 with sparse part having weight 52070590.
Pruned matrix : 452893 x 455457 with weight 34748113.
Total sieving time: 46.16 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 46.34 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Dec 28, 2007

By Sinkiti Sibata / PFGW

7·10¹²⁷⁵⁵-9 and 7·10¹⁵¹⁴²-9 are PRPs.

Dec 27, 2007 (5th)

By Yousuke Koide

(10¹⁸⁰⁹-1)/9 is divisible by 23016857713231589991096649713043507_<35>

(10¹⁸⁶³-1)/9 is divisible by 7506789884668978259450285467_<28>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 27, 2007 (4th)

By Jo Yeong Uk / GGNFS, GMP-ECM

7·10¹³⁷-9 = 6(9)₁₃₆1_<138> = 9041 · 162129560783_<12> · C123

C123 = P50 · P73

P50 = 63195768153342995547599618615921084920365446753767_<50>

P73 = 7556685842419476053247753995520570438772601000514461987314342496480958991_<73>

Number: 69991_137
N=477550566505190610831339497667016508356659514844638240871039919937869611141038512390547786684479527858687496804388001769097
  ( 123 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=63195768153342995547599618615921084920365446753767 (pp50)
 r2=7556685842419476053247753995520570438772601000514461987314342496480958991 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.07 hours.
Scaled time: 8.67 units (timescale=2.130).
Factorization parameters were as follows:
n: 477550566505190610831339497667016508356659514844638240871039919937869611141038512390547786684479527858687496804388001769097
m: 1000000000000000000000000000
c5: 700
c0: -9
skew: 0.42
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1450001)
Primes: RFBsize:107126, AFBsize:107093, largePrimes:2316731 encountered
Relations: rels:2429777, finalFF:264060
Max relations in full relation-set: 28
Initial matrix: 214287 x 264060 with sparse part having weight 22014166.
Pruned matrix : 198204 x 199339 with weight 13643617.
Total sieving time: 3.87 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 4.07 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

7·10¹⁶²-9 = 6(9)₁₆₁1_<163> = 859 · 118247 · 2662639391_<10> · 68628329971_<11> · C135

C135 = P30 · P105

P30 = 436977788659416077831566216483_<30>

P105 = 863057237779628902143622988929371538585971609219344275040457451654589439284920068001169478963439353329509_<105>

Dec 27, 2007 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

5·10¹⁷¹-9 = 4(9)₁₇₀1_<172> = 7 · 41 · C170

C170 = P43 · P128

P43 = 1363684689367687199660001585916252959225073_<43>

P128 = 12775389298778802140820274185385735600606854567622114532762344954306460995067145385939039085787137146377153359945100703455866041_<128>

7·10¹⁴³-9 = 6(9)₁₄₂1_<144> = 97 · 317 · 571 · C137

C137 = P68 · P70

P68 = 11669963674208858774803484401760836297661604636382205067928038771673_<68>

P70 = 3416342715437805134104596866257027736379971208960481691857755728114273_<70>

Number: n
N=39868595387807238075146492882117277574103046308113959709594872989761346018457223189921629162943461946194596677613254006978940667499388729
  ( 137 digits)
SNFS difficulty: 143 digits.
Divisors found:

Thu Dec 27 16:03:21 2007  prp68 factor: 11669963674208858774803484401760836297661604636382205067928038771673
Thu Dec 27 16:03:21 2007  prp70 factor: 3416342715437805134104596866257027736379971208960481691857755728114273
Thu Dec 27 16:03:21 2007  elapsed time 00:58:19 (Msieve 1.32)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 10.12 hours.
Scaled time: 13.24 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_6_9_142_1
n: 39868595387807238075146492882117277574103046308113959709594872989761346018457223189921629162943461946194596677613254006978940667499388729
skew: 0.26
deg: 5
c5: 7000
c0: -9
m: 10000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1100001)
Primes: RFBsize:203362, AFBsize:202857, largePrimes:6879960 encountered
Relations: rels:6390626, finalFF:531267
Max relations in full relation-set: 28
Initial matrix: 406287 x 531267 with sparse part having weight 31643740.
Pruned matrix : 
Total sieving time: 9.91 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 10.12 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁹⁴-9 = 6(9)₁₉₃1_<195> = 59 · 503 · 19009 · 4546319117_<10> · 3201890183553739545421_<22> · 3663534177803835316717_<22> · 5453825411908180414535101_<25> · C109

C109 = P47 · P62

P47 = 52063286361231377503035962252713421659616793211_<47>

P62 = 81944416344344076297954674797070896167668217005498046483209993_<62>

Number: n
N=4266295613839554521455940618914223009809176846224270626203668901679911671717662492929960969596044736169757523
  ( 109 digits)
Divisors found:

Thu Dec 27 21:14:40 2007  prp47 factor: 52063286361231377503035962252713421659616793211
Thu Dec 27 21:14:40 2007  prp62 factor: 81944416344344076297954674797070896167668217005498046483209993
Thu Dec 27 21:14:40 2007  elapsed time 01:21:04 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 15.97 hours.
Scaled time: 28.00 units (timescale=1.753).
Factorization parameters were as follows:
name: KA_6_9_193_1
n: 4266295613839554521455940618914223009809176846224270626203668901679911671717662492929960969596044736169757523
skew: 20303.21
# norm 3.02e+15
c5: 64260
c4: -5524240892
c3: 33370301956429
c2: 2960552805759545129
c1: 13268125763144698600299
c0: -427943730192357035630844
# alpha -6.40
Y1: 410046852743
Y0: -581336125346552761433
# Murphy_E 1.18e-09
# M 835049287715849898352208609708011149328452835128639575533350171456753898162996679714302558410477726301170271
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:230209, AFBsize:229921, largePrimes:6992043 encountered
Relations: rels:6742934, finalFF:579789
Max relations in full relation-set: 28
Initial matrix: 460216 x 579789 with sparse part having weight 39572835.
Pruned matrix : 350884 x 353249 with weight 18553288.
Total sieving time: 15.64 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 15.97 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁰⁸-9 = 6(9)₁₀₇1_<109> = 404321 · 378807857 · C95

C95 = P46 · P50

P46 = 2663967441313171836581746263544242756268412123_<46>

P50 = 17156308633252668896929507566790813539577265672261_<50>

Number: n
N=45703847612105192551412600444051943138121632548159102877835632289400552214113597792942597220103
  ( 95 digits)
Divisors found:
 r1=2663967441313171836581746263544242756268412123 (pp46)
 r2=17156308633252668896929507566790813539577265672261 (pp50)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.81 hours.
Scaled time: 8.43 units (timescale=1.754).
Factorization parameters were as follows:
name: KA_6_9_107_1
n:  45703847612105192551412600444051943138121632548159102877835632289400552214113597792942597220103
m:  5492465041505502450157
deg: 4
c4: 50220792
c3: 473490998762
c2: -150320131923816106
c1: -1840155014132418213
c0: 240325391527681110358680
skew: 1635.250
type: gnfs
# adj. I(F,S) = 54.908
# E(F1,F2) = 4.085225e-05
# GGNFS version 0.77.1-20050930-k8 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1198729570.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved  special-q in [100000, 100000)
Primes: RFBsize:92938, AFBsize:92993, largePrimes:1857627 encountered
Relations: rels:1908164, finalFF:212612
Max relations in full relation-set: 28
Initial matrix: 186005 x 212612 with sparse part having weight 16282353.
Pruned matrix : 174218 x 175212 with weight 11293718.
Total sieving time: 4.41 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.30 hours.
Total square root time: 0.04 hours, sqrts: 14.
Prototype def-par.txt line would be:
gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 4.81 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁴⁵-9 = 6(9)₁₄₄1_<146> = 94261 · C141

C141 = P34 · P108

P34 = 1021695068102849396044532089064863_<34>

P108 = 726849841772289840962937682508573633040889067399121266108989206433699098743911136797514039693842951036128037_<108>

Dec 27, 2007 (2nd)

By Sinkiti Sibata / GGNFS

7·10¹¹³-9 = 6(9)₁₁₂1_<114> = 491 · 2423 · 4003873 · C102

C102 = P48 · P54

P48 = 184432465107840005841929350652158018855881137453_<48>

P54 = 796792925041443202307060294296189274485989498333919823_<54>

Number: 69991_113
N=146954483345879750650262027109056915485927149646071893433452883477538598863216027684838960521344430819
  ( 102 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=184432465107840005841929350652158018855881137453 (pp48)
 r2=796792925041443202307060294296189274485989498333919823 (pp54)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.40 hours.
Scaled time: 1.62 units (timescale=0.675).
Factorization parameters were as follows:
name: 69991_113
n: 146954483345879750650262027109056915485927149646071893433452883477538598863216027684838960521344430819
m: 10000000000000000000000
c5: 7000
c0: -9
skew: 0.26
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63823, largePrimes:2223893 encountered
Relations: rels:2457553, finalFF:359535
Max relations in full relation-set: 28
Initial matrix: 112989 x 359535 with sparse part having weight 31384555.
Pruned matrix : 71414 x 72042 with weight 5203701.
Total sieving time: 2.19 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.40 hours.
 --------- CPU info (if available) ----------

7·10¹³⁵-9 = 6(9)₁₃₄1_<136> = 3673 · 255019 · 84498497 · 15088353311_<11> · C109

C109 = P37 · P73

P37 = 2619090469168430611738435623980583053_<37>

P73 = 2238016293251830424874207565385593578321653128229251831899397482529153343_<73>

Number: 69991_135
N=5861567143499528535945249491745181774451528037501922335500468042836092047603598088439983509779689035584096179
  ( 109 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=2619090469168430611738435623980583053 (pp37)
 r2=2238016293251830424874207565385593578321653128229251831899397482529153343 (pp73)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.83 hours.
Scaled time: 13.67 units (timescale=2.003).
Factorization parameters were as follows:
name: 69991_135
n: 5861567143499528535945249491745181774451528037501922335500468042836092047603598088439983509779689035584096179
m: 1000000000000000000000000000
c5: 7
c0: -9
skew: 1.05
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1225001)
Primes: RFBsize:78498, AFBsize:63908, largePrimes:1579365 encountered
Relations: rels:1604122, finalFF:195607
Max relations in full relation-set: 28
Initial matrix: 142472 x 195607 with sparse part having weight 16386599.
Pruned matrix : 126424 x 127200 with weight 8919279.
Total sieving time: 6.60 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.83 hours.
 --------- CPU info (if available) ----------

7·10¹⁴⁷-9 = 6(9)₁₄₆1_<148> = 44253346650419_<14> · 640263926981563_<15> · 2384930862846177191492797_<25> · C96

C96 = P36 · P60

P36 = 345533806013666402094028972113839143_<36>

P60 = 299796493353162488095487968396822078060268288441471385866693_<60>

Number: 69991_147
N=103589823377869076072607851794326081481578050618794143412322232850520425835300380055682643364099
  ( 96 digits)
Divisors found:
 r1=345533806013666402094028972113839143 (pp36)
 r2=299796493353162488095487968396822078060268288441471385866693 (pp60)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 11.00 hours.
Scaled time: 7.42 units (timescale=0.675).
Factorization parameters were as follows:
name: 69991_147
n:  103589823377869076072607851794326081481578050618794143412322232850520425835300380055682643364099
m:  7455843658268344282957
deg: 4
c4: 33522000
c3: 140814788
c2: 77276617925738599
c1: 69424401729227304416
c0: 2357246899800669557952
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.016
# E(F1,F2) = 2.812171e-05
# GGNFS version 0.77.1-20060513-pentium4 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1198709841.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1500001)
Primes: RFBsize:92938, AFBsize:92936, largePrimes:1911524 encountered
Relations: rels:2002935, finalFF:233843
Max relations in full relation-set: 28
Initial matrix: 185950 x 233843 with sparse part having weight 21496159.
Pruned matrix : 166071 x 167064 with weight 13108251.
Polynomial selection time: 0.17 hours.
Total sieving time: 9.92 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.72 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,95,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 11.00 hours.
 --------- CPU info (if available) ----------

Dec 27, 2007

By Sinkiti Sibata / GGNFS

7·10¹³³-9 = 6(9)₁₃₂1_<134> = 449 · 1493 · 90917 · 94389114492319_<14> · C110

C110 = P44 · P66

P44 = 85173022756831337810382828011673697322037311_<44>

P66 = 142864005459473961587757841830261127716190760624346731496837517471_<66>

Number: 69991_133
N=12168159188131852215584768023354461103145336764833774484034596076561291835579447472592128168069219417276360481
  ( 110 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=85173022756831337810382828011673697322037311 (pp44)
 r2=142864005459473961587757841830261127716190760624346731496837517471 (pp66)
Version: GGNFS-0.77.1-20060513-k8
Total time: 8.35 hours.
Scaled time: 16.72 units (timescale=2.003).
Factorization parameters were as follows:
name: 69991_133
n: 12168159188131852215584768023354461103145336764833774484034596076561291835579447472592128168069219417276360481
m: 100000000000000000000000000
c5: 7000
c0: -9
skew: 0.26
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1375001)
Primes: RFBsize:78498, AFBsize:63823, largePrimes:1568311 encountered
Relations: rels:1565951, finalFF:168189
Max relations in full relation-set: 28
Initial matrix: 142389 x 168189 with sparse part having weight 15197800.
Pruned matrix : 134600 x 135375 with weight 10638770.
Total sieving time: 8.08 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.35 hours.
 --------- CPU info (if available) ----------

Dec 26, 2007 (6th)

By Sinkiti Sibata / PRIMO

(2·10²⁹⁷⁸-17)/3 is prime.

Dec 26, 2007 (5th)

By Sinkiti Sibata / GGNFS

7·10¹¹⁸-9 = 6(9)₁₁₇1_<119> = 29 · 281 · 479 · 564899 · C107

C107 = P34 · P74

P34 = 1984136958064167375045366373528421_<34>

P74 = 15999844291278446970836451631567805232288393575182670206207520554418064299_<74>

Number: 69991_118
N=31745882381597551712985680104483070892222684616727431250512197757342182638804213346559326046812565481941879
  ( 107 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=1984136958064167375045366373528421 (pp34)
 r2=15999844291278446970836451631567805232288393575182670206207520554418064299 (pp74)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.24 hours.
Scaled time: 4.45 units (timescale=1.991).
Factorization parameters were as follows:
name: 69991_118
n: 31745882381597551712985680104483070892222684616727431250512197757342182638804213346559326046812565481941879
m: 100000000000000000000000
c5: 7000
c0: -9
skew: 0.26
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63823, largePrimes:2167506 encountered
Relations: rels:2281489, finalFF:242097
Max relations in full relation-set: 28
Initial matrix: 112989 x 242097 with sparse part having weight 22238741.
Pruned matrix : 87145 x 87773 with weight 5534433.
Total sieving time: 2.10 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.24 hours.
 --------- CPU info (if available) ----------

7·10¹²²-9 = 6(9)₁₂₁1_<123> = 83 · 13523 · 244861 · 1071691642724939_<16> · C97

C97 = P44 · P53

P44 = 82895830946665960950649287503567133316049651_<44>

P53 = 28669805558837951631417683899953649248910278323675131_<53>

Number: 69991_122
N=2376607354879214865611819176528989671083739593311572594941837848584100495761234335579813189929281
  ( 97 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=82895830946665960950649287503567133316049651 (pp44)
 r2=28669805558837951631417683899953649248910278323675131 (pp53)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.38 hours.
Scaled time: 6.77 units (timescale=2.003).
Factorization parameters were as follows:
name: 69991_122
n: 2376607354879214865611819176528989671083739593311572594941837848584100495761234335579813189929281
m: 1000000000000000000000000
c5: 700
c0: -9
skew: 0.42
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63803, largePrimes:2446192 encountered
Relations: rels:2891407, finalFF:532620
Max relations in full relation-set: 28
Initial matrix: 112969 x 532620 with sparse part having weight 52760048.
Pruned matrix : 76482 x 77110 with weight 9438717.
Total sieving time: 3.23 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.38 hours.
 --------- CPU info (if available) ----------

7·10¹³²-9 = 6(9)₁₃₁1_<133> = 1292567 · 190646486287_<12> · C116

C116 = P41 · P76

P41 = 10653299394346279999189253853948866948741_<41>

P76 = 2666441366915221621544897168193843156735547511317187784920639757035112567619_<76>

Number: 69991_132
N=28406398199217797464553546226922521246087029329926717717175210835294924586217098258316437679183181636843102569417679
  ( 116 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=10653299394346279999189253853948866948741 (pp41)
 r2=2666441366915221621544897168193843156735547511317187784920639757035112567619 (pp76)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.77 hours.
Scaled time: 11.49 units (timescale=1.991).
Factorization parameters were as follows:
name: 69991_132
n: 28406398199217797464553546226922521246087029329926717717175210835294924586217098258316437679183181636843102569417679
m: 100000000000000000000000000
c5: 700
c0: -9
skew: 0.42
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1150001)
Primes: RFBsize:63951, AFBsize:63803, largePrimes:1538473 encountered
Relations: rels:1545151, finalFF:170046
Max relations in full relation-set: 28
Initial matrix: 127822 x 170046 with sparse part having weight 14925657.
Pruned matrix : 117194 x 117897 with weight 8533990.
Total sieving time: 5.57 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.77 hours.
 --------- CPU info (if available) ----------

Dec 26, 2007 (4th)

By Jo Yeong Uk / GGNFS, GMP-ECM

7·10¹¹⁷-9 = 6(9)₁₁₆1_<118> = C118

C118 = P48 · P70

P48 = 965127703405741647531200158987421082342396773977_<48>

P70 = 7252926193392239386243000349720048960099140101219877063658000208088783_<70>

Number: 69991_117
N=6999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
  ( 118 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=965127703405741647531200158987421082342396773977 (pp48)
 r2=7252926193392239386243000349720048960099140101219877063658000208088783 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.05 hours.
Scaled time: 2.25 units (timescale=2.145).
Factorization parameters were as follows:
n: 6999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
m: 100000000000000000000000
c5: 700
c0: -9
skew: 0.42
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 450001)
Primes: RFBsize:49098, AFBsize:49186, largePrimes:1878131 encountered
Relations: rels:1929377, finalFF:194599
Max relations in full relation-set: 28
Initial matrix: 98352 x 194599 with sparse part having weight 16935639.
Pruned matrix : 78199 x 78754 with weight 4525630.
Total sieving time: 1.00 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 1.05 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

7·10¹⁵²-9 = 6(9)₁₅₁1_<153> = 642738965504016239_<18> · C136

C136 = P32 · P104

P32 = 12499425996572633795685838286539_<32>

P104 = 87131128901653143200613872829832683606052695848751370614553206443217691319643034696885938619060585421771_<104>

Dec 26, 2007 (3rd)

By matsui / GGNFS

2·10¹⁶⁷+9 = 2(0)₁₆₆9_<168> = 47 · 184481867 · 10008810089_<11> · 118729587401_<12> · 10440234088181_<14> · C124

C124 = P61 · P63

P61 = 6290280740566369228935563961231140837620944228695383054749943_<61>

P63 = 295567569227359507343672924451640185453395509237894904088703543_<63>

N=1859202988246876566381452884068131590659953240147645274080909534187043414526270082207047941221587915349634178688954923148049
  ( 124 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=6290280740566369228935563961231140837620944228695383054749943 (pp61)
 r2=295567569227359507343672924451640185453395509237894904088703543 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 127.80 hours.
Scaled time: 166.65 units (timescale=1.304).
Factorization parameters were as follows:
n: 1859202988246876566381452884068131590659953240147645274080909534187043414526270082207047941221587915349634178688954923148049
m: 1000000000000000000000000000000000
c5: 200
c0: 9
skew: 0.54
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 5450001)
Primes: RFBsize:380800, AFBsize:380082, largePrimes:5892464 encountered
Relations: rels:6135246, finalFF:894339
Max relations in full relation-set: 28
Initial matrix: 760947 x 894339 with sparse part having weight 44957251.
Pruned matrix : 648054 x 651922 with weight 30819584.
Total sieving time: 114.05 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 13.26 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 127.80 hours.

Dec 26, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(22·10¹⁶⁶-1)/3 = 7(3)₁₆₆_<167> = 13 · 2501184977_<10> · C157

C157 = P47 · P111

P47 = 20970006021949093438264942952242363969867903567_<47>

P111 = 107550815343039437975417504676624224363468612606306698519306645404641567204160857189344675377069667152654245399_<111>

Number: n
N=2255341245409071967907084403148340605774006950236708152769712418205381307006397248573287358922524681798311083347365571924927256446185523776892981730485438233
  ( 157 digits)
SNFS difficulty: 167 digits.
Divisors found:

Wed Dec 26 05:26:18 2007  prp47 factor: 20970006021949093438264942952242363969867903567
Wed Dec 26 05:26:18 2007  prp111 factor: 107550815343039437975417504676624224363468612606306698519306645404641567204160857189344675377069667152654245399
Wed Dec 26 05:26:18 2007  elapsed time 02:18:47 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 78.83 hours.
Scaled time: 138.12 units (timescale=1.752).
Factorization parameters were as follows:
name: KA_7_3_166
n: 2255341245409071967907084403148340605774006950236708152769712418205381307006397248573287358922524681798311083347365571924927256446185523776892981730485438233
type: snfs
skew: 0.34
deg: 5
c5: 220
c0: -1
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3500001)
Primes: RFBsize:230209, AFBsize:230048, largePrimes:7684784 encountered
Relations: rels:7152361, finalFF:475660
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 78.54 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.6,2.6,100000
total time: 78.83 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹²⁰-9 = 6(9)₁₁₉1_<121> = 197 · 419 · C116

C116 = P52 · P65

P52 = 1323129079639263647678527821934298050401138159281717_<52>

P65 = 64093734415499366088944419295581630353010019359658087508532919861_<65>

Number: n
N=84804283827823074034139781689543631804029414971590564917679270198563173134002883345650145984517160752577444483481337
  ( 116 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=1323129079639263647678527821934298050401138159281717 (pp52)
 r2=64093734415499366088944419295581630353010019359658087508532919861 (pp65)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.47 hours.
Scaled time: 2.59 units (timescale=1.755).
Factorization parameters were as follows:
name: KA_6_9_119_1
n: 84804283827823074034139781689543631804029414971590564917679270198563173134002883345650145984517160752577444483481337
type: snfs
skew: 1.05
deg: 5
c5: 7
c0: -9
m: 1000000000000000000000000
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 220001)
Primes: RFBsize:78498, AFBsize:78361, largePrimes:4117883 encountered
Relations: rels:3508482, finalFF:209284
Max relations in full relation-set: 28
Initial matrix: 156925 x 209284 with sparse part having weight 9419779.
Pruned matrix : 113353 x 114201 with weight 3874739.
Total sieving time: 1.28 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.10 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.4,2.4,50000
total time: 1.47 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(8·10¹⁶⁶-17)/9 = (8)₁₆₅7_<166> = 4083907 · 43094378617_<11> · C149

C149 = P41 · P51 · P58

P41 = 38584081030692973979026508694832853174717_<41>

P51 = 418114217260780904751406897239535819468897448269121_<51>

P58 = 3130746579328069205359019081831876161205414051790095798089_<58>

Number: n
N=1309009655457622967425044640452475241525607022021852781211536044491653424923374629964185236322257748149509769
  ( 109 digits)
Divisors found:

Thu Dec 27 01:08:55 2007  prp51 factor: 418114217260780904751406897239535819468897448269121
Thu Dec 27 01:08:55 2007  prp58 factor: 3130746579328069205359019081831876161205414051790095798089
Thu Dec 27 01:08:55 2007  elapsed time 00:56:09 (Msieve 1.32)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 14.81 hours.
Scaled time: 19.34 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_8_165_7
n: 1309009655457622967425044640452475241525607022021852781211536044491653424923374629964185236322257748149509769
skew: 17293.45
# norm 1.67e+15
c5: 69840
c4: 7463998242
c3: -78994172254267
c2: -2236017190191479429
c1: 14571241816633004474387
c0: 2943605098409076728592987
# alpha -6.80
Y1: 379170613327
Y0: -451398307899860421580
# Murphy_E 1.27e-09
# M 913262407536112418797141648337235351640361187128809490900940893449426725706506274192425043867981484896313502
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1500000)
Primes: RFBsize:230209, AFBsize:230668, largePrimes:6776674 encountered
Relations: rels:6460557, finalFF:550004
Max relations in full relation-set: 28
Initial matrix: 460957 x 550004 with sparse part having weight 33437232.
Pruned matrix : 373838 x 376206 with weight 17048281.
Total sieving time: 13.36 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 14.81 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 26, 2007

By Yousuke Koide

(10¹⁷⁹¹-1)/9 is divisible by 430713366297695220680641963_<27>

(10¹⁸²⁷-1)/9 is divisible by 223755556979749662730993077361_<30>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 25, 2007 (6th)

By Bruce Dodson

(10³⁰¹-1)/9 is divisible by 1141240390081433457327371568501745249133720840602413587_<55>, cofactor is prime.

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 25, 2007 (5th)

By Yousuke Koide

(10¹⁷⁰⁷-1)/9 is divisible by 75920820144562528214807220511_<29>

(10¹⁷¹³-1)/9 is divisible by 21378384423167366346901350575839_<32>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 25, 2007 (4th)

By Robert Backstrom / GGNFS, Msieve

(4·10¹⁶⁷-13)/9 = (4)₁₆₆3_<167> = 7 · 199 · 178417 · C159

C159 = P73 · P87

P73 = 1485476151933583531111398308948380526129750464603540854114915552692816459_<73>

P87 = 120382802341518563935422558643399557108880046309548748111160170924304751890414156384017_<87>

Number: n
N=178825781981260185544919324400362315519182373617989035689700410480589420542722308843419223897366923093762619358223783664573201072908733661591929401830902135803
  ( 159 digits)
SNFS difficulty: 167 digits.
Divisors found:

prp73 factor: 1485476151933583531111398308948380526129750464603540854114915552692816459
prp87 factor: 120382802341518563935422558643399557108880046309548748111160170924304751890414156384017
elapsed time 02:46:27 (Msieve 1.32)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 82.93 hours.
Scaled time: 108.55 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_4_166_3
n: 178825781981260185544919324400362315519182373617989035689700410480589420542722308843419223897366923093762619358223783664573201072908733661591929401830902135803
skew: 1.01
deg: 5
c5: 25
c0: -26
m: 2000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3900397)
Primes: RFBsize:230209, AFBsize:230867, largePrimes:7730813 encountered
Relations: rels:7172093, finalFF:452321
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 82.63 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 82.93 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 25, 2007 (3rd)

By Sinkiti Sibata / GGNFS

(4·10¹⁶¹+41)/9 = (4)₁₆₀9_<161> = 18094688609_<11> · 26999490049546734407_<20> · C131

C131 = P57 · P75

P57 = 661800895912546464100385070921509481515371228023099756833_<57>

P75 = 137462252416217059157918563636603097318468429817984026396850545706670319831_<75>

Number: 44449_161
N=90972641803209054654671943300688174982440708379689549892031878497530778160414254242799972773189906368931128996322659002194437655223
  ( 131 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=661800895912546464100385070921509481515371228023099756833 (pp57)
 r2=137462252416217059157918563636603097318468429817984026396850545706670319831 (pp75)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 83.42 hours.
Scaled time: 166.08 units (timescale=1.991).
Factorization parameters were as follows:
name: 44449_161
n: 90972641803209054654671943300688174982440708379689549892031878497530778160414254242799972773189906368931128996322659002194437655223
m: 100000000000000000000000000000000
c5: 40
c0: 41
skew: 1
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4950001)
Primes: RFBsize:315948, AFBsize:314247, largePrimes:6029218 encountered
Relations: rels:6254224, finalFF:838574
Max relations in full relation-set: 32
Initial matrix: 630261 x 838574 with sparse part having weight 63869247.
Pruned matrix : 474489 x 477704 with weight 46325545.
Total sieving time: 79.60 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.37 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 83.42 hours.
 --------- CPU info (if available) ----------

Dec 25, 2007 (2nd)

By Jo Yeong Uk / GGNFS

9·10¹⁸¹-7 = 8(9)₁₈₀3_<182> = 3613 · 3761 · 17011 · 2340581 · 730684027 · 15300750882422633_<17> · 979400478501517858241_<21> · C119

C119 = P53 · P66

P53 = 16940272774462961564775996098870506033529998386074873_<53>

P66 = 896797988999442350354441292775914106811664777578919757946243069497_<66>

Number: 89993_181
N=15192002557240387749167059448579590970166470920242453316132075745911229316132758666921505340614262736034804889184448881
  ( 119 digits)
Divisors found:
 r1=16940272774462961564775996098870506033529998386074873 (pp53)
 r2=896797988999442350354441292775914106811664777578919757946243069497 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 38.34 hours.
Scaled time: 82.16 units (timescale=2.143).
Factorization parameters were as follows:
name: 89993_181
n: 15192002557240387749167059448579590970166470920242453316132075745911229316132758666921505340614262736034804889184448881
skew: 98114.36
# norm 2.21e+16
c5: 31560
c4: -1924665624
c3: -412313060325580
c2: 47672706443648087839
c1: 1442560992222373548243522
c0: -146358796049818815151457984880
# alpha -6.24
Y1: 3744248581117
Y0: -54512483709568246234133
# Murphy_E 3.34e-10
# M 5312090155304946753032180946674168126337529924282533139667763695347823533748345268463219266442595271493810276031748175
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4125001)
Primes: RFBsize:315948, AFBsize:316143, largePrimes:7687286 encountered
Relations: rels:7809081, finalFF:793940
Max relations in full relation-set: 28
Initial matrix: 632175 x 793940 with sparse part having weight 66592823.
Pruned matrix : 496253 x 499477 with weight 40203065.
Polynomial selection time: 2.37 hours.
Total sieving time: 34.05 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.57 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000
total time: 38.34 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

Dec 25, 2007

The factor table of 699...991 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Dec 24, 2007

By Robert Backstrom / GGNFS, Msieve

(64·10¹⁶⁹-1)/9 = 7(1)₁₆₉_<170> = 191 · 227 · 23599 · C161

C161 = P68 · P94

P68 = 11931889546918933708321958997600760626322617766055953766899623909449_<68>

P94 = 5824724856908681664958265245672136436260835730449256750908837269949436735995268697884565220373_<94>

Number: n
N=69499973633827580647471586447132751857395021337483909114981344631924934491933816608111087357431841283281168537224630080843910275596154330028617514385574482004477
  ( 161 digits)
SNFS difficulty: 171 digits.
Divisors found:

Mon Dec 24 19:01:19 2007  prp68 factor: 11931889546918933708321958997600760626322617766055953766899623909449
Mon Dec 24 19:01:19 2007  prp94 factor: 5824724856908681664958265245672136436260835730449256750908837269949436735995268697884565220373
Mon Dec 24 19:01:19 2007  elapsed time 01:27:33 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 72.40 hours.
Scaled time: 131.56 units (timescale=1.817).
Factorization parameters were as follows:
name: KA_7_1_169
n: 69499973633827580647471586447132751857395021337483909114981344631924934491933816608111087357431841283281168537224630080843910275596154330028617514385574482004477
skew: 0.35
deg: 5
c5: 1
c0: -5
m: 20000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4900001)
Primes: RFBsize:250150, AFBsize:249616, largePrimes:7898818 encountered
Relations: rels:7354029, finalFF:555685
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 72.21 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 72.40 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Dec 23, 2007 (5th)

By matsui / GGNFS

3·10¹⁶⁶+1 = 3(0)₁₆₅1_<167> = 19² · 31 · 373 · 193939 · 23755628747941_<14> · 447212374355192497_<18> · C124

C124 = P45 · P79

P45 = 625649191871122082626948379908529671729699051_<45>

P79 = 5575285937796913330137969587393113913079322142661733106598322245299860531890319_<79>

N=3488173141433069844672322710287029279310821431486754226005972594141095952219346638593373912893212468814594969707770010387269
  ( 124 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=625649191871122082626948379908529671729699051 (pp45)
 r2=5575285937796913330137969587393113913079322142661733106598322245299860531890319 (pp79)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 108.27 hours.
Scaled time: 184.28 units (timescale=1.702).
Factorization parameters were as follows:
n: 3488173141433069844672322710287029279310821431486754226005972594141095952219346638593373912893212468814594969707770010387269
m: 1000000000000000000000000000000000
c5: 30
c0: 1
skew: 0.51
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 5200001)
Primes: RFBsize:348513, AFBsize:347321, largePrimes:5907563 encountered
Relations: rels:6145608, finalFF:870306
Max relations in full relation-set: 28
Initial matrix: 695901 x 870306 with sparse part having weight 52151957.
Pruned matrix : 553239 x 556782 with weight 35119544.
Total sieving time: 103.81 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 4.08 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 108.27 hours.

Dec 23, 2007 (4th)

By Sinkiti Sibata / GGNFS

(22·10¹⁶¹-1)/3 = 7(3)₁₆₁_<162> = 73 · 34653533 · 22935196665910109914667553700279_<32> · C122

C122 = P53 · P69

P53 = 15456307151502000419816734779747252856782558221670037_<53>

P69 = 817754305715924564199835791161046377202886980231427415903294669859419_<69>

Number: 73333_161
N=12639461723608598020994817140915197006312553495483248231488432539680347420405192366902367090348663282604229103442194528503
  ( 122 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=15456307151502000419816734779747252856782558221670037 (pp53)
 r2=817754305715924564199835791161046377202886980231427415903294669859419 (pp69)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 94.57 hours.
Scaled time: 64.40 units (timescale=0.681).
Factorization parameters were as follows:
name: 73333_161
n: 12639461723608598020994817140915197006312553495483248231488432539680347420405192366902367090348663282604229103442194528503
m: 100000000000000000000000000000000
c5: 220
c0: -1
skew: 0.34
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4550001)
Primes: RFBsize:315948, AFBsize:315952, largePrimes:5839234 encountered
Relations: rels:5995706, finalFF:784221
Max relations in full relation-set: 32
Initial matrix: 631967 x 784221 with sparse part having weight 49430510.
Pruned matrix : 512955 x 516178 with weight 33232195.
Total sieving time: 82.14 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 11.76 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 94.57 hours.
 --------- CPU info (if available) ----------

5·10¹⁶⁷+9 = 5(0)₁₆₆9_<168> = 17 · 1989241 · 4503242489106295715733929_<25> · 13375753468061863141381463203_<29> · C108

C108 = P33 · P75

P33 = 247594231851496673861477854899257_<33>

P75 = 991401494836260862208699840210242066186026283682422229091025681417922365483_<75>

Number: 50009_167
N=245465291570409554408333235492955931297544893177855395881640586610749416809020286506572455808735126099146131
  ( 108 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=247594231851496673861477854899257 (pp33)
 r2=991401494836260862208699840210242066186026283682422229091025681417922365483 (pp75)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 148.51 hours.
Scaled time: 295.68 units (timescale=1.991).
Factorization parameters were as follows:
name: 50009_167
n: 245465291570409554408333235492955931297544893177855395881640586610749416809020286506572455808735126099146131
m: 1000000000000000000000000000000000
c5: 500
c0: 9
skew: 0.45
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 7250001)
Primes: RFBsize:380800, AFBsize:380707, largePrimes:6144009 encountered
Relations: rels:6397329, finalFF:900175
Max relations in full relation-set: 32
Initial matrix: 761574 x 900175 with sparse part having weight 67509735.
Pruned matrix : 652300 x 656171 with weight 49587514.
Total sieving time: 142.12 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 5.80 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 148.51 hours.
 --------- CPU info (if available) ----------

Dec 23, 2007 (3rd)

By Jo Yeong Uk / GGNFS

2·10¹⁸⁷+9 = 2(0)₁₈₆9_<188> = 61 · 149 · 283 · 70663 · 2939271579080203_<16> · 4012670006992512529_<19> · 5937247290902120471857247_<25> · C118

C118 = P48 · P70

P48 = 875378053458562890900671686629987206094799966703_<48>

P70 = 1795070177818256857278501924746661172178297270528928854534971402770967_<70>

Number: 20009_187
N=1571365038080062045688276537552192603928436205005459284020038961717757775228192637376787221670115377779946873535111801
  ( 118 digits)
Divisors found:
 r1=875378053458562890900671686629987206094799966703 (pp48)
 r2=1795070177818256857278501924746661172178297270528928854534971402770967 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 33.41 hours.
Scaled time: 71.01 units (timescale=2.125).
Factorization parameters were as follows:
name: 20009_187
n: 1571365038080062045688276537552192603928436205005459284020038961717757775228192637376787221670115377779946873535111801
skew: 86841.90
# norm 2.08e+16
c5: 18720
c4: 8005758744
c3: -417143604761414
c2: -54242084718394161427
c1: 1422581424753045528714126
c0: 43918391624543280113635161840
# alpha -6.35
Y1: 1252807503029
Y0: -38440854919115622102169
# Murphy_E 3.88e-10
# M 1529114244625491084620152441929551187310300433953474676067635486861415835076684651925957412555777624572292435341208442
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 100
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3975001)
Primes: RFBsize:315948, AFBsize:316044, largePrimes:7583161 encountered
Relations: rels:7616240, finalFF:734012
Max relations in full relation-set: 28
Initial matrix: 632072 x 734011 with sparse part having weight 59496583.
Pruned matrix : 544994 x 548218 with weight 38635632.
Total sieving time: 31.36 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.72 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000
total time: 33.41 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

Dec 23, 2007 (2nd)

By Robert Backstrom / GMP-ECM

(13·10¹⁶⁵-31)/9 = 1(4)₁₆₄1_<166> = 11 · 499 · 1319876500333999_<16> · C147

C147 = P40 · P107

P40 = 1994429019434361543756357833325269071763_<40>

P107 = 99966786327320553004552683264048083299808115979086757765172472797852861187379110833799751735350193567159837_<107>

Dec 23, 2007

By Yousuke Koide

(10¹⁴⁶⁵-1)/9 is divisible by 750351062900043426795315702791_<30>

(10¹⁵⁴⁷-1)/9 is divisible by 223088287829064817231566124802627_<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 22, 2007

By Robert Backstrom / GGNFS, Msieve

5·10¹⁵³+9 = 5(0)₁₅₂9_<154> = 113 · 283 · C150

C150 = P64 · P86

P64 = 9652395741655011049538026702985684108326820233080272800634433481_<64>

P86 = 16198321181881033533347435589236482009169983223746311965676775774243157661743075509891_<86>

Number: n
N=156352606397948653804058913662090747052753369398667875793489477469589418055598986835110541292723349698239469651959098158166296632164858188185997060571
  ( 150 digits)
SNFS difficulty: 154 digits.
Divisors found:

Sat Dec 22 17:46:28 2007  prp64 factor: 9652395741655011049538026702985684108326820233080272800634433481
Sat Dec 22 17:46:28 2007  prp86 factor: 16198321181881033533347435589236482009169983223746311965676775774243157661743075509891
Sat Dec 22 17:46:28 2007  elapsed time 00:41:58 (Msieve 1.31)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 20.36 hours.
Scaled time: 35.68 units (timescale=1.752).
Factorization parameters were as follows:
name: KA_5_0_152_9
n: 156352606397948653804058913662090747052753369398667875793489477469589418055598986835110541292723349698239469651959098158166296632164858188185997060571
type: snfs
skew: 1.41
deg: 5
c5: 8
c0: 45
m: 5000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1200000)
Primes: RFBsize:216816, AFBsize:215956, largePrimes:6188331 encountered
Relations: rels:5704176, finalFF:531554
Max relations in full relation-set: 28
Initial matrix: 432837 x 531554 with sparse part having weight 24767036.
Pruned matrix : 
Total sieving time: 20.20 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 20.36 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 21, 2007 (3rd)

By Yousuke Koide

(10¹³³⁹-1)/9 is divisible by 5775107139441156343356533814929_<31>

(10¹³⁵¹-1)/9 is divisible by 1782854636817021657923017573_<28>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 21, 2007 (2nd)

By NFSNet

(10²³⁹-1)/9 = (1)₂₃₉_<239> = 479 · 142847911 · C228

C228 = P54 · P81 · P94

P54 = 383155477843726029783939406113226468701730728790004161_<54>

P81 = 128780300340244872385688233345188210841783983757299260103530718169486826135819357_<81>

P94 = 3290967632861131703281828943635774383301940171982919699073443165222894023742681701403432993547_<94>

Reference: NFSNet current status

Dec 21, 2007

By Robert Backstrom / GGNFS, Msieve

5·10¹⁶³+9 = 5(0)₁₆₂9_<164> = 470209 · 29802628633_<11> · C148

C148 = P39 · P44 · P66

P39 = 994274499440732115855225384785607465089_<39>

P44 = 20388243227799757288129029804812187656347787_<44>

P66 = 176010423833552850724204320884474640196768850687932515195507552179_<66>

Number: n
N=3567997124893726715042848190931992165491965877318560254922568110615225565901811932175902351214161088571608357164392386147216979036661072219279275697
  ( 148 digits)
SNFS difficulty: 164 digits.
Divisors found:

Fri Dec 21 19:06:29 2007  prp39 factor: 994274499440732115855225384785607465089
Fri Dec 21 19:06:29 2007  prp44 factor: 20388243227799757288129029804812187656347787
Fri Dec 21 19:06:29 2007  prp66 factor: 176010423833552850724204320884474640196768850687932515195507552179
Fri Dec 21 19:06:29 2007  elapsed time 01:29:29 (Msieve 1.31)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 46.82 hours.
Scaled time: 61.47 units (timescale=1.313).
Factorization parameters were as follows:
name: KA_5_0_162_9
n: 3567997124893726715042848190931992165491965877318560254922568110615225565901811932175902351214161088571608357164392386147216979036661072219279275697
skew: 1.41
deg: 5
c5: 8
c0: 45
m: 500000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2200000)
Primes: RFBsize:230209, AFBsize:229217, largePrimes:7357077 encountered
Relations: rels:6869781, finalFF:531314
Max relations in full relation-set: 28
Initial matrix: 459491 x 531314 with sparse part having weight 41024110.
Pruned matrix : 405664 x 408025 with weight 28167530.
Total sieving time: 46.52 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 46.82 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 20, 2007 (2nd)

By Sinkiti Sibata / GGNFS

5·10¹⁵⁷+9 = 5(0)₁₅₆9_<158> = 1097 · 14897 · 26348627 · 158905115827_<12> · 230706227803_<12> · C121

C121 = P59 · P63

P59 = 25360542995799645970199393340105446955335067305527210019419_<59>

P63 = 124896659843040259553684977555818906011332891068066978344194417_<63>

Number: 50009_157
N=3167447111981185564662038922263931214905167097009116697762326586042626329656257920880146946528001824003871576052481383723
  ( 121 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=25360542995799645970199393340105446955335067305527210019419 (pp59)
 r2=124896659843040259553684977555818906011332891068066978344194417 (pp63)
Version: GGNFS-0.77.1-20060513-k8
Total time: 49.75 hours.
Scaled time: 99.65 units (timescale=2.003).
Factorization parameters were as follows:
name: 50009_157
n: 3167447111981185564662038922263931214905167097009116697762326586042626329656257920880146946528001824003871576052481383723
m: 10000000000000000000000000000000
c5: 500
c0: 9
skew: 0.45
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3200001)
Primes: RFBsize:216816, AFBsize:216721, largePrimes:5704293 encountered
Relations: rels:5645688, finalFF:500017
Max relations in full relation-set: 28
Initial matrix: 433604 x 500017 with sparse part having weight 46100082.
Pruned matrix : 406183 x 408415 with weight 34369135.
Total sieving time: 46.98 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.40 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 49.75 hours.
 --------- CPU info (if available) ----------

Dec 20, 2007

By Robert Backstrom / GGNFS, Msieve

5·10¹⁵⁹+9 = 5(0)₁₅₈9_<160> = 158855819 · C152

C152 = P51 · P101

P51 = 595062504831659452988979151082530531460782679178587_<51>

P101 = 52893741733194472069753410091559437984333289639309186156142766882448531546650531764689412803138414753_<101>

Number: n
N=31475082445673582785154379519455941365295532548291479331959504738066913368782543622150851143828731889261167071254720609258890289690930364974543362494011
  ( 152 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=595062504831659452988979151082530531460782679178587 (pp51)
 r2=52893741733194472069753410091559437984333289639309186156142766882448531546650531764689412803138414753 (pp101)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 20.39 hours.
Scaled time: 37.07 units (timescale=1.818).
Factorization parameters were as follows:
name: KA_5_0_158_9
n: 31475082445673582785154379519455941365295532548291479331959504738066913368782543622150851143828731889261167071254720609258890289690930364974543362494011
skew: 1.78
deg: 5
c5: 1
c0: 18
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:216816, AFBsize:216936, largePrimes:6939749 encountered
Relations: rels:6405566, finalFF:494197
Max relations in full relation-set: 48
Initial matrix: 433819 x 494197 with sparse part having weight 37620448.
Pruned matrix : 385615 x 387848 with weight 23915069.
Total sieving time: 19.02 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 1.08 hours.
Total square root time: 0.14 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 20.39 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

8·10¹⁶³-7 = 7(9)₁₆₂3_<164> = 1511 · 9661 · 321227 · 564463 · C146

C146 = P42 · P104

P42 = 725182024346650930487852356735252779350207_<42>

P104 = 41678193707764674563769995598226622228791564423366352341260784993112394124120101447997247395973034963569_<104>

Number: n
N=30224276884108635845705620161872665740218373338594605309453520593775179206533817870115077142218894679107820860767648488655970203393799663737608783
  ( 146 digits)
SNFS difficulty: 165 digits.
Divisors found:

Thu Dec 20 18:40:55 2007  prp42 factor: 725182024346650930487852356735252779350207
Thu Dec 20 18:40:55 2007  prp104 factor: 41678193707764674563769995598226622228791564423366352341260784993112394124120101447997247395973034963569
Thu Dec 20 18:40:55 2007  elapsed time 02:14:03 (Msieve 1.31)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 113.19 hours.
Scaled time: 198.19 units (timescale=1.751).
Factorization parameters were as follows:
name: KA_7_9_162_3
n: 30224276884108635845705620161872665740218373338594605309453520593775179206533817870115077142218894679107820860767648488655970203393799663737608783
type: snfs
skew: 0.49
deg: 5
c5: 2
c0: -175
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4400001)
Primes: RFBsize:230209, AFBsize:231247, largePrimes:7814161 encountered
Relations: rels:7249012, finalFF:516556
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 112.81 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 113.19 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 19, 2007 (5th)

By Yousuke Koide

(10¹²⁴⁹-1)/9 is divisible by 3859327619352771895471324837_<28>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 19, 2007 (4th)

By Jo Yeong Uk / GMP-ECM

5·10¹⁶²+9 = 5(0)₁₆₁9_<163> = 7 · 29² · 271229879065601402201623_<24> · C136

C136 = P35 · P101

P35 = 64374435181365818315554180691915647_<35>

P101 = 48643521375868913517679138570941692047144478517809618044912143356711058007954967110653981808106775647_<101>

Dec 19, 2007 (3rd)

By matsui / GGNFS

(7·10¹⁶⁶+11)/9 = (7)₁₆₅9_<166> = 3 · 40361 · 205111360920457_<15> · 12389475956090072848518619_<26> · C122

C122 = P47 · P75

P47 = 55943227542338151602426973986475076889992624589_<47>

P75 = 451837410354294038053223198387566184140151017305302109616973764868158183999_<75>

N=25277243059591087751933230830792917038072519013701850924280163483893165455099071542202433152586138066004172655689993751411
  ( 122 
digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=55943227542338151602426973986475076889992624589 (pp47)
 r2=451837410354294038053223198387566184140151017305302109616973764868158183999 (pp75)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 10.74 hours.
Scaled time: 18.27 units (timescale=1.701).
Factorization parameters were as follows:
n: 25277243059591087751933230830792917038072519013701850924280163483893165455099071542202433152586138066004172655689993751411
m: 1000000000000000000000000000000000
c5: 70
c0: 11
skew: 0.69
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 6000001)
Primes: , , largePrimes:5871705 encountered
Relations: rels:5969485, finalFF:743203
Max relations in full relation-set: 28
Initial matrix: 696897 x 743203 with sparse part having weight 52810271.
Pruned matrix : 665688 x 669236 with weight 44065470.
Total sieving time: 2.91 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 7.59 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 10.74 hours.

Dec 19, 2007 (2nd)

By Sinkiti Sibata / GGNFS

5·10¹⁵⁶+9 = 5(0)₁₅₅9_<157> = 7 · 37447 · 28194483512088014904108943_<26> · C126

C126 = P62 · P64

P62 = 74881270812473695723895111402915691073452855235176557355117707_<62>

P64 = 9034780048660293802053456177468412100175147936351538480358818021_<64>

Number: 50009_156
N=676535811554865734658433221423933641105523804759318323019495315982034160190227630983735165481246914074639192835621689847797847
  ( 126 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=74881270812473695723895111402915691073452855235176557355117707 (pp62)
 r2=9034780048660293802053456177468412100175147936351538480358818021 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 32.37 hours.
Scaled time: 64.84 units (timescale=2.003).
Factorization parameters were as follows:
name: 50009_156
n: 676535811554865734658433221423933641105523804759318323019495315982034160190227630983735165481246914074639192835621689847797847
m: 10000000000000000000000000000000
c5: 50
c0: 9
skew: 0.71
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:215821, largePrimes:5559380 encountered
Relations: rels:5479029, finalFF:518470
Max relations in full relation-set: 28
Initial matrix: 432702 x 518470 with sparse part having weight 40228570.
Pruned matrix : 380168 x 382395 with weight 26863487.
Total sieving time: 30.33 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.72 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.37 hours.
 --------- CPU info (if available) ----------

Dec 19, 2007

By Robert Backstrom / GGNFS, Msieve

5·10¹⁴⁷+9 = 5(0)₁₄₆9_<148> = C148

C148 = P40 · P108

P40 = 5849697884884838262743075248501338289883_<40>

P108 = 854744996817632047461743936663945403195159505305631899758967978986218123868623742456524092166116733189586923_<108>

Number: n
N=5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 148 digits)
SNFS difficulty: 149 digits.
Divisors found:

Wed Dec 19 02:59:00 2007  prp40 factor: 5849697884884838262743075248501338289883
Wed Dec 19 02:59:00 2007  prp108 factor: 854744996817632047461743936663945403195159505305631899758967978986218123868623742456524092166116733189586923
Wed Dec 19 02:59:00 2007  elapsed time 00:54:34 (Msieve 1.31)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 12.29 hours.
Scaled time: 16.07 units (timescale=1.308).
Factorization parameters were as follows:
name: KA_5_0_146_9
n: 5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
skew: 2.24
deg: 5
c5: 4
c0: 225
m: 500000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1500001)
Primes: RFBsize:203362, AFBsize:203297, largePrimes:6971350 encountered
Relations: rels:6423924, finalFF:479679
Max relations in full relation-set: 28
Initial matrix: 406723 x 479679 with sparse part having weight 30923173.
Pruned matrix : 
Total sieving time: 12.09 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 12.29 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 18, 2007 (4th)

By Jo Yeong Uk / GGNFS, GMP-ECM

5·10¹⁶⁴+9 = 5(0)₁₆₃9_<165> = C165

C165 = P79 · P86

P79 = 6673964901781837641922867159706054031558290898862034367879686441388466755506249_<79>

P86 = 74917984640061309718805919117074967560324362619058281263115508699855177428830489506241_<86>

Number: 50009_164
N=500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 165 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=6673964901781837641922867159706054031558290898862034367879686441388466755506249 (pp79)
 r2=74917984640061309718805919117074967560324362619058281263115508699855177428830489506241 (pp86)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 39.42 hours.
Scaled time: 84.59 units (timescale=2.146).
Factorization parameters were as follows:
n: 500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
m: 1000000000000000000000000000000000
c5: 1
c0: 18
skew: 1.78
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [2500000, 4600001)
Primes: RFBsize:348513, AFBsize:348406, largePrimes:6566352 encountered
Relations: rels:6735729, finalFF:809660
Max relations in full relation-set: 28
Initial matrix: 696986 x 809660 with sparse part having weight 54958042.
Pruned matrix : 606950 x 610498 with weight 38013089.
Total sieving time: 37.13 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 2.13 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,49,49,2.5,2.5,100000
total time: 39.42 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹⁸⁵+9 = 5(0)₁₈₄9_<186> = C186

C186 = P42 · C144

P42 = 862676558302067280404855791214660371447819_<42>

C144 = [579591499488646557153454224836516440632324855138225561082733176963781513205559091433257936622764264592554118739834167338788722441133338317646011_<144>]

Dec 18, 2007 (3rd)

By Sinkiti Sibata / GGNFS

5·10¹⁵⁴+9 = 5(0)₁₅₃9_<155>= 829 · 15683 · 56596823 · 44630287349_<11> · C130

C130 = P58 · P72

P58 = 6547416756766895807011708792092633881889587619560266369321_<58>

P72 = 232538362293215384924110022839616818354212477256510811617282792627275661_<72>

Number: 50009_154
N=1522525569869729691381144278511493679974899677541911790344380065429203883992934588841549407329972980911637269126252640383900396181
  ( 130 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=6547416756766895807011708792092633881889587619560266369321 (pp58)
 r2=232538362293215384924110022839616818354212477256510811617282792627275661 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 32.09 hours.
Scaled time: 64.08 units (timescale=1.997).
Factorization parameters were as follows:
name: 50009_154
n: 1522525569869729691381144278511493679974899677541911790344380065429203883992934588841549407329972980911637269126252640383900396181
m: 10000000000000000000000000000000
c5: 1
c0: 18
skew: 1.78
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216936, largePrimes:5911757 encountered
Relations: rels:6144438, finalFF:787955
Max relations in full relation-set: 28
Initial matrix: 433819 x 787955 with sparse part having weight 63391684.
Pruned matrix : 273376 x 275609 with weight 35731953.
Total sieving time: 30.69 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.09 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.09 hours.
 --------- CPU info (if available) ----------

Dec 18, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

5·10¹⁶³+3 = 5(0)₁₆₂3_<164> = 29 · 227 · 1372379 · 3452401427_<10> · C145

C145 = P58 · P87

P58 = 1652368488234263596749387089016071429414818510198454291329_<58>

P87 = 970161182233720701578804573039325030395254397715312007695070136323727969873955547645013_<87>

Number: n
N=1603063766031098986258777513442487052832641665579047108880335847996162488378285630331639750683924926169543565709805927302627011252569149775992277
  ( 145 digits)
SNFS difficulty: 164 digits.
Divisors found:

Tue Dec 18 13:14:30 2007  prp58 factor: 1652368488234263596749387089016071429414818510198454291329
Tue Dec 18 13:14:30 2007  prp87 factor: 970161182233720701578804573039325030395254397715312007695070136323727969873955547645013
Tue Dec 18 13:14:30 2007  elapsed time 01:41:34 (Msieve 1.31)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 65.55 hours.
Scaled time: 85.80 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_5_0_162_3
n: 1603063766031098986258777513442487052832641665579047108880335847996162488378285630331639750683924926169543565709805927302627011252569149775992277
skew: 1.13
deg: 5
c5: 8
c0: 15
m: 500000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100001)
Primes: RFBsize:230209, AFBsize:229672, largePrimes:7196433 encountered
Relations: rels:6672971, finalFF:503221
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 65.18 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 65.55 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

5·10¹⁴⁵+9 = 5(0)₁₄₄9_<146> = 480587 · 664114531 · 173304257326374916002763_<24> · C108

C108 = P40 · P69

P40 = 8011859098238196250376857716817447795633_<40>

P69 = 112826851275727796887800559483225541997057785219800577879840211604843_<69>

Number: n
N=903952834919007588982726744512079025688319216306952508354097362135326614270017939800842749245239175617050619
  ( 108 digits)
SNFS difficulty: 145 digits.
Divisors found:

Tue Dec 18 15:02:49 2007  prp40 factor: 8011859098238196250376857716817447795633
Tue Dec 18 15:02:49 2007  prp69 factor: 112826851275727796887800559483225541997057785219800577879840211604843
Tue Dec 18 15:02:49 2007  elapsed time 00:24:54 (Msieve 1.31)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.79 hours.
Scaled time: 8.75 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_5_0_144_9
n: 903952834919007588982726744512079025688319216306952508354097362135326614270017939800842749245239175617050619
skew: 1.12
deg: 5
c5: 5
c0: 9
m: 100000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 900000)
Primes: RFBsize:183072, AFBsize:182621, largePrimes:6411156 encountered
Relations: rels:5849768, finalFF:448390
Max relations in full relation-set: 28
Initial matrix: 365759 x 448390 with sparse part having weight 26854576.
Pruned matrix : 294774 x 296666 with weight 13333677.
Total sieving time: 4.67 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 4.79 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Dec 18, 2007

By Yousuke Koide

(10¹¹⁷¹-1)/9 is divisible by 822720687271610738727673132529_<30>, cofactor is prime

(10¹¹⁹³-1)/9 is divisible by 14202873041760299228830573_<26>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 17, 2007 (3rd)

By Yousuke Koide

(10¹⁵⁰⁹-1)/9 is divisible by 276617318087890951973712854116609_<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 17, 2007 (2nd)

By Sinkiti Sibata / GGNFS

5·10¹¹⁶+9 = 5(0)₁₁₅9_<117> = 5647 · 14738747 · C106

C106 = P37 · P70

P37 = 1770527491110016131038045568525078001_<37>

P70 = 3393039989462346591698405537211579666741526697212892785900831616289301_<70>

Number: 50009_116
N=6007470579778724082070197662126840225249465868554753560298389981872307218603794018676645158186753206767301
  ( 106 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=1770527491110016131038045568525078001 (pp37)
 r2=3393039989462346591698405537211579666741526697212892785900831616289301 (pp70)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.65 hours.
Scaled time: 1.11 units (timescale=0.674).
Factorization parameters were as follows:
name: 50009_116
n: 6007470579778724082070197662126840225249465868554753560298389981872307218603794018676645158186753206767301
m: 100000000000000000000000
c5: 50
c0: 9
skew: 0.71
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:64058, largePrimes:1928320 encountered
Relations: rels:1872426, finalFF:132412
Max relations in full relation-set: 28
Initial matrix: 113221 x 132412 with sparse part having weight 9758667.
Pruned matrix : 104806 x 105436 with weight 6199905.
Total sieving time: 1.39 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.65 hours.
 --------- CPU info (if available) ----------

5·10¹³⁷+9 = 5(0)₁₃₆9_<138> = 97 · 1506773568889_<13> · 226074463554510734010057673_<27> · C98

C98 = P38 · P60

P38 = 54141127725421474038977984368371957931_<38>

P60 = 279493344149482372551112704180571406141518303948937390507771_<60>

Number: 50009_137
N=15132084844002305813551973140721593577879529754928485014234706791511561393412085501945537540581801
  ( 98 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=54141127725421474038977984368371957931 (pp38)
 r2=279493344149482372551112704180571406141518303948937390507771 (pp60)
Version: GGNFS-0.77.1-20060513-k8
Total time: 12.19 hours.
Scaled time: 24.20 units (timescale=1.985).
Factorization parameters were as follows:
name: 50009_137
n: 15132084844002305813551973140721593577879529754928485014234706791511561393412085501945537540581801
m: 1000000000000000000000000000
c5: 500
c0: 9
skew: 0.45
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1975001)
Primes: RFBsize:78498, AFBsize:64083, largePrimes:1684652 encountered
Relations: rels:1727895, finalFF:191071
Max relations in full relation-set: 28
Initial matrix: 142648 x 191071 with sparse part having weight 20882416.
Pruned matrix : 131206 x 131983 with weight 12913225.
Total sieving time: 11.87 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 12.19 hours.
 --------- CPU info (if available) ----------

5·10¹⁵¹+9 = 5(0)₁₅₀9_<152> = 17 · 43 · 107 · C147

C147 = P48 · P100

P48 = 334673882571236023305008947620488003064113918729_<48>

P100 = 1910060078664050756982889449663405594416053618701081486519366050468241477476722382784210606901891513_<100>

Number: 50009_151
N=639247222470818364294207141669969443982765894882186736898628175460577623790224631473976245573212984389582827262615543935461600419346177940856846977
  ( 147 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=334673882571236023305008947620488003064113918729 (pp48)
 r2=1910060078664050756982889449663405594416053618701081486519366050468241477476722382784210606901891513 (pp100)
Version: GGNFS-0.77.1-20060513-k8
Total time: 20.92 hours.
Scaled time: 41.16 units (timescale=1.967).
Factorization parameters were as follows:
name 50009_151
n: 639247222470818364294207141669969443982765894882186736898628175460577623790224631473976245573212984389582827262615543935461600419346177940856846977
m: 1000000000000000000000000000000
c5: 50
c0: 9
skew: 0.71
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:175768, largePrimes:5442675 encountered
Relations: rels:5368300, finalFF:498395
Max relations in full relation-set: 28
Initial matrix: 352135 x 498395 with sparse part having weight 42380181.
Pruned matrix : 282161 x 283985 with weight 22301234.
Total sieving time: 19.66 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 1.00 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 20.92 hours.
 --------- CPU info (if available) ----------

Dec 17, 2007

By Jo Yeong Uk / GGNFS

5·10¹³⁸+9 = 5(0)₁₃₇9_<139> = 7 · 67 · 24062444319260058179401_<23> · C114

C114 = P45 · P69

P45 = 946212734975879332729540202137182929419049849_<45>

P69 = 468240129107916666081642626977725725851067323112806555638980157404389_<69>

Number: 50009_138
N=443054773188660674408303607729086637392367280159933140054775228028741936788471173247150308418917853949686442387261
  ( 114 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=946212734975879332729540202137182929419049849 (pp45)
 r2=468240129107916666081642626977725725851067323112806555638980157404389 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.63 hours.
Scaled time: 9.87 units (timescale=2.129).
Factorization parameters were as follows:
n: 443054773188660674408303607729086637392367280159933140054775228028741936788471173247150308418917853949686442387261
m: 10000000000000000000000000000
c5: 1
c0: 180
skew: 2.83
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1000001)
Primes: RFBsize:107126, AFBsize:107118, largePrimes:2193538 encountered
Relations: rels:2294860, finalFF:267501
Max relations in full relation-set: 28
Initial matrix: 214308 x 267501 with sparse part having weight 20336589.
Pruned matrix : 188484 x 189619 with weight 11495582.
Total sieving time: 4.48 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 4.63 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹⁴⁹+9 = 5(0)₁₄₈9_<150> = 614655261608425773017_<21> · C129

C129 = P43 · P87

P43 = 1292831320258423031896200514838978324604313_<43>

P87 = 629211332393361618328576188689966621539549657057208953485058442782747222654866355168729_<87>

Number: 50009_149
N=813464117579671160481609861465604632683977337341874220218641873074098242561055665721518223145604420413125413994385245321276128177
  ( 129 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=1292831320258423031896200514838978324604313 (pp43)
 r2=629211332393361618328576188689966621539549657057208953485058442782747222654866355168729 (pp87)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.28 hours.
Scaled time: 24.19 units (timescale=2.145).
Factorization parameters were as follows:
n: 813464117579671160481609861465604632683977337341874220218641873074098242561055665721518223145604420413125413994385245321276128177
m: 1000000000000000000000000000000
c5: 1
c0: 18
skew: 1.78
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1650001)
Primes: RFBsize:135072, AFBsize:134903, largePrimes:3896038 encountered
Relations: rels:4055635, finalFF:434303
Max relations in full relation-set: 28
Initial matrix: 270042 x 434303 with sparse part having weight 42347910.
Pruned matrix : 218215 x 219629 with weight 20005906.
Total sieving time: 10.98 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 11.28 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

Dec 16, 2007 (4th)

By Sinkiti Sibata / GGNFS

5·10¹²¹+9 = 5(0)₁₂₀9_<122> = 401 · C120

C120 = P39 · P81

P39 = 234394740470022334833839226247804877881_<39>

P81 = 531958520279564508033197824266783726238632647326464705045488524626649705389905089_<81>

Number: 50009_121
N=124688279301745635910224438902743142144638403990024937655860349127182044887780548628428927680798004987531172069825436409
  ( 120 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=234394740470022334833839226247804877881 (pp39)
 r2=531958520279564508033197824266783726238632647326464705045488524626649705389905089 (pp81)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.07 hours.
Scaled time: 4.13 units (timescale=1.992).
Factorization parameters were as follows:
name: 50009_121
n: 124688279301745635910224438902743142144638403990024937655860349127182044887780548628428927680798004987531172069825436409
m: 1000000000000000000000000
c5: 50
c0: 9
skew: 0.71
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64058, largePrimes:2256398 encountered
Relations: rels:2489942, finalFF:350248
Max relations in full relation-set: 28
Initial matrix: 113221 x 350248 with sparse part having weight 32201932.
Pruned matrix : 75006 x 75636 with weight 5986172.
Total sieving time: 1.95 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.07 hours.
 --------- CPU info (if available) ----------

5·10¹⁰⁷+9 = 5(0)₁₀₆9_<108> = 19 · C107

C107 = P35 · P73

P35 = 22161612064368328651072431710802457_<35>

P73 = 1187449243189082427047892522175799526276103441537325771419337450292326123_<73>

Number: 50009_107
N=26315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684211
  ( 107 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=22161612064368328651072431710802457 (pp35)
 r2=1187449243189082427047892522175799526276103441537325771419337450292326123 (pp73)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.95 hours.
Scaled time: 1.31 units (timescale=0.674).
Factorization parameters were as follows:
name: 50009_107
n: 26315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684211
m: 1000000000000000000000
c5: 500
c0: 9
skew: 0.45
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:64083, largePrimes:2414537 encountered
Relations: rels:2970085, finalFF:672208
Max relations in full relation-set: 28
Initial matrix: 113248 x 672208 with sparse part having weight 51031416.
Pruned matrix : 58155 x 58785 with weight 4968824.
Total sieving time: 1.78 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,107,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.95 hours.
 --------- CPU info (if available) ----------

5·10¹¹⁴+9 = 5(0)₁₁₃9_<115> = 7 · 83 · 463 · 48623 · C105

C105 = P38 · P67

P38 = 70541614319082877066125526339209355501_<38>

P67 = 5419082164403195929289385747756719945734828037540124137574223619561_<67>

Number: 50009_114
N=382270804004751115685801549224284849574629336415081490606549481511433152190319400016180865627738226555061
  ( 105 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=70541614319082877066125526339209355501 (pp38)
 r2=5419082164403195929289385747756719945734828037540124137574223619561 (pp67)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.67 hours.
Scaled time: 1.13 units (timescale=0.674).
Factorization parameters were as follows:
name: 50009_114
n: 382270804004751115685801549224284849574629336415081490606549481511433152190319400016180865627738226555061
m: 100000000000000000000000
c5: 1
c0: 18
skew: 1.78
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:63888, largePrimes:2196933 encountered
Relations: rels:2439165, finalFF:379789
Max relations in full relation-set: 28
Initial matrix: 113053 x 379789 with sparse part having weight 30408564.
Pruned matrix : 65611 x 66240 with weight 4277422.
Total sieving time: 1.50 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.67 hours.
 --------- CPU info (if available) ----------

Dec 16, 2007 (3rd)

By Robert Backstrom / GMP-ECM

5·10¹⁰²+9 = 5(0)₁₀₁9_<103> = 7 · 23 · 7001 · C97

C97 = P41 · P57

P41 = 31854706908327006451053849450780933259103_<41>

P57 = 139254884403520782870512217316445103008038584589836414223_<57>

Dec 16, 2007 (2nd)

By Jo Yeong Uk / GGNFS

5·10¹³³+9 = 5(0)₁₃₂9_<134> = C134

C134 = P55 · P80

P55 = 1808856091842673778141469519200801928271629226769243833_<55>

P80 = 27641778815618891492508230793764960546620767858028425576294203682615206075499473_<80>

Number: 50009_133
N=50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 134 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=1808856091842673778141469519200801928271629226769243833 (pp55)
 r2=27641778815618891492508230793764960546620767858028425576294203682615206075499473 (pp80)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.70 hours.
Scaled time: 5.79 units (timescale=2.145).
Factorization parameters were as follows:
n: 50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
m: 1000000000000000000000000000
c5: 1
c0: 180
skew: 2.83
type: snfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [600000, 1150001)
Primes: RFBsize:92938, AFBsize:92784, largePrimes:1635992 encountered
Relations: rels:1676140, finalFF:218361
Max relations in full relation-set: 28
Initial matrix: 185786 x 218361 with sparse part having weight 11337457.
Pruned matrix : 170705 x 171697 with weight 7105532.
Total sieving time: 2.59 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1200000,1200000,25,25,46,46,2.2,2.2,50000
total time: 2.70 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹²⁶+9 = 5(0)₁₂₅9_<127> = 7 · 541 · C124

C124 = P62 · P62

P62 = 18583998288422002372740046473239078846323774567438627504014367_<62>

P62 = 71045331073170059497410700220270620432737612295639886159776421_<62>

Number: 50009_126
N=1320306311064166886717718510694481119619751782413519936625297068919989437549511486664906258251914444151043041985740691840507
  ( 124 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=18583998288422002372740046473239078846323774567438627504014367 (pp62)
 r2=71045331073170059497410700220270620432737612295639886159776421 (pp62)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.52 hours.
Scaled time: 3.25 units (timescale=2.136).
Factorization parameters were as follows:
n: 1320306311064166886717718510694481119619751782413519936625297068919989437549511486664906258251914444151043041985740691840507
m: 10000000000000000000000000
c5: 50
c0: 9
skew: 0.71
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [400000, 720001)
Primes: RFBsize:63951, AFBsize:64058, largePrimes:1387334 encountered
Relations: rels:1376239, finalFF:164736
Max relations in full relation-set: 28
Initial matrix: 128074 x 164736 with sparse part having weight 7959278.
Pruned matrix : 112535 x 113239 with weight 4175510.
Total sieving time: 1.46 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000
total time: 1.52 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹²⁹+9 = 5(0)₁₂₈9_<130> = 1283 · 6673 · 421483 · C118

C118 = P35 · P36 · P48

P35 = 55851141761388119444538473036013289_<35>

P36 = 188165401070611685235607528162110379_<36>

P48 = 131847024827184141097638546699400890537611235187_<48>

Number: 50009_129
N=1385613673935590348953591613436489741829549505362287644707221680889335587698736375275354448321494087870618987366346297
  ( 118 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=55851141761388119444538473036013289 (pp35)
 r2=188165401070611685235607528162110379 (pp36)
 r3=131847024827184141097638546699400890537611235187 (pp48)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.96 hours.
Scaled time: 4.16 units (timescale=2.127).
Factorization parameters were as follows:
n: 1385613673935590348953591613436489741829549505362287644707221680889335587698736375275354448321494087870618987366346297
m: 100000000000000000000000000
c5: 1
c0: 18
skew: 1.78
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 900001)
Primes: RFBsize:78498, AFBsize:78486, largePrimes:1556493 encountered
Relations: rels:1609896, finalFF:225323
Max relations in full relation-set: 28
Initial matrix: 157051 x 225323 with sparse part having weight 11609462.
Pruned matrix : 126069 x 126918 with weight 5246803.
Total sieving time: 1.89 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.96 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

Dec 16, 2007

By Sinkiti Sibata / PRIMO

(2·10²⁴⁰³+1)/3 is prime.

Dec 15, 2007 (4th)

By matsui / GGNFS

(5·10¹⁶⁶+7)/3 = 1(6)₁₆₅9_<167> = 38609 · 75787 · 156630091583671031730558418871436461_<36> · C122

C122 = P52 · P71

P52 = 2264388869748319451290164995673979200391552839732379_<52>

P71 = 16059767993409165566619664888931389674520944070045699328877175122292297_<71>

N=36365559895016016644306948036519971789440001831406469011965021801985852343260659678682774063764231328439857717070493184563
  ( 122 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=2264388869748319451290164995673979200391552839732379 (pp52)
 r2=16059767993409165566619664888931389674520944070045699328877175122292297 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 125.39 hours.
Scaled time: 238.73 units (timescale=1.904).
Factorization parameters were as follows:
n: 36365559895016016644306948036519971789440001831406469011965021801985852343260659678682774063764231328439857717070493184563
m: 1000000000000000000000000000000000
c5: 50
c0: 7
skew: 0.67
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 6400001)
Primes: RFBsize:348513, AFBsize:349596, largePrimes:6068375 encountered
Relations: rels:6296703, finalFF:852370
Max relations in full relation-set: 28
Initial matrix: 698174 x 852370 with sparse part having weight 63956552.
Pruned matrix : 581570 x 585124 with weight 46821531.
Total sieving time: 110.75 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 14.13 hours.
Time per square root: 0.35 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 125.39 hours.

Dec 15, 2007 (3rd)

By Yousuke Koide

(10¹³⁷⁵-1)/9 is divisible by 584213416911071661540509773751_<30>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 15, 2007 (2nd)

The factor table of 500...009 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Dec 15, 2007

By Alfred Reich

10¹⁸¹³+1 is divisible by 1341949101412826358472947603971939_<34>

10¹⁹⁶⁶+1 is divisible by 4955902500081447124888466401899581_<34>

Reference: Factorizations of numbers of the form 10ⁿ+1 (Alfred Reich)

Dec 14, 2007 (4th)

By Yousuke Koide

(10¹³¹⁵-1)/9 is divisible by 155872807295141767753013971998423271_<36>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 14, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(2·10²³⁶²+43)/9 is prime.

Dec 14, 2007 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(5·10¹⁶³+31)/9 = (5)₁₆₂9_<163> = 3² · 11503 · 2014594707737_<13> · C146

C146 = P35 · P44 · P68

P35 = 30188843843595259209660847329747917_<35>

P44 = 35971250079769021640351453407071430175983319_<44>

P68 = 24529244107054551003240215672832228187869914838761899129142536396667_<68>

Number: n
N=882347574042559821772402450073629885235585583487871518473855136881851884014580940306573631458996102973759197773
  ( 111 digits)
Divisors found:

Fri Dec 14 06:00:23 2007  prp44 factor: 35971250079769021640351453407071430175983319
Fri Dec 14 06:00:23 2007  prp68 factor: 24529244107054551003240215672832228187869914838761899129142536396667
Fri Dec 14 06:00:23 2007  elapsed time 01:21:20 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 23.38 hours.
Scaled time: 40.42 units (timescale=1.729).
Factorization parameters were as follows:
name: KA_5_162_9
n: 882347574042559821772402450073629885235585583487871518473855136881851884014580940306573631458996102973759197773
skew: 19044.42
# norm 6.38e+15
c5: 111600
c4: 14885090508
c3: 145705138135436
c2: -5337155657782209549
c1: 9745908703860354342290
c0: 107907444208141710319877800
# alpha -6.45
Y1: 212966576537
Y0: -1512145107533754160601
# Murphy_E 8.60e-10
# M 496213671955529285371696094504443999209726698467323627075527118570036745236814734332119703037015817317104508841
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1200001)
Primes: RFBsize:230209, AFBsize:230305, largePrimes:6818981 encountered
Relations: rels:6507373, finalFF:543771
Max relations in full relation-set: 28
Initial matrix: 460599 x 543771 with sparse part having weight 35789432.
Pruned matrix : 
Total sieving time: 23.12 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 23.38 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(4·10¹⁶¹+23)/9 = (4)₁₆₀7_<161> = 13³ · 132253376785665958621_<21> · C138

C138 = P39 · P99

P39 = 208122669820059734018270507907490349851_<39>

P99 = 734955876882058340201805409936009321630527412736093444708338848258488834565508219522142315629339181_<99>

5·10¹⁵²-9 = 4(9)₁₅₁1_<153> = 19 · 199 · 1451 · 94201 · C141

C141 = P52 · P90

P52 = 2456042554669170698593684758425118153245909492210089_<52>

P90 = 393916809814646016551948100067256455621282070935459752206741992118247884075792950119651649_<90>

Number: n
N=967476447904293055909635216958020112332090895404733428215992995669631565708561959491679428666082918940760232731437093604988438320239803286761
  ( 141 digits)
SNFS difficulty: 152 digits.
Divisors found:

Fri Dec 14 22:19:20 2007  prp52 factor: 2456042554669170698593684758425118153245909492210089
Fri Dec 14 22:19:20 2007  prp90 factor: 393916809814646016551948100067256455621282070935459752206741992118247884075792950119651649
Fri Dec 14 22:19:20 2007  elapsed time 01:04:26 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 22.64 hours.
Scaled time: 29.75 units (timescale=1.314).
Factorization parameters were as follows:
name: KA_4_9_151_1
n: 967476447904293055909635216958020112332090895404733428215992995669631565708561959491679428666082918940760232731437093604988438320239803286761
skew: 0.45
deg: 5
c5: 500
c0: -9
m: 1000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1100000)
Primes: RFBsize:203362, AFBsize:203297, largePrimes:6755039 encountered
Relations: rels:6230916, finalFF:474146
Max relations in full relation-set: 28
Initial matrix: 406726 x 474146 with sparse part having weight 31631044.
Pruned matrix : 349533 x 351630 with weight 19468857.
Total sieving time: 22.45 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 22.64 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 14, 2007

By Jo Yeong Uk / GGNFS

5·10¹⁵⁸-9 = 4(9)₁₅₇1_<159> = 192370543578919_<15> · 255761895497279_<15> · 6553146809446631_<16> · C115

C115 = P36 · P79

P36 = 916954738515527411860196269384889891_<36>

P79 = 1691210995646724198680462578472437912581425581533448011756847939729769453981971_<79>

Number: 49991_158
N=1550763936287826755654564895336804649264066034246143513988755304298815619485742512321951624878705182064449334155161
  ( 115 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=916954738515527411860196269384889891 (pp36)
 r2=1691210995646724198680462578472437912581425581533448011756847939729769453981971 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 25.62 hours.
Scaled time: 54.41 units (timescale=2.124).
Factorization parameters were as follows:
n: 1550763936287826755654564895336804649264066034246143513988755304298815619485742512321951624878705182064449334155161
m: 100000000000000000000000000000000
c5: 1
c0: -180
skew: 2.83
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3500001)
Primes: RFBsize:283146, AFBsize:282037, largePrimes:5639108 encountered
Relations: rels:5690607, finalFF:673567
Max relations in full relation-set: 28
Initial matrix: 565247 x 673567 with sparse part having weight 41646735.
Pruned matrix : 476541 x 479431 with weight 26834784.
Total sieving time: 24.40 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 1.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 25.62 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

(67·10¹⁶¹+23)/9 = 7(4)₁₆₀7_<162> = 3 · 11 · 1399 · 1523 · 87433 · 21320365267_<11> · 40377356857463_<14> · C126

C126 = P37 · P89

P37 = 6578288242353527353007952811929293213_<37>

P89 = 21383556043195314533903891888116589234987504067784812619439791414098469151797015018035563_<89>

Dec 13, 2007

By Sinkiti Sibata / PRIMO

(2·10²¹⁷⁵-17)/3 is prime.

Dec 12, 2007

By Sinkiti Sibata / PFGW

2·10¹²⁹⁸⁴-7 and 2·10¹³⁶¹⁴-7 are PRP.

Dec 11, 2007 (2nd)

By Yousuke Koide

10¹¹²¹+1 is divisible by 69849282640264627005884025897913761023_<38>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 11, 2007

By Robert Backstrom / GGNFS, Msieve

5·10¹⁵⁵-9 = 4(9)₁₅₄1_<156> = 52249831 · C148

C148 = P68 · P81

P68 = 12577330540482969770037590027834896246509937898150565038352486568081_<68>

P81 = 760845786107138460535930299805308106874138122028043088814610693093595148504742881_<81>

Number: n
N=9569408942203085786057374998973680890948719049445346531360072724445749881946986584511632200303193325161185688811127446517482515876462834875006581361
  ( 148 digits)
SNFS difficulty: 155 digits.
Divisors found:

Tue Dec 11 14:10:53 2007  prp68 factor: 12577330540482969770037590027834896246509937898150565038352486568081
Tue Dec 11 14:10:53 2007  prp81 factor: 760845786107138460535930299805308106874138122028043088814610693093595148504742881
Tue Dec 11 14:10:53 2007  elapsed time 01:06:58 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 25.92 hours.
Scaled time: 44.94 units (timescale=1.734).
Factorization parameters were as follows:
name: KA_4_9_154_1
n: 9569408942203085786057374998973680890948719049445346531360072724445749881946986584511632200303193325161185688811127446517482515876462834875006581361
type: snfs
skew: 1.12
deg: 5
c5: 5
c0: -9
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1200000)
Primes: RFBsize:216816, AFBsize:216491, largePrimes:6390484 encountered
Relations: rels:5934433, finalFF:556300
Max relations in full relation-set: 28
Initial matrix: 433373 x 556300 with sparse part having weight 28717637.
Pruned matrix : 323054 x 325284 with weight 14040928.
Total sieving time: 25.73 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 25.92 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 10, 2007 (5th)

By Sinkiti Sibata / PFGW

(8·10¹⁰⁷¹⁷-11)/3, (8·10¹⁴⁶⁷³-11)/3, (8·10¹⁶⁷⁵⁴-11)/3 and (8·10¹⁷⁶⁰⁶-11)/3 are PRP.

Dec 10, 2007 (4th)

By suberi / GMP-ECM

(16·10¹⁷⁶-61)/9 = 1(7)₁₇₅1_<177> = 3 · 5261 · C173

C173 = P36 · C137

P36 = 817155339792930387676948727914630841_<36>

C137 = [13784254841763201401763506838527012403768451779816402753683122065119425484587917320413953839479488490114718629521019279324075409499402757_<137>]

Dec 10, 2007 (3rd)

By Jo Yeong Uk / GGNFS

5·10¹⁶⁶-9 = 4(9)₁₆₅1_<167> = 41 · 89 · 809 · 16811 · 1289694079831_<13> · 47803986587156910009154269051461_<32> · C113

C113 = P48 · P65

P48 = 423642819486377500810088159556192139680472557229_<48>

P65 = 38574774798609590656685912133706632252046886635615382500322326219_<65>

Number: 49991_166
N=16341926356735026827094185515432260422814688809284832362536839593066759444529868046049647268284701680004884687151
  ( 113 digits)
Divisors found:
 r1=423642819486377500810088159556192139680472557229 (pp48)
 r2=38574774798609590656685912133706632252046886635615382500322326219 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 20.00 hours.
Scaled time: 42.48 units (timescale=2.124).
Factorization parameters were as follows:
name: 49991_166
n: 16341926356735026827094185515432260422814688809284832362536839593066759444529868046049647268284701680004884687151
skew: 27295.93
# norm 2.18e+15
c5: 33120
c4: 4441313622
c3: -62567391423243
c2: -2850563779112809232
c1: 20403393653491258023492
c0: 412100355487556686774922021
# alpha -5.81
Y1: 642727557923
Y0: -3456530699039931079782
# Murphy_E 7.71e-10
# M 1551685654449727006542580819033466558148370987093910726938703232431161248973769563550852895364742766086059152787
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1400000, 2380001)
Primes: RFBsize:203362, AFBsize:203153, largePrimes:7633589 encountered
Relations: rels:7513780, finalFF:534371
Max relations in full relation-set: 28
Initial matrix: 406594 x 534371 with sparse part having weight 51341064.
Pruned matrix : 315342 x 317438 with weight 31467716.
Polynomial selection time: 1.06 hours.
Total sieving time: 18.10 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.58 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000
total time: 20.00 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 10, 2007 (2nd)

By Sinkiti Sibata / GGNFS

4·10¹⁷⁹+9 = 4(0)₁₇₈9_<180> = C180

C180 = P45 · P135

P45 = 921163045658547580756150590548571589420901651_<45>

P135 = 434233659160780244149695889605425366477201748488030257510308420904369547799589597822903126508104998452818212276951470860768875906012659_<135>

Number: 40009_179
N=400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 180 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=921163045658547580756150590548571589420901651 (pp45)
 r2=434233659160780244149695889605425366477201748488030257510308420904369547799589597822903126508104998452818212276951470860768875906012659 (pp135)
Version: GGNFS-0.77.1-20060513-k8
Total time: 514.08 hours.
Scaled time: 1025.58 units (timescale=1.995).
Factorization parameters were as follows:
name: 40009_179
n: 400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
m: 1000000000000000000000000000000000000
c5: 2
c0: 45
skew: 1.86
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 9400001)
Primes: RFBsize:501962, AFBsize:502481, largePrimes:6588779 encountered
Relations: rels:7085432, finalFF:1174582
Max relations in full relation-set: 28
Initial matrix: 1004508 x 1174582 with sparse part having weight 72170055.
Pruned matrix : 861753 x 866839 with weight 54190298.
Total sieving time: 503.52 hours.
Total relation processing time: 0.48 hours.
Matrix solve time: 9.74 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 514.08 hours.
 --------- CPU info (if available) ----------

Dec 10, 2007

By Robert Backstrom / GGNFS, Msieve

5·10¹⁴⁶-9 = 4(9)₁₄₅1_<147> = 41 · 59 · 5970268730389741_<16> · C128

C128 = P59 · P69

P59 = 89514634314987140562070529941642327551603414368208045052321_<59>

P69 = 386764152467374483050690533716910166621405836972248541038074724385249_<69>

Number: n
N=34621051674262958248832730437816687088862152041094871343262841750725698980225021240368058000790564138392180385545468782765612929
  ( 128 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=89514634314987140562070529941642327551603414368208045052321 (pp59)
 r2=386764152467374483050690533716910166621405836972248541038074724385249 (pp69)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.86 hours.
Scaled time: 12.82 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_4_9_145_1
n: 34621051674262958248832730437816687088862152041094871343262841750725698980225021240368058000790564138392180385545468782765612929
skew: 0.71
deg: 5
c5: 50
c0: -9
m: 100000000000000000000000000000
type: snfs
rlim: 1800000
alim: 1800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:135072, AFBsize:134503, largePrimes:6508918 encountered
Relations: rels:5845525, finalFF:310973
Max relations in full relation-set: 28
Initial matrix: 269640 x 310973 with sparse part having weight 24290713.
Pruned matrix : 244308 x 245720 with weight 16377793.
Total sieving time: 7.07 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 1.51 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.5,2.5,100000
total time: 8.86 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

4·10¹⁵⁴+9 = 4(0)₁₅₃9_<155> = 17 · 13913 · 1396989572897_<13> · 61059519554988608394921409_<26> · C112

C112 = P56 · P56

P56 = 42618868918024524866536599051397923694814520254443166653_<56>

P56 = 46520226216352324323002797548303105981922548494168073941_<56>

Number: n
N=1982639423151567720765887757879743509716301779332394742489381947815103365988434494345777849480504756361889489473
  ( 112 digits)
SNFS difficulty: 155 digits.
Divisors found:

Mon Dec 10 21:43:43 2007  prp56 factor: 42618868918024524866536599051397923694814520254443166653
Mon Dec 10 21:43:43 2007  prp56 factor: 46520226216352324323002797548303105981922548494168073941
Mon Dec 10 21:43:43 2007  elapsed time 01:00:47 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 24.01 hours.
Scaled time: 31.77 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_4_0_153_9
n: 1982639423151567720765887757879743509716301779332394742489381947815103365988434494345777849480504756361889489473
skew: 1.86
deg: 5
c5: 2
c0: 45
m: 10000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1200000)
Primes: RFBsize:203362, AFBsize:203302, largePrimes:6863368 encountered
Relations: rels:6330906, finalFF:483438
Max relations in full relation-set: 28
Initial matrix: 406729 x 483438 with sparse part having weight 36996653.
Pruned matrix : 344289 x 346386 with weight 21435247.
Total sieving time: 23.83 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 24.01 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 9, 2007 (2nd)

By Yousuke Koide

(10¹¹⁷⁷-1)/9 is divisible by 15112598396753272691345143612337643317_<38>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 9, 2007

By Jo Yeong Uk / GGNFS

5·10¹⁵⁴-9 = 4(9)₁₅₃1_<155> = 20431 · 52699109 · 32997845429069_<14> · 307535008641326161_<18> · C112

C112 = P35 · P78

P35 = 29858758013316752254424575775237339_<35>

P78 = 153258730444147188544171970047926818140030968120876657797177159787574781970379_<78>

Number: 49991_154
N=4576115345759931963273148602487874485867641118618536902522504884305530749801301398793635737836618902146792781481
  ( 112 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=29858758013316752254424575775237339 (pp35)
 r2=153258730444147188544171970047926818140030968120876657797177159787574781970379 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 16.32 hours.
Scaled time: 34.73 units (timescale=2.128).
Factorization parameters were as follows:
n: 4576115345759931963273148602487874485867641118618536902522504884305530749801301398793635737836618902146792781481
m: 10000000000000000000000000000000
c5: 1
c0: -18
skew: 1.78
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2500001)
Primes: RFBsize:216816, AFBsize:216936, largePrimes:5614449 encountered
Relations: rels:5616644, finalFF:590726
Max relations in full relation-set: 28
Initial matrix: 433819 x 590726 with sparse part having weight 45178149.
Pruned matrix : 324617 x 326850 with weight 28243374.
Total sieving time: 15.65 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.55 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 16.32 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

4·10¹⁶⁶+9 = 4(0)₁₆₅9_<167> = 95273 · 8165188054910845523309_<22> · 14974400622659504557368769453_<29> · C112

C112 = P50 · P63

P50 = 16787178947577077116058498947766265186683375867777_<50>

P63 = 204548731765952768246248790510940164302339098214505480636361977_<63>

Number: 40009_166
N=3433796163654992834720717303856461988726115533311254786924829579654454831482818646616432841788029058212662315129
  ( 112 digits)
Divisors found:
 r1=16787178947577077116058498947766265186683375867777 (pp50)
 r2=204548731765952768246248790510940164302339098214505480636361977 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 17.28 hours.
Scaled time: 37.04 units (timescale=2.144).
Factorization parameters were as follows:
name: 40009_166
n: 3433796163654992834720717303856461988726115533311254786924829579654454831482818646616432841788029058212662315129
skew: 32399.49
# norm 4.04e+15
c5: 43260
c4: -2582623147
c3: -129295358935911
c2: -427069562025293841
c1: 24893025188825634820574
c0: -213047928497871312783824304
# alpha -6.19
Y1: 8847912799
Y0: -2398488377529493938175
# Murphy_E 7.74e-10
# M 1450873548697470902964069406047257719289617562836590192062108198415984904995949699924035264821588859357326623899
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1400000, 2240001)
Primes: RFBsize:203362, AFBsize:203291, largePrimes:7436972 encountered
Relations: rels:7186524, finalFF:474824
Max relations in full relation-set: 28
Initial matrix: 406739 x 474824 with sparse part having weight 42851975.
Pruned matrix : 354327 x 356424 with weight 28562696.
Polynomial selection time: 0.94 hours.
Total sieving time: 15.41 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.68 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000
total time: 17.28 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 8, 2007 (3rd)

By matsui / GMP-ECM

(37·10¹⁷⁸-1)/9 = 4(1)₁₇₈_<179> = 7 · 137 · C176

C176 = P33 · C144

P33 = 256606801414902925624321820940911_<33>

C144 = [167059987357085613333034797110824057589025658340318711449285988164500386196628719375549643795216399404461119111310119558935462349796606422281239_<144>]

Dec 8, 2007 (2nd)

By Jo Yeong Uk / GGNFS

5·10¹⁶²-9 = 4(9)₁₆₁1_<163> = C163

C163 = P44 · P56 · P64

P44 = 68385977371361886229008858431010504877885471_<44>

P56 = 10358845079111018892823016494495871163939965326959587059_<56>

P64 = 7058161771042422170571387133040680162138563583374078964992316019_<64>

Number: 49991_162
N=4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
  ( 163 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=68385977371361886229008858431010504877885471 (pp44)
 r2=10358845079111018892823016494495871163939965326959587059 (pp56)
 r3=7058161771042422170571387133040680162138563583374078964992316019 (pp64)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 48.82 hours.
Scaled time: 104.66 units (timescale=2.144).
Factorization parameters were as follows:
n: 4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
m: 500000000000000000000000000000000
c5: 4
c0: -225
skew: 2.24
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [2500000, 5100001)
Primes: RFBsize:348513, AFBsize:348286, largePrimes:6727746 encountered
Relations: rels:6971731, finalFF:855302
Max relations in full relation-set: 28
Initial matrix: 696863 x 855302 with sparse part having weight 63866792.
Pruned matrix : 578415 x 581963 with weight 45564381.
Total sieving time: 46.21 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 2.42 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,49,49,2.5,2.5,100000
total time: 48.82 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

5·10¹⁵¹-9 = 4(9)₁₅₀1_<152> = 41 · 71 · 5849 · 301673 · 2377056670405894456247259031_<28> · C112

C112 = P34 · P78

P34 = 7216593624182899656979319751461431_<34>

P78 = 567463522224990994815587976391783657930851218965846028456860191438113244343673_<78>

Number: 49991_151
N=4095153636445241190206816689343683703674815019630873708328681246983802788485970229898316586832416033236168376063
  ( 112 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=7216593624182899656979319751461431 (pp34)
 r2=567463522224990994815587976391783657930851218965846028456860191438113244343673 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 12.78 hours.
Scaled time: 27.42 units (timescale=2.146).
Factorization parameters were as follows:
n: 4095153636445241190206816689343683703674815019630873708328681246983802788485970229898316586832416033236168376063
m: 1000000000000000000000000000000
c5: 50
c0: -9
skew: 0.71
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:175768, largePrimes:5401564 encountered
Relations: rels:5292212, finalFF:469027
Max relations in full relation-set: 28
Initial matrix: 352135 x 469027 with sparse part having weight 39728717.
Pruned matrix : 293297 x 295121 with weight 22323023.
Total sieving time: 12.29 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 12.78 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 8, 2007

By Robert Backstrom / GMP-ECM

5·10¹⁵⁷-9 = 4(9)₁₅₆1_<158> = 23 · 47 · 32993 · C151

C151 = P41 · P110

P41 = 64414577002263313514982818321328963237311_<41>

P110 = 21763981302826500962913776820417810329105314486317929333032864905086682541577240814547337472885523445053489457_<110>

Dec 7, 2007 (4th)

By Jo Yeong Uk / GGNFS

5·10¹⁴⁸-9 = 4(9)₁₄₇1_<149> = 29 · 79² · 109 · 752100379 · C133

C133 = P34 · P99

P34 = 3528305141284807144178302848697901_<34>

P99 = 955101178320483387652564653901091192062550077009781733001890240341202021273986351553940732976675729_<99>

Number: 49991_148
N=3369888397915338921258428641420141674023216060199260547003287810058336759881465047437666734012844616469309629039403567538331159944829
  ( 133 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=3528305141284807144178302848697901 (pp34)
 r2=955101178320483387652564653901091192062550077009781733001890240341202021273986351553940732976675729 (pp99)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.19 hours.
Scaled time: 21.63 units (timescale=2.123).
Factorization parameters were as follows:
n: 3369888397915338921258428641420141674023216060199260547003287810058336759881465047437666734012844616469309629039403567538331159944829
m: 1000000000000000000000000000000
c5: 1
c0: -180
skew: 2.83
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1575001)
Primes: RFBsize:135072, AFBsize:134763, largePrimes:3725528 encountered
Relations: rels:3800513, finalFF:378509
Max relations in full relation-set: 28
Initial matrix: 269899 x 378509 with sparse part having weight 33652982.
Pruned matrix : 230441 x 231854 with weight 17271651.
Total sieving time: 9.90 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 10.19 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 7, 2007 (3rd)

By Jo Yeong Uk / GGNFS

8·10¹⁸⁶-7 = 7(9)₁₈₅3_<187> = C187

C187 = P59 · P129

P59 = 23673718891878340687652156651068165346397873316066209701723_<59>

P129 = 337927472930521778199552160468265760927553690616358987625083967033589270515553679435711873302636879244937694756967161283401298491_<129>

Number: 79993_186
N=7999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 187 digits)
SNFS difficulty: 187 digits.
Divisors found:
 r1=23673718891878340687652156651068165346397873316066209701723 (pp59)
 r2=337927472930521778199552160468265760927553690616358987625083967033589270515553679435711873302636879244937694756967161283401298491 (pp129)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 403.36 hours.
Scaled time: 859.97 units (timescale=2.132).
Factorization parameters were as follows:
n: 7999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
m: 20000000000000000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [6000000, 12600001)
Primes: RFBsize:788060, AFBsize:788254, largePrimes:11493077 encountered
Relations: rels:12030057, finalFF:1799960
Max relations in full relation-set: 28
Initial matrix: 1576379 x 1799960 with sparse part having weight 101413617.
Pruned matrix : 1375471 x 1383416 with weight 74538419.
Total sieving time: 389.01 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 13.95 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,12000000,12000000,28,28,50,50,2.6,2.6,100000
total time: 403.36 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 7, 2007 (2nd)

By Sinkiti Sibata / PFGW

5·10¹⁰⁸²⁰-9 and 5·10¹⁴⁵⁹²-9 are PRP.

Dec 7, 2007

By Yousuke Koide

(10¹⁰⁹³-1)/9 is divisible by 199506195135220536755902065305293_<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 6, 2007 (5th)

By Jo Yeong Uk / GMP-ECM

5·10¹⁹⁹-9 = 4(9)₁₉₈1_<200> = C200

C200 = P34 · P167

P34 = 1224112416041742410052808832168959_<34>

P167 = 40845921783620723265274965609618243098936302659169196754666765677273901878095642440080026040452661066087357309697423682859960350348666458327845592281510888305426519049_<167>

Dec 6, 2007 (4th)

By Robert Backstrom / GGNFS, Msieve

(16·10¹⁶²-7)/9 = 1(7)₁₆₂_<163>= 149 · 12918999672424547147_<20> · C141

C141 = P53 · P89

P53 = 42410911175907381021122531054551380413053150932223867_<53>

P89 = 21776331263493214068135261250146977053996751440377507135716102961789622007528024777905477_<89>

Number: n
N=923554050953145651757115932207095054219542878393925009149107585156454700784480736260600830105563687523730018039673296026246046433409929419559
  ( 141 digits)
SNFS difficulty: 163 digits.
Divisors found:

Thu Dec 06 08:21:53 2007  prp53 factor: 42410911175907381021122531054551380413053150932223867
Thu Dec 06 08:21:53 2007  prp89 factor: 21776331263493214068135261250146977053996751440377507135716102961789622007528024777905477
Thu Dec 06 08:21:53 2007  elapsed time 02:06:15 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 67.27 hours.
Scaled time: 88.59 units (timescale=1.317).
Factorization parameters were as follows:
name: KA_1_7_162
n: 923554050953145651757115932207095054219542878393925009149107585156454700784480736260600830105563687523730018039673296026246046433409929419559
skew: 0.67
deg: 5
c5: 50
c0: -7
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2600000)
Primes: RFBsize:216816, AFBsize:217591, largePrimes:7393862 encountered
Relations: rels:6850636, finalFF:494540
Max relations in full relation-set: 28
Initial matrix: 434472 x 494540 with sparse part having weight 50632783.
Pruned matrix : 
Total sieving time: 67.01 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 67.27 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10¹⁵²+9 = 4(0)₁₅₁9_<153> = 26713 · 1234873 · 1996467668952176494127953_<25> · C118

C118 = P41 · P78

P41 = 35974049014171230767387935670841612478177_<41>

P78 = 168835367899724431687288680957130059518243845115630566914418157002167566445961_<78>

Number: n
N=6073691800150318752219511984753628781476739145121835518994745689916081064629478208333175321810209710086068549562293097
  ( 118 digits)
SNFS difficulty: 152 digits.
Divisors found:

Thu Dec 06 16:08:51 2007  prp41 factor: 35974049014171230767387935670841612478177
Thu Dec 06 16:08:51 2007  prp78 factor: 168835367899724431687288680957130059518243845115630566914418157002167566445961
Thu Dec 06 16:08:51 2007  elapsed time 00:47:53 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 22.03 hours.
Scaled time: 31.99 units (timescale=1.452).
Factorization parameters were as follows:
name: KA_4_0_151_9
n: 6073691800150318752219511984753628781476739145121835518994745689916081064629478208333175321810209710086068549562293097
skew: 0.94
deg: 5
c5: 25
c0: 18
m: 2000000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1200000)
Primes: RFBsize:148933, AFBsize:148625, largePrimes:7017509 encountered
Relations: rels:6462685, finalFF:361511
Max relations in full relation-set: 28
Initial matrix: 297622 x 361511 with sparse part having weight 34777349.
Pruned matrix : 266133 x 267685 with weight 22914288.
Total sieving time: 21.83 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 22.03 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(34·10¹⁶¹-7)/9 = 3(7)₁₆₁_<162> = 197 · 9371 · 110183 · 694182710171_<12> · C139

C139 = P58 · P82

P58 = 2616862112205494779410765284481436663033222318232195981387_<58>

P82 = 1022386293766035950048848925429858897403553614981437089485799152210536157188516281_<82>

Number: n
N=2675443956194536316022798734239381743434700299393259205203764910786567960718170468410719273526054038360896452757923210295394590633222461747
  ( 139 digits)
SNFS difficulty: 162 digits.
Divisors found:

Thu Dec 06 23:56:31 2007  prp58 factor: 2616862112205494779410765284481436663033222318232195981387
Thu Dec 06 23:56:31 2007  prp82 factor: 1022386293766035950048848925429858897403553614981437089485799152210536157188516281
Thu Dec 06 23:56:31 2007  elapsed time 02:44:21 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 69.26 hours.
Scaled time: 83.04 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_3_7_161
n: 2675443956194536316022798734239381743434700299393259205203764910786567960718170468410719273526054038360896452757923210295394590633222461747
type: snfs
skew: 0.46
deg: 5
c5: 340
c0: -7
m: 100000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3000001)
Primes: RFBsize:230209, AFBsize:229397, largePrimes:7454855 encountered
Relations: rels:6893700, finalFF:514080
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 68.95 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 69.26 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Dec 6, 2007 (3rd)

By Sinkiti Sibata / GGNFS

5·10¹⁴³-9 = 4(9)₁₄₂1_<144> = 17 · C143

C143 = P60 · P84

P60 = 285720265191441664337755675562698371459936363289423581013937_<60>

P84 = 102939022145228428989427304065983196665834399279521532082685405829806319911074359479_<84>

Number: 49991_143
N=29411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823
  ( 143 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=285720265191441664337755675562698371459936363289423581013937 (pp60)
 r2=102939022145228428989427304065983196665834399279521532082685405829806319911074359479 (pp84)
Version: GGNFS-0.77.1-20060513-k8
Total time: 11.80 hours.
Scaled time: 23.49 units (timescale=1.991).
Factorization parameters were as follows:
name: 49991_143
n: 29411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823
m: 50000000000000000000000000000
c5: 8
c0: -45
skew: 1.41
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1950001)
Primes: RFBsize:100021, AFBsize:99898, largePrimes:2740628 encountered
Relations: rels:2726242, finalFF:266126
Max relations in full relation-set: 28
Initial matrix: 199984 x 266126 with sparse part having weight 25911863.
Pruned matrix : 180593 x 181656 with weight 15619042.
Total sieving time: 11.27 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.36 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 11.80 hours.
 --------- CPU info (if available) ----------

5·10¹³⁵-9 = 4(9)₁₃₄1_<136> = 7 · 23 · 79 · 17536644897128650802233_<23> · C110

C110 = P46 · P65

P46 = 1719936531432379284578110469620659745107108719_<46>

P65 = 13033411521941582112132234407177385128654436282436915981843640207_<65>

Number: 49991_135
N=22416640605779012272061571478739422204655514974373750892597086537285582773909365228492465712874266775868664833
  ( 110 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=1719936531432379284578110469620659745107108719 (pp46)
 r2=13033411521941582112132234407177385128654436282436915981843640207 (pp65)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.81 hours.
Scaled time: 11.61 units (timescale=2.000).
Factorization parameters were as follows:
name: 49991_135
n: 22416640605779012272061571478739422204655514974373750892597086537285582773909365228492465712874266775868664833
m: 1000000000000000000000000000
c5: 5
c0: -9
skew: 1.12
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:63763, largePrimes:1597471 encountered
Relations: rels:1658522, finalFF:230632
Max relations in full relation-set: 28
Initial matrix: 142327 x 230632 with sparse part having weight 17325623.
Pruned matrix : 115642 x 116417 with weight 7445126.
Total sieving time: 5.63 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.81 hours.
 --------- CPU info (if available) ----------

5·10¹⁴²-9 = 4(9)₁₄₁1_<143> = 2339 · 7678802901535212851801_<22> · C118

C118 = P30 · P44 · P46

P30 = 117630389300918643864328074179_<30>

P44 = 13290764272933581140590846123083681578082559_<44>

P46 = 1780642654590329845797643787582718386220435529_<46>

Number: 49991_142
N=2783852765203771242392062028278372201075337622567765162596504687226524568762724852814366472811671739409898543364743269
  ( 118 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=117630389300918643864328074179 (pp30)
 r2=13290764272933581140590846123083681578082559 (pp44)
 r3=1780642654590329845797643787582718386220435529 (pp46)
Version: GGNFS-0.77.1-20060513-k8
Total time: 15.52 hours.
Scaled time: 30.95 units (timescale=1.994).
Factorization parameters were as follows:
name: 49991_142
n: 2783852765203771242392062028278372201075337622567765162596504687226524568762724852814366472811671739409898543364743269
m: 10000000000000000000000000000
c5: 500
c0: -9
skew: 0.45
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2350001)
Primes: RFBsize:100021, AFBsize:99988, largePrimes:2795102 encountered
Relations: rels:2767439, finalFF:225205
Max relations in full relation-set: 28
Initial matrix: 200076 x 225205 with sparse part having weight 24651803.
Pruned matrix : 193526 x 194590 with weight 19788059.
Total sieving time: 14.86 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.47 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 15.52 hours.
 --------- CPU info (if available) ----------

Dec 6, 2007 (2nd)

By Sinkiti Sibata / PFGW

(22·10¹¹⁴³¹-7)/3 and (22·10¹²⁹²⁷-7)/3 are PRP.

Dec 6, 2007

By Robert Backstrom / GGNFS, Msieve 1.30

9·10¹⁶¹+7 = 9(0)₁₆₀7_<162> = 32742491009_<11> · 15305913553837_<14> · C139

C139 = P61 · P78

P61 = 2871374186022696036738055549847702632759229312163023359543043_<61>

P78 = 625434371370412843235342091358846490870084281799111208724718685614180061274753_<78>

Number: n
N=1795856109004335763698691572087419453798364220434114608269312678179761222742470512062548832927933855893213113194030583971753238970152693379
  ( 139 digits)
SNFS difficulty: 161 digits.
Divisors found:

Thu Dec 06 02:15:29 2007  prp61 factor: 2871374186022696036738055549847702632759229312163023359543043
Thu Dec 06 02:15:29 2007  prp78 factor: 625434371370412843235342091358846490870084281799111208724718685614180061274753
Thu Dec 06 02:15:29 2007  elapsed time 01:54:10 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 65.06 hours.
Scaled time: 84.97 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_9_0_160_7
n: 1795856109004335763698691572087419453798364220434114608269312678179761222742470512062548832927933855893213113194030583971753238970152693379
skew: 0.60
deg: 5
c5: 90
c0: 7
m: 100000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300001)
Primes: RFBsize:230209, AFBsize:230767, largePrimes:7363359 encountered
Relations: rels:6836918, finalFF:495414
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 64.81 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 65.06 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 5, 2007 (3rd)

By Jo Yeong Uk / GMP-ECM

5·10¹⁵³-9 = 4(9)₁₅₂1_<154> = 7² · 31 · 233 · 367 · 190668767 · 15049933389679_<14> · C125

C125 = P36 · P89

P36 = 394436722224962502210435443374249441_<36>

P89 = 34009384186180731129927406696605787600972387399376193654041569409619395347174902797719823_<89>

Dec 5, 2007 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS

5·10¹²³-9 = 4(9)₁₂₂1_<124> = 7 · 31 · 103668634195146479_<18> · C105

C105 = P33 · P72

P33 = 529652772019323584350569475910017_<33>

P72 = 419634942345057429532843777824194673588852290057980851002408093562224161_<72>

5·10¹²⁴-9 = 4(9)₁₂₃1_<125> = 112834510063289823811_<21> · C105

C105 = P45 · P60

P45 = 449489779543195000651111258759942012797389869_<45>

P60 = 985844086264210902762592892891295128151928079697441377159249_<60>

Number: n
N=443126840998862673372330594167340785125969505774279345379238258715809495060385177703056868837181152248381
  ( 105 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=449489779543195000651111258759942012797389869 (pp45)
 r2=985844086264210902762592892891295128151928079697441377159249 (pp60)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.96 hours.
Scaled time: 2.60 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_4_9_123_1
n: 443126840998862673372330594167340785125969505774279345379238258715809495060385177703056868837181152248381
skew: 1.78
deg: 5
c5: 1
c0: -18
m: 10000000000000000000000000
type: snfs
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 250001)
Primes: RFBsize:63951, AFBsize:63888, largePrimes:4613515 encountered
Relations: rels:4003172, finalFF:210650
Max relations in full relation-set: 48
Initial matrix: 127906 x 210650 with sparse part having weight 17161578.
Pruned matrix : 98518 x 99221 with weight 4907911.
Total sieving time: 1.71 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.10 hours.
Total square root time: 0.06 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000
total time: 1.96 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 5, 2007

By Sinkiti Sibata / GGNFS

5·10¹²⁸-9 = 4(9)₁₂₇1_<129> = 17981 · 3843931457165509_<16> · C109

C109 = P45 · P64

P45 = 942477006562110761447064968719904363145782491_<45>

P64 = 7675554588296651640866311850875593032012524032228064348193639269_<64>

Number: 49991_128
N=7234033712081902712464612958999569631054058842077060936513763588440193920136568538523951971389190729990239079
  ( 109 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=942477006562110761447064968719904363145782491 (pp45)
 r2=7675554588296651640866311850875593032012524032228064348193639269 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.04 hours.
Scaled time: 6.11 units (timescale=2.010).
Factorization parameters were as follows:
name: 49991_128
n: 7234033712081902712464612958999569631054058842077060936513763588440193920136568538523951971389190729990239079
m: 50000000000000000000000000
c5: 8
c0: -45
skew: 1.41
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:63951, AFBsize:63928, largePrimes:1408145 encountered
Relations: rels:1391646, finalFF:160862
Max relations in full relation-set: 28
Initial matrix: 127944 x 160862 with sparse part having weight 8338899.
Pruned matrix : 116420 x 117123 with weight 4694100.
Total sieving time: 2.90 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 3.04 hours.
 --------- CPU info (if available) ----------

5·10¹²⁹-9 = 4(9)₁₂₈1_<130> = 7 · 399271 · C124

C124 = P37 · P88

P37 = 1719378230348833617587044366277777273_<37>

P88 = 1040477691594168476615746126692780490295108691699389255395317590980581957687501917021311_<88>

Number: 49991_129
N=1788974692090620870822788818335702532150558678906592979991749248720078056543765297969835739921721623372882793176278052464903
  ( 124 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=1719378230348833617587044366277777273 (pp37)
 r2=1040477691594168476615746126692780490295108691699389255395317590980581957687501917021311 (pp88)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.02 hours.
Scaled time: 6.07 units (timescale=2.010).
Factorization parameters were as follows:
name: 49991_129
n: 1788974692090620870822788818335702532150558678906592979991749248720078056543765297969835739921721623372882793176278052464903
m: 100000000000000000000000000
c5: 1
c0: -18
skew: 1.78
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:63951, AFBsize:63888, largePrimes:1400726 encountered
Relations: rels:1379152, finalFF:155356
Max relations in full relation-set: 28
Initial matrix: 127906 x 155356 with sparse part having weight 8163928.
Pruned matrix : 118614 x 119317 with weight 4886712.
Total sieving time: 2.88 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 3.02 hours.
 --------- CPU info (if available) ----------

5·10¹³¹-9 = 4(9)₁₃₀1_<132> = 41 · 5547391 · C124

C124 = P60 · P64

P60 = 331708005539959846200945699830264904120183676134446346135329_<60>

P64 = 6627373043733457754101972925473022695394088807721914419175039809_<64>

Number: 49991_131
N=2198352694306118352775557233934329691552518925057765344324838864814459845991060504289533496412119129734953277157126876312161
  ( 124 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=331708005539959846200945699830264904120183676134446346135329 (pp60)
 r2=6627373043733457754101972925473022695394088807721914419175039809 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.40 hours.
Scaled time: 8.73 units (timescale=1.985).
Factorization parameters were as follows:
name: 49991_131
n: 2198352694306118352775557233934329691552518925057765344324838864814459845991060504289533496412119129734953277157126876312161
m: 100000000000000000000000000
c5: 50
c0: -9
skew: 0.71
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64058, largePrimes:1540929 encountered
Relations: rels:1578173, finalFF:205413
Max relations in full relation-set: 28
Initial matrix: 128074 x 205413 with sparse part having weight 14981903.
Pruned matrix : 107027 x 107731 with weight 6295031.
Total sieving time: 4.24 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.40 hours.
 --------- CPU info (if available) ----------

5·10¹³³-9 = 4(9)₁₃₂1_<134> = 1388981393_<10> · C125

C125 = P46 · P79

P46 = 4580943858133272901234098370518760018593679951_<46>

P79 = 7858119105566310646465581070947787541968136461241464994014105774627915529998537_<79>

Number: 49991_133
N=35997602453123718699088433361036392227609920185590275938275294088118860783040021616761859674530571627319128529175336476231687
  ( 125 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=4580943858133272901234098370518760018593679951 (pp46)
 r2=7858119105566310646465581070947787541968136461241464994014105774627915529998537 (pp79)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.68 hours.
Scaled time: 9.29 units (timescale=1.985).
Factorization parameters were as follows:
name: 49991_133
n: 35997602453123718699088433361036392227609920185590275938275294088118860783040021616761859674530571627319128529175336476231687
m: 500000000000000000000000000
c5: 8
c0: -45
skew: 1.41
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 925001)
Primes: RFBsize:78498, AFBsize:63928, largePrimes:1457680 encountered
Relations: rels:1439431, finalFF:160358
Max relations in full relation-set: 28
Initial matrix: 142491 x 160358 with sparse part having weight 10506246.
Pruned matrix : 136383 x 137159 with weight 7567068.
Total sieving time: 4.48 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 4.68 hours.
 --------- CPU info (if available) ----------

5·10¹³⁴-9 = 4(9)₁₃₃1_<135> = 19 · 4294946301634720547509_<22> · C112

C112 = P40 · P72

P40 = 7661951585715267309757814664269644345249_<40>

P72 = 799685573994862057768981025766325851378881906722550433228529476184746329_<72>

Number: 49991_134
N=6127152151743557074542844552870042019610302481794247517939862406771161342106351861871786326029301318444361340921
  ( 112 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=7661951585715267309757814664269644345249 (pp40)
 r2=799685573994862057768981025766325851378881906722550433228529476184746329 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.82 hours.
Scaled time: 11.55 units (timescale=1.986).
Factorization parameters were as follows:
name: 49991_134
n: 6127152151743557074542844552870042019610302481794247517939862406771161342106351861871786326029301318444361340921
m: 1000000000000000000000000000
c5: 1
c0: -18
skew: 1.78
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:63888, largePrimes:1619441 encountered
Relations: rels:1697010, finalFF:245323
Max relations in full relation-set: 28
Initial matrix: 142453 x 245323 with sparse part having weight 18456007.
Pruned matrix : 112751 x 113527 with weight 7450413.
Total sieving time: 5.64 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.82 hours.
 --------- CPU info (if available) ----------

Dec 4, 2007 (5th)

By Jo Yeong Uk / GGNFS

5·10¹¹⁸-9 = 4(9)₁₁₇1_<119> = C119

C119 = P60 · P60

P60 = 113451761893099661361741916560523265424931846016438394824059_<60>

P60 = 440715940992725025596348804318707127294139212236448645152949_<60>

Number: 49991_118
N=49999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
  ( 119 digits)
SNFS difficulty: 120 digits.
Divisors found:

r1=113451761893099661361741916560523265424931846016438394824059
(pp60)

r2=440715940992725025596348804318707127294139212236448645152949
(pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.74 hours.
Scaled time: 1.58 units (timescale=2.145).
Factorization parameters were as follows:
n:
49999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
m: 1000000000000000000000000
c5: 1
c0: -180
skew: 2.83
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 420001)
Primes: RFBsize:49098, AFBsize:49121,
largePrimes:1721640 encountered
Relations: rels:1663175, finalFF:113797
Max relations in full relation-set: 28
Initial matrix: 98283 x 113797 with sparse part having
weight 8423002.
Pruned matrix : 92995 x 93550 with weight 5618322.
Total sieving time: 0.68 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.74 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz
stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz
stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz
stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz
stepping 07
Memory: 8167512k/8912896k available (2114k kernel
code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine..
4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine..
4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine..
4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine..
4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 4, 2007 (4th)

By Robert Backstrom / GMP-ECM

5·10¹¹³-9 = 4(9)₁₁₂1_<114> = 23 · 263 · 200041 · 2035289 · C99

C99 = P30 · P69

P30 = 443952373522730358003023095039_<30>

P69 = 457303931730390724716183370178707280616570660476664818059347925723369_<69>

Dec 4, 2007 (3rd)

By matsui / GMP-ECM

(4·10¹⁸⁵-13)/9 = (4)₁₈₄3_<185> = 7 · 1451 · C181

C181 = P33 · C149

P33 = 164277524510786827843488693745099_<33>

C149 = [26636298892028694012587941153238062628591187075841112023861911522751253412947765247273184353075516238787560153594780836262462832930974948643067577301_<149>]

Dec 4, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

4·10¹⁶¹+9 = 4(0)₁₆₀9_<162> = 4051 · 127235411 · 1969369859_<10> · C141

C141 = P40 · P102

P40 = 3315928709727846416041854024938819789689_<40>

P102 = 118838532278963278232537809676524506390734233220677222531873601915306217550488799630909789562805027619_<102>

Number: n
N=394060101005733730854944506185225543063987154654543968918320787847903391279563079348777846305919632986249125213107544098370152142181416420491
  ( 141 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Dec 04 13:47:12 2007  prp40 factor: 3315928709727846416041854024938819789689
Tue Dec 04 13:47:12 2007  prp102 factor: 118838532278963278232537809676524506390734233220677222531873601915306217550488799630909789562805027619
Tue Dec 04 13:47:12 2007  elapsed time 01:05:12 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 31.49 hours.
Scaled time: 45.35 units (timescale=1.440).
Factorization parameters were as follows:
name: KA_4_0_160_9
n: 394060101005733730854944506185225543063987154654543968918320787847903391279563079348777846305919632986249125213107544098370152142181416420491
skew: 0.74
deg: 5
c5: 40
c0: 9
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:203362, AFBsize:203082, largePrimes:7092138 encountered
Relations: rels:6575017, finalFF:473191
Max relations in full relation-set: 28
Initial matrix: 406511 x 473191 with sparse part having weight 37652625.
Pruned matrix : 356677 x 358773 with weight 25275013.
Total sieving time: 31.28 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 31.49 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Dec 4, 2007

The factor table of 499...991 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Dec 3, 2007 (3rd)

By Yousuke Koide

(10¹⁰¹⁹-1)/9 is divisible by 1164875952920329463736875905335015089_<37>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 3, 2007 (2nd)

By Robert Backstrom / GMP-ECM

(64·10²³⁴+53)/9 = 7(1)₂₃₃7_<235> = 13 · 1181 · 7451 · 1471598307214747_<16> · 3052073285905649_<16> · 172548225862787861_<18> · 2699321912890730492306803_<25> · C155

C155 = P47 · P109

P47 = 26652891282185821045577962549160542412294508503_<47>

P109 = 1114899980065870331232905973592925067977812491581216317251152807767466063464285258166500582274270472922906037_<109>

Dec 3, 2007

By Jo Yeong Uk / GGNFS

(4·10¹⁸⁷-1)/3 = 1(3)₁₈₇_<188> = 13² · 71 · 641 · 4354373 · C174

C174 = P52 · P122

P52 = 5361712371792973170896785910460906141853462256912209_<52>

P122 = 74251719049861199442807051707488431927072858194646024738993713156188070400742301801156540569317981596338173399436320309791_<122>

Number: 13333_187
N=398116360656536779984902594959659524762886894764740907788961498125477543559005946143561502786041981375439529374284451922273986560056748206834695296451854204990252061970138319
  ( 174 digits)
SNFS difficulty: 187 digits.
Divisors found:
 r1=5361712371792973170896785910460906141853462256912209 (pp52)
 r2=74251719049861199442807051707488431927072858194646024738993713156188070400742301801156540569317981596338173399436320309791 (pp122)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 361.56 hours.
Scaled time: 773.01 units (timescale=2.138).
Factorization parameters were as follows:
n: 398116360656536779984902594959659524762886894764740907788961498125477543559005946143561502786041981375439529374284451922273986560056748206834695296451854204990252061970138319
m: 20000000000000000000000000000000000000
c5: 25
c0: -2
skew: 0.6
type: snfs
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [6000000, 11900001)
Primes: RFBsize:788060, AFBsize:788149, largePrimes:11393019 encountered
Relations: rels:11956011, finalFF:1824015
Max relations in full relation-set: 28
Initial matrix: 1576273 x 1824015 with sparse part having weight 91057329.
Pruned matrix : 1349070 x 1357015 with weight 64635248.
Total sieving time: 348.71 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 12.46 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,12000000,12000000,28,28,50,50,2.6,2.6,100000
total time: 361.56 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Jo Yeong Uk completed factorizations up to n=200 of 133...33. Congratulations!

Dec 2, 2007

By Sinkiti Sibata / PFGW

2·10¹³⁵⁶¹+9, 2·10¹⁵⁹⁵⁵+9, (23·10¹³⁰⁹²-11)/3, (17·10¹¹⁰⁴⁶+7)/3, (17·10¹⁵⁴⁴⁸+7)/3, (17·10¹⁶⁶²⁸+7)/3, (17·10¹⁶⁹¹⁸+7)/3 and (17·10¹⁸⁷³⁴+7)/3 are PRP.

Dec 1, 2007 (5th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

4·10¹⁶⁰+9 = 4(0)₁₅₉9_<161> = 277 · 138637 · 247609 · 15173733529_<11> · C138

C138 = P62 · P76

P62 = 60797126856307127135595444344471160234256633836042739865882569_<62>

P76 = 4559940072470123498850798447077277366305328269178339465898539108054593612449_<76>

Number: n
N=277231255043124412962563195334423003572989349824918726484343257938458321577544020345163333731927265082665578558503965730046567209330501481
  ( 138 digits)
SNFS difficulty: 160 digits.
Divisors found:

Sat Dec 01 14:19:53 2007  prp62 factor: 60797126856307127135595444344471160234256633836042739865882569
Sat Dec 01 14:19:53 2007  prp76 factor: 4559940072470123498850798447077277366305328269178339465898539108054593612449
Sat Dec 01 14:19:53 2007  elapsed time 01:19:11

Version: GGNFS-0.77.1-20051202-athlon
Total time: 27.74 hours.
Scaled time: 40.22 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_4_0_159_9
n: 277231255043124412962563195334423003572989349824918726484343257938458321577544020345163333731927265082665578558503965730046567209330501481
skew: 1.18
deg: 5
c5: 4
c0: 9
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1500000)
Primes: RFBsize:203362, AFBsize:203477, largePrimes:7032527 encountered
Relations: rels:6512477, finalFF:474011
Max relations in full relation-set: 28
Initial matrix: 406903 x 474011 with sparse part having weight 35734018.
Pruned matrix : 354822 x 356920 with weight 23455777.
Total sieving time: 27.55 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 27.74 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 3400+

4·10¹⁵¹+9 = 4(0)₁₅₀9_<152> = 7 · 131 · 197 · 1531 · 47933 · 2296496011_<10> · 1404598779340570579_<19> · C111

C111 = P31 · P81

P31 = 6104431168415592413869608635611_<31>

P81 = 153232696611883288817148088275635599149717352290249536018399392505789557880036813_<81>

4·10¹⁵⁷+9 = 4(0)₁₅₆9_<158> = 7 · 87972114341735599736283329579_<29> · C128

C128 = P53 · P76

P53 = 22156740177008454467142813185853133375535106690625343_<53>

P76 = 2931642819433829612544003364072511581602586787125479620745479951967818422771_<76>

Number: n
N=64955648241987874447117430039138259202002854155007541960018688539768478636343303641089348405672723770075499054458421913940885453
  ( 128 digits)
SNFS difficulty: 157 digits.
Divisors found:

Sat Dec 01 21:40:37 2007  prp53 factor: 22156740177008454467142813185853133375535106690625343
Sat Dec 01 21:40:37 2007  prp76 factor: 2931642819433829612544003364072511581602586787125479620745479951967818422771
Sat Dec 01 21:40:37 2007  elapsed time 01:33:31 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 37.39 hours.
Scaled time: 48.71 units (timescale=1.303).
Factorization parameters were as follows:
name: KA_4_0_156_9
n: 64955648241987874447117430039138259202002854155007541960018688539768478636343303641089348405672723770075499054458421913940885453
skew: 0.94
deg: 5
c5: 25
c0: 18
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1600001)
Primes: RFBsize:216816, AFBsize:216551, largePrimes:7116928 encountered
Relations: rels:6581195, finalFF:473861
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 37.16 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 37.39 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10¹⁶²+9 = 4(0)₁₆₁9_<163> = 13 · C162

C162 = P77 · P86

P77 = 14484959608208348655122569360348676482871487639034491862149522347733039174529_<77>

P86 = 21242193006733989503775579532646316990712184952355071124010335682117913659526189758317_<86>

Number: n
N=307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307693
  ( 162 digits)
SNFS difficulty: 162 digits.
Divisors found:

Sun Dec 02 00:56:26 2007  prp77 factor: 14484959608208348655122569360348676482871487639034491862149522347733039174529
Sun Dec 02 00:56:26 2007  prp86 factor: 21242193006733989503775579532646316990712184952355071124010335682117913659526189758317
Sun Dec 02 00:56:26 2007  elapsed time 01:38:38 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 57.08 hours.
Scaled time: 75.52 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_4_0_161_9
n: 307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307693
skew: 0.94
deg: 5
c5: 25
c0: 18
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2800000)
Primes: RFBsize:216816, AFBsize:216551, largePrimes:7515407 encountered
Relations: rels:6986522, finalFF:507662
Max relations in full relation-set: 28
Initial matrix: 433431 x 507662 with sparse part having weight 54891344.
Pruned matrix : 403528 x 405759 with weight 36508693.
Total sieving time: 56.79 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 57.08 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 1, 2007 (4th)

By Yousuke Koide

10¹⁴⁹⁷+1 is divisible by 7016092401376747085885131800303253_<34>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 1, 2007 (3rd)

By Robert Backstrom / GGNFS

4·10¹⁵⁵+9 = 4(0)₁₅₄9_<156> = 1975423 · 3095912878954409_<16> · C134

C134 = P65 · P70

P65 = 34448312105302906122201979845692525321041884536529688865372252369_<65>

P70 = 1898642540091341888277141518857734481586769553402869501770427156234223_<70>

Number: n
N=65405030797471631024897797203292080268700559470205742591870217011703486438834669678697175888566047633668436172058302458077017630624287
  ( 134 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=34448312105302906122201979845692525321041884536529688865372252369 (pp65)
 r2=1898642540091341888277141518857734481586769553402869501770427156234223 (pp70)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.75 hours.
Scaled time: 32.02 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_4_0_154_9
n: 65405030797471631024897797203292080268700559470205742591870217011703486438834669678697175888566047633668436172058302458077017630624287
type: snfs
skew: 1.17
deg: 5
c5: 4
c0: 9
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:216816, AFBsize:216936, largePrimes:6166954 encountered
Relations: rels:5660881, finalFF:507771
Max relations in full relation-set: 28
Initial matrix: 433816 x 507771 with sparse part having weight 24265495.
Pruned matrix : 362409 x 364642 with weight 13836447.
Total sieving time: 24.20 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.29 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 26.75 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Dec 1, 2007 (2nd)

By Sinkiti Sibata / Msieve

4·10¹⁷²+9 = 4(0)₁₇₁9_<173> = 379417 · 2183353693_<10> · 369214042069_<12> · 10392906827609765461_<20> · 1432364659536702101368956541_<28> · C100

C100 = P45 · P56

P45 = 521485688834094616003641826229481656646415453_<45>

P56 = 16846429736694498814138730507079319979241737624177166277_<56>

Thu Nov 29 14:35:06 2007  Msieve v. 1.30
Thu Nov 29 14:35:06 2007  random seeds: 5e6160f2 130a07ab
Thu Nov 29 14:35:06 2007  factoring 8785172015635305902166850873310561627369223602890592020277003775916249170381081979472941403203278481 (100 digits)
Thu Nov 29 14:35:06 2007  commencing quadratic sieve (100-digit input)
Thu Nov 29 14:35:07 2007  using multiplier of 1
Thu Nov 29 14:35:07 2007  using 64kb Pentium 4 sieve core
Thu Nov 29 14:35:07 2007  sieve interval: 18 blocks of size 65536
Thu Nov 29 14:35:07 2007  processing polynomials in batches of 6
Thu Nov 29 14:35:07 2007  using a sieve bound of 2825051 (102331 primes)
Thu Nov 29 14:35:07 2007  using large prime bound of 423757650 (28 bits)
Thu Nov 29 14:35:07 2007  using double large prime bound of 3379182069851550 (43-52 bits)
Thu Nov 29 14:35:07 2007  using trial factoring cutoff of 52 bits
Thu Nov 29 14:35:07 2007  polynomial 'A' values have 13 factors
Sat Dec  1 08:30:49 2007  102586 relations (23428 full + 79158 combined from 1560356 partial), need 102427
Sat Dec  1 08:30:56 2007  begin with 1583784 relations
Sat Dec  1 08:30:59 2007  reduce to 275743 relations in 14 passes
Sat Dec  1 08:30:59 2007  attempting to read 275743 relations
Sat Dec  1 08:31:11 2007  recovered 275743 relations
Sat Dec  1 08:31:11 2007  recovered 267629 polynomials
Sat Dec  1 08:31:11 2007  attempting to build 102586 cycles
Sat Dec  1 08:31:11 2007  found 102586 cycles in 5 passes
Sat Dec  1 08:31:11 2007  distribution of cycle lengths:
Sat Dec  1 08:31:11 2007     length 1 : 23428
Sat Dec  1 08:31:11 2007     length 2 : 17036
Sat Dec  1 08:31:11 2007     length 3 : 16856
Sat Dec  1 08:31:11 2007     length 4 : 14145
Sat Dec  1 08:31:11 2007     length 5 : 11048
Sat Dec  1 08:31:11 2007     length 6 : 7584
Sat Dec  1 08:31:11 2007     length 7 : 5024
Sat Dec  1 08:31:11 2007     length 9+: 7465
Sat Dec  1 08:31:11 2007  largest cycle: 20 relations
Sat Dec  1 08:31:12 2007  matrix is 102331 x 102586 with weight 6915312 (avg 67.41/col)
Sat Dec  1 08:31:15 2007  filtering completed in 3 passes
Sat Dec  1 08:31:15 2007  matrix is 98799 x 98863 with weight 6691681 (avg 67.69/col)
Sat Dec  1 08:31:16 2007  saving the first 48 matrix rows for later
Sat Dec  1 08:31:16 2007  matrix is 98751 x 98863 with weight 5212412 (avg 52.72/col)
Sat Dec  1 08:31:16 2007  matrix includes 64 packed rows
Sat Dec  1 08:31:16 2007  using block size 21845 for processor cache size 512 kB
Sat Dec  1 08:31:17 2007  commencing Lanczos iteration
Sat Dec  1 08:32:59 2007  lanczos halted after 1563 iterations (dim = 98750)
Sat Dec  1 08:32:59 2007  recovered 16 nontrivial dependencies
Sat Dec  1 08:33:01 2007  prp45 factor: 521485688834094616003641826229481656646415453
Sat Dec  1 08:33:01 2007  prp56 factor: 16846429736694498814138730507079319979241737624177166277
Sat Dec  1 08:33:01 2007  elapsed time 41:57:55

Dec 1, 2007

By Sinitiki Sibata / PFGW

4·10¹⁹⁶⁷⁹-9 is PRP.

November 2007

Nov 30, 2007 (3rd)

By Alfred Reich

10¹⁶⁵⁵+1 is divisible by 18802215938788787651629737655497612041_<38>

10¹⁸¹³+1 is divisible by 1341949101412826358472947603971939_<34>

Reference: Factorizations of numbers of the form 10ⁿ+1 (Alfred Reich)

Nov 30, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM

(19·10¹⁶¹-1)/9 = 2(1)₁₆₁_<162> = 727717 · 384816673 · 674074250329_<12> · C136

C136 = P35 · P101

P35 = 14467529402478870760723338650411987_<35>

P101 = 77302329134119121600032539311233102902267933504106572342606708487422816772928441334860645111491619777_<101>

Nov 30, 2007

By Bruce Dodson

10²⁴²+1 is divisible by 209363088773816814667969748813613304559806235889961_<51> and cofactor is prime.

Reference: Factoring and Prime Identification (Torbjörn Granlund)

Nov 29, 2007

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

4·10¹⁵⁸+9 = 4(0)₁₅₇9_<159> = 29 · 617 · C155

C155 = P59 · P97

P59 = 16694516335098246170350962150521377733606416852014894432101_<59>

P97 = 1339069098410419305684551449267723355927167683871174848884295909043052511734794797656249685854513_<97>

Number: n
N=22355110937238026043704241882300340915441792879897166489688705080198960487341418431788967752752473034147431956631084781758229475213770748337338624042921813
  ( 155 digits)
SNFS difficulty: 160 digits.
Divisors found:

Thu Nov 29 08:24:10 2007  prp59 factor: 16694516335098246170350962150521377733606416852014894432101
Thu Nov 29 08:24:10 2007  prp97 factor: 1339069098410419305684551449267723355927167683871174848884295909043052511734794797656249685854513
Thu Nov 29 08:24:10 2007  elapsed time 01:05:46 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 33.00 hours.
Scaled time: 43.14 units (timescale=1.307).
Factorization parameters were as follows:
name: KA_4_0_157_9
n: 22355110937238026043704241882300340915441792879897166489688705080198960487341418431788967752752473034147431956631084781758229475213770748337338624042921813
skew: 2.95
deg: 5
c5: 1
c0: 225
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1450000)
Primes: RFBsize:216816, AFBsize:216371, largePrimes:7014483 encountered
Relations: rels:6490308, finalFF:490288
Max relations in full relation-set: 28
Initial matrix: 433251 x 490288 with sparse part having weight 34015211.
Pruned matrix : 387237 x 389467 with weight 22902473.
Total sieving time: 31.53 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 1.22 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 33.00 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10¹⁵³+9 = 4(0)₁₅₂9_<154> = 211 · 499 · 823 · 7213 · 5983931 · 20484293 · C128

C128 = P34 · P95

P34 = 1674567153955540249123309372823653_<34>

P95 = 31178204285060110569074580607563260199102302136786304734413870091585370032227633400052324234081_<95>

Nov 28, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

4·10¹⁷¹+9 = 4(0)₁₇₀9_<172> = 4727579 · 42758299609_<11> · 70786206663533_<14> · 52842317195285609_<17> · 1749706642519018677552131_<25> · C100

C100 = P44 · P57

P44 = 13309174465738976322573197980572388901369971_<44>

P57 = 227171538029579664285228640378502521594404174584065064527_<57>

Number: n
N=30234656332859324703546336715738054258309704996708157961949684440936332
94526234496732144750815118717
  ( 100 digits)
Divisors found:

Wed Nov 28 06:36:31 2007  recovered 43 nontrivial dependencies
...
Wed Nov 28 07:11:14 2007  reading relations for dependency 7
...
Wed Nov 28 07:16:43 2007  prp44 factor: 
13309174465738976322573197980572388901369971
Wed Nov 28 07:16:43 2007  prp57 factor: 
227171538029579664285228640378502521594404174584065064527
Wed Nov 28 07:16:43 2007  elapsed time 00:53:58 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.30 hours.
Scaled time: 7.53 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_4_0_170_9
n: 
3023465633285932470354633671573805425830970499670815796194968444093633294
526234496732144750815118717
skew: 13066.21
# norm 1.20e+14
c5: 13380
c4: -91502224
c3: -7858450792205
c2: -14686422473786386
c1: -36147477295763868464
c0: 769155274794014273908275
# alpha -6.05
Y1: 15220904303
Y0: -11770923922825153852
# Murphy_E 3.35e-09
# M 
9956905416872819849530372527310632673808913467304665376913463743595106352
33511921121477064551418045
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved  special-q in [100000, 800000)
Primes: RFBsize:135072, AFBsize:134812, largePrimes:3453555 encountered
Relations: rels:3414232, finalFF:377182
Max relations in full relation-set: 28
Initial matrix: 269962 x 377182 with sparse part having weight 19839270.
Pruned matrix : 171344 x 172757 with weight 6919700.
Total sieving time: 6.15 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,
26,48,48,2.5,2.5,100000
total time: 6.30 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(2·10¹⁶⁷+7)/9 = (2)₁₆₆3_<167> = 17 · 22549 · 56437 · 85331 · C152

C152 = P58 · P94

P58 = 2871978723164024191549374139558544135462013900057318167591_<58>

P94 = 4191401889447764303388864665063780609861896939555630361153238115797687072530286019054001194603_<94>

Number: n
N=12037617046723468605626924896371158078923549938485194482958855970507181664139302569091093571951782614912001181491026391397577812391492441451368958711373
  ( 152 digits)
SNFS difficulty: 167 digits.
Divisors found:

Wed Nov 28 16:26:47 2007  prp58 factor: 2871978723164024191549374139558544135462013900057318167591
Wed Nov 28 16:26:47 2007  prp94 factor: 4191401889447764303388864665063780609861896939555630361153238115797687072530286019054001194603
Wed Nov 28 16:26:47 2007  elapsed time 01:44:43 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 74.04 hours.
Scaled time: 106.55 units (timescale=1.439).
Factorization parameters were as follows:
name: KA_2_166_3
n: 12037617046723468605626924896371158078923549938485194482958855970507181664139302569091093571951782614912001181491026391397577812391492441451368958711373
skew: 0.51
deg: 5
c5: 200
c0: 7
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3700001)
Primes: RFBsize:216816, AFBsize:216921, largePrimes:7734112 encountered
Relations: rels:7208772, finalFF:447988
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 73.76 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 74.04 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Nov 28, 2007

By JMB / GMP-ECM

4·10¹⁶⁵+9 = 4(0)₁₆₄9_<166> = 19 · 1877 · 8893 · 11427643437022285783_<20> · 128867463506675408316022657357_<30> · C109

C109 = P39 · P71

P39 = 467807742471873906594101709631462254293_<39>

P71 = 18307391061578173853638901084078048550027933080852242492899530687116597_<71>

Nov 27, 2007 (4th)

By Robert Backstrom / GGNFS, Msieve

(5·10¹⁶²-23)/9 = (5)₁₆₁3_<162> = 916781 · 51222224362217_<14> · C143

C143 = P53 · P90

P53 = 88251067479212923009474772487688631800999197025093157_<53>

P90 = 134055145824349829678858500491427751894659830463832718793400933405117679808822762144065977_<90>

Number: n
N=11830509720080425325375598472836094119415647645200888882018736825250641
682747740385363305803723965653576539279961713632444852447675173179219389
  ( 143 digits)
SNFS difficulty: 162 digits.
Divisors found:

Wed Nov 28 01:46:13 2007  prp53 factor: 
88251067479212923009474772487688631800999197025093157
Wed Nov 28 01:46:13 2007  prp90 factor: 
1340551458243498296788585004914277518946598304638327187934009334051176798
08822762144065977
Wed Nov 28 01:46:13 2007  elapsed time 01:49:31 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 57.66 hours.
Scaled time: 76.39 units (timescale=1.325).
Factorization parameters were as follows:
name: KA_5_161_3
n: 
1183050972008042532537559847283609411941564764520088888201873682525064168
2747740385363305803723965653576539279961713632444852447675173179219389
skew: 0.54
deg: 5
c5: 500
c0: -23
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2700000)
Primes: RFBsize:216816, AFBsize:216551, largePrimes:7434136 encountered
Relations: rels:6877587, finalFF:488281
Max relations in full relation-set: 28
Initial matrix: 433433 x 488281 with sparse part having weight 51570740.
Pruned matrix : 409705 x 411936 with weight 36845788.
Total sieving time: 57.40 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 57.66 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 27, 2007 (3rd)

By Sinkiti Sibata / GGNFS

4·10¹⁴¹+9 = 4(0)₁₄₀9_<142> = 3264208176022063_<16> · 1989887208412614157281179_<25> · C102

C102 = P38 · P65

P38 = 12560245906602427344287633654384461339_<38>

P65 = 49029282824428429410597115467691293631272803877265436025347251103_<65>

Number: 40009_141
N=615819848899179877938710121407036005167041262827473023425282772740726134822493088078335262461028606917
  ( 102 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=12560245906602427344287633654384461339 (pp38)
 r2=49029282824428429410597115467691293631272803877265436025347251103 (pp65)
Version: GGNFS-0.77.1-20060513-k8
Total time: 8.54 hours.
Scaled time: 17.10 units (timescale=2.003).
Factorization parameters were as follows:
name: 40009_141
n: 615819848899179877938710121407036005167041262827473023425282772740726134822493088078335262461028606917
m: 10000000000000000000000000000
c5: 40
c0: 9
skew: 0.74
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1550001)
Primes: RFBsize:100021, AFBsize:99568, largePrimes:2682501 encountered
Relations: rels:2667799, finalFF:280425
Max relations in full relation-set: 28
Initial matrix: 199656 x 280425 with sparse part having weight 23554506.
Pruned matrix : 173823 x 174885 with weight 12458201.
Total sieving time: 8.15 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 8.54 hours.
 --------- CPU info (if available) ----------

4·10¹³⁵+9 = 4(0)₁₃₄9_<136> = 4432543729_<10> · 350104414826237_<15> · C112

C112 = P32 · P34 · P47

P32 = 50076108520827966913691944342129_<32>

P34 = 4390119913201648970056724078503841_<34>

P47 = 11724718391352138352586053521568560187634367997_<47>

Number: 40009_135
N=25775635121078719114580793852241494535899517591251721059647750320822687095
16545156309460784839303831716228099533
  ( 112 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=50076108520827966913691944342129 (pp32)
 r2=4390119913201648970056724078503841 (pp34)
 r3=11724718391352138352586053521568560187634367997 (pp47)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.32 hours.
Scaled time: 12.66 units (timescale=2.003).
Factorization parameters were as follows:
name: 40009_135
n:
2577563512107871911458079385224149453589951759125172105964775032082268709516
545156309460784839303831716228099533
m: 1000000000000000000000000000
c5: 4
c0: 9
skew: 1.18
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:64053, largePrimes:1576550 encountered
Relations: rels:1619234, finalFF:212791
Max relations in full relation-set: 28
Initial matrix: 142615 x 212791 with sparse part having weight 15765979.
Pruned matrix : 120857 x 121634 with weight 7446674.
Total sieving time: 6.12 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.32 hours.
 --------- CPU info (if available) ----------

Nov 27, 2007 (2nd)

By Sinkiti Sibata / GGNFS

4·10¹⁴⁵+9 = 4(0)₁₄₄9_<146> = 7 · 23 · 16196138573250129419_<20> · 270390616492056889150461299_<27> · C98

C98 = P40 · P59

P40 = 1605173021880918410125104138533069730893_<40>

P59 = 35343468163557001022907513872788192718182385124531802470493_<59>

Number: 40009_145
N=56732381595848825220588411669623668386053143977130622031227669941751645504214351435599936083040249
  ( 98 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=1605173021880918410125104138533069730893 (pp40)
 r2=35343468163557001022907513872788192718182385124531802470493 (pp59)
Version: GGNFS-0.77.1-20060513-k8
Total time: 11.67 hours.
Scaled time: 23.46 units (timescale=2.010).
Factorization parameters were as follows:
name: 40009_145
n: 56732381595848825220588411669623668386053143977130622031227669941751645504214351435599936083040249
m: 100000000000000000000000000000
c5: 4
c0: 9
skew: 1.18
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1950001)
Primes: RFBsize:100021, AFBsize:100078, largePrimes:2670477 encountered
Relations: rels:2616911, finalFF:229148
Max relations in full relation-set: 28
Initial matrix: 200163 x 229148 with sparse part having weight 21999475.
Pruned matrix : 191898 x 192962 with weight 16653697.
Total sieving time: 11.09 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 11.67 hours.
 --------- CPU info (if available) ----------

Nov 27, 2007

By Robert Backstrom / GGNFS, Msieve

4·10¹³⁷+9 = 4(0)₁₃₆9_<138> = 47 · 210996161 · 27663076039007_<14> · C115

C115 = P48 · P68

P48 = 144128879329630272184991648078450696106391196441_<48>

P68 = 10116635425360137333667412655105196323996222926944429943963917753921_<68>

Number: n
N=1458099326443594054045323972411079454526604785894103274387642346249087765340142012336087436548886974989376608995161
  ( 115 digits)
SNFS difficulty: 137 digits.
Divisors found:

Tue Nov 27 03:12:55 2007  prp48 factor: 144128879329630272184991648078450696106391196441
Tue Nov 27 03:12:55 2007  prp68 factor: 10116635425360137333667412655105196323996222926944429943963917753921
Tue Nov 27 03:12:55 2007  elapsed time 00:26:19 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 6.20 hours.
Scaled time: 8.01 units (timescale=1.293).
Factorization parameters were as follows:
name: KA_4_0_136_9
n: 1458099326443594054045323972411079454526604785894103274387642346249087765340142012336087436548886974989376608995161
skew: 0.94
deg: 5
c5: 25
c0: 18
m: 2000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 800000)
Primes: RFBsize:114155, AFBsize:113992, largePrimes:6288087 encountered
Relations: rels:5665178, finalFF:314490
Max relations in full relation-set: 28
Initial matrix: 228211 x 314490 with sparse part having weight 25079773.
Pruned matrix : 185311 x 186516 with weight 11952601.
Total sieving time: 6.00 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,75000
total time: 6.20 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10¹⁴⁶+9 = 4(0)₁₄₅9_<147> = 220681 · 486209806553_<12> · C130

C130 = P39 · P91

P39 = 764412203911204700836054966106935734613_<39>

P91 = 4876898556751362048961362794806390789746536739262210158192817562689449702712780913893826501_<91>

Number: n
N=3727960774017682077509562283847137837199147716353152979632032702775892834651891935886292568866270350371012428874815801170002379113
  ( 130 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=764412203911204700836054966106935734613 (pp39)
 r2=4876898556751362048961362794806390789746536739262210158192817562689449702712780913893826501 (pp91)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 10.26 hours.
Scaled time: 12.27 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_4_0_145_9
n: 3727960774017682077509562283847137837199147716353152979632032702775892834651891935886292568866270350371012428874815801170002379113
type: snfs
skew: 0.74
deg: 5
c5: 40
c0: 9
m: 100000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1150001)
Primes: RFBsize:148933, AFBsize:148405, largePrimes:5927738 encountered
Relations: rels:5289921, finalFF:359602
Max relations in full relation-set: 28
Initial matrix: 297405 x 359602 with sparse part having weight 20581544.
Pruned matrix : 247886 x 249437 with weight 11630633.
Total sieving time: 8.79 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.21 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 10.26 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 26, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(10²¹⁵³+53)/9 is prime.

Nov 26, 2007 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

4·10¹²⁶+9 = 4(0)₁₂₅9_<127> = 13² · 1093 · 157478185310284045321_<21> · C102

C102 = P32 · P70

P32 = 51219530045909995936125110786993_<32>

P70 = 2684708475243401264102954877320619544959453611256556529626076156285909_<70>

Number: 40009_126
N=137509506412238603536864415063538192494400116628332569921903945385237808208535294351993306538906381637
  ( 102 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=51219530045909995936125110786993 (pp32)
 r2=2684708475243401264102954877320619544959453611256556529626076156285909 (pp70)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.80 hours.
Scaled time: 5.61 units (timescale=2.003).
Factorization parameters were as follows:
name: 40009_126
n: 137509506412238603536864415063538192494400116628332569921903945385237808208535294351993306538906381637
m: 10000000000000000000000000
c5: 40
c0: 9
skew: 0.74
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63733, largePrimes:2383131 encountered
Relations: rels:2755788, finalFF:468753
Max relations in full relation-set: 28
Initial matrix: 112898 x 468753 with sparse part having weight 45593086.
Pruned matrix : 76412 x 77040 with weight 8664530.
Total sieving time: 2.66 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.80 hours.
 --------- CPU info (if available) ----------

4·10¹²⁸+9 = 4(0)₁₂₇9_<129> = 1993 · 51913 · 1430797079340329352472921_<25> · C97

C97 = P48 · P50

P48 = 181803558476376236283955641729897094029004670893_<48>

P50 = 14862646249026576411818998493115073085499220973317_<50>

Number: 40009_128
N=2702081976448597109558698566520468643612755318410534419392185730772033180107476795736942719562081
  ( 97 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=181803558476376236283955641729897094029004670893 (pp48)
 r2=14862646249026576411818998493115073085499220973317 (pp50)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.78 hours.
Scaled time: 7.55 units (timescale=1.997).
Factorization parameters were as follows:
name: 40009_128
n: 2702081976448597109558698566520468643612755318410534419392185730772033180107476795736942719562081
m: 20000000000000000000000000
c5: 125
c0: 9
skew: 0.59
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:63951, AFBsize:64093, largePrimes:1557590 encountered
Relations: rels:1625431, finalFF:234022
Max relations in full relation-set: 28
Initial matrix: 128110 x 234022 with sparse part having weight 14826718.
Pruned matrix : 98552 x 99256 with weight 5347992.
Total sieving time: 3.66 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 3.78 hours.
 --------- CPU info (if available) ----------

4·10¹²⁹+9 = 4(0)₁₂₈9_<130> = 19 · 13921 · 42456366769_<11> · 1961107985919825167_<19> · C96

C96 = P32 · P64

P32 = 90496029963707513725625363116699_<32>

P64 = 2007068038467510110982557191892561779029831762757164209225700983_<64>

Number: 40009_129
N=181631689348355459790962688701929834427428033812142412776081374439007954060590809771261908015117
  ( 96 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=90496029963707513725625363116699 (pp32)
 r2=2007068038467510110982557191892561779029831762757164209225700983 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.35 hours.
Scaled time: 8.78 units (timescale=2.016).
Factorization parameters were as follows:
name: 40009_129
n: 181631689348355459790962688701929834427428033812142412776081374439007954060590809771261908015117
m: 100000000000000000000000000
c5: 2
c0: 45
skew: 1.86
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64093, largePrimes:1536620 encountered
Relations: rels:1564442, finalFF:196332
Max relations in full relation-set: 28
Initial matrix: 128109 x 196332 with sparse part having weight 14524685.
Pruned matrix : 109268 x 109972 with weight 6465733.
Total sieving time: 4.20 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.35 hours.
 --------- CPU info (if available) ----------

4·10¹³³+9 = 4(0)₁₃₂9_<134> = 7 · 14039910954930703_<17> · C117

C117 = P54 · P64

P54 = 212045331507039776360742002829387808898620546351104409_<54>

P64 = 1919414992157459171757261776221197366678153779688615271444343881_<64>

Number: 40009_133
N=407002988311610582561227888701054777787770001367652789611232968795378225157190752222575768698744823864819960731271329
  ( 117 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=212045331507039776360742002829387808898620546351104409 (pp54)
 r2=1919414992157459171757261776221197366678153779688615271444343881 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.87 hours.
Scaled time: 11.73 units (timescale=1.997).
Factorization parameters were as follows:
name: 40009_133
n: 407002988311610582561227888701054777787770001367652789611232968795378225157190752222575768698744823864819960731271329
m: 200000000000000000000000000
c5: 125
c0: 9
skew: 0.59
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:64093, largePrimes:1612445 encountered
Relations: rels:1679680, finalFF:236889
Max relations in full relation-set: 28
Initial matrix: 142657 x 236889 with sparse part having weight 18018688.
Pruned matrix : 114736 x 115513 with weight 7558893.
Total sieving time: 5.69 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.87 hours.
 --------- CPU info (if available) ----------

4·10¹⁴⁷+9 = 4(0)₁₄₆9_<148> = 19 · 4057594903_<10> · 44338326960703_<14> · 256008644002393841860575255628769_<33> · C91

C91 = P39 · P53

P39 = 404664799012214157417672549706061106703_<39>

P53 = 11295575051062064761509401409725052595688718501423797_<53>

Mon Nov 26 07:03:06 2007  Msieve v. 1.28
Mon Nov 26 07:03:06 2007  random seeds: 806018b8 fde7d0ee
Mon Nov 26 07:03:06 2007  factoring 4570921607765411105037991565791212407235592613498883380616910429784125813855670791040411291 (91 digits)
Mon Nov 26 07:03:07 2007  commencing quadratic sieve (91-digit input)
Mon Nov 26 07:03:07 2007  using multiplier of 3
Mon Nov 26 07:03:07 2007  using 64kb Pentium 2 sieve core
Mon Nov 26 07:03:07 2007  sieve interval: 18 blocks of size 65536
Mon Nov 26 07:03:07 2007  processing polynomials in batches of 6
Mon Nov 26 07:03:07 2007  using a sieve bound of 1719869 (64508 primes)
Mon Nov 26 07:03:07 2007  using large prime bound of 165107424 (27 bits)
Mon Nov 26 07:03:07 2007  using double large prime bound of 619412223763104 (42-50 bits)
Mon Nov 26 07:03:07 2007  using trial factoring cutoff of 50 bits
Mon Nov 26 07:03:07 2007  polynomial 'A' values have 12 factors
Mon Nov 26 18:54:49 2007  64777 relations (16555 full + 48222 combined from 769817 partial), need 64604
Mon Nov 26 18:54:55 2007  begin with 786372 relations
Mon Nov 26 18:55:11 2007  reduce to 163091 relations in 10 passes
Mon Nov 26 18:55:11 2007  attempting to read 163091 relations
Mon Nov 26 18:55:23 2007  recovered 163091 relations
Mon Nov 26 18:55:23 2007  recovered 145695 polynomials
Mon Nov 26 18:55:45 2007  attempting to build 64777 cycles
Mon Nov 26 18:55:45 2007  found 64777 cycles in 6 passes
Mon Nov 26 18:55:48 2007  distribution of cycle lengths:
Mon Nov 26 18:55:48 2007     length 1 : 16555
Mon Nov 26 18:55:48 2007     length 2 : 11833
Mon Nov 26 18:55:48 2007     length 3 : 11147
Mon Nov 26 18:55:48 2007     length 4 : 8679
Mon Nov 26 18:55:48 2007     length 5 : 6323
Mon Nov 26 18:55:48 2007     length 6 : 4272
Mon Nov 26 18:55:48 2007     length 7 : 2648
Mon Nov 26 18:55:48 2007     length 9+: 3320
Mon Nov 26 18:55:48 2007  largest cycle: 18 relations
Mon Nov 26 18:55:49 2007  matrix is 64508 x 64777 with weight 4021806 (avg 62.09/col)
Mon Nov 26 18:55:53 2007  filtering completed in 3 passes
Mon Nov 26 18:55:53 2007  matrix is 61073 x 61137 with weight 3812110 (avg 62.35/col)
Mon Nov 26 18:55:56 2007  saving the first 48 matrix rows for later
Mon Nov 26 18:55:56 2007  matrix is 61025 x 61137 with weight 3042466 (avg 49.76/col)
Mon Nov 26 18:55:56 2007  matrix includes 64 packed rows
Mon Nov 26 18:55:56 2007  using block size 10922 for processor cache size 256 kB
Mon Nov 26 18:55:58 2007  commencing Lanczos iteration
Mon Nov 26 18:59:10 2007  lanczos halted after 966 iterations
Mon Nov 26 18:59:11 2007  recovered 16 nontrivial dependencies
Mon Nov 26 18:59:37 2007  prp39 factor: 404664799012214157417672549706061106703
Mon Nov 26 18:59:37 2007  prp53 factor: 11295575051062064761509401409725052595688718501423797
Mon Nov 26 18:59:37 2007  elapsed time 11:56:31

Nov 26, 2007

By Robert Backstrom / GGNFS, Msieve

4·10¹¹⁰+9 = 4(0)₁₀₉9_<111> = 113 · 2393 · 251419167001_<12> · C94

C94 = P36 · P59

P36 = 165181848872234857617062189249532241_<36>

P59 = 35618706443028798016568330143685321380313564206887456692761_<59>

Number: n
N=5883563784696880916434650652243177524072887965464968204171469084560963632896817817164100807401
  ( 94 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=165181848872234857617062189249532241 (pp36)
 r2=35618706443028798016568330143685321380313564206887456692761 (pp59)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.95 hours.
Scaled time: 1.13 units (timescale=1.193).
Factorization parameters were as follows:
name: KA_4_0_109_9
n: 5883563784696880916434650652243177524072887965464968204171469084560963632896817817164100807401
type: snfs
skew: 1.18
deg: 5
c5: 4
c0: 9
m: 10000000000000000000000
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:63951, AFBsize:64053, largePrimes:3675896 encountered
Relations: rels:3189891, finalFF:232392
Max relations in full relation-set: 28
Initial matrix: 128068 x 232392 with sparse part having weight 9272010.
Pruned matrix : 64275 x 64979 with weight 2367167.
Total sieving time: 0.80 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.04 hours.
Total square root time: 0.04 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.4,2.4,50000
total time: 0.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

4·10¹¹⁹+9 = 4(0)₁₁₈9_<120> = 59011 · C115

C115 = P44 · P72

P44 = 10299709529696676595537272509874674618354731_<44>

P72 = 658115379703367141596436109463234164314654145602057711013672694021719049_<72>

Number: n
N=6778397247970717323888766501160800528714985341715951263323787090542441239768856653844198539255393062310416701970819
  ( 115 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=10299709529696676595537272509874674618354731 (pp44)
 r2=658115379703367141596436109463234164314654145602057711013672694021719049 (pp72)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.09 hours.
Scaled time: 2.49 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_4_0_118_9
n: 6778397247970717323888766501160800528714985341715951263323787090542441239768856653844198539255393062310416701970819
type: snfs
skew: 1.86
deg: 5
c5: 2
c0: 45
m: 1000000000000000000000000
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 240001)
Primes: RFBsize:78498, AFBsize:78531, largePrimes:4067301 encountered
Relations: rels:3437845, finalFF:191917
Max relations in full relation-set: 28
Initial matrix: 157094 x 191917 with sparse part having weight 8634183.
Pruned matrix : 126308 x 127157 with weight 4290229.
Total sieving time: 1.70 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.17 hours.
Total square root time: 0.12 hours, sqrts: 5.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.4,2.4,50000
total time: 2.09 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(52·10¹⁶⁴-7)/9 = 5(7)₁₆₄_<165> = 29 · 7019 · 6320886474787_<13> · C147

C147 = P52 · P96

P52 = 1253831070899856312688601931720582966577047750139261_<52>

P96 = 358154634908081150423440098044503617839531497495445248785010282856127665013429077944232929344361_<96>

Number: n
N=449065409434546449622971187681183740755523201415900451788832840460807324862141335905611317885561982939064087542226259352648468932390312211175057221
  ( 147 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Nov 26 16:37:58 2007  prp52 factor: 1253831070899856312688601931720582966577047750139261
Mon Nov 26 16:37:58 2007  prp96 factor: 358154634908081150423440098044503617839531497495445248785010282856127665013429077944232929344361
Mon Nov 26 16:37:58 2007  elapsed time 02:02:22 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 108.78 hours.
Scaled time: 140.77 units (timescale=1.294).
Factorization parameters were as follows:
name: KA_5_7_164
n: 449065409434546449622971187681183740755523201415900451788832840460807324862141335905611317885561982939064087542226259352648468932390312211175057221
skew: 1.06
deg: 5
c5: 26
c0: -35
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3600001)
Primes: RFBsize:230209, AFBsize:230477, largePrimes:7720364 encountered
Relations: rels:7181991, finalFF:477241
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 108.43 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 108.78 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10¹³¹+9 = 4(0)₁₃₀9_<132> = 619 · 194167 · 14543527 · C117

C117 = P44 · P73

P44 = 80094272947449979071432758202536808045156517_<44>

P73 = 2857082077051308573674020837361541499660528541802562865615658481450429087_<73>

Number: n
N=228835911712614820963407007506081825552432657431830205371716856226255647416792245683256227303671261195144781724409979
  ( 117 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=80094272947449979071432758202536808045156517 (pp44)
 r2=2857082077051308573674020837361541499660528541802562865615658481450429087 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.68 hours.
Scaled time: 4.40 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_4_0_130_9
n: 228835911712614820963407007506081825552432657431830205371716856226255647416792245683256227303671261195144781724409979
type: snfs
skew: 0.74
deg: 5
c5: 40
c0: 9
m: 100000000000000000000000000
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 460001)
Primes: RFBsize:114155, AFBsize:113572, largePrimes:4179030 encountered
Relations: rels:3531412, finalFF:259869
Max relations in full relation-set: 28
Initial matrix: 227794 x 259869 with sparse part having weight 7780095.
Pruned matrix : 168810 x 170012 with weight 4136104.
Total sieving time: 3.28 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.26 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.2,2.2,50000
total time: 3.68 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

4·10¹¹⁷+9 = 4(0)₁₁₆9_<118> = 163890451 · 119008224119929_<15> · C96

C96 = P34 · P63

P34 = 1049848161996414833607686052033851_<34>

P63 = 195345258444219449654150537877637812726731604913236518703820721_<63>

Number: n
N=205082860532378423488589379837991228596967004928112301824211634341274075328421533654926527226571
  ( 96 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=1049848161996414833607686052033851 (pp34)
 r2=195345258444219449654150537877637812726731604913236518703820721 (pp63)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.75 hours.
Scaled time: 2.09 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_4_0_116_9
n: 205082860532378423488589379837991228596967004928112301824211634341274075328421533654926527226571
type: snfs
skew: 0.94
deg: 5
c5: 25
c0: 18
m: 200000000000000000000000
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 220001)
Primes: RFBsize:78498, AFBsize:78241, largePrimes:3946046 encountered
Relations: rels:3317892, finalFF:182434
Max relations in full relation-set: 28
Initial matrix: 156803 x 182434 with sparse part having weight 7590913.
Pruned matrix : 131548 x 132396 with weight 4205854.
Total sieving time: 1.36 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.18 hours.
Total square root time: 0.11 hours, sqrts: 5.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.4,2.4,50000
total time: 1.75 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 25, 2007 (5th)

By Jo Yeong Uk / GGNFS

4·10¹¹⁸+9 = 4(0)₁₁₇9_<119> = C119

C119 = P52 · P68

P52 = 3728574790867178284745181738866780429302431068160529_<52>

P68 = 10727959674558907354142285722781332734722136495462711094331511744121_<68>

Number: 40009_118
N=40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 119 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=3728574790867178284745181738866780429302431068160529 (pp52)
 r2=10727959674558907354142285722781332734722136495462711094331511744121 (pp68)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.90 hours.
Scaled time: 1.93 units (timescale=2.144).
Factorization parameters were as follows:
n: 40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
m: 1000000000000000000000000
c5: 1
c0: 225
skew: 2.95
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 450001)
Primes: RFBsize:49098, AFBsize:49111, largePrimes:1886445 encountered
Relations: rels:1942478, finalFF:199895
Max relations in full relation-set: 28
Initial matrix: 98273 x 199895 with sparse part having weight 17093793.
Pruned matrix : 77103 x 77658 with weight 4340439.
Total sieving time: 0.85 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.90 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Nov 25, 2007 (4th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(4·10¹⁶⁴-7)/3 = 1(3)₁₆₃1_<165> = 983 · 6424123 · 8002014907_<10> · C145

C145 = P41 · P44 · P61

P41 = 38845079894049413226636666173926767146741_<41>

P44 = 37241278615967782300259863150917251444291063_<44>

P61 = 1823943632731313508599180109626448102079347834135801509470639_<61>

Number: n
N=67925993006367260173084306432034998810393910129667030593595794518859702769290352728359242093103768599257
  ( 104 digits)
Divisors found:

Mon Nov 26 00:08:03 2007  prp44 factor: 37241278615967782300259863150917251444291063
Mon Nov 26 00:08:03 2007  prp61 factor: 1823943632731313508599180109626448102079347834135801509470639
Mon Nov 26 00:08:03 2007  elapsed time 01:07:26 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 18.97 hours.
Scaled time: 22.69 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_1_3_163_1
n: 67925993006367260173084306432034998810393910129667030593595794518859702769290352728359242093103768599257
skew: 14548.83
# norm 4.31e+14
c5: 15540
c4: 662881441
c3: -30284510564936
c2: -70420841882984262
c1: 1380105811745476751310
c0: 213375504826872901606500
# alpha -5.63
Y1: 56183257309
Y0: -84745088989414396159
# Murphy_E 1.94e-09
# M 35605800172212779601640616997983630603863264454095218451097658761114576612953147801228187028086397273557
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved  special-q in [100000, 1200000)
Primes: RFBsize:169511, AFBsize:169993, largePrimes:4092500 encountered
Relations: rels:4001895, finalFF:381407
Max relations in full relation-set: 28
Initial matrix: 339591 x 381407 with sparse part having weight 23210863.
Pruned matrix : 297455 x 299216 with weight 14265146.
Total sieving time: 18.76 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 18.97 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 25, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(22·10²¹⁵⁹-31)/9 is prime.

Nov 25, 2007 (2nd)

By matsui / GMP-ECM

(5·10¹⁸⁷-23)/9 = (5)₁₈₆3_<187> = 3 · C187

C187 = P34 · C154

P34 = 1249569676018218532056891295863517_<34>

C154 = [1481991670726852801036337564124989580909663768841067210637083024250974479404992726846367777814579781927851301822010278319654383652691909116064846052888903_<154>]

Nov 25, 2007

The factor table of 400...009 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Nov 24, 2007 (4th)

By matsui / GMP-ECM

(2·10¹⁸⁹+61)/9 = (2)₁₈₈9_<189> = 31 · 107 · C185

C185 = P36 · C149

P36 = 927349548463379812942637190276565777_<36>

C149 = [72243462018069324109887983093635000589160560432323063168326829250562665832911989665414796383191130798805708121654081515508917870686847094978760612881_<149>]

Nov 24, 2007 (3rd)

By Sinkiti Sibata / GGNFS

4·10¹⁵⁹-9 = 3(9)₁₅₈1_<160> = 13 · 199 · 2130173 · 64929089 · 24131072597_<11> · 952589489681209_<15> · C117

C117 = P44 · P73

P44 = 74079493501806378527450601403663790436099271_<44>

P73 = 6564912794659200412500871081575072082513907943647734630671406825808638043_<73>

Number: 39991_159
N=486325414711881789179913696860213450928824568538724820830782157801328627106326427776063177946853247455134006055166653
  ( 117 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=74079493501806378527450601403663790436099271 (pp44)
 r2=6564912794659200412500871081575072082513907943647734630671406825808638043 (pp73)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 77.01 hours.
Scaled time: 51.98 units (timescale=0.675).
Factorization parameters were as follows:
name: 39991_159
n: 486325414711881789179913696860213450928824568538724820830782157801328627106326427776063177946853247455134006055166653
m: 100000000000000000000000000000000
c5: 2
c0: -45
skew: 1.86
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3900001)
Primes: RFBsize:283146, AFBsize:283407, largePrimes:5742291 encountered
Relations: rels:5806571, finalFF:681486
Max relations in full relation-set: 28
Initial matrix: 566618 x 681486 with sparse part having weight 45436461.
Pruned matrix : 483086 x 485983 with weight 31035378.
Total sieving time: 66.61 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 9.87 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 77.01 hours.
 --------- CPU info (if available) ----------

Nov 24, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

(32·10¹⁶²-23)/9 = 3(5)₁₆₁3_<163> = 79 · 353 · 10831 · 2304545063_<10> · C145

C145 = P59 · P87

P59 = 11418294572176870102030727526262175468766886077048774464453_<59>

P87 = 447353324129822631187220179321823753744991839539223628912706731724334093004388243879691_<87>

Number: n
N=5108012032756833801090420940354909442473568947558897114792618109230650012286452899825548147198860702329357055515312908368542021336328083488124023
  ( 145 digits)
SNFS difficulty: 163 digits.
Divisors found:

Sat Nov 24 02:02:22 2007  prp59 factor: 11418294572176870102030727526262175468766886077048774464453
Sat Nov 24 02:02:22 2007  prp87 factor: 447353324129822631187220179321823753744991839539223628912706731724334093004388243879691
Sat Nov 24 02:02:22 2007  elapsed time 01:45:11 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 44.69 hours.
Scaled time: 59.13 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_3_5_161_3
n: 5108012032756833801090420940354909442473568947558897114792618109230650012286452899825548147198860702329357055515312908368542021336328083488124023
skew: 0.75
deg: 5
c5: 100
c0: -23
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100000)
Primes: RFBsize:216816, AFBsize:217116, largePrimes:7231197 encountered
Relations: rels:6696431, finalFF:498681
Max relations in full relation-set: 28
Initial matrix: 433996 x 498681 with sparse part having weight 44598884.
Pruned matrix : 388932 x 391165 with weight 29632951.
Total sieving time: 44.45 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 44.69 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 24, 2007

By Yousuke Koide

10¹⁷⁴⁹+1 is divisible by 1107787169378395599401257233239538397_<37>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 22, 2007 (3rd)

By Robert Backstrom / GGNFS

(5·10¹⁶¹-41)/9 = (5)₁₆₀1_<161> = 3² · 68196269 · 15233617008611_<14> · C139

C139 = P50 · P90

P50 = 16440538531421432078827696011643851667074412930711_<50>

P90 = 361414271751827151353177663968973256352972286750998069364546030733668065300904591141591911_<90>

Number: n
N=5941845260541530719336256541742219880917628765154081949520232045063493647492461579811333302877434609513809414777144042637306700263481078721
  ( 139 digits)
SNFS difficulty: 161 digits.
Divisors found:

Thu Nov 22 18:28:14 2007  prp50 factor: 16440538531421432078827696011643851667074412930711
Thu Nov 22 18:28:14 2007  prp90 factor: 361414271751827151353177663968973256352972286750998069364546030733668065300904591141591911
Thu Nov 22 18:28:14 2007  elapsed time 02:27:05 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 48.96 hours.
Scaled time: 58.56 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_5_160_1
n: 5941845260541530719336256541742219880917628765154081949520232045063493647492461579811333302877434609513809414777144042637306700263481078721
type: snfs
skew: 0.96
deg: 5
c5: 50
c0: -41
m: 100000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100000)
Primes: RFBsize:250150, AFBsize:250567, largePrimes:7178290 encountered
Relations: rels:6709445, finalFF:607497
Max relations in full relation-set: 28
Initial matrix: 500782 x 607497 with sparse part having weight 34954359.
Pruned matrix : 408203 x 410770 with weight 20239156.
Total sieving time: 48.70 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.3,2.3,100000
total time: 48.96 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 22, 2007 (2nd)

By Jo Yeong Uk / GGNFS

8·10¹⁸¹-7 = 7(9)₁₈₀3_<182> = C182

C182 = P48 · P135

P48 = 216148982655435929699114314027715477553384103519_<48>

P135 = 370115089218478356758654535607364677329573694364240237802979699121028544430300307143621280593966654455367748978194923424449434078433447_<135>

Number: 79993_181
N=79999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 182 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=216148982655435929699114314027715477553384103519 (pp48)
 r2=370115089218478356758654535607364677329573694364240237802979699121028544430300307143621280593966654455367748978194923424449434078433447 (pp135)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 248.23 hours.
Scaled time: 529.98 units (timescale=2.135).
Factorization parameters were as follows:
n: 79999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
m: 2000000000000000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [5000000, 9100001)
Primes: RFBsize:664579, AFBsize:665480, largePrimes:11067378 encountered
Relations: rels:11387297, finalFF:1536217
Max relations in full relation-set: 28
Initial matrix: 1330124 x 1536217 with sparse part having weight 93212688.
Pruned matrix : 1143509 x 1150223 with weight 64319333.
Total sieving time: 238.30 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 9.59 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000
total time: 248.23 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 22, 2007

By Yousuke Koide

10¹⁰⁷⁹+1 is divisible by 12872791513686398145408033283561_<32>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 21, 2007 (2nd)

By Robert Backstrom / GGNFS

2·10¹⁶²+9 = 2(0)₁₆₁9_<163> = 11 · 113 · 2081 · 2657 · C153

C153 = P47 · P107

P47 = 27122851242050836906551105038309233622985323233_<47>

P107 = 10729015936115722072912979992395528159519097329221924474233456905349010539193520511048503243582233656097483_<107>

Number: n
N=291001503208859535061564265651302436861094295924708253361979542649323701281159624158760359646784825637743314939558512723565886104522114020560808112722539
  ( 153 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=27122851242050836906551105038309233622985323233 (pp47)
 r2=10729015936115722072912979992395528159519097329221924474233456905349010539193520511048503243582233656097483 (pp107)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 36.87 hours.
Scaled time: 48.12 units (timescale=1.305).
Factorization parameters were as follows:
name: KA_2_0_161_9
n: 291001503208859535061564265651302436861094295924708253361979542649323701281159624158760359646784825637743314939558512723565886104522114020560808112722539
skew: 1.08
deg: 5
c5: 25
c0: 36
m: 200000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1550001)
Primes: RFBsize:230209, AFBsize:230472, largePrimes:7089581 encountered
Relations: rels:6599696, finalFF:530658
Max relations in full relation-set: 28
Initial matrix: 460745 x 530658 with sparse part having weight 35163360.
Pruned matrix : 401897 x 404264 with weight 22662170.
Total sieving time: 33.35 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 3.15 hours.
Total square root time: 0.12 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 36.87 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 21, 2007

By Sinkiti Sibata / GGNFS

4·10¹⁵¹-9 = 3(9)₁₅₀1_<152> = 31 · 5519 · 371213 · 1158569 · 54827975693_<11> · 85431185431_<11> · C114

C114 = P48 · P66

P48 = 683451293547552766493247508223331705485919834283_<48>

P66 = 169811308556460662649467994337463527761352643619555931552038754243_<66>

Number: 39991_151
N=116057758491915655173344214309582763419377248961382375191490426117901521122776418083702863212981536767552323112769
  ( 114 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=683451293547552766493247508223331705485919834283 (pp48)
 r2=169811308556460662649467994337463527761352643619555931552038754243 (pp66)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 27.46 hours.
Scaled time: 18.54 units (timescale=0.675).
Factorization parameters were as follows:
name: 39991_151
n: 116057758491915655173344214309582763419377248961382375191490426117901521122776418083702863212981536767552323112769
m: 1000000000000000000000000000000
c5: 40
c0: -9
skew: 0.74
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:175758, largePrimes:5240539 encountered
Relations: rels:5083135, finalFF:433587
Max relations in full relation-set: 28
Initial matrix: 352127 x 433587 with sparse part having weight 34832429.
Pruned matrix : 302527 x 304351 with weight 21729699.
Total sieving time: 23.97 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.16 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 27.46 hours.
 --------- CPU info (if available) ----------

4·10¹⁸⁵+3 = 4(0)₁₈₄3_<186> = 59 · C184

C184 = P68 · P117

P68 = 11020580464970018963281153740355391062570795450373519356122648057289_<68>

P117 = 615181844413636911986288389296689173200938369983514842349545281535581167010170014581500501046126500380108078763742353_<117>

Number: 40003_185
N=6779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661017
  ( 184 digits)
SNFS difficulty: 185 digits.
Divisors found:
 r1=11020580464970018963281153740355391062570795450373519356122648057289 (pp68)
 r2=615181844413636911986288389296689173200938369983514842349545281535581167010170014581500501046126500380108078763742353 (pp117)
Version: GGNFS-0.77.1-20060513-k8
Total time: 676.35 hours.
Scaled time: 1350.68 units (timescale=1.997).
Factorization parameters were as follows:
name: 40003_185
n: 6779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661017
m: 10000000000000000000000000000000000000
c5: 4
c0: 3
skew: 0.94
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 11400001)
Primes: RFBsize:501962, AFBsize:502056, largePrimes:6651477 encountered
Relations: rels:7134496, finalFF:1151991
Max relations in full relation-set: 28
Initial matrix: 1004085 x 1151991 with sparse part having weight 85952580.
Pruned matrix : 882609 x 887693 with weight 67545486.
Total sieving time: 663.68 hours.
Total relation processing time: 0.62 hours.
Matrix solve time: 11.72 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 676.35 hours.
 --------- CPU info (if available) ----------

Nov 20, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

4·10¹⁶¹-9 = 3(9)₁₆₀1_<162> = 53 · C160

C160 = P41 · P120

P41 = 21806825430466113390135407080568754712841_<41>

P120 = 346092091000860392504443010316442896408178789678554842890548184933093473061870388053493738110298874615414662714544919267_<120>

Number: n
N=7547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547
  ( 160 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Nov 20 21:05:11 2007  prp41 factor: 21806825430466113390135407080568754712841
Tue Nov 20 21:05:11 2007  prp120 factor: 346092091000860392504443010316442896408178789678554842890548184933093473061870388053493738110298874615414662714544919267
Tue Nov 20 21:05:11 2007  elapsed time 01:33:02 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 32.27 hours.
Scaled time: 42.73 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_3_9_160_1
n: 7547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547
skew: 0.74
deg: 5
c5: 40
c0: -9
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1600000)
Primes: RFBsize:216816, AFBsize:216336, largePrimes:7059026 encountered
Relations: rels:6542964, finalFF:512046
Max relations in full relation-set: 28
Initial matrix: 433219 x 512046 with sparse part having weight 41365043.
Pruned matrix : 370773 x 373003 with weight 24932021.
Total sieving time: 32.05 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 32.27 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 20, 2007 (2nd)

By matsui / GMP-ECM

(2·10¹⁸⁶-17)/3 = (6)₁₈₅1_<186> = 577 · C184

C184 = P35 · C149

P35 = 56045655546039900196398563598407527_<35>

C149 = [20615362435591879186624607699826768353984778680961983009624827499187120028491903918962048793936194257434728540858949740169821440639266289814167775059_<149>]

Nov 20, 2007

By JMB / GMP-ECM

9·10²⁰⁰+7 = 9(0)₁₉₉7_<201> = 16363 · 1185871 · 11041256557141927631_<20> · C172

C172 = P40 · P133

P40 = 1129520353150946514870638937980393951891_<40>

P133 = 3719029026601584878459985815308542356310526920113885973087730339593263375620616238307141131837874615521876099561714963205165591240279_<133>

Nov 19, 2007 (2nd)

By Robert Backstrom / GGNFS, GMP-ECM, Msieve

4·10¹⁴⁷-9 = 3(9)₁₄₆1_<148> = 13 · 89 · 6167403400563579766175239_<25> · C120

C120 = P43 · P77

P43 = 9859117276170965916528849893551257536137453_<43>

P77 = 56857301497661450675385390309929156870609092238968154609890852061865551467889_<77>

Number: n
N=560562803472055342614818809179881640621418269258805647401713026165934061851143305328751575837660941339806278907419746717
  ( 120 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=9859117276170965916528849893551257536137453 (pp43)
 r2=56857301497661450675385390309929156870609092238968154609890852061865551467889 (pp77)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 16.03 hours.
Scaled time: 19.11 units (timescale=1.192).
Factorization parameters were as follows:
name: KA_3_9_146_1
n: 560562803472055342614818809179881640621418269258805647401713026165934061851143305328751575837660941339806278907419746717
type: snfs
skew: 0.94
deg: 5
c5: 25
c0: -18
m: 200000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1800001)
Primes: RFBsize:148933, AFBsize:148625, largePrimes:6504113 encountered
Relations: rels:5821520, finalFF:335213
Max relations in full relation-set: 28
Initial matrix: 297622 x 335213 with sparse part having weight 24954157.
Pruned matrix : 280576 x 282128 with weight 18024050.
Total sieving time: 13.38 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 2.30 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 16.03 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

2·10¹⁵⁸+9 = 2(0)₁₅₇9_<159> = 11 · 41 · 97 · 4773739 · 7061641 · C141

C141 = P34 · P107

P34 = 3675342336556885802003207981173427_<34>

P107 = 36899426515186775228625677333483856599631170454625200580800988523050776047130897857948345990003506238466139_<107>

(14·10¹⁶⁶-41)/9 = 1(5)₁₆₅1_<167> = 17 · 2011 · C162

C162 = P32 · P40 · P45 · P47

P32 = 35081134283933574559653611257097_<32>

P40 = 2728630078335383137189177941861782066861_<40>

P45 = 126411714129835466690844912764467931579339687_<45>

P47 = 37602690897693034145575177417896418231525935887_<47>

Number: n
N=12970326457624057370940093292765884024967210652070161540053382611780691229396033766335056809054710948583510049684525069811157738709
  ( 131 digits)
SNFS difficulty: 167 digits.
Divisors found:

Mon Nov 19 08:29:02 2007  prp40 factor: 2728630078335383137189177941861782066861
Mon Nov 19 08:29:02 2007  prp45 factor: 126411714129835466690844912764467931579339687
Mon Nov 19 08:29:02 2007  prp47 factor: 37602690897693034145575177417896418231525935887
Mon Nov 19 08:29:02 2007  elapsed time 03:38:46 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 212.15 hours.
Scaled time: 254.37 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_1_5_165_1

n: 12970326457624057370940093292765884024967210652070161540053382611780691229396033766335056809054710948583510049684525069811157738709

# n: 455013764166366032572485317680859846010341812839838405111754630577574971642892197488974041464754308817841739712626306945785109999577487218988374398325549347867773

type: snfs
skew: 0.78
deg: 5
c5: 140
c0: -41
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3400001)
Primes: RFBsize:250150, AFBsize:250097, largePrimes:7703762 encountered
Relations: rels:7182168, finalFF:528137
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 211.32 hours.
Total relation processing time: 0.83 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.6,2.6,100000
total time: 212.15 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 19, 2007

By Jo Yeong Uk / GGNFS

2·10¹⁵³+9 = 2(0)₁₅₂9_<154> = 7 · 23 · 41 · 83 · 3482753797249_<13> · 36236576853259787647_<20> · C116

C116 = P52 · P64

P52 = 2959271181514799226974060568985564239580538542286449_<52>

P64 = 9774340558371489481440431760860958181256487808303078991400909109_<64>

Number: 20009_153
N=28924924332700020078102154409371603648546043054508471127824139389385626667861861974281623089899076036621178091363941
  ( 116 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=2959271181514799226974060568985564239580538542286449 (pp52)
 r2=9774340558371489481440431760860958181256487808303078991400909109 (pp64)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 13.75 hours.
Scaled time: 29.35 units (timescale=2.134).
Factorization parameters were as follows:
n: 28924924332700020078102154409371603648546043054508471127824139389385626667861861974281623089899076036621178091363941
m: 10000000000000000000000000000000
c5: 1
c0: 450
skew: 3.39
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2300001)
Primes: RFBsize:216816, AFBsize:216826, largePrimes:5458908 encountered
Relations: rels:5374729, finalFF:530472
Max relations in full relation-set: 28
Initial matrix: 433706 x 530472 with sparse part having weight 36351069.
Pruned matrix : 358650 x 360882 with weight 22220315.
Total sieving time: 13.03 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.61 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 13.75 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 18, 2007 (5th)

By Robert Backstrom / GGNFS, Msieve

2·10¹⁶¹+9 = 2(0)₁₆₀9_<162> = 89 · C160

C160 = P74 · P86

P74 = 34658477847360659014058595102069167012530568460007500101714626375633760287_<74>

P86 = 64838133432541527475079803698431770081537553848180889286332859833318730119895305215663_<86>

Number: n
N=2247191011235955056179775280898876404494382022471910112359550561797752808988764044943820224719101123595505617977528089887640449438202247191011235955056179775281
  ( 160 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=34658477847360659014058595102069167012530568460007500101714626375633760287 (pp74)
 r2=64838133432541527475079803698431770081537553848180889286332859833318730119895305215663 (pp86)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 44.07 hours.
Scaled time: 58.35 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_2_0_160_9
n: 2247191011235955056179775280898876404494382022471910112359550561797752808988764044943820224719101123595505617977528089887640449438202247191011235955056179775281
skew: 0.85
deg: 5
c5: 20
c0: 9
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:216816, AFBsize:216651, largePrimes:7001649 encountered
Relations: rels:6463003, finalFF:491333
Max relations in full relation-set: 48
Initial matrix: 433534 x 491333 with sparse part having weight 39251584.
Pruned matrix : 388274 x 390505 with weight 25421104.
Total sieving time: 39.34 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 4.37 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 44.07 hours.
 --------- CPU info (if available) ----------

2·10¹⁵⁴+9 = 2(0)₁₅₃9_<155> = 11 · 139 · 123307 · C147

C147 = P57 · P90

P57 = 830079215274331883817516423026643554541585944243418276953_<57>

P90 = 127795405115706014236248092068937621366157768320616692605819506501989361071666161673603051_<90>

Number: n
N=106080309594110586696617947039119018304385493129409072262824490186120714311071268289763648455730854269029413911116146625540532880538725457703783603
  ( 147 digits)
SNFS difficulty: 155 digits.
Divisors found:

Sun Nov 18 21:03:15 2007  prp57 factor: 830079215274331883817516423026643554541585944243418276953
Sun Nov 18 21:03:15 2007  prp90 factor: 127795405115706014236248092068937621366157768320616692605819506501989361071666161673603051
Sun Nov 18 21:03:15 2007  elapsed time 00:52:25 (Msieve 1.29)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 17.88 hours.
Scaled time: 23.42 units (timescale=1.310).
Factorization parameters were as follows:
name: KA_2_0_153_9
n: 106080309594110586696617947039119018304385493129409072262824490186120714311071268289763648455730854269029413911116146625540532880538725457703783603
skew: 2.14
deg: 5
c5: 1
c0: 45
m: 10000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 750000)
Primes: RFBsize:203362, AFBsize:203572, largePrimes:6377392 encountered
Relations: rels:5863802, finalFF:471912
Max relations in full relation-set: 28
Initial matrix: 406998 x 471912 with sparse part having weight 26578410.
Pruned matrix : 347290 x 349388 with weight 15627841.
Total sieving time: 17.71 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 17.88 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 18, 2007 (4th)

By Jo Yeong Uk / GGNFS

4·10¹⁴¹-9 = 3(9)₁₄₀1_<142> = 13 · 191 · 20359 · 195319 · 12420177806754397_<17> · C113

C113 = P36 · P78

P36 = 163736308730108767707475962968700893_<36>

P78 = 199209262950089812594969876563503547961581096151892699792833892052250192212997_<78>

Number: 39991_141
N=32617789380293323671116887710598264533701832802595148777896193264079821368295646222589206276954325334265840106321
  ( 113 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=163736308730108767707475962968700893 (pp36)
 r2=199209262950089812594969876563503547961581096151892699792833892052250192212997 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.44 hours.
Scaled time: 11.55 units (timescale=2.123).
Factorization parameters were as follows:
n: 32617789380293323671116887710598264533701832802595148777896193264079821368295646222589206276954325334265840106321
m: 20000000000000000000000000000
c5: 5
c0: -36
skew: 1.48
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1100001)
Primes: RFBsize:114155, AFBsize:113572, largePrimes:3187730 encountered
Relations: rels:3200509, finalFF:325241
Max relations in full relation-set: 28
Initial matrix: 227794 x 325241 with sparse part having weight 26244758.
Pruned matrix : 187279 x 188481 with weight 12048136.
Total sieving time: 5.27 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 5.44 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 18, 2007 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

2·10¹⁴⁸+9 = 2(0)₁₄₇9_<149> = 11 · 17 · 41 · 89819 · C140

C140 = P33 · P45 · P63

P33 = 609146353706828448793174289718131_<33>

P45 = 150327116082360350342458857196514705709372161_<45>

P63 = 317159220689745360562169219217954642762236170568071499368229363_<63>

Number: 20009_148
N=29042655068025427477641936744710994528214215510409132260749261322213369262621494629040875043696308199191832070407911191359581261140499285033
  ( 140 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=609146353706828448793174289718131 (pp33)
 r2=150327116082360350342458857196514705709372161 (pp45)
 r3=317159220689745360562169219217954642762236170568071499368229363 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 20.82 hours.
Scaled time: 14.06 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_148
n: 29042655068025427477641936744710994528214215510409132260749261322213369262621494629040875043696308199191832070407911191359581261140499285033
m: 200000000000000000000000000000
c5: 125
c0: 18
skew: 0.68
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2650001)
Primes: RFBsize:114155, AFBsize:113727, largePrimes:2759008 encountered
Relations: rels:2717014, finalFF:256815
Max relations in full relation-set: 28
Initial matrix: 227948 x 256815 with sparse part having weight 24576686.
Pruned matrix : 218819 x 220022 with weight 19196213.
Total sieving time: 19.03 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.53 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 20.82 hours.
 --------- CPU info (if available) ----------

4·10¹¹⁷-9 = 3(9)₁₁₆1_<118> = 13 · 9973 · 214363 · 581922332049027043_<18> · C90

C90 = P42 · P48

P42 = 531991308851942132115845825480210110671439_<42>

P48 = 464912723832181683082293085018597257414298049209_<48>

Sat Nov 17 15:56:48 2007  Msieve v. 1.28
Sat Nov 17 15:56:48 2007  random seeds: 515dd9e0 50f90094
Sat Nov 17 15:56:48 2007  factoring 247329528453403843265964841503467900787215031507298040842564825634927508129438170852841751 (90 digits)
Sat Nov 17 15:56:49 2007  commencing quadratic sieve (89-digit input)
Sat Nov 17 15:56:49 2007  using multiplier of 1
Sat Nov 17 15:56:49 2007  using 64kb Pentium 2 sieve core
Sat Nov 17 15:56:49 2007  sieve interval: 18 blocks of size 65536
Sat Nov 17 15:56:49 2007  processing polynomials in batches of 6
Sat Nov 17 15:56:49 2007  using a sieve bound of 1575281 (59464 primes)
Sat Nov 17 15:56:49 2007  using large prime bound of 126022480 (26 bits)
Sat Nov 17 15:56:49 2007  using double large prime bound of 380896014563600 (42-49 bits)
Sat Nov 17 15:56:49 2007  using trial factoring cutoff of 49 bits
Sat Nov 17 15:56:49 2007  polynomial 'A' values have 11 factors
Sat Nov 17 23:25:48 2007  59782 relations (15877 full + 43905 combined from 635165 partial), need 59560
Sat Nov 17 23:25:52 2007  begin with 651042 relations
Sat Nov 17 23:25:54 2007  reduce to 146575 relations in 9 passes
Sat Nov 17 23:25:54 2007  attempting to read 146575 relations
Sat Nov 17 23:26:02 2007  recovered 146575 relations
Sat Nov 17 23:26:02 2007  recovered 123038 polynomials
Sat Nov 17 23:26:14 2007  attempting to build 59782 cycles
Sat Nov 17 23:26:14 2007  found 59782 cycles in 5 passes
Sat Nov 17 23:26:16 2007  distribution of cycle lengths:
Sat Nov 17 23:26:16 2007     length 1 : 15877
Sat Nov 17 23:26:16 2007     length 2 : 11295
Sat Nov 17 23:26:17 2007     length 3 : 10499
Sat Nov 17 23:26:17 2007     length 4 : 7977
Sat Nov 17 23:26:17 2007     length 5 : 5541
Sat Nov 17 23:26:17 2007     length 6 : 3771
Sat Nov 17 23:26:17 2007     length 7 : 2219
Sat Nov 17 23:26:17 2007     length 9+: 2603
Sat Nov 17 23:26:17 2007  largest cycle: 19 relations
Sat Nov 17 23:26:18 2007  matrix is 59464 x 59782 with weight 3654625 (avg 61.13/col)
Sat Nov 17 23:26:21 2007  filtering completed in 3 passes
Sat Nov 17 23:26:21 2007  matrix is 55555 x 55619 with weight 3417406 (avg 61.44/col)
Sat Nov 17 23:26:23 2007  saving the first 48 matrix rows for later
Sat Nov 17 23:26:23 2007  matrix is 55507 x 55619 with weight 2798607 (avg 50.32/col)
Sat Nov 17 23:26:23 2007  matrix includes 64 packed rows
Sat Nov 17 23:26:23 2007  using block size 10922 for processor cache size 256 kB
Sat Nov 17 23:26:26 2007  commencing Lanczos iteration
Sat Nov 17 23:29:02 2007  lanczos halted after 879 iterations
Sat Nov 17 23:29:03 2007  recovered 17 nontrivial dependencies
Sat Nov 17 23:29:33 2007  prp42 factor: 531991308851942132115845825480210110671439
Sat Nov 17 23:29:33 2007  prp48 factor: 464912723832181683082293085018597257414298049209
Sat Nov 17 23:29:33 2007  elapsed time 07:32:45

4·10¹⁰⁵-9 = 3(9)₁₀₄1_<106> = 13 · 4049 · 230177683 · C93

C93 = P34 · P59

P34 = 5089468623085822110371775885182959_<34>

P59 = 64868403116863325702101470038639463824085108816719708634719_<59>

Number: 39991_105
N=330145702292958441592211172106378607837842790909434221456259170903001863735703019123414553521
  ( 93 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=5089468623085822110371775885182959 (pp34)
 r2=64868403116863325702101470038639463824085108816719708634719 (pp59)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.24 hours.
Scaled time: 0.84 units (timescale=0.675).
Factorization parameters were as follows:
name: 39991_105
n: 330145702292958441592211172106378607837842790909434221456259170903001863735703019123414553521
m: 1000000000000000000000
c5: 4
c0: -9
skew: 1.18
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:64053, largePrimes:2165320 encountered
Relations: rels:2447143, finalFF:427386
Max relations in full relation-set: 28
Initial matrix: 113215 x 427386 with sparse part having weight 29087007.
Pruned matrix : 55181 x 55811 with weight 3194505.
Total sieving time: 1.11 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,105,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.24 hours.
 --------- CPU info (if available) ----------

4·10¹²³-9 = 3(9)₁₂₂1_<124> = 13 · 15601 · 14877774143167099699747_<23> · C97

C97 = P48 · P49

P48 = 470762130228440485791543763322013994572073144603_<48>

P49 = 2815948587112211304623095233966680241651606098227_<49>

Number: 39991_123
N=1325641955482711805978372001349693249395454462809784497501309555808926827572054827616211192918881
  ( 97 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=470762130228440485791543763322013994572073144603 (pp48)
 r2=2815948587112211304623095233966680241651606098227 (pp49)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.60 hours.
Scaled time: 1.75 units (timescale=0.675).
Factorization parameters were as follows:
name: 39991_123
n: 1325641955482711805978372001349693249395454462809784497501309555808926827572054827616211192918881
m: 2000000000000000000000000
c5: 125
c0: -9
skew: 0.59
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:64093, largePrimes:2072753 encountered
Relations: rels:2079058, finalFF:159271
Max relations in full relation-set: 28
Initial matrix: 113257 x 159271 with sparse part having weight 13679756.
Pruned matrix : 100109 x 100739 with weight 6360731.
Total sieving time: 2.31 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.60 hours.
 --------- CPU info (if available) ----------

Nov 18, 2007 (2nd)

By Yousuke Koide

(10¹⁶⁸³-1)/9 is divisible by 2597072697640403933361917807092159369_<37>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 18, 2007

By Robert Backstrom / GGNFS

4·10¹⁰⁹-9 = 3(9)₁₀₈1_<110> = 53 · C108

C108 = P49 · P59

P49 = 7969641884935205730310904257533114365615152149547_<49>

P59 = 94698982969196667127271104615127284069462500623071914214001_<59>

Number: n
N=754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547
  ( 108 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=7969641884935205730310904257533114365615152149547 (pp49)
 r2=94698982969196667127271104615127284069462500623071914214001 (pp59)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.96 hours.
Scaled time: 1.15 units (timescale=1.192).
Factorization parameters were as follows:
name: KA_3_9_108_1
n: 754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547
type: snfs
skew: 1.86
deg: 5
c5: 2
c0: -45
m: 10000000000000000000000
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:63951, AFBsize:64093, largePrimes:3342545 encountered
Relations: rels:2790483, finalFF:160806
Max relations in full relation-set: 28
Initial matrix: 128109 x 160806 with sparse part having weight 5905277.
Pruned matrix : 96382 x 97086 with weight 2618908.
Total sieving time: 0.81 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.4,2.4,50000
total time: 0.96 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

4·10¹²¹-9 = 3(9)₁₂₀1_<122> = 31 · C121

C121 = P48 · P73

P48 = 207550763771542349075740138245104441965655783933_<48>

P73 = 6216901143594248208194826668257714111385850652570251799400319368993225117_<73>

Number: n
N=1290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161
  ( 121 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=207550763771542349075740138245104441965655783933 (pp48)
 r2=6216901143594248208194826668257714111385850652570251799400319368993225117 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.55 hours.
Scaled time: 2.05 units (timescale=1.318).
Factorization parameters were as follows:
name: KA_3_9_120_1
n: 1290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161
skew: 0.74
deg: 5
c5: 40
c0: -9
m: 1000000000000000000000000
type: snfs
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:63951, AFBsize:63733, largePrimes:4298910 encountered
Relations: rels:3675690, finalFF:181805
Max relations in full relation-set: 48
Initial matrix: 127751 x 181805 with sparse part having weight 12806423.
Pruned matrix : 102487 x 103189 with weight 4549576.
Total sieving time: 1.36 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.10 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000
total time: 1.55 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 17, 2007 (4th)

By Jo Yeong Uk / GGNFS

(4·10¹⁹⁵-1)/3 = 1(3)₁₉₅_<196> = 919 · 2815092622300365139319_<22> · 1616772208578912506305058572743036521_<37> · C135

C135 = P49 · P86

P49 = 9750955237361634372618257316599424244951087381213_<49>

P86 = 32691476708214933835165765723715218661077209696240370449876399876944717064876363130561_<86>

Number: 13333_195
N=318773126025054291670957797550571273589430793561728712537650216394184484148701462662385921621852455278537160766090492754352887897550493
  ( 135 digits)
Divisors found:
 r1=9750955237361634372618257316599424244951087381213 (pp49)
 r2=32691476708214933835165765723715218661077209696240370449876399876944717064876363130561 (pp86)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 386.78 hours.
Scaled time: 823.45 units (timescale=2.129).
Factorization parameters were as follows:
name: 13333_195
n: 318773126025054291670957797550571273589430793561728712537650216394184484148701462662385921621852455278537160766090492754352887897550493
skew: 131671.97
# norm 3.05e+18
c5: 197280
c4: -307423178886
c3: -58612697870847169
c2: 3978958100881520574793
c1: 213561147801238145597164433
c0: -11098269473779960898804283038595
# alpha -5.90
Y1: 773059969233563
Y0: -69451436841457195078837658
# Murphy_E 4.23e-11
# M 56576599863178588454020620146065243601482425869774777937223046811868572601341632692068072510368265616104157355536434726657596047407882
type: gnfs
rlim: 12000000
alim: 12000000
lpbr: 28
lpba: 28
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 51/51
Sieved algebraic special-q in [6000000, 11600001)
Primes: RFBsize:788060, AFBsize:788407, largePrimes:12637468 encountered
Relations: rels:13248927, finalFF:1826316
Max relations in full relation-set: 28
Initial matrix: 1576544 x 1826316 with sparse part having weight 125344949.
Pruned matrix : 1341143 x 1349089 with weight 79768099.
Polynomial selection time: 23.32 hours.
Total sieving time: 349.55 hours.
Total relation processing time: 0.39 hours.
Matrix solve time: 13.52 hours.
Time per square root: 0.67 hours.
Prototype def-par.txt line would be:
gnfs,134,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,12000000,12000000,28,28,51,51,2.6,2.6,100000
total time: 386.78 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

4·10¹³¹-9 = 3(9)₁₃₀1_<132> = 83 · 157 · 43427 · 89517934664444970329_<20> · C103

C103 = P37 · P67

P37 = 2706709430006427754108248781033420387_<37>

P67 = 2917230383237813120633073932480522042054906957099018520221291471441_<67>

Number: 39991_131
N=7896094987811053945775833802148765097844972873029553301959921686999250192636341021809147450036357667667
  ( 103 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=2706709430006427754108248781033420387 (pp37)
 r2=2917230383237813120633073932480522042054906957099018520221291471441 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.06 hours.
Scaled time: 4.43 units (timescale=2.145).
Factorization parameters were as follows:
n: 7896094987811053945775833802148765097844972873029553301959921686999250192636341021809147450036357667667
m: 200000000000000000000000000
c5: 5
c0: -36
skew: 1.48
type: snfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [600000, 1000001)
Primes: RFBsize:92938, AFBsize:92554, largePrimes:1605182 encountered
Relations: rels:1657757, finalFF:229082
Max relations in full relation-set: 28
Initial matrix: 185559 x 229082 with sparse part having weight 10774169.
Pruned matrix : 157627 x 158618 with weight 5983307.
Total sieving time: 1.97 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1200000,1200000,25,25,46,46,2.2,2.2,50000
total time: 2.06 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 17, 2007 (3rd)

By Robert Backstrom / GGNFS

2·10¹⁵²+9 = 2(0)₁₅₁9_<153> = 11 · 5689 · C148

C148 = P69 · P80

P69 = 246315360411796404596074328483957549191621049813614560388841748191993_<69>

P80 = 12975075126577197804004996961447593348172069718738575880540661517804485822477547_<80>

Number: n
N=3195960306172997331373144345547228303424471468064366640566324166253855127119321178030968855366816344141005768708352642260183128525543712747087681171
  ( 148 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=246315360411796404596074328483957549191621049813614560388841748191993 (pp69)
 r2=12975075126577197804004996961447593348172069718738575880540661517804485822477547 (pp80)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 16.67 hours.
Scaled time: 14.62 units (timescale=0.877).
Factorization parameters were as follows:
name: KA_2_0_151_9
n: 3195960306172997331373144345547228303424471468064366640566324166253855127119321178030968855366816344141005768708352642260183128525543712747087681171
skew: 0.54
deg: 5
c5: 200
c0: 9
m: 1000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 650001)
Primes: RFBsize:203362, AFBsize:203482, largePrimes:6183842 encountered
Relations: rels:5700058, finalFF:479667
Max relations in full relation-set: 28
Initial matrix: 406909 x 479667 with sparse part having weight 26262880.
Pruned matrix : 339138 x 341236 with weight 14609906.
Total sieving time: 14.71 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.47 hours.
Total square root time: 0.32 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 16.67 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 17, 2007 (2nd)

By Sinkiti Sibata / GGNFS

2·10¹⁴⁷+9 = 2(0)₁₄₆9_<148> = 7 · 188393823755666606087_<21> · C127

C127 = P35 · P92

P35 = 48974472633629490212445941599538267_<35>

P92 = 30966742771240142891864085906864765198542074244953818306582481386219016872212029624089901403_<92>

Number: 20009_147
N=1516579896402744219014433937457116142826101612462661029810181639049330302450011786700883958686428599152590539537076162355488601
  ( 127 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=48974472633629490212445941599538267 (pp35)
 r2=30966742771240142891864085906864765198542074244953818306582481386219016872212029624089901403 (pp92)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 17.87 hours.
Scaled time: 12.06 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_147
n: 1516579896402744219014433937457116142826101612462661029810181639049330302450011786700883958686428599152590539537076162355488601
m: 100000000000000000000000000000
c5: 200
c0: 9
skew: 0.54
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2350001)
Primes: RFBsize:114155, AFBsize:114287, largePrimes:2723540 encountered
Relations: rels:2681399, finalFF:265609
Max relations in full relation-set: 28
Initial matrix: 228507 x 265609 with sparse part having weight 23794062.
Pruned matrix : 215996 x 217202 with weight 17271817.
Total sieving time: 16.25 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.37 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 17.87 hours.
 --------- CPU info (if available) ----------

Nov 17, 2007

The factor table of 399...991 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Nov 16, 2007 (3rd)

By Jo Yeong Uk / GGNFS, GMP-ECM

2·10¹⁴⁹+9 = 2(0)₁₄₈9_<150> = 467 · 1867 · 4621 · 108421 · C135

C135 = P40 · P96

P40 = 1863452397272640607861076350654167212689_<40>

P96 = 245697714723845525541313190866322224591579633478192557941408979790414184607140661966923663278569_<96>

Number: 20009_149
N=457845995506559311920071361063861840226353200596349254744820183599147637255647440000439776818147406947190006280979032862128666078562041
  ( 135 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=1863452397272640607861076350654167212689 (pp40)
 r2=245697714723845525541313190866322224591579633478192557941408979790414184607140661966923663278569 (pp96)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 9.32 hours.
Scaled time: 19.79 units (timescale=2.123).
Factorization parameters were as follows:
n: 457845995506559311920071361063861840226353200596349254744820183599147637255647440000439776818147406947190006280979032862128666078562041
m: 1000000000000000000000000000000
c5: 1
c0: 45
skew: 2.14
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1500001)
Primes: RFBsize:135072, AFBsize:135163, largePrimes:3697267 encountered
Relations: rels:3741082, finalFF:354567
Max relations in full relation-set: 28
Initial matrix: 270299 x 354567 with sparse part having weight 30900567.
Pruned matrix : 237134 x 238549 with weight 17237573.
Total sieving time: 9.00 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 9.32 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10¹⁹¹+9 = 2(0)₁₉₀9_<192> = C192

C192 = P45 · C148

P45 = 139787422364207720750158040677389843257571643_<45>

C148 = [1430743886806296706788516093667434949145159858014350886258366962866810355411884866166709798529837275207436439253831768696683312353651987615427655563_<148>]

2·10¹³⁷+9 = 2(0)₁₃₆9_<138> = 1747 · 187546628295101_<15> · 17157672728274349_<17> · 1099656391248576163177704783751416330647_<40> · 32352842794331493715586477085068987078828228518142150588757859949_<65>

C104 = P40 · P65

P40 = 1099656391248576163177704783751416330647_<40>

P65 = 32352842794331493715586477085068987078828228518142150588757859949_<65>

Number: 20009_137
N=35577010353847071166627381630160508224933719406788362654288006111043429068247910493731177879457902557003
  ( 104 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=1099656391248576163177704783751416330647 (pp40)
 r2=32352842794331493715586477085068987078828228518142150588757859949 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 8.22 hours.
Scaled time: 5.55 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_137
n: 35577010353847071166627381630160508224933719406788362654288006111043429068247910493731177879457902557003
m: 1000000000000000000000000000
c5: 200
c0: 9
skew: 0.54
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1225001)
Primes: RFBsize:78498, AFBsize:63988, largePrimes:1552634 encountered
Relations: rels:1574611, finalFF:193594
Max relations in full relation-set: 28
Initial matrix: 142551 x 193594 with sparse part having weight 15125767.
Pruned matrix : 126553 x 127329 with weight 8216971.
Total sieving time: 7.78 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.22 hours.
 --------- CPU info (if available) ----------

Nov 16, 2007

By Robert Backstrom / GGNFS, Msieve

2·10¹⁴⁶+9 = 2(0)₁₄₅9_<147> = 11 · 19 · 443 · C142

C142 = P43 · P99

P43 = 5697591929599718777554446090898432894508443_<43>

P99 = 379130428884937776481991873307188799908650024737963391395977785501700705423478684413792248504210049_<99>

Number: n
N=2160130471880501582295570652467409031505502932377115577780897966237160724507760268720230701934396837568989166945683519284564787713177875943707
  ( 142 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=5697591929599718777554446090898432894508443 (pp43)
 r2=379130428884937776481991873307188799908650024737963391395977785501700705423478684413792248504210049 (pp99)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.11 hours.
Scaled time: 10.69 units (timescale=1.318).
Factorization parameters were as follows:
name: KA_2_0_145_9
n: 2160130471880501582295570652467409031505502932377115577780897966237160724507760268720230701934396837568989166945683519284564787713177875943707
skew: 0.85
deg: 5
c5: 20
c0: 9
m: 100000000000000000000000000000
type: snfs
rlim: 2200000
alim: 2200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 850001)
Primes: RFBsize:162662, AFBsize:162600, largePrimes:6215071 encountered
Relations: rels:5583240, finalFF:372600
Max relations in full relation-set: 48
Initial matrix: 325329 x 372600 with sparse part having weight 24152920.
Pruned matrix : 286219 x 287909 with weight 14211438.
Total sieving time: 6.19 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.66 hours.
Total square root time: 0.10 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2200000,2200000,28,28,48,48,2.5,2.5,100000
total time: 8.11 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

2·10¹⁶⁷-9 = 1(9)₁₆₆1_<168> = 11 · 25693999 · C159

C159 = P51 · P54 · P56

P51 = 213778048882883699682952867750597400299228114685941_<51>

P54 = 253294029617274149322595661355934135791715095080163601_<54>

P56 = 13068253350533572176578369071664035808002504957074122959_<56>

Number: n
N=707628975225622987615972826254806883824577800513582250010277426328933141866387485335318251478947211830209140203586766770644842719181945240138828454917359567819
  ( 159 digits)
SNFS difficulty: 167 digits.
Divisors found:

Fri Nov 16 05:59:23 2007  prp51 factor: 213778048882883699682952867750597400299228114685941
Fri Nov 16 05:59:23 2007  prp54 factor: 253294029617274149322595661355934135791715095080163601
Fri Nov 16 05:59:23 2007  prp56 factor: 13068253350533572176578369071664035808002504957074122959
Fri Nov 16 05:59:23 2007  elapsed time 01:49:33 (Msieve 1.29)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 62.94 hours.
Scaled time: 82.45 units (timescale=1.310).
Factorization parameters were as follows:
name: KA_1_9_166_1
n: 707628975225622987615972826254806883824577800513582250010277426328933141866387485335318251478947211830209140203586766770644842719181945240138828454917359567819
skew: 0.54
deg: 5
c5: 200
c0: -9
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2600001)
Primes: RFBsize:230209, AFBsize:230472, largePrimes:7397646 encountered
Relations: rels:6871280, finalFF:499906
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 62.61 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 62.94 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 15, 2007 (4th)

By Sinkiti Sibata / GGNFS

2·10¹³³+9 = 2(0)₁₃₂9_<134> = 41 · 106261 · 138657907177600053240515967083_<30> · C98

C98 = P30 · P68

P30 = 337482959187671618348715804443_<30>

P68 = 98101523251692854700293015379351134705420468393200528633582388590261_<68>

Number: 20009_133
N=33107592367799477994531315875696566699102396778630104307460969147141634839210559134468289330329623
  ( 98 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=337482959187671618348715804443 (pp30)
 r2=98101523251692854700293015379351134705420468393200528633582388590261 (pp68)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 5.55 hours.
Scaled time: 3.75 units (timescale=0.676).
Factorization parameters were as follows:
name: 20009_133
n: 33107592367799477994531315875696566699102396778630104307460969147141634839210559134468289330329623
m: 200000000000000000000000000
c5: 125
c0: 18
skew: 0.68
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 925001)
Primes: RFBsize:78498, AFBsize:63828, largePrimes:1467588 encountered
Relations: rels:1461357, finalFF:170545
Max relations in full relation-set: 28
Initial matrix: 142392 x 170545 with sparse part having weight 10197756.
Pruned matrix : 131765 x 132540 with weight 6330275.
Total sieving time: 5.15 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.55 hours.
 --------- CPU info (if available) ----------

2·10¹³⁶+9 = 2(0)₁₃₅9_<137> = 11 · 626113 · 1638117457_<10> · 14068805453502347862038393_<26> · C96

C96 = P37 · P59

P37 = 7479989621822215707304648726870274177_<37>

P59 = 16845400134770192015265810071674311005731257071385123440419_<59>

Number: 20009_136
N=126003418183523590081005231307316729274954208236469757844274078817776161403684503808348053760163
  ( 96 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=7479989621822215707304648726870274177 (pp37)
 r2=16845400134770192015265810071674311005731257071385123440419 (pp59)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 7.86 hours.
Scaled time: 5.31 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_136
n: 126003418183523590081005231307316729274954208236469757844274078817776161403684503808348053760163
m: 1000000000000000000000000000
c5: 20
c0: 9
skew: 0.85
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1150001)
Primes: RFBsize:78498, AFBsize:63843, largePrimes:1536871 encountered
Relations: rels:1552675, finalFF:189444
Max relations in full relation-set: 28
Initial matrix: 142408 x 189444 with sparse part having weight 14166681.
Pruned matrix : 126873 x 127649 with weight 7809355.
Total sieving time: 7.43 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 7.86 hours.
 --------- CPU info (if available) ----------

Nov 15, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

(2·10¹⁶⁷+1)/3 = (6)₁₆₆7_<167> = 67 · 163 · 154247 · 105057409 · C150

C150 = P44 · P45 · P62

P44 = 35110383512037779258731687752743501077616849_<44>

P45 = 144490044053633250534088853071686157579676183_<45>

P62 = 74255636529996781604025069037975869335914287473493040697234147_<62>

Number: n
N=376706333569452881833796963898895894903820904576725150866190626909505248384898760572288876235614404361232252029198354520001692450611622477750149560949
  ( 150 digits)
SNFS difficulty: 167 digits.
Divisors found:

Thu Nov 15 11:40:38 2007  prp44 factor: 35110383512037779258731687752743501077616849
Thu Nov 15 11:40:38 2007  prp45 factor: 144490044053633250534088853071686157579676183
Thu Nov 15 11:40:38 2007  prp62 factor: 74255636529996781604025069037975869335914287473493040697234147
Thu Nov 15 11:40:38 2007  elapsed time 03:04:59 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 61.61 hours.
Scaled time: 81.70 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_6_166_7
n: 376706333569452881833796963898895894903820904576725150866190626909505248384898760572288876235614404361232252029198354520001692450611622477750149560949
skew: 0.35
deg: 5
c5: 200
c0: 1
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2850000)
Primes: RFBsize:250150, AFBsize:249566, largePrimes:7551318 encountered
Relations: rels:7059925, finalFF:577979
Max relations in full relation-set: 28
Initial matrix: 499781 x 577979 with sparse part having weight 49191823.
Pruned matrix : 444384 x 446946 with weight 33215771.
Total sieving time: 61.30 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 61.61 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 15, 2007 (2nd)

By Jo Yeong Uk / GGNFS

2·10¹³⁸+9 = 2(0)₁₃₇9_<139> = 11² · 41 · 9034909729_<10> · C125

C125 = P30 · P38 · P58

P30 = 799755820751262322119275375033_<30>

P38 = 20766309102022228980253099855875658537_<38>

P58 = 2686706507069958673687375702336773298121688744721734859241_<58>

Number: 20009_138
N=44620758746381241841688897721867317475788276748995108314229042673027347676487429597124584059980824714622578162566104956058761
  ( 125 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=799755820751262322119275375033 (pp30)
 r2=20766309102022228980253099855875658537 (pp38)
 r3=2686706507069958673687375702336773298121688744721734859241 (pp58)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.74 hours.
Scaled time: 10.09 units (timescale=2.126).
Factorization parameters were as follows:
n: 44620758746381241841688897721867317475788276748995108314229042673027347676487429597124584059980824714622578162566104956058761
m: 10000000000000000000000000000
c5: 1
c0: 450
skew: 3.39
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1000001)
Primes: RFBsize:107126, AFBsize:106598, largePrimes:2324281 encountered
Relations: rels:2569529, finalFF:387303
Max relations in full relation-set: 28
Initial matrix: 213788 x 387303 with sparse part having weight 31262275.
Pruned matrix : 152381 x 153513 with weight 10650969.
Total sieving time: 4.62 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 4.74 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10¹⁴¹+9 = 2(0)₁₄₀9_<142> = 7 · 29 · 84089 · 1843241 · C128

C128 = P39 · P45 · P45

P39 = 193589288637298059074525377001965216949_<39>

P45 = 468214580957084640590379178323139739604088747_<45>

P45 = 701271823576894703710295051061370970173632749_<45>

Number: 20009_141
N=63564209137520160828475746211489351888520291688068698024161891639200326972468705608592258442484833328985146148995415235418800347
  ( 128 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=193589288637298059074525377001965216949 (pp39)
 r2=468214580957084640590379178323139739604088747 (pp45)
 r3=701271823576894703710295051061370970173632749 (pp45)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.50 hours.
Scaled time: 11.67 units (timescale=2.123).
Factorization parameters were as follows:
n: 63564209137520160828475746211489351888520291688068698024161891639200326972468705608592258442484833328985146148995415235418800347
m: 10000000000000000000000000000
c5: 20
c0: 9
skew: 0.85
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1100001)
Primes: RFBsize:114155, AFBsize:113962, largePrimes:3318316 encountered
Relations: rels:3434745, finalFF:413798
Max relations in full relation-set: 28
Initial matrix: 228184 x 413798 with sparse part having weight 34667463.
Pruned matrix : 162968 x 164172 with weight 12380892.
Total sieving time: 5.34 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 5.50 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 15, 2007

By JMB / GMP-ECM

9·10¹⁷⁸+7 = 9(0)₁₇₇7_<179> = 149 · C177

C177 = P35 · C143

P35 = 34477381911603229695013790339605181_<35>

C143 = [17519510245477803843772234672206519263441432562534062592219996721821259842723144120268391140425192935308257597913633559158414046764815248848903_<143>]

Nov 14, 2007 (3rd)

By Jo Yeong Uk / GGNFS, Msieve

2·10¹⁵¹+9 = 2(0)₁₅₀9_<152> = C152

C152 = P64 · P88

P64 = 5361545627942898041009151470006806437953024698709373565545033283_<64>

P88 = 3730267610848168946728870898319835513379653329283710892077298113553792162530729021571523_<88>

Number: 20009_151
N=20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 152 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=5361545627942898041009151470006806437953024698709373565545033283 (pp64)
 r2=3730267610848168946728870898319835513379653329283710892077298113553792162530729021571523 (pp88)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.44 hours.
Scaled time: 24.53 units (timescale=2.145).
Factorization parameters were as follows:
n: 20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
m: 1000000000000000000000000000000
c5: 20
c0: 9
skew: 0.85
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:176393, largePrimes:5255231 encountered
Relations: rels:5101022, finalFF:437517
Max relations in full relation-set: 28
Initial matrix: 352762 x 437517 with sparse part having weight 35441926.
Pruned matrix : 301643 x 303470 with weight 21914347.
Total sieving time: 10.89 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.44 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 11.44 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10¹¹⁵+9 = 2(0)₁₁₄9_<116> = 2549 · C112

C112 = P34 · P36 · P43

P34 = 3610985855871191931623417922834769_<34>

P36 = 347349964829672312277520077897474727_<36>

P43 = 6255573247015228068683536228478645049008707_<43>

Number: 20009_115
N=7846214201647704982346018046292663789721459395841506473126716359356610435464888191447626520204001569242840329541
  ( 112 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=3610985855871191931623417922834769 (pp34)
 r2=347349964829672312277520077897474727 (pp36)
 r3=6255573247015228068683536228478645049008707 (pp43)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.64 hours.
Scaled time: 1.37 units (timescale=2.143).
Factorization parameters were as follows:
n: 7846214201647704982346018046292663789721459395841506473126716359356610435464888191447626520204001569242840329541
m: 100000000000000000000000
c5: 2
c0: 9
skew: 1.35
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 390001)
Primes: RFBsize:49098, AFBsize:48886, largePrimes:1863902 encountered
Relations: rels:1959876, finalFF:245084
Max relations in full relation-set: 28
Initial matrix: 98049 x 245084 with sparse part having weight 19250215.
Pruned matrix : 66805 x 67359 with weight 3521221.
Total sieving time: 0.60 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.64 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10¹²⁸+9 = 2(0)₁₂₇9_<129> = 11 · 19 · 41 · 3628268961937_<13> · C112

C112 = P30 · P82

P30 = 838738174203331430476288994347_<30>

P82 = 7669622162401410990558076424963758890890607406854931844023679051213111668308932099_<82>

Number: 20009_128
N=6432804889321966154737940019106072881085761416381139523418545975573334342986996964229572138342044269550217844353
  ( 112 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=838738174203331430476288994347 (pp30)
 r2=7669622162401410990558076424963758890890607406854931844023679051213111668308932099 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.75 hours.
Scaled time: 3.75 units (timescale=2.146).
Factorization parameters were as follows:
n: 6432804889321966154737940019106072881085761416381139523418545975573334342986996964229572138342044269550217844353
m: 100000000000000000000000000
c5: 1
c0: 450
skew: 3.39
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 850001)
Primes: RFBsize:78498, AFBsize:78411, largePrimes:1572335 encountered
Relations: rels:1653001, finalFF:250088
Max relations in full relation-set: 28
Initial matrix: 156973 x 250088 with sparse part having weight 11746162.
Pruned matrix : 112238 x 113086 with weight 4590998.
Total sieving time: 1.69 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.75 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10¹²⁹+9 = 2(0)₁₂₈9_<130> = 7³ · 163 · 4507 · C121

C121 = P41 · P80

P41 = 82003635083982433094568610504258544735069_<41>

P80 = 96789357905979190059916421135822880484975096215801511141201084498141280349953947_<80>

Number: 20009_129
N=7937079185734887593874167046697325195980474197859232432137387602376763124415823530918175646633742048331470586833465867343
  ( 121 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=82003635083982433094568610504258544735069 (pp41)
 r2=96789357905979190059916421135822880484975096215801511141201084498141280349953947 (pp80)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.72 hours.
Scaled time: 3.68 units (timescale=2.139).
Factorization parameters were as follows:
n: 7937079185734887593874167046697325195980474197859232432137387602376763124415823530918175646633742048331470586833465867343
m: 100000000000000000000000000
c5: 1
c0: 45
skew: 2.14
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 850001)
Primes: RFBsize:78498, AFBsize:78411, largePrimes:1567044 encountered
Relations: rels:1646980, finalFF:248901
Max relations in full relation-set: 28
Initial matrix: 156973 x 248901 with sparse part having weight 11659733.
Pruned matrix : 112684 x 113532 with weight 4605631.
Total sieving time: 1.66 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.72 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10¹⁴³+9 = 2(0)₁₄₂9_<144> = 41 · 67 · 3331649 · 14935649 · 82226933119967_<14> · 1277854822563168097967_<22> · C92

C92 = P39 · P53

P39 = 378442673724566134246810453283328526129_<39>

P53 = 36795294718689337041099821264332695452995703051552587_<53>

Wed Nov 14 21:20:40 2007  
Wed Nov 14 21:20:40 2007  
Wed Nov 14 21:20:40 2007  Msieve v. 1.28
Wed Nov 14 21:20:40 2007  random seeds: 3b93c2a8 eb1b55fc
Wed Nov 14 21:20:40 2007  factoring 13924909713824200219224541074202380892627126993472216666474137256898926894158453179847045723 (92 digits)
Wed Nov 14 21:20:41 2007  commencing quadratic sieve (91-digit input)
Wed Nov 14 21:20:41 2007  using multiplier of 3
Wed Nov 14 21:20:41 2007  using 32kb Intel Core sieve core
Wed Nov 14 21:20:41 2007  sieve interval: 36 blocks of size 32768
Wed Nov 14 21:20:41 2007  processing polynomials in batches of 6
Wed Nov 14 21:20:41 2007  using a sieve bound of 1753547 (65732 primes)
Wed Nov 14 21:20:41 2007  using large prime bound of 177108247 (27 bits)
Wed Nov 14 21:20:41 2007  using double large prime bound of 702796695147472 (42-50 bits)
Wed Nov 14 21:20:41 2007  using trial factoring cutoff of 50 bits
Wed Nov 14 21:20:41 2007  polynomial 'A' values have 12 factors
Wed Nov 14 22:27:23 2007  66322 relations (17638 full + 48684 combined from 795835 partial), need 65828
Wed Nov 14 22:27:23 2007  begin with 813473 relations
Wed Nov 14 22:27:24 2007  reduce to 163711 relations in 11 passes
Wed Nov 14 22:27:24 2007  attempting to read 163711 relations
Wed Nov 14 22:27:25 2007  recovered 163711 relations
Wed Nov 14 22:27:25 2007  recovered 140908 polynomials
Wed Nov 14 22:27:25 2007  attempting to build 66322 cycles
Wed Nov 14 22:27:25 2007  found 66322 cycles in 5 passes
Wed Nov 14 22:27:25 2007  distribution of cycle lengths:
Wed Nov 14 22:27:25 2007     length 1 : 17638
Wed Nov 14 22:27:25 2007     length 2 : 12531
Wed Nov 14 22:27:25 2007     length 3 : 11404
Wed Nov 14 22:27:25 2007     length 4 : 8950
Wed Nov 14 22:27:25 2007     length 5 : 6342
Wed Nov 14 22:27:25 2007     length 6 : 4034
Wed Nov 14 22:27:25 2007     length 7 : 2526
Wed Nov 14 22:27:25 2007     length 9+: 2897
Wed Nov 14 22:27:25 2007  largest cycle: 17 relations
Wed Nov 14 22:27:25 2007  matrix is 65732 x 66322 with weight 3973198 (avg 59.91/col)
Wed Nov 14 22:27:26 2007  filtering completed in 3 passes
Wed Nov 14 22:27:26 2007  matrix is 61414 x 61478 with weight 3685100 (avg 59.94/col)
Wed Nov 14 22:27:27 2007  saving the first 48 matrix rows for later
Wed Nov 14 22:27:27 2007  matrix is 61366 x 61478 with weight 2818330 (avg 45.84/col)
Wed Nov 14 22:27:27 2007  matrix includes 64 packed rows
Wed Nov 14 22:27:27 2007  using block size 24591 for processor cache size 4096 kB
Wed Nov 14 22:27:28 2007  commencing Lanczos iteration
Wed Nov 14 22:27:44 2007  lanczos halted after 972 iterations
Wed Nov 14 22:27:44 2007  recovered 16 nontrivial dependencies
Wed Nov 14 22:27:45 2007  prp39 factor: 378442673724566134246810453283328526129
Wed Nov 14 22:27:45 2007  prp53 factor: 36795294718689337041099821264332695452995703051552587
Wed Nov 14 22:27:45 2007  elapsed time 01:07:05

Nov 14, 2007 (2nd)

By matsuix / GMP-ECM

(79·10¹⁸⁸-7)/9 = 8(7)₁₈₈_<189> = 17 · 293 · C186

C186 = P32 · C154

P32 = 21765125120660595551469602307679_<32>

C154 = [8096678074753473185944039706917079992623437626274897607442886516416138091715794569583278042469134900566577085836441842147205791368296429713363394770501523_<154>]

Nov 14, 2007

By Sinkiti Sibata / Msieve, GGNFS

2·10¹¹³+9 = 2(0)₁₁₂9_<114> = 29 · 41 · 43 · 66063586712481298029647_<23> · C86

C86 = P30 · P57

P30 = 126503094686428494316629112361_<30>

P57 = 468076014118751200598434885891146498395685059990909881001_<57>

Tue Nov 13 19:16:24 2007  
Tue Nov 13 19:16:24 2007  Msieve v. 1.28
Tue Nov 13 19:16:24 2007  random seeds: 79b93950 914c419f
Tue Nov 13 19:16:24 2007  factoring 59213064334510423889180281278137633024927225091119261905297311496666472844090768153361 (86 digits)
Tue Nov 13 19:16:25 2007  commencing quadratic sieve (86-digit input)
Tue Nov 13 19:16:25 2007  using multiplier of 1
Tue Nov 13 19:16:25 2007  using 64kb Pentium 2 sieve core
Tue Nov 13 19:16:25 2007  sieve interval: 8 blocks of size 65536
Tue Nov 13 19:16:25 2007  processing polynomials in batches of 13
Tue Nov 13 19:16:25 2007  using a sieve bound of 1450331 (55667 primes)
Tue Nov 13 19:16:25 2007  using large prime bound of 116026480 (26 bits)
Tue Nov 13 19:16:25 2007  using double large prime bound of 328248542117840 (41-49 bits)
Tue Nov 13 19:16:25 2007  using trial factoring cutoff of 49 bits
Tue Nov 13 19:16:25 2007  polynomial 'A' values have 11 factors
Wed Nov 14 00:52:54 2007  55802 relations (15557 full + 40245 combined from 585823 partial), need 55763
Wed Nov 14 00:52:57 2007  begin with 601380 relations
Wed Nov 14 00:52:59 2007  reduce to 134103 relations in 9 passes
Wed Nov 14 00:52:59 2007  attempting to read 134103 relations
Wed Nov 14 00:53:05 2007  recovered 134103 relations
Wed Nov 14 00:53:05 2007  recovered 113504 polynomials
Wed Nov 14 00:53:06 2007  attempting to build 55802 cycles
Wed Nov 14 00:53:06 2007  found 55802 cycles in 5 passes
Wed Nov 14 00:53:09 2007  distribution of cycle lengths:
Wed Nov 14 00:53:09 2007     length 1 : 15557
Wed Nov 14 00:53:09 2007     length 2 : 10981
Wed Nov 14 00:53:09 2007     length 3 : 9922
Wed Nov 14 00:53:09 2007     length 4 : 7142
Wed Nov 14 00:53:09 2007     length 5 : 4933
Wed Nov 14 00:53:09 2007     length 6 : 3153
Wed Nov 14 00:53:09 2007     length 7 : 1922
Wed Nov 14 00:53:09 2007     length 9+: 2192
Wed Nov 14 00:53:09 2007  largest cycle: 17 relations
Wed Nov 14 00:53:10 2007  matrix is 55667 x 55802 with weight 2940878 (avg 52.70/col)
Wed Nov 14 00:53:15 2007  filtering completed in 3 passes
Wed Nov 14 00:53:15 2007  matrix is 51377 x 51441 with weight 2736176 (avg 53.19/col)
Wed Nov 14 00:53:17 2007  saving the first 48 matrix rows for later
Wed Nov 14 00:53:17 2007  matrix is 51329 x 51441 with weight 2040428 (avg 39.67/col)
Wed Nov 14 00:53:17 2007  matrix includes 64 packed rows
Wed Nov 14 00:53:17 2007  using block size 5461 for processor cache size 128 kB
Wed Nov 14 00:53:18 2007  commencing Lanczos iteration
Wed Nov 14 00:55:31 2007  lanczos halted after 813 iterations
Wed Nov 14 00:55:32 2007  recovered 17 nontrivial dependencies
Wed Nov 14 00:55:33 2007  prp30 factor: 126503094686428494316629112361
Wed Nov 14 00:55:33 2007  prp57 factor: 468076014118751200598434885891146498395685059990909881001
Wed Nov 14 00:55:33 2007  elapsed time 05:39:09

2·10¹²⁴+9 = 2(0)₁₂₃9_<125> = 11 · 7699 · 530843 · C114

C114 = P50 · P65

P50 = 12933342699273453806862343859989698555609089656801_<50>

P65 = 34397439116451164611055979433447141435329163111083759614363162267_<65>

Number: 20009_124
N=444873868070456791285157294883334653826114223009391544914693262254988985036803067248867103876557666800384103127867
  ( 114 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=12933342699273453806862343859989698555609089656801 (pp50)
 r2=34397439116451164611055979433447141435329163111083759614363162267 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.57 hours.
Scaled time: 1.74 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_124
n: 444873868070456791285157294883334653826114223009391544914693262254988985036803067248867103876557666800384103127867
m: 10000000000000000000000000
c5: 1
c0: 45
skew: 2.14
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:63918, largePrimes:2172125 encountered
Relations: rels:2319136, finalFF:277481
Max relations in full relation-set: 28
Initial matrix: 113080 x 277481 with sparse part having weight 24656124.
Pruned matrix : 81390 x 82019 with weight 5386144.
Total sieving time: 2.35 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.57 hours.
 --------- CPU info (if available) ----------

2·10¹³¹+9 = 2(0)₁₃₀9_<132> = 23 · 5816239007_<10> · 74887441003_<11> · C110

C110 = P50 · P60

P50 = 57062021722090451670266439953685372616833385097687_<50>

P60 = 349867635331476129784259517594411816903548623239985088658229_<60>

Number: 20009_131
N=19964154607141111700061809502715420631256369551377576495671386457041725733903887371073728671212925530921416323
  ( 110 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=57062021722090451670266439953685372616833385097687 (pp50)
 r2=349867635331476129784259517594411816903548623239985088658229 (pp60)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 4.46 hours.
Scaled time: 3.01 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_131
n: 19964154607141111700061809502715420631256369551377576495671386457041725733903887371073728671212925530921416323
m: 100000000000000000000000000
c5: 20
c0: 9
skew: 0.85
type: snfs

Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:63951, AFBsize:63843, largePrimes:1417127 encountered
Relations: rels:1397458, finalFF:156815
Max relations in full relation-set: 28
Initial matrix: 127861 x 156815 with sparse part having weight 9252290.
Pruned matrix : 118504 x 119207 with weight 5490939.
Total sieving time: 4.16 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.46 hours.
 --------- CPU info (if available) ----------

2·10¹³²+9 = 2(0)₁₃₁9_<133> = 11 · 17 · 338993 · 2059033 · 22755127841_<11> · 113606374765035095179_<21> · C88

C88 = P41 · P47

P41 = 64553585691076468757776709697760029089923_<41>

P47 = 91818881868322405255423164024086685058772234099_<47>

Number: 20009_132
N=5927238058745577841908105029284969199323891268952962791663876711778527940853004477884377
  ( 88 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=64553585691076468757776709697760029089923 (pp41)
 r2=91818881868322405255423164024086685058772234099 (pp47)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 4.49 hours.
Scaled time: 3.03 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_132
n: 5927238058745577841908105029284969199323891268952962791663876711778527940853004477884377
m: 100000000000000000000000000
c5: 200
c0: 9
skew: 0.54
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:63951, AFBsize:63988, largePrimes:1398569 encountered
Relations: rels:1367313, finalFF:147644
Max relations in full relation-set: 28
Initial matrix: 128004 x 147644 with sparse part having weight 8145619.
Pruned matrix : 122053 x 122757 with weight 5454428.
Total sieving time: 4.18 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.49 hours.
 --------- CPU info (if available) ----------

2·10¹²¹+9 = 2(0)₁₂₀9_<122> = 47 · 25022303 · 6042247621_<10> · C103

C103 = P50 · P54

P50 = 23276367811865773221842316006407580116078609884723_<50>

P54 = 120918048180665503779004167358585435298916357823336103_<54>

Number: 20009_121
N=2814532964546077252871970629316708556510168734465584891122419326288554907143692044303039418256114054469
  ( 103 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=23276367811865773221842316006407580116078609884723 (pp50)
 r2=120918048180665503779004167358585435298916357823336103 (pp54)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.13 hours.
Scaled time: 1.44 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_121
n: 2814532964546077252871970629316708556510168734465584891122419326288554907143692044303039418256114054469
m: 1000000000000000000000000
c5: 20
c0: 9
skew: 0.85
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63843, largePrimes:2088965 encountered
Relations: rels:2160713, finalFF:219066
Max relations in full relation-set: 28
Initial matrix: 113008 x 219066 with sparse part having weight 18684530.
Pruned matrix : 87485 x 88114 with weight 4996495.
Total sieving time: 1.91 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.13 hours.
 --------- CPU info (if available) ----------

Nov 13, 2007 (5th)

By Jo Yeong Uk / GMP-ECM

2·10¹⁴⁴+9 = 2(0)₁₄₃9_<145> = 11 · 42923 · C139

C139 = P33 · P107

P33 = 128461577505546794238270375795409_<33>

P107 = 32974179012994192473352789524852599153449785137428491442089586166492685253837254412846376457647278813227617_<107>

Nov 13, 2007 (4th)

By Sinkiti Sibata / GGNFS

2·10¹⁰⁹+9 = 2(0)₁₀₈9_<110> = 23 · 95905845140127483764287_<23> · C85

C85 = P42 · P44

P42 = 748402279230484392743519946043122325419467_<42>

P44 = 12114959912210466897728207722918366529921027_<44>

Number: 20009_109
N=9066863611084262532391767761617834512428564112384343014130227238186317203834158432609
  ( 85 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=748402279230484392743519946043122325419467 (pp42)
 r2=12114959912210466897728207722918366529921027 (pp44)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.20 hours.
Scaled time: 0.81 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_109
n: 9066863611084262532391767761617834512428564112384343014130227238186317203834158432609
m: 10000000000000000000000
c5: 1
c0: 45
skew: 2.14
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:63918, largePrimes:1920083 encountered
Relations: rels:1935524, finalFF:195943
Max relations in full relation-set: 28
Initial matrix: 113080 x 195943 with sparse part having weight 13085661.
Pruned matrix : 82364 x 82993 with weight 3462543.
Total sieving time: 1.04 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.20 hours.
 --------- CPU info (if available) ----------

2·10¹¹²+9 = 2(0)₁₁₁9_<113> = 11 · 83 · 10859 · 4136577279787441_<16> · C90

C90 = P31 · P59

P31 = 9206018018107001474355735891329_<31>

P59 = 52973226058227628382351941365777895979723862883622018652443_<59>

Number: 20009_112
N=487672473569298877322950209283462946924937198672763413701237098246837153702239074068366747
  ( 90 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=9206018018107001474355735891329 (pp31)
 r2=52973226058227628382351941365777895979723862883622018652443 (pp59)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.05 hours.
Scaled time: 1.38 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_112
n: 487672473569298877322950209283462946924937198672763413701237098246837153702239074068366747
m: 10000000000000000000000
c5: 200
c0: 9
skew: 0.54
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:63988, largePrimes:2409465 encountered
Relations: rels:3030076, finalFF:735233
Max relations in full relation-set: 28
Initial matrix: 113151 x 735233 with sparse part having weight 52489673.
Pruned matrix : 56354 x 56983 with weight 4802576.
Total sieving time: 1.89 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,112,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.05 hours.
 --------- CPU info (if available) ----------

2·10¹⁴²+9 = 2(0)₁₄₁9_<143> = 11 · 449 · 183695312580749129_<18> · 470754046684836857_<18> · 237679956825681386323_<21> · C84

C84 = P35 · P49

P35 = 36136781193374500273671200283243499_<35>

P49 = 5452012051103151492998305179171168472959562758251_<49>

Tue Nov 13 17:25:38 2007  Msieve v. 1.28
Tue Nov 13 17:25:38 2007  random seeds: 101e150d 418d085c
Tue Nov 13 17:25:38 2007  factoring 197018166554355499780407837997782804306340474278893940041682769225414512357104360249 (84 digits)
Tue Nov 13 17:25:39 2007  commencing quadratic sieve (83-digit input)
Tue Nov 13 17:25:40 2007  using multiplier of 29
Tue Nov 13 17:25:40 2007  using 64kb Pentium 2 sieve core
Tue Nov 13 17:25:40 2007  sieve interval: 6 blocks of size 65536
Tue Nov 13 17:25:40 2007  processing polynomials in batches of 17
Tue Nov 13 17:25:40 2007  using a sieve bound of 1392707 (53151 primes)
Tue Nov 13 17:25:40 2007  using large prime bound of 121165509 (26 bits)
Tue Nov 13 17:25:40 2007  using double large prime bound of 354880447655010 (41-49 bits)
Tue Nov 13 17:25:40 2007  using trial factoring cutoff of 49 bits
Tue Nov 13 17:25:40 2007  polynomial 'A' values have 11 factors
Tue Nov 13 21:04:22 2007  53343 relations (15805 full + 37538 combined from 575786 partial), need 53247
Tue Nov 13 21:04:28 2007  begin with 591591 relations
Tue Nov 13 21:04:31 2007  reduce to 124728 relations in 11 passes
Tue Nov 13 21:04:31 2007  attempting to read 124728 relations
Tue Nov 13 21:04:40 2007  recovered 124728 relations
Tue Nov 13 21:04:40 2007  recovered 100888 polynomials
Tue Nov 13 21:04:54 2007  attempting to build 53343 cycles
Tue Nov 13 21:04:55 2007  found 53343 cycles in 5 passes
Tue Nov 13 21:04:57 2007  distribution of cycle lengths:
Tue Nov 13 21:04:57 2007     length 1 : 15805
Tue Nov 13 21:04:57 2007     length 2 : 10899
Tue Nov 13 21:04:57 2007     length 3 : 9489
Tue Nov 13 21:04:57 2007     length 4 : 6716
Tue Nov 13 21:04:57 2007     length 5 : 4439
Tue Nov 13 21:04:57 2007     length 6 : 2729
Tue Nov 13 21:04:57 2007     length 7 : 1532
Tue Nov 13 21:04:57 2007     length 9+: 1734
Tue Nov 13 21:04:57 2007  largest cycle: 17 relations
Tue Nov 13 21:04:57 2007  matrix is 53151 x 53343 with weight 2794558 (avg 52.39/col)
Tue Nov 13 21:04:59 2007  filtering completed in 3 passes
Tue Nov 13 21:04:59 2007  matrix is 48275 x 48339 with weight 2547868 (avg 52.71/col)
Tue Nov 13 21:05:01 2007  saving the first 48 matrix rows for later
Tue Nov 13 21:05:01 2007  matrix is 48227 x 48339 with weight 1924721 (avg 39.82/col)
Tue Nov 13 21:05:01 2007  matrix includes 64 packed rows
Tue Nov 13 21:05:02 2007  commencing Lanczos iteration
Tue Nov 13 21:09:26 2007  lanczos halted after 764 iterations
Tue Nov 13 21:09:27 2007  recovered 17 nontrivial dependencies
Tue Nov 13 21:09:49 2007  prp35 factor: 36136781193374500273671200283243499
Tue Nov 13 21:09:49 2007  prp49 factor: 5452012051103151492998305179171168472959562758251
Tue Nov 13 21:09:49 2007  elapsed time 03:44:11

Nov 13, 2007 (3rd)

By matsuix / GMP-ECM

2·10¹⁷⁷+3 = 2(0)₁₇₆3_<178> = 19 · 23 · 107 · C173

C173 = P30 · C144

P30 = 221303620588838744540899263379_<30>

C144 = [193275258075082552732257542798544930147975742565477273667881259410088142299640908729176984976444019569373369657540183408799360677960504958362823_<144>]

Nov 13, 2007 (2nd)

By JMB / GMP-ECM

9·10¹⁷⁹+7 = 9(0)₁₇₈7_<180> = 367699 · 313009111137872717_<18> · C157

C157 = P34 · P124

P34 = 1707358559977705545311234918697001_<34>

P124 = 4580030236511827524816894288626065240922568714998170751384355667293248449614016116415020750898340461128531874477462326513929_<124>

Nov 13, 2007

The factor table of 200...009 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Nov 12, 2007 (5th)

By Yousuke Koide

(10¹³⁰⁹-1)/9 is divisible by 1163807225003295831984120638730881_<34>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 12, 2007 (4th)

By matsuix / GMP-ECM

6·10¹⁹⁴-1 = 5(9)₁₉₄_<195> = 19 · C194

C194 = P30 · P164

P30 = 552558220648518327302187386107_<30>

P164 = 57150443497805430547760194830899991379283534240795388543593799035627131426642721828037543684764910233345763252213386580962086660768427630404724977220097501462854303_<164>

Nov 12, 2007 (3rd)

By Jo Yeong Uk / GGNFS

(8·10¹⁷⁸+7)/3 = 2(6)₁₇₇9_<179> = C179

C179 = P78 · P101

P78 = 767662720421063505818715038954728721321787934050897941208611795952414246856909_<78>

P101 = 34737477745486953572334913721147854658092970596516908814796404141305652988617311793270855849086732641_<101>

Number: 26669_178
N=26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 179 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=767662720421063505818715038954728721321787934050897941208611795952414246856909 (pp78)
 r2=34737477745486953572334913721147854658092970596516908814796404141305652988617311793270855849086732641 (pp101)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 229.96 hours.
Scaled time: 491.89 units (timescale=2.139).
Factorization parameters were as follows:
n: 26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
m: 1000000000000000000000000000000000000
c5: 2
c0: 175
skew: 2.45
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [5000000, 8800001)
Primes: RFBsize:664579, AFBsize:665250, largePrimes:11139695 encountered
Relations: rels:11517589, finalFF:1584544
Max relations in full relation-set: 28
Initial matrix: 1329894 x 1584544 with sparse part having weight 95324120.
Pruned matrix : 1095649 x 1102362 with weight 62665643.
Total sieving time: 220.70 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 8.91 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000
total time: 229.96 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 12, 2007 (2nd)

By Robert Backstrom / GMP-ECM

2·10¹⁶⁵+3 = 2(0)₁₆₄3_<166> = 94136405394950299_<17> · C149

C149 = P36 · P113

P36 = 838305023383274289860418539450587157_<36>

P113 = 25343717347214324824522098723663613215893017202640604427624247481323908812513490062007103784101162836271292998421_<113>

Nov 12, 2007

By JMB / GMP-ECM, Msieve

9·10¹⁷⁷+7 = 9(0)₁₇₆7_<178> = 153438528657199_<15> · 32667044190772508911_<20> · C145

C145 = P33 · P112

P33 = 231363885166211856645528826109773_<33>

P112 = 7760731807961019750154843183467424612751080704744319434512584619725381829268383039969389480897051376995338032131_<112>

9·10¹⁸²+7 = 9(0)₁₈₁7_<183> = 681997 · 5371290194501118001753_<22> · 15159963126712966411921_<23> · C134

C134 = P37 · P41 · P57

P37 = 6744944339966240521048365048076011509_<37>

P41 = 19234654468418325743668292529120757280653_<41>

P57 = 124916706233941797813783021695951936693773474351449547931_<57>

9·10¹⁹¹+7 = 9(0)₁₉₀7_<192> = 19² · 71 · 223 · 5348430907_<10> · 7081217033400011183081_<22> · 4467601201156530952852184773_<28> · C126

C126 = P32 · P38 · P58

P32 = 16211565179348756515840607697259_<32>

P38 = 21676057655573837315308075461982724731_<38>

P58 = 2648244977702149059480307274983753320329588866774945947601_<58>

Nov 11, 2007 (4th)

By Robert Backstrom / GGNFS, Msieve

(17·10¹⁶⁵-71)/9 = 1(8)₁₆₄1_<166> = 3² · 11 · 19 · 239 · 2301857 · C154

C154 = P52 · P103

P52 = 1104452615085621808528281839929327507501092871162291_<52>

P103 = 1652700990864867075451213479344319367803780935121458431710865579015107058129083254411956069524400585357_<103>

Number: n
N=1825329931315300800903828355172001996656416128933119005508117804769257585582659512383777143680106332212925711617403703267839837227789771348804185345172887
  ( 154 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Nov 12 01:18:09 2007  prp52 factor: 1104452615085621808528281839929327507501092871162291
Mon Nov 12 01:18:09 2007  prp103 factor: 1652700990864867075451213479344319367803780935121458431710865579015107058129083254411956069524400585357
Mon Nov 12 01:18:09 2007  elapsed time 01:38:44 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 45.96 hours.
Scaled time: 60.94 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_1_8_164_1
n: 1825329931315300800903828355172001996656416128933119005508117804769257585582659512383777143680106332212925711617403703267839837227789771348804185345172887
skew: 1.33
deg: 5
c5: 17
c0: -71
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100000)
Primes: RFBsize:250150, AFBsize:249087, largePrimes:7336079 encountered
Relations: rels:6862148, finalFF:583606
Max relations in full relation-set: 28
Initial matrix: 499302 x 583606 with sparse part having weight 42516043.
Pruned matrix : 429944 x 432504 with weight 26149440.
Total sieving time: 45.69 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 45.96 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 11, 2007 (3rd)

By matsuix / GMP-ECM

4·10¹⁷⁶+7 = 4(0)₁₇₅7_<177> = 11 · 37 · C174

C174 = P37 · C138

P37 = 7135210354090040619550238567081980993_<37>

C138 = [137739594774192223139709541988016487305378968971069153072936288397790444184230544651923302551708474913403317389091953092751175896905333457_<138>]

(14·10¹⁹⁶-41)/9 = 1(5)₁₉₅1_<197> = 43 · C195

C195 = P29 · C167

P29 = 12991941439670998826484083573_<29>

C167 = [27844730337109139843652566781414443973010019917901912124608905800374293093913322511112990355973246182909621326436655829024147474787381586660026718061075677175452115209_<167>]

Nov 11, 2007 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

9·10¹⁶³+7 = 9(0)₁₆₂7_<164> = 47 · 349 · 859 · 58211 · C153

C153 = P33 · P42 · P78

P33 = 818470811192938112676337938572201_<33>

P42 = 873583190755642325776044428797599382814221_<42>

P78 = 153466481365034760327052932409167822889494591377902353931701362171082781011161_<78>

Number: n
N=134065738464908389294733191862713080806437886653151154389264336165712868499470848705785633116618319074552541740190520581
  ( 120 digits)
SNFS difficulty: 163 digits.
Divisors found:

Sun Nov 11 08:08:38 2007  prp42 factor: 873583190755642325776044428797599382814221
Sun Nov 11 08:08:38 2007  prp78 factor: 153466481365034760327052932409167822889494591377902353931701362171082781011161
Sun Nov 11 08:08:38 2007  elapsed time 01:40:59 (Msieve 1.29)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 63.94 hours.
Scaled time: 83.51 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_9_0_162_7

n: 134065738464908389294733191862713080806437886653151154389264336165712868499470848705785633116618319074552541740190520581

# n: 109728893714553854980742941642496184479539542626049635609986238428007354105418652745423356276793313693697545479480233833467867898192710425178858044968781

skew: 0.16
deg: 5
c5: 9000
c0: 7
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2950001)
Primes: RFBsize:216816, AFBsize:217011, largePrimes:7516572 encountered
Relations: rels:6969287, finalFF:457940
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 63.56 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 63.94 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 11, 2007

By JMB / GMP-ECM

9·10¹⁸³+7 = 9(0)₁₈₂7_<184> = 59 · 5879009045374855927_<19> · C164

C164 = P35 · P129

P35 = 81464545498575947436007410472506863_<35>

P129 = 318506082558980426195556346049653444619519149682263511747011957601975589600934055977483795167502851069663481908650764978825371373_<129>

9·10¹⁶⁴+7 = 9(0)₁₆₃7_<165> = 883 · 24573393591862132649_<20> · C143

C143 = P34 · P110

P34 = 2564993881968404917452325855647781_<34>

P110 = 16170756423913671663934778083625100661998605305949217253030068605305369307115708420697061171260255444165225841_<110>

9·10¹⁷³+7 = 9(0)₁₇₂7_<174> = 19 · 647 · 224401 · C165

C165 = P31 · P134

P31 = 4204449134966651726234511502249_<31>

P134 = 77598037366254001837116882823105292830227805356149887771917581121716866409828186604482406682111147355193961123945624774784312354859251_<134>

9·10¹⁶⁹+7 = 9(0)₁₆₈7_<170> = 2111 · 1429958609_<10> · C158

C158 = P32 · P126

P32 = 56769904881370799699375018291651_<32>

P126 = 525185398197314224568248713026766256427182001005757531713576174925963787257959304880282840700874560113146274753741218461103843_<126>

Nov 10, 2007 (2nd)

By Sinkiti Sibata / PFGW

(23·10¹⁰⁵⁹⁸+7)/3, (23·10¹²⁴⁶⁵+7)/3, (23·10¹⁵⁸⁷⁵+7)/3 and (23·10¹⁸⁸⁹⁵+7)/3 are PRPs. There is no other PRP of the form (23·10ⁿ+7)/3 (10001≤n≤20000).

Nov 10, 2007

By matsuix / GMP-ECM

6·10¹⁶⁶-1 = 5(9)₁₆₆_<167> = 1415744095201_<13> · C155

C155 = P26 · C130

P26 = 12712979409464320156621733_<26>

C130 = [3333643448967159954626524687734330724615407100378702091659234658746271899362005594705868470962976554854259399799326518042378430003_<130>]

Nov 9, 2007

By matsuix / GMP-ECM

(55·10¹⁸⁰-1)/9 = 6(1)₁₈₀_<181> = 3 · 23 · C179

C179 = P30 · P150

P30 = 101498619902504222710961733499_<30>

P150 = 872591447867335155263871338215982008049920291961559255672354899684344056901549523294371067281499223907198249217989811855244487724718971598186664829281_<150>

Nov 8, 2007 (2nd)

By matsuix / GMP-ECM

(8·10¹⁷⁴-53)/9 = (8)₁₇₃3_<174> = 2309 · C171

C171 = P29 · C143

P29 = 28200513448768426338019164149_<29>

C143 = [13651064825355236966422593727849148145450828300351719858603135500864608496173059635187685618753649483887590160393912399962653031892990513454363_<143>]

Nov 8, 2007

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

9·10¹⁵³+7 = 9(0)₁₅₂7_<154> = 907 · 1567 · 51635332541907318461_<20> · C129

C129 = P61 · P68

P61 = 4772486568530653705948719675085861919871051034726502704647793_<61>

P68 = 25696533054533355691086868666739471157508323084478430890473067987511_<68>

Number: n
N=122636358860564412039100336767082272939485086621808173675665794174642554988798630986018211854909258720752103550308799860577713223
  ( 129 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=4772486568530653705948719675085861919871051034726502704647793 (pp61)
 r2=25696533054533355691086868666739471157508323084478430890473067987511 (pp68)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.78 hours.
Scaled time: 35.54 units (timescale=1.327).
Factorization parameters were as follows:
name: KA_9_0_152_7
n: 122636358860564412039100336767082272939485086621808173675665794174642554988798630986018211854909258720752103550308799860577713223
skew: 0.24
deg: 5
c5: 9000
c0: 7
m: 1000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:183072, AFBsize:183101, largePrimes:6782121 encountered
Relations: rels:6200134, finalFF:427533
Max relations in full relation-set: 48
Initial matrix: 366240 x 427533 with sparse part having weight 38208097.
Pruned matrix : 321175 x 323070 with weight 23509586.
Total sieving time: 23.39 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 3.08 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 26.78 hours.
 --------- CPU info (if available) ----------

Cywin on AMD 64 3200+

(67·10¹⁶⁵+23)/9 = 7(4)₁₆₄7_<166> = 11 · 17 · 113417 · C159

C159 = P76 · P84

P76 = 3436383816970356938534318813689175226044935882855602276600499748816862981373_<76>

P84 = 102143530795393078870771512077719961217354103402463760765008945031833455587257908841_<84>

Number: n
N=351004376233502067423634322257777917760418568213229144337614952819956323425302295053639519584815678512598105002812461856105588319194641309439952033732715018693
  ( 159 digits)
SNFS difficulty: 166 digits.
Divisors found:

Thu Nov 08 15:26:03 2007  prp76 factor: 3436383816970356938534318813689175226044935882855602276600499748816862981373
Thu Nov 08 15:26:03 2007  prp84 factor: 102143530795393078870771512077719961217354103402463760765008945031833455587257908841
Thu Nov 08 15:26:03 2007  elapsed time 02:17:33 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 81.97 hours.
Scaled time: 98.04 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_7_4_164_7
n: 351004376233502067423634322257777917760418568213229144337614952819956323425302295053639519584815678512598105002812461856105588319194641309439952033732715018693
type: snfs
skew: 0.81
deg: 5
c5: 67
c0: 23
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2600000)
Primes: RFBsize:250150, AFBsize:249876, largePrimes:7471694 encountered
Relations: rels:6998321, finalFF:574667
Max relations in full relation-set: 28
Initial matrix: 500091 x 574667 with sparse part having weight 41672522.
Pruned matrix : 442380 x 444944 with weight 28636697.
Total sieving time: 81.66 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 81.97 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(71·10¹⁶⁵-17)/9 = 7(8)₁₆₄7_<166> = 3 · 11 · 79 · 467 · 1619 · 377387 · C152

C152 = P31 · P41 · P81

P31 = 1719997418393992940622623083871_<31>

P41 = 38022766744779558259291504973562443163143_<41>

P81 = 162163322041498669991056527746571842965333158652283809975565132898038976089503147_<81>

Nov 7, 2007 (4th)

By Jo Yeong Uk / GGNFS

9·10¹⁶⁰+7 = 9(0)₁₅₉7_<161> = 193 · 233 · 43499 · 1514405906081012721338467999_<28> · C125

C125 = P58 · P67

P58 = 9539345889759064940903674568760087065552798466254478738629_<58>

P67 = 3184850972645850020285709503660847208668237617514389096861847478007_<67>

Number: 90007_160
N=30381395035404349559261482175363386501616068379879041925147514635035093035613293267212425275525857274850151785739806178832403
  ( 125 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=9539345889759064940903674568760087065552798466254478738629 (pp58)
 r2=3184850972645850020285709503660847208668237617514389096861847478007 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 30.91 hours.
Scaled time: 66.06 units (timescale=2.137).
Factorization parameters were as follows:
n: 30381395035404349559261482175363386501616068379879041925147514635035093035613293267212425275525857274850151785739806178832403
m: 100000000000000000000000000000000
c5: 9
c0: 7
skew: 0.95
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3800001)
Primes: RFBsize:283146, AFBsize:283337, largePrimes:5671469 encountered
Relations: rels:5709779, finalFF:661423
Max relations in full relation-set: 28
Initial matrix: 566547 x 661423 with sparse part having weight 42662144.
Pruned matrix : 495804 x 498700 with weight 29440637.
Total sieving time: 29.54 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.24 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 30.91 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 7, 2007 (3rd)

By Sinkiti Sibata / PFGW

9·10¹⁵⁷¹⁰+7, 9·10¹⁶⁴⁵³+7, 9·10¹⁷⁴⁸⁸+7 and 9·10¹⁸¹⁰⁹+7 are PRPs. There is no other PRP of the form 9·10ⁿ+7 (10001≤n≤20000).

Nov 7, 2007 (2nd)

By Sinkiti Sibata / Msieve, GGNFS

9·10¹²¹+7 = 9(0)₁₂₀7_<122> = 71 · 10733 · 14298301 · 13437563210843_<14> · C96

C96 = P47 · P50

P47 = 46754707307478264058557236237372093839004268587_<47>

P50 = 13147183761460396406902731745730328931732164333889_<50>

Mon Nov 05 07:44:28 2007  
Mon Nov 05 07:44:28 2007  Msieve v. 1.28
Mon Nov 05 07:44:28 2007  random seeds: cd76d0a4 bee9a5b5
Mon Nov 05 07:44:28 2007  factoring 614692728684711966341285537593488278848176917343378079725035602868779219670052351614028502244843 (96 digits)
Mon Nov 05 07:44:29 2007  commencing quadratic sieve (96-digit input)
Mon Nov 05 07:44:30 2007  using multiplier of 11
Mon Nov 05 07:44:30 2007  using 64kb Pentium 2 sieve core
Mon Nov 05 07:44:30 2007  sieve interval: 18 blocks of size 65536
Mon Nov 05 07:44:30 2007  processing polynomials in batches of 6
Mon Nov 05 07:44:30 2007  using a sieve bound of 2297747 (84706 primes)
Mon Nov 05 07:44:30 2007  using large prime bound of 344662050 (28 bits)
Mon Nov 05 07:44:30 2007  using double large prime bound of 2329744160961150 (43-52 bits)
Mon Nov 05 07:44:30 2007  using trial factoring cutoff of 52 bits
Mon Nov 05 07:44:30 2007  polynomial 'A' values have 13 factors
Tue Nov 06 21:50:05 2007  85254 relations (21080 full + 64174 combined from 1274004 partial), need 84802
Tue Nov 06 21:50:26 2007  begin with 1295084 relations
Tue Nov 06 21:53:11 2007  reduce to 222278 relations in 12 passes
Tue Nov 06 21:53:12 2007  attempting to read 222278 relations
Tue Nov 06 21:53:48 2007  recovered 222278 relations
Tue Nov 06 21:53:48 2007  recovered 207893 polynomials
Tue Nov 06 21:56:08 2007  attempting to build 85254 cycles
Tue Nov 06 21:56:15 2007  found 85254 cycles in 6 passes
Tue Nov 06 21:56:21 2007  distribution of cycle lengths:
Tue Nov 06 21:56:21 2007     length 1 : 21080
Tue Nov 06 21:56:21 2007     length 2 : 14945
Tue Nov 06 21:56:21 2007     length 3 : 14297
Tue Nov 06 21:56:21 2007     length 4 : 11531
Tue Nov 06 21:56:21 2007     length 5 : 8635
Tue Nov 06 21:56:21 2007     length 6 : 5795
Tue Nov 06 21:56:21 2007     length 7 : 3728
Tue Nov 06 21:56:21 2007     length 9+: 5243
Tue Nov 06 21:56:21 2007  largest cycle: 20 relations
Tue Nov 06 21:56:42 2007  matrix is 84706 x 85254 with weight 5719147 (avg 67.08/col)
Tue Nov 06 21:57:55 2007  filtering completed in 3 passes
Tue Nov 06 21:57:55 2007  matrix is 80583 x 80647 with weight 5410769 (avg 67.09/col)
Tue Nov 06 21:57:59 2007  saving the first 48 matrix rows for later
Tue Nov 06 21:58:00 2007  matrix is 80535 x 80647 with weight 4352733 (avg 53.97/col)
Tue Nov 06 21:58:00 2007  matrix includes 64 packed rows
Tue Nov 06 21:58:00 2007  using block size 10922 for processor cache size 256 kB
Tue Nov 06 21:58:03 2007  commencing Lanczos iteration
Tue Nov 06 22:04:03 2007  lanczos halted after 1275 iterations
Tue Nov 06 22:04:05 2007  recovered 15 nontrivial dependencies
Tue Nov 06 23:20:29 2007  prp47 factor: 46754707307478264058557236237372093839004268587
Tue Nov 06 23:20:29 2007  prp50 factor: 13147183761460396406902731745730328931732164333889
Tue Nov 06 23:20:29 2007  elapsed time 39:36:01

9·10¹⁶⁶-7 = 8(9)₁₆₅3_<167> = 42709 · 1578482099_<10> · C154

C154 = P39 · P115

P39 = 326236852168633890020751838911718198217_<39>

P115 = 4092139473970466337231565660348581447470351547418909019180227591362356350317132972423887166170348215102482040007519_<115>

Number: 89993_166
N=1335006700623134276833509278792951544459029456753960978279183880064673180289547757171082237750647795330058324252033450827327369675772426590179731812393623
  ( 154 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=326236852168633890020751838911718198217 (pp39)
 r2=4092139473970466337231565660348581447470351547418909019180227591362356350317132972423887166170348215102482040007519 (pp115)
Version: GGNFS-0.77.1-20060513-k8
Total time: 124.14 hours.
Scaled time: 248.65 units (timescale=2.003).
Factorization parameters were as follows:
name: 89993_166
n: 1335006700623134276833509278792951544459029456753960978279183880064673180289547757171082237750647795330058324252033450827327369675772426590179731812393623
m: 1000000000000000000000000000000000
c5: 90
c0: -7
skew: 0.6
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 6400001)
Primes: RFBsize:348513, AFBsize:349111, largePrimes:5986344 encountered
Relations: rels:6137431, finalFF:783376
Max relations in full relation-set: 28
Initial matrix: 697691 x 783376 with sparse part having weight 60293050.
Pruned matrix : 635609 x 639161 with weight 46938360.
Total sieving time: 117.98 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 5.62 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 124.14 hours.
 --------- CPU info (if available) ----------

Nov 7, 2007

By Robert Backstrom / GGNFS, Msieve

9·10¹⁵⁴+7 = 9(0)₁₅₃7_<155> = C155

C155 = P75 · P81

P75 = 342774283579171568600971909894532466448184589420657720323497289127488139607_<75>

P81 = 262563454469922156375323276959104849917481523961677799993943153957816466910677201_<81>

Number: n
N=90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
  ( 155 digits)
SNFS difficulty: 155 digits.
Divisors found:

Wed Nov 07 02:43:42 2007  prp75 factor: 342774283579171568600971909894532466448184589420657720323497289127488139607
Wed Nov 07 02:43:42 2007  prp81 factor: 262563454469922156375323276959104849917481523961677799993943153957816466910677201
Wed Nov 07 02:43:42 2007  elapsed time 01:08:12 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 31.83 hours.
Scaled time: 38.16 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_9_0_153_7
n: 90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
type: snfs
skew: 1.51
deg: 5
c5: 9
c0: 70
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1350000)
Primes: RFBsize:216816, AFBsize:217291, largePrimes:6508656 encountered
Relations: rels:6015638, finalFF:533595
Max relations in full relation-set: 28
Initial matrix: 434171 x 533595 with sparse part having weight 29453920.
Pruned matrix : 345128 x 347362 with weight 15856430.
Total sieving time: 31.59 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 31.83 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 6, 2007 (7th)

By JMB / GGNFS

9·10¹⁵²+7 = 9(0)₁₅₁7_<153> = 4761397 · 170458908643_<12> · 49688519499466733076979_<23> · C113

C113 = P39 · P74

P39 = 703840987201156095759020645169329337871_<39>

P74 = 31707193373284828223436939712373236806907701314756561688871528206762760813_<74>

Nov 6, 2007 (6th)

By Jo Yeong Uk / GGNFS, GMP-ECM

9·10¹⁵⁰+7 = 9(0)₁₄₉7_<151> = 19732343 · 326052556279_<12> · C133

C133 = P39 · P94

P39 = 589499724724831441087810448027951375963_<39>

P94 = 2372972128635709558872684003447910854760650370032899324921933688620430554494554451055042317237_<94>

Number: 90007_150
N=1398866416610448089159839440560263500294515545943113810621260052431416451996375989188510257329362504846021037950153661991966102374231
  ( 133 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=589499724724831441087810448027951375963 (pp39)
 r2=2372972128635709558872684003447910854760650370032899324921933688620430554494554451055042317237 (pp94)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 12.90 hours.
Scaled time: 27.68 units (timescale=2.146).
Factorization parameters were as follows:
n: 1398866416610448089159839440560263500294515545943113810621260052431416451996375989188510257329362504846021037950153661991966102374231
m: 1000000000000000000000000000000
c5: 9
c0: 7
skew: 0.95
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:176458, largePrimes:5458981 encountered
Relations: rels:5399088, finalFF:508783
Max relations in full relation-set: 28
Initial matrix: 352824 x 508783 with sparse part having weight 43914106.
Pruned matrix : 281114 x 282942 with weight 22700108.
Total sieving time: 12.40 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.39 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 12.90 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹⁶²+7 = 9(0)₁₆₁7_<163> = 5675476123_<10> · 19653188594940718862107501_<26> · C128

C128 = P36 · P93

P36 = 688903506523745903246622831283151599_<36>

P93 = 117124780898551182812517761055884645674869174813318998257172923202640159324081908982573296791_<93>

Nov 6, 2007 (5th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

9·10¹⁶⁴-7 = 8(9)₁₆₃3_<165> = 19 · 1847353 · C158

C158 = P40 · P56 · P63

P40 = 5195304037384876588643582502770703788863_<40>

P56 = 44521045988937219971985542168110282187182538753337627749_<56>

P63 = 110856890051938744122912238100452821884732080214861054731598977_<63>

Number: n
N=4935464700192921827044022834990668957767855479530538704420183216532608252538248713711246307900524500214451242775212773
  ( 118 digits)
SNFS difficulty: 165 digits.
Divisors found:

Tue Nov 06 10:24:21 2007  prp56 factor: 44521045988937219971985542168110282187182538753337627749
Tue Nov 06 10:24:21 2007  prp63 factor: 110856890051938744122912238100452821884732080214861054731598977
Tue Nov 06 10:24:21 2007  elapsed time 01:29:30 (Msieve 1.29)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 64.39 hours.
Scaled time: 84.09 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_8_9_163_3
n: 4935464700192921827044022834990668957767855479530538704420183216532608252538248713711246307900524500214451242775212773

# n: 25641239683282826264048301029977258784524896461386415561816513169184004869328396388038224934470250706081392645243448898305618334648776412862933585172092747099

skew: 1.51
deg: 5
c5: 9
c0: -70
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3200000)
Primes: RFBsize:216816, AFBsize:217291, largePrimes:7651039 encountered
Relations: rels:7167373, finalFF:504847
Max relations in full relation-set: 28
Initial matrix: 434171 x 504847 with sparse part having weight 46676546.
Pruned matrix : 406046 x 408280 with weight 34115092.
Total sieving time: 64.06 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 64.39 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(2·10¹⁶⁶+1)/3 = (6)₁₆₅7_<166> = 132420593 · C158

C158 = P36 · P123

P36 = 472608263478122255214913213813840403_<36>

P123 = 106525087996081326022960925559747436760122308821013875848798824526842994763515192581889447596719018370039169071680038462873_<123>

Nov 6, 2007 (4th)

By matsuix / GMP-ECM

(19·10¹⁶⁵-1)/9 = 2(1)₁₆₅_<166> = 97 · 28030207 · 678175727 · 28933389748066579_<17> · C131

C131 = P40 · P92

P40 = 1004850910964957079601987123021515538751_<40>

P92 = 39379469642482560582795123873781476067047647244625665707647850841194751914774629866823998323_<92>

Nov 6, 2007 (3rd)

By Sinkiti Sibata / GGNFS

9·10¹³³+7 = 9(0)₁₃₂7_<134> = 5881 · 26930082287_<11> · 176964956297383872307_<21> · C100

C100 = P44 · P57

P44 = 25264976655443100325796147326226279933324489_<44>

P57 = 127100563245798676374051740186784449244832505678728530547_<57>

Number: 90007_133
N=3211192763298772886403404485557143401237610375947392799399813124253179761582114633674548555499665483
  ( 100 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=25264976655443100325796147326226279933324489 (pp44)
 r2=127100563245798676374051740186784449244832505678728530547 (pp57)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 8.81 hours.
Scaled time: 5.96 units (timescale=0.676).
Factorization parameters were as follows:
name: 90007_133
n: 3211192763298772886403404485557143401237610375947392799399813124253179761582114633674548555499665483
m: 100000000000000000000000000
c5: 9000
c0: 7
skew: 0.24
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1300001)
Primes: RFBsize:78498, AFBsize:63803, largePrimes:1571280 encountered
Relations: rels:1590409, finalFF:190659
Max relations in full relation-set: 28
Initial matrix: 142368 x 190659 with sparse part having weight 15771459.
Pruned matrix : 127262 x 128037 with weight 8863354.
Total sieving time: 8.34 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.32 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.81 hours.
 --------- CPU info (if available) ----------

9·10¹¹⁷+7 = 9(0)₁₁₆7_<118> = 47 · 443867 · C111

C111 = P41 · P71

P41 = 17471857037357853190634584935442902072067_<41>

P71 = 24691798610564857752888526692177153472802870226100236461016311059115929_<71>

Number: 90007_117
N=431411575319020471390006657639299562083696817558297724701797533850110074663442648073275160198696667283265655243
  ( 111 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=17471857037357853190634584935442902072067 (pp41)
 r2=24691798610564857752888526692177153472802870226100236461016311059115929 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.78 hours.
Scaled time: 1.88 units (timescale=0.676).
Factorization parameters were as follows:
name: 90007_117
n: 431411575319020471390006657639299562083696817558297724701797533850110074663442648073275160198696667283265655243
m: 100000000000000000000000
c5: 900
c0: 7
skew: 0.38
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:63823, largePrimes:2291621 encountered
Relations: rels:2546258, finalFF:364912
Max relations in full relation-set: 28
Initial matrix: 112985 x 364912 with sparse part having weight 33871287.
Pruned matrix : 74587 x 75215 with weight 6217223.
Total sieving time: 2.55 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.78 hours.
 --------- CPU info (if available) ----------

Nov 6, 2007 (2nd)

By JMB / GGNFS

9·10¹⁸⁴+7 = 9(0)₁₈₃7_<185> = 617 · 3725507 · 159746791 · 1198459567_<10> · 80746431532206891622049_<23> · 666062407088402900138543_<24> · C112

C112 = P53 · P60

P53 = 11636058351571852705216457129789359016330456971195199_<53>

P60 = 326792650541123463809952364790176505238645003791330917413293_<60>

Nov 6, 2007

By Torbjörn Granlund

(10⁸⁴³-1)/9 is divisible by 769166959867961874063651865987632601_<36>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 5, 2007 (5th)

By JMB / GMP-ECM, Msieve

9·10¹⁴⁷+7 = 9(0)₁₄₆7_<148> = 25951 · 1738969 · 197021917 · 92978880982634662097_<20> · C110

C110 = P30 · P40 · P41

P30 = 102931531869565976194616134711_<30>

P40 = 2005256885602141410291462050850625780121_<40>

P41 = 52744753108364828721861464937342277420987_<41>

9·10¹⁵¹+7 = 9(0)₁₅₀7_<152> = 269 · 21613 · 67791928153_<11> · 44970969250703_<14> · 383031576676808952277813_<24> · C98

C98 = P40 · P58

P40 = 6810025963958582438251862479127272552967_<40>

P58 = 1946621858651143417424307752923064400610721325684111628979_<58>

Nov 5, 2007 (4th)

By Sinkiti Sibata / GGNFS

9·10¹²⁰+7 = 9(0)₁₁₉7_<121> = 29 · 281 · 386471 · 142583653 · C104

C104 = P33 · P71

P33 = 266099299493114096677875328801409_<33>

P71 = 75319566589929176165358361692126958829966221213822132241587381268023129_<71>

Number: 90007_120
N=20042483907705114278411372506196732936640720090441885904393246630974136265348532459246920117086459788761
  ( 104 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=266099299493114096677875328801409 (pp33)
 r2=75319566589929176165358361692126958829966221213822132241587381268023129 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.09 hours.
Scaled time: 1.41 units (timescale=0.676).
Factorization parameters were as follows:
name: 90007_120
n: 20042483907705114278411372506196732936640720090441885904393246630974136265348532459246920117086459788761
m: 1000000000000000000000000
c5: 9
c0: 7
skew: 0.95
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63908, largePrimes:2006815 encountered
Relations: rels:1988282, finalFF:148363
Max relations in full relation-set: 28
Initial matrix: 113070 x 148363 with sparse part having weight 12012483.
Pruned matrix : 101019 x 101648 with weight 6176663.
Total sieving time: 1.81 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.09 hours.
 --------- CPU info (if available) ----------

9·10¹²⁶+7 = 9(0)₁₂₅7_<127> = 18386461 · 1742218293047_<13> · C108

C108 = P32 · P77

P32 = 13822662893206118250744627949841_<32>

P77 = 20325913755563927082639117313372686004914219990075373791674260136282142256981_<77>

Number: 90007_126
N=280958253839541308962636479299682207592405666050712699120756569825329538777009922534463258852005274600090021
  ( 108 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=13822662893206118250744627949841 (pp32)
 r2=20325913755563927082639117313372686004914219990075373791674260136282142256981 (pp77)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 3.97 hours.
Scaled time: 2.69 units (timescale=0.676).
Factorization parameters were as follows:
name: 90007_126
n: 280958253839541308962636479299682207592405666050712699120756569825329538777009922534463258852005274600090021
m: 10000000000000000000000000
c5: 90
c0: 7
skew: 0.6
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:49098, AFBsize:64083, largePrimes:2196928 encountered
Relations: rels:2262442, finalFF:171270
Max relations in full relation-set: 28
Initial matrix: 113248 x 171270 with sparse part having weight 16894508.
Pruned matrix : 103160 x 103790 with weight 7851326.
Total sieving time: 3.61 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.97 hours.
 --------- CPU info (if available) ----------

Nov 5, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

4·10¹⁶¹-3 = 3(9)₁₆₀7_<162> = 13 · 71 · 738953 · 17948851 · 743599950371757358081470341_<27> · C119

C119 = P43 · P77

P43 = 2846805213519635781879812334100609838888539_<43>

P77 = 15435038486874269067278126927452408807037060575563649377214970000125309743587_<77>

Number: n
N=43940548035309899548763925751595996999472868799993550808813202591598052489814547810338118021293899624001452203163049393
  ( 119 digits)
SNFS difficulty: 161 digits.
Divisors found:

Mon Nov 05 02:38:02 2007  prp43 factor: 2846805213519635781879812334100609838888539
Mon Nov 05 02:38:02 2007  prp77 factor: 15435038486874269067278126927452408807037060575563649377214970000125309743587
Mon Nov 05 02:38:02 2007  elapsed time 01:17:03 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 33.21 hours.
Scaled time: 43.87 units (timescale=1.321).
Factorization parameters were as follows:
name: KA_3_9_160_7
n: 43940548035309899548763925751595996999472868799993550808813202591598052489814547810338118021293899624001452203163049393
skew: 0.60
deg: 5
c5: 40
c0: -3
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:216816, AFBsize:215821, largePrimes:7042289 encountered
Relations: rels:6514886, finalFF:501112
Max relations in full relation-set: 28
Initial matrix: 432703 x 501112 with sparse part having weight 40819259.
Pruned matrix : 378693 x 380920 with weight 25477509.
Total sieving time: 33.00 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 33.21 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

9·10¹¹¹+7 = 9(0)₁₁₀7_<112> = 131 · 859 · C107

C107 = P33 · P35 · P40

P33 = 682916690512923260407060455419117_<33>

P35 = 51118310350528656363520883890560151_<35>

P40 = 2291046123805509364111583138403788910949_<40>

9·10¹²⁷+7 = 9(0)₁₂₆7_<128> = 344206321 · C120

C120 = P35 · P85

P35 = 33157853781215682395478284485540807_<35>

P85 = 7885645618034098004254139912968642957732499669205257892740457352566043261860258601681_<85>

9·10¹³⁵+7 = 9(0)₁₃₄7_<136> = 1002121 · 14760091 · C123

C123 = P54 · P70

P54 = 588447254183867044277609191468715934421424931568990421_<54>

P70 = 1034012456449314522976535796820781617144073180839915839118262268905897_<70>

Number: n
N=608461790789514535341427955241331643019831322889419400572308896788480722510373845551247628493647294880837405891288543412637
  ( 123 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=588447254183867044277609191468715934421424931568990421 (pp54)
 r2=1034012456449314522976535796820781617144073180839915839118262268905897 (pp70)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.84 hours.
Scaled time: 6.28 units (timescale=1.297).
Factorization parameters were as follows:
name: KA_9_0_134_7
n: 608461790789514535341427955241331643019831322889419400572308896788480722510373845551247628493647294880837405891288543412637
skew: 0.95
deg: 5
c5: 9
c0: 7
m: 1000000000000000000000000000
type: snfs
rlim: 2400000
alim: 2400000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 440001)
Primes: RFBsize:176302, AFBsize:176458, largePrimes:5339208 encountered
Relations: rels:4827042, finalFF:398527
Max relations in full relation-set: 48
Initial matrix: 352824 x 398527 with sparse part having weight 16282983.
Pruned matrix : 297861 x 299689 with weight 9125460.
Total sieving time: 3.68 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.99 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,48,48,2.5,2.5,75000
total time: 4.84 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

9·10¹⁴³+7 = 9(0)₁₄₂7_<144> = 67 · 14449 · C138

C138 = P32 · P107

P32 = 16764671435106466291549252481783_<32>

P107 = 55454254267525152340965490394347806129765919513362592966669387843539324159605808600050322487693263291392363_<107>

Nov 5, 2007 (2nd)

By Jo Yeong Uk / Msieve, GGNFS, GMP-ECM

9·10¹⁰⁸+7 = 9(0)₁₀₇7_<109> = 37871 · 3406331833_<10> · 88079868587_<11> · C84

C84 = P33 · P52

P33 = 144064331776620889004606685503461_<33>

P52 = 5498138252554114429604456503865744400402842973430807_<52>

Mon Nov  5 01:24:55 2007  
Mon Nov  5 01:24:55 2007  
Mon Nov  5 01:24:55 2007  Msieve v. 1.28
Mon Nov  5 01:24:55 2007  random seeds: 152d9442 e6816ec9
Mon Nov  5 01:24:55 2007  factoring 792085613369686554167223683559223742655367466905587896034275024581697823391242523027 (84 digits)
Mon Nov  5 01:24:55 2007  commencing quadratic sieve (84-digit input)
Mon Nov  5 01:24:55 2007  using multiplier of 43
Mon Nov  5 01:24:55 2007  using 32kb Intel Core sieve core
Mon Nov  5 01:24:55 2007  sieve interval: 12 blocks of size 32768
Mon Nov  5 01:24:55 2007  processing polynomials in batches of 17
Mon Nov  5 01:24:55 2007  using a sieve bound of 1401067 (53824 primes)
Mon Nov  5 01:24:55 2007  using large prime bound of 119090695 (26 bits)
Mon Nov  5 01:24:55 2007  using double large prime bound of 344017052465110 (41-49 bits)
Mon Nov  5 01:24:55 2007  using trial factoring cutoff of 49 bits
Mon Nov  5 01:24:55 2007  polynomial 'A' values have 11 factors
Mon Nov  5 01:43:23 2007  54205 relations (16445 full + 37760 combined from 563337 partial), need 53920
Mon Nov  5 01:43:23 2007  begin with 579782 relations
Mon Nov  5 01:43:24 2007  reduce to 124756 relations in 9 passes
Mon Nov  5 01:43:24 2007  attempting to read 124756 relations
Mon Nov  5 01:43:25 2007  recovered 124756 relations
Mon Nov  5 01:43:25 2007  recovered 99117 polynomials
Mon Nov  5 01:43:25 2007  attempting to build 54205 cycles
Mon Nov  5 01:43:25 2007  found 54205 cycles in 5 passes
Mon Nov  5 01:43:25 2007  distribution of cycle lengths:
Mon Nov  5 01:43:25 2007     length 1 : 16445
Mon Nov  5 01:43:25 2007     length 2 : 11224
Mon Nov  5 01:43:25 2007     length 3 : 9837
Mon Nov  5 01:43:25 2007     length 4 : 6662
Mon Nov  5 01:43:25 2007     length 5 : 4386
Mon Nov  5 01:43:25 2007     length 6 : 2611
Mon Nov  5 01:43:25 2007     length 7 : 1468
Mon Nov  5 01:43:25 2007     length 9+: 1572
Mon Nov  5 01:43:25 2007  largest cycle: 15 relations
Mon Nov  5 01:43:25 2007  matrix is 53824 x 54205 with weight 2718225 (avg 50.15/col)
Mon Nov  5 01:43:25 2007  filtering completed in 3 passes
Mon Nov  5 01:43:25 2007  matrix is 48768 x 48832 with weight 2453195 (avg 50.24/col)
Mon Nov  5 01:43:26 2007  saving the first 48 matrix rows for later
Mon Nov  5 01:43:26 2007  matrix is 48720 x 48832 with weight 1746320 (avg 35.76/col)
Mon Nov  5 01:43:26 2007  matrix includes 64 packed rows
Mon Nov  5 01:43:26 2007  commencing Lanczos iteration
Mon Nov  5 01:44:06 2007  lanczos halted after 771 iterations
Mon Nov  5 01:44:07 2007  recovered 17 nontrivial dependencies
Mon Nov  5 01:44:07 2007  prp33 factor: 144064331776620889004606685503461
Mon Nov  5 01:44:07 2007  prp52 factor: 5498138252554114429604456503865744400402842973430807
Mon Nov  5 01:44:07 2007  elapsed time 00:19:12

9·10¹³¹+7 = 9(0)₁₃₀7_<132> = 38921 · 632971 · 968437 · 83275116371_<11> · 274255609394142444443_<21> C85

C85 = P40 · P45

P40 = 2288057282169860293574275141471863042313_<40>

P45 = 721881101657780564083407600404226856588479089_<45>

Mon Nov  5 01:45:50 2007  
Mon Nov  5 01:45:50 2007  
Mon Nov  5 01:45:50 2007  Msieve v. 1.28
Mon Nov  5 01:45:50 2007  random seeds: 72177c0e 693b4483
Mon Nov  5 01:45:50 2007  factoring 1651705311508886027462420179604336574242886949428131140156014177945487040201122692857 (85 digits)
Mon Nov  5 01:45:50 2007  commencing quadratic sieve (84-digit input)
Mon Nov  5 01:45:50 2007  using multiplier of 5
Mon Nov  5 01:45:50 2007  using 32kb Intel Core sieve core
Mon Nov  5 01:45:50 2007  sieve interval: 12 blocks of size 32768
Mon Nov  5 01:45:50 2007  processing polynomials in batches of 17
Mon Nov  5 01:45:50 2007  using a sieve bound of 1413031 (54118 primes)
Mon Nov  5 01:45:50 2007  using large prime bound of 118694604 (26 bits)
Mon Nov  5 01:45:50 2007  using double large prime bound of 341960341070040 (41-49 bits)
Mon Nov  5 01:45:50 2007  using trial factoring cutoff of 49 bits
Mon Nov  5 01:45:50 2007  polynomial 'A' values have 11 factors
Mon Nov  5 02:05:58 2007  54588 relations (16316 full + 38272 combined from 571175 partial), need 54214
Mon Nov  5 02:05:58 2007  begin with 587491 relations
Mon Nov  5 02:05:58 2007  reduce to 126754 relations in 10 passes
Mon Nov  5 02:05:58 2007  attempting to read 126754 relations
Mon Nov  5 02:05:59 2007  recovered 126754 relations
Mon Nov  5 02:05:59 2007  recovered 102596 polynomials
Mon Nov  5 02:05:59 2007  attempting to build 54588 cycles
Mon Nov  5 02:05:59 2007  found 54588 cycles in 5 passes
Mon Nov  5 02:05:59 2007  distribution of cycle lengths:
Mon Nov  5 02:05:59 2007     length 1 : 16316
Mon Nov  5 02:05:59 2007     length 2 : 11199
Mon Nov  5 02:05:59 2007     length 3 : 9830
Mon Nov  5 02:05:59 2007     length 4 : 6838
Mon Nov  5 02:05:59 2007     length 5 : 4545
Mon Nov  5 02:05:59 2007     length 6 : 2670
Mon Nov  5 02:05:59 2007     length 7 : 1519
Mon Nov  5 02:05:59 2007     length 9+: 1671
Mon Nov  5 02:05:59 2007  largest cycle: 18 relations
Mon Nov  5 02:05:59 2007  matrix is 54118 x 54588 with weight 2840617 (avg 52.04/col)
Mon Nov  5 02:06:00 2007  filtering completed in 3 passes
Mon Nov  5 02:06:00 2007  matrix is 49044 x 49108 with weight 2553112 (avg 51.99/col)
Mon Nov  5 02:06:00 2007  saving the first 48 matrix rows for later
Mon Nov  5 02:06:00 2007  matrix is 48996 x 49108 with weight 1908309 (avg 38.86/col)
Mon Nov  5 02:06:00 2007  matrix includes 64 packed rows
Mon Nov  5 02:06:00 2007  commencing Lanczos iteration
Mon Nov  5 02:06:41 2007  lanczos halted after 776 iterations
Mon Nov  5 02:06:42 2007  recovered 16 nontrivial dependencies
Mon Nov  5 02:06:42 2007  prp40 factor: 2288057282169860293574275141471863042313
Mon Nov  5 02:06:42 2007  prp45 factor: 721881101657780564083407600404226856588479089
Mon Nov  5 02:06:42 2007  elapsed time 00:20:52

9·10¹¹²+7 = 9(0)₁₁₁7_<113> = 1706363 · 6132851 · 14021233 · C93

C93 = P45 · P49

P45 = 366287276724937330096345104351579811913585089_<45>

P49 = 1674559682769946750885495255184227109771029382647_<49>

Number: 90007_112
N=613369905915178755561126474140880398319161319784569225022227103519115609390857587884174550583
  ( 93 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=366287276724937330096345104351579811913585089 (pp45)
 r2=1674559682769946750885495255184227109771029382647 (pp49)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.89 hours.
Scaled time: 1.90 units (timescale=2.119).
Factorization parameters were as follows:
n: 613369905915178755561126474140880398319161319784569225022227103519115609390857587884174550583
m: 10000000000000000000000
c5: 900
c0: 7
skew: 0.38
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 360001)
Primes: RFBsize:30757, AFBsize:30859, largePrimes:1047627 encountered
Relations: rels:958703, finalFF:81871
Max relations in full relation-set: 28
Initial matrix: 61680 x 81871 with sparse part having weight 4265106.
Pruned matrix : 57019 x 57391 with weight 2165245.
Total sieving time: 0.86 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,112,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.89 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹¹⁴+7 = 9(0)₁₁₃7_<115> = 653 · 4287299 · 249763385813_<12> · C95

C95 = P42 · P54

P42 = 115630510169949718409527011290812428381853_<42>

P54 = 111312603505914666012718121697883345483669372301240129_<54>

Number: 90007_114
N=12871133131734246468791789551870388883140990287398533490691419410177257253759609146868658979037
  ( 95 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=115630510169949718409527011290812428381853 (pp42)
 r2=111312603505914666012718121697883345483669372301240129 (pp54)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.90 hours.
Scaled time: 1.93 units (timescale=2.145).
Factorization parameters were as follows:
n: 12871133131734246468791789551870388883140990287398533490691419410177257253759609146868658979037
m: 100000000000000000000000
c5: 9
c0: 70
skew: 1.51
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 420001)
Primes: RFBsize:49098, AFBsize:49341, largePrimes:1898932 encountered
Relations: rels:2001615, finalFF:245554
Max relations in full relation-set: 28
Initial matrix: 98503 x 245554 with sparse part having weight 19808415.
Pruned matrix : 69060 x 69616 with weight 3831506.
Total sieving time: 0.85 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.90 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹⁴⁶+7 = 9(0)₁₄₅7_<147> = 23 · 4271 · 437543 · 5421833 · 8849681 · C123

C123 = P35 · P89

P35 = 23988971368700909013664451648647553_<35>

P89 = 18191938657561789126660465345836496511300044062263632583171015546703249344891910371448337_<89>

9·10¹³²+7 = 9(0)₁₃₁7_<133> = 491 · 85117573 · C123

C123 = P51 · P73

P51 = 139221663158686554389864242499707408798312738177711_<51>

P73 = 1546802865177850881667388439251649501422697254868710734255734319160698559_<73>

Number: 90007_132
N=215348467468682007507192912246188645535589219763134333352082775267400780424803384796810560313123800212289002220311443618449
  ( 123 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=139221663158686554389864242499707408798312738177711 (pp51)
 r2=1546802865177850881667388439251649501422697254868710734255734319160698559 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.77 hours.
Scaled time: 8.02 units (timescale=2.125).
Factorization parameters were as follows:
n: 215348467468682007507192912246188645535589219763134333352082775267400780424803384796810560313123800212289002220311443618449
m: 100000000000000000000000000
c5: 900
c0: 7
skew: 0.38
type: snfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [600000, 1350001)
Primes: RFBsize:92938, AFBsize:92634, largePrimes:1721351 encountered
Relations: rels:1789708, finalFF:239139
Max relations in full relation-set: 28
Initial matrix: 185636 x 239139 with sparse part having weight 15179814.
Pruned matrix : 164618 x 165610 with weight 8472390.
Total sieving time: 3.64 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1200000,1200000,25,25,46,46,2.2,2.2,50000
total time: 3.77 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹⁴⁰+7 = 9(0)₁₃₉7_<141> = 151 · 160910339138441_<15> · C125

C125 = P33 · P46 · P48

P33 = 119266962910373522768317901849023_<33>

P46 = 1073502048919627741496999269090973341811523617_<46>

P48 = 289306754986378993892936910082750693641415226647_<48>

Number: 90007_140
N=37040906958342008436196962352631290237631464821269784853671653578621103961679404648708146669704204687383872089120977255061577
  ( 125 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=119266962910373522768317901849023 (pp33)
 r2=1073502048919627741496999269090973341811523617 (pp46)
 r3=289306754986378993892936910082750693641415226647 (pp48)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.15 hours.
Scaled time: 13.17 units (timescale=2.142).
Factorization parameters were as follows:
n: 37040906958342008436196962352631290237631464821269784853671653578621103961679404648708146669704204687383872089120977255061577
m: 10000000000000000000000000000
c5: 9
c0: 7
skew: 0.95
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:113992, largePrimes:3368728 encountered
Relations: rels:3487641, finalFF:407793
Max relations in full relation-set: 28
Initial matrix: 228211 x 407793 with sparse part having weight 35263251.
Pruned matrix : 168183 x 169388 with weight 13199446.
Total sieving time: 5.98 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.15 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 5, 2007

The factor table of 900...007 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Nov 4, 2007 (3rd)

By Sinkiti Sibata / PFGW

9·10¹⁰⁸⁵⁵-7 is PRP. It is the only PRP of the form 9·10ⁿ-7 (10001≤n≤20000).

Nov 4, 2007 (2nd)

By Jo Yeong Uk / GGNFS

9·10¹⁶⁰+1 = 9(0)₁₅₉1_<161> = 196668336511615844317373683402996797341833_<42> · C120

C120 = P52 · P69

P52 = 1739150909232723432175836807853304310816643860207313_<52>

P69 = 263130261241924464291801141224892605010946153371020043305094966475369_<69>

Number: 90001_160
N=457623233085536978487969224809644797039838287759370817200669676684400841774026444495529209155367065867115087869248173497
  ( 120 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=1739150909232723432175836807853304310816643860207313 (pp52)
 r2=263130261241924464291801141224892605010946153371020043305094966475369 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 27.70 hours.
Scaled time: 59.42 units (timescale=2.145).
Factorization parameters were as follows:
n: 457623233085536978487969224809644797039838287759370817200669676684400841774026444495529209155367065867115087869248173497
m: 100000000000000000000000000000000
c5: 9
c0: 1
skew: 0.64
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:282992, largePrimes:5669639 encountered
Relations: rels:5735722, finalFF:684749
Max relations in full relation-set: 28
Initial matrix: 566202 x 684749 with sparse part having weight 43062449.
Pruned matrix : 470596 x 473491 with weight 28108258.
Total sieving time: 26.39 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.17 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 27.70 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 4, 2007

By Sinkiti Sibata / GGNFS

9·10¹⁶¹-7 = 8(9)₁₆₀3_<162> = 53 · 710382599 · 3193863019_<10> · 14169121763_<11> · C132

C132 = P39 · P93

P39 = 637003641965194182950788890954509239897_<39>

P93 = 829226536019218470577471928756725407087718463007725782007729866451066972588969963334914455291_<93>

Number: 89993_161
N=528220323458424440646483477713402912362372432295144177626701835540702260229176792484870656015751898878654984062057672951330199945027
  ( 132 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=637003641965194182950788890954509239897 (pp39)
 r2=829226536019218470577471928756725407087718463007725782007729866451066972588969963334914455291 (pp93)
Version: GGNFS-0.77.1-20060513-k8
Total time: 72.73 hours.
Scaled time: 146.18 units (timescale=2.010).
Factorization parameters were as follows:
name: 89993_161
n: 528220323458424440646483477713402912362372432295144177626701835540702260229176792484870656015751898878654984062057672951330199945027
m: 100000000000000000000000000000000
c5: 90
c0: -7
skew: 0.6
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4550001)
Primes: RFBsize:315948, AFBsize:316641, largePrimes:5828768 encountered
Relations: rels:5947621, finalFF:747210
Max relations in full relation-set: 28
Initial matrix: 632656 x 747210 with sparse part having weight 48277826.
Pruned matrix : 546815 x 550042 with weight 33888020.
Total sieving time: 68.82 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 3.49 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 72.73 hours.
 --------- CPU info (if available) ----------

Nov 3, 2007 (2nd)

By suberi / GGNFS

3·10¹⁵⁸-7 = 2(9)₁₅₇3_<159> = 17 · 41 · 47 · 3041 · 841123744137979613_<18> · C133

C133 = P51 · P83

P51 = 263885431718243596975433066048441779693678318105769_<51>

P83 = 13567470651611743221749122292261888185172901056388384006891037144978168857382893251_<83>

Number: 29993_158
N=3580257850225164627404836853606844290357386870515998826943797062408011849614535981097388373034324355416498626742076743203763054265019
  ( 133 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=263885431718243596975433066048441779693678318105769 (pp51)
 r2=13567470651611743221749122292261888185172901056388384006891037144978168857382893251 (pp83)
Version: GGNFS-0.77.1-20060722-k8
Total time: 49.54 hours.
Scaled time: 72.72 units (timescale=1.468).
Factorization parameters were as follows:
n: 3580257850225164627404836853606844290357386870515998826943797062408011849614535981097388373034324355416498626742076743203763054265019
m: 10000000000000000000000000000000
c5: 3000
c0: -7
skew: 0.3
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3300001)
Primes: RFBsize:283146, AFBsize:283037, largePrimes:5584207 encountered
Relations: rels:5598336, finalFF:647691
Max relations in full relation-set: 32
Initial matrix: 566250 x 647691 with sparse part having weight 39597994.
Pruned matrix : 499206 x 502101 with weight 26364073.
Total sieving time: 45.55 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.63 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 49.54 hours.
 --------- CPU info (if available) ----------

Nov 3, 2007

By Jo Yeong Uk / GGNFS

(8·10¹⁶⁰+1)/9 = (8)₁₅₉9_<160> = 3 · 825027643337_<12> · 4496569364490716593_<19> · C129

C129 = P45 · P85

P45 = 584055110117804933562252574038305701305028939_<45>

P85 = 1367485081849265048121060885327005302341443223828135540212293179914394095612984131937_<85>

Number: 88889_160
N=798686650063927990314125701018237249713184766388387794727385204591609598499027731309396698824991490472673979526416377225579124843
  ( 129 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=584055110117804933562252574038305701305028939 (pp45)
 r2=1367485081849265048121060885327005302341443223828135540212293179914394095612984131937 (pp85)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 27.65 hours.
Scaled time: 59.31 units (timescale=2.145).
Factorization parameters were as follows:
n: 798686650063927990314125701018237249713184766388387794727385204591609598499027731309396698824991490472673979526416377225579124843
m: 200000000000000000000000000000000
c5: 1
c0: 4
skew: 1.32
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:282707, largePrimes:5654427 encountered
Relations: rels:5714441, finalFF:680834
Max relations in full relation-set: 28
Initial matrix: 565917 x 680834 with sparse part having weight 42328056.
Pruned matrix : 473624 x 476517 with weight 27571459.
Total sieving time: 26.35 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.16 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 27.65 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 2, 2007 (6th)

By Sinkiti Sibata / GGNFS

9·10¹⁵⁹-7 = 8(9)₁₅₈3_<160> = 18104666690449826252281753693_<29> · C132

C132 = P56 · P77

P56 = 22392329597836817510288640646341074175512979619336814351_<56>

P77 = 22199985850784836127380389132731731977501124190563051137404670084573603137251_<77>

Number: 89993_159
N=497109400238087848582031566032851660055020853947195342757531373490526734611539481118145584113295135923191327086633995939773759489101
  ( 132 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=22392329597836817510288640646341074175512979619336814351 (pp56)
 r2=22199985850784836127380389132731731977501124190563051137404670084573603137251 (pp77)
Version: GGNFS-0.77.1-20060513-k8
Total time: 59.23 hours.
Scaled time: 118.63 units (timescale=2.003).
Factorization parameters were as follows:
name: 89993_159
n: 497109400238087848582031566032851660055020853947195342757531373490526734611539481118145584113295135923191327086633995939773759489101
m: 100000000000000000000000000000000
c5: 9
c0: -70
skew: 1.51
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3900001)
Primes: RFBsize:283146, AFBsize:284062, largePrimes:5877832 encountered
Relations: rels:6049555, finalFF:771663
Max relations in full relation-set: 28
Initial matrix: 567272 x 771663 with sparse part having weight 50943228.
Pruned matrix : 418651 x 421551 with weight 36252838.
Total sieving time: 56.43 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 2.38 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 59.23 hours.
 --------- CPU info (if available) ----------

Nov 2, 2007 (5th)

By Robert Backstrom / GGNFS, Msieve

6·10¹⁶⁷+7 = 6(0)₁₆₆7_<168> = 157 · C166

C166 = P47 · P120

P47 = 30141491732912660764138607233343720887304110987_<47>

P120 = 126790541251891655395868197515952259522258968043055404184000880238481113593670765322134091338218303304135490412872342073_<120>

Number: n
N=3821656050955414012738853503184713375796178343949044585987261146496815286624203821656050955414012738853503184713375796178343949044585987261146496815286624203821656051
  ( 166 digits)
SNFS difficulty: 168 digits.
Divisors found:

Fri Nov 02 11:53:15 2007  prp47 factor: 30141491732912660764138607233343720887304110987
Fri Nov 02 11:53:15 2007  prp120 factor: 126790541251891655395868197515952259522258968043055404184000880238481113593670765322134091338218303304135490412872342073
Fri Nov 02 11:53:15 2007  elapsed time 05:00:20 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 142.75 hours.
Scaled time: 170.45 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_6_0_166_7
n: 3821656050955414012738853503184713375796178343949044585987261146496815286624203821656050955414012738853503184713375796178343949044585987261146496815286624203821656051
type: snfs
skew: 0.82
deg: 5
c5: 75
c0: 28
m: 2000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5000213)
Primes: RFBsize:250150, AFBsize:250046, largePrimes:8066210 encountered
Relations: rels:7523828, finalFF:472612
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 142.32 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.6,2.6,100000
total time: 142.75 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

3·10¹⁶⁰-1 = 2(9)₁₆₀_<161> = 3119 · 62171 · 716003 · 80479894854409_<14> · C133

C133 = P59 · P75

P59 = 22773127470380768369771978355584433053642892841637684786821_<59>

P75 = 117894381311324651726376382743763178993218466198694259251340381195966953253_<75>

Number: n
N=2684823773644472499695314004905933113030245860446596390581560505765323424678107700978354714731235290256104741769394425383100177478713
  ( 133 digits)
SNFS difficulty: 160 digits.
Divisors found:

Fri Nov 02 21:39:00 2007  prp59 factor: 22773127470380768369771978355584433053642892841637684786821
Fri Nov 02 21:39:00 2007  prp75 factor: 117894381311324651726376382743763178993218466198694259251340381195966953253
Fri Nov 02 21:39:00 2007  elapsed time 01:07:33 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 28.18 hours.
Scaled time: 37.37 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_2_9_160
n: 2684823773644472499695314004905933113030245860446596390581560505765323424678107700978354714731235290256104741769394425383100177478713
skew: 0.95
deg: 5
c5: 3
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1400000)
Primes: RFBsize:216816, AFBsize:216846, largePrimes:7002342 encountered
Relations: rels:6502743, finalFF:523807
Max relations in full relation-set: 28
Initial matrix: 433727 x 523807 with sparse part having weight 39790411.
Pruned matrix : 360363 x 362595 with weight 22732739.
Total sieving time: 27.98 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 28.18 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 2, 2007 (4th)

By matsui / GMP-ECM

(5·10¹⁶⁶+7)/3 = 1(6)₁₆₅9_<167> = 38609 · 75787 · C157

C157 = P36 · C122

P36 = 156630091583671031730558418871436461_<36>

C122 = [36365559895016016644306948036519971789440001831406469011965021801985852343260659678682774063764231328439857717070493184563_<122>]

Nov 2, 2007 (3rd)

By Jo Yeong Uk / GGNFS, GMP-ECM

2·10¹⁶⁰-3 = 1(9)₁₅₉7_<161> = 15073 · 1023361 · 2269267633_<10> · 51894756337_<11> · C131

C131 = P49 · P82

P49 = 1244702530203678363132386159041482385491409469399_<49>

P82 = 8845587159376599603050287573778844195307606321990000300773593282138846596884883531_<82>

Number: 19997_160
N=11010124718413221462280367876462346322453582439931705506709272261862462870251427913507922600641649990825847478334158897252623567869
  ( 131 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=1244702530203678363132386159041482385491409469399 (pp49)
 r2=8845587159376599603050287573778844195307606321990000300773593282138846596884883531 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 25.76 hours.
Scaled time: 54.81 units (timescale=2.128).
Factorization parameters were as follows:
n: 11010124718413221462280367876462346322453582439931705506709272261862462870251427913507922600641649990825847478334158897252623567869
m: 100000000000000000000000000000000
c5: 2
c0: -3
skew: 1.08
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3500001)
Primes: RFBsize:283146, AFBsize:283187, largePrimes:5679964 encountered
Relations: rels:5762216, finalFF:699117
Max relations in full relation-set: 28
Initial matrix: 566398 x 699117 with sparse part having weight 43937665.
Pruned matrix : 457329 x 460224 with weight 27759676.
Total sieving time: 24.56 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 1.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 25.76 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

(7·10¹⁶¹+11)/9 = (7)₁₆₀9_<161> = 13 · 1181 · 188695951 · 13069034534977941833_<20> · C130

C130 = P34 · P96

P34 = 6012553105775282745767182262190667_<34>

P96 = 341662463922226905047290637587563518265187529653427259070665961826179127070588201628147242777463_<96>

Nov 2, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

9·10¹⁶⁰-7 = 8(9)₁₅₉3_<161> = 619 · 31247 · 201823 · C149

C149 = P44 · P44 · P61

P44 = 44832592826645189491277561661890927333335849_<44>

P44 = 58928729369518409469720209631759471783420671_<44>

P61 = 8726738097012509717654043907256703264726239277870739541104253_<61>

Number: n
N=23055411367586615082003261341128857444920360386517972549304906315835176876756217183769848071125522085298104115328957218756792728520856138498005089787
  ( 149 digits)
SNFS difficulty: 160 digits.
Divisors found:

Fri Nov 02 05:43:45 2007  prp44 factor: 44832592826645189491277561661890927333335849
Fri Nov 02 05:43:45 2007  prp44 factor: 58928729369518409469720209631759471783420671
Fri Nov 02 05:43:45 2007  prp61 factor: 8726738097012509717654043907256703264726239277870739541104253
Fri Nov 02 05:43:45 2007  elapsed time 01:21:01 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.14 hours.
Scaled time: 50.08 units (timescale=1.425).
Factorization parameters were as follows:
name: KA_8_9_159_3
n: 23055411367586615082003261341128857444920360386517972549304906315835176876756217183769848071125522085298104115328957218756792728520856138498005089787
skew: 0.95
deg: 5
c5: 9
c0: -7
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1800179)
Primes: RFBsize:203362, AFBsize:203517, largePrimes:7126574 encountered
Relations: rels:6588475, finalFF:452122
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 34.95 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 35.14 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Nov 2, 2007

By Jo Yeong Uk / GGNFS, GMP-ECM

(4·10¹⁹⁰-31)/9 = (4)₁₈₉1_<190> = C190

C190 = P89 · P101

P89 = 56633002372177889917787382603024134082794402810604184699423290284260806567232850743196879_<89>

P101 = 78477994425170505252478126430623716163551522942533133685072386085630247384183834818134344179505629079_<101>

Number: 44441_190
N=4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
  ( 190 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=56633002372177889917787382603024134082794402810604184699423290284260806567232850743196879 (pp89)
 r2=78477994425170505252478126430623716163551522942533133685072386085630247384183834818134344179505629079 (pp101)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 506.30 hours.
Scaled time: 1086.00 units (timescale=2.145).
Factorization parameters were as follows:
n: 4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
m: 100000000000000000000000000000000000000
c5: 4
c0: -31
skew: 1.51
type: snfs
Factor base limits: 13000000/13000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 51/51
Sieved algebraic special-q in [6500000, 14600001)
Primes: RFBsize:849252, AFBsize:849764, largePrimes:12825340 encountered
Relations: rels:13582667, finalFF:1936815
Max relations in full relation-set: 28
Initial matrix: 1699080 x 1936815 with sparse part having weight 144996551.
Pruned matrix : 1492822 x 1501381 with weight 111522440.
Total sieving time: 485.19 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 20.54 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,13000000,13000000,28,28,51,51,2.6,2.6,100000
total time: 506.30 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific ro2utine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

P89 is the biggest factor which was found in our tables so far. Congratulations!

I was surprized that two P89s had been found continuously from the same near-repdigit sequence.

(5·10¹⁶⁰-23)/9 = (5)₁₅₉3_<160> = 3 · 47 · 36583 · 391183217 · 13416202562095777_<17> · C129

C129 = P36 · P93

P36 = 557467334877805199211719058269920279_<36>

P93 = 368128820889923730632432710032916764064373628070399222255862045362828218454119475627959989141_<93>

Nov 1, 2007 (5th)

By matsui / Msieve

(5·10¹⁷³+7)/3 = 1(6)₁₇₂9_<174> = 79 · 141073 · 154543 · 165887 · 63473899 · 133660440077_<12> · 1862230537518772176753410725489813_<34> · C104

C104 = P43 · P61

P43 = 5917523119420196943705339866721088586618339_<43>

P61 = 6239425363430810864236794554166498878991514867897846161057107_<61>

Nov 1, 2007 (4th)

By Robert Backstrom / GMP-ECM, GGNFS

9·10¹⁵⁴-7 = 8(9)₁₅₃3_<155> = 31 · 59 · 3116155837_<10> · C143

C143 = P34 · P47 · P63

P34 = 3792154237087773328323098510929643_<34>

P47 = 13515254733080096925398066307959108515533417271_<47>

P63 = 308105468835983009135964692963347948427570307230290780677274397_<63>

prp34 factors: 3792154237087773328323098510929643
prp47 factor:  13515254733080096925398066307959108515533417271 (pp47)
prp63 factor:  308105468835983009135964692963347948427570307230290780677274397 (pp63)

GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM]
Input number is 15791000075873905536643005674835499743042023035608132996665252198463383016350684288596800392658129485982981128379660782197197761083905185830441 (143 digits)
Using B1=1030000, B2=875663603, polynomial Dickson(3), sigma=1277051764
Step 1 took 15188ms
Step 2 took 8703ms
********** Factor found in step 2: 3792154237087773328323098510929643
Found probable prime factor of 34 digits: 3792154237087773328323098510929643
Composite cofactor 4164123895973381665684521031919367758331000757893159498628020621881612855280700051156426496919521695565910587 has 109 digits

Number: n
N=4164123895973381665684521031919367758331000757893159498628020621881612855280700051156426496919521695565910587
  ( 109 digits)
Divisors found:
 r1=13515254733080096925398066307959108515533417271 (pp47)
 r2=308105468835983009135964692963347948427570307230290780677274397 (pp63)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 15.47 hours.
Scaled time: 20.19 units (timescale=1.305).
Factorization parameters were as follows:
name: KA_8_9_153_3
n: 4164123895973381665684521031919367758331000757893159498628020621881612855280700051156426496919521695565910587
skew: 13433.88
# norm 5.58e+14
c5: 62340
c4: -1730045296
c3: -31252455735533
c2: 59780409705258362
c1: 594864083607926757768
c0: 4226538018654160771217904
# alpha -5.88
Y1: 54837503413
Y0: -582038343536829418255
# Murphy_E 1.28e-09
# M 775188593700025757374907442535572328332511394125380113220895912641476417303724565829169862375221504000062036
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:230209, AFBsize:230238, largePrimes:6848426 encountered
Relations: rels:6590432, finalFF:586768
Max relations in full relation-set: 28
Initial matrix: 460530 x 586768 with sparse part having weight 36842357.
Pruned matrix : 341921 x 344287 with weight 16084571.
Total sieving time: 13.36 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 1.49 hours.
Total square root time: 0.31 hours, sqrts: 2.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 15.47 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 1, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(85·10²⁹⁶⁰-31)/9 is prime.

Nov 1, 2007 (2nd)

By Sinkiti Sibata / GGNFS

9·10¹⁵²-7 = 8(9)₁₅₁3_<153> = 27487 · 2387449 · 5618769997_<10> · C133

C133 = P44 · P89

P44 = 75820868126956676281536230696860571433120407_<44>

P89 = 32192229601894986931087007258474395061004652068487123300133829248970334366365297350334109_<89>

Number: 89993_152
N=2440842795357990826312342895539487490184328387705207959270387795925092533977126288036775251949678234292518146093908937568969876062363
  ( 133 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=75820868126956676281536230696860571433120407 (pp44)
 r2=32192229601894986931087007258474395061004652068487123300133829248970334366365297350334109 (pp89)
Version: GGNFS-0.77.1-20060513-k8
Total time: 37.53 hours.
Scaled time: 72.25 units (timescale=1.925).
Factorization parameters were as follows:
name: 89993_152
n: 2440842795357990826312342895539487490184328387705207959270387795925092533977126288036775251949678234292518146093908937568969876062363
m: 1000000000000000000000000000000
c5: 900
c0: -7
skew: 0.38
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2500001)
Primes: RFBsize:176302, AFBsize:175703, largePrimes:5892665 encountered
Relations: rels:5985872, finalFF:583936
Max relations in full relation-set: 28
Initial matrix: 352069 x 583936 with sparse part having weight 61282735.
Pruned matrix : 277434 x 279258 with weight 33988858.
Total sieving time: 35.96 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.27 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 37.53 hours.
 --------- CPU info (if available) ----------

Nov 1, 2007

By Yousuke Koide

(10¹²⁶⁵-1)/9 is divisible by 7973059286225484515918622191263721_<34>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

October 2007

Oct 31, 2007 (5th)

By Robert Backstrom / GGNFS, Msieve

9·10¹⁵⁷-7 = 8(9)₁₅₆3_<158> = 23 · 64057787 · C149

C149 = P73 · P76

P73 = 8547312778918799179387612593474476828728823510172134540253167241939987973_<73>

P76 = 7146824962215572093535969278319248184705372720242480746696150650147917691641_<76>

Number: n
N=61086148328241023456170774434462215920080438294417426293679106525704877121001087183439811795314562241854476205041713894715231040563014033617462633693
  ( 149 digits)
SNFS difficulty: 157 digits.
Divisors found:

Thu Nov 01 00:37:53 2007  prp73 factor: 8547312778918799179387612593474476828728823510172134540253167241939987973
Thu Nov 01 00:37:53 2007  prp76 factor: 7146824962215572093535969278319248184705372720242480746696150650147917691641
Thu Nov 01 00:37:53 2007  elapsed time 01:22:09 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 37.30 hours.
Scaled time: 49.46 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_8_9_156_3
n: 61086148328241023456170774434462215920080438294417426293679106525704877121001087183439811795314562241854476205041713894715231040563014033617462633693
skew: 0.38
deg: 5
c5: 900
c0: -7
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1900000)
Primes: RFBsize:216816, AFBsize:216321, largePrimes:7229719 encountered
Relations: rels:6721021, finalFF:520151
Max relations in full relation-set: 28
Initial matrix: 433201 x 520151 with sparse part having weight 46044664.
Pruned matrix : 368182 x 370412 with weight 28093041.
Total sieving time: 37.05 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 37.30 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 31, 2007 (4th)

By Jo Yeong Uk / GGNFS, Msieve

9·10¹⁵⁰-7 = 8(9)₁₄₉3_<151> = 859 · 352963277 · 18139634852382632412042997_<26> · C115

C115 = P41 · P74

P41 = 55504280314514112186236174411054189440309_<41>

P74 = 29482533885016913889484106257918099812603456906714576053691076225565509087_<74>

Number: 89993_150
N=1636406825136139563104533988910623283706494518193323744963557735997068458160508983884811204786788623931439183587883
  ( 115 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=55504280314514112186236174411054189440309 (pp41)
 r2=29482533885016913889484106257918099812603456906714576053691076225565509087 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 12.99 hours.
Scaled time: 27.87 units (timescale=2.146).
Factorization parameters were as follows:
n: 1636406825136139563104533988910623283706494518193323744963557735997068458160508983884811204786788623931439183587883
m: 1000000000000000000000000000000
c5: 9
c0: -7
skew: 0.95
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:176458, largePrimes:5472027 encountered
Relations: rels:5419693, finalFF:513988
Max relations in full relation-set: 28
Initial matrix: 352824 x 513988 with sparse part having weight 44556647.
Pruned matrix : 279117 x 280945 with weight 22936374.
Total sieving time: 12.50 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 12.99 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹⁵³-7 = 8(9)₁₅₂3_<154> = 235483 · 15771126802857831503737789_<26> · 2469438507084583723424410362013_<31> · C93

C93 = P35 · P59

P35 = 29916323560200857306637278521712341_<35>

P59 = 32803016936544339453376593485631195739277624165372655627383_<59>

Wed Oct 31 08:32:17 2007  
Wed Oct 31 08:32:17 2007  
Wed Oct 31 08:32:17 2007  Msieve v. 1.28
Wed Oct 31 08:32:17 2007  random seeds: 78b84c31 5c438943
Wed Oct 31 08:32:17 2007  factoring 981345668424409173005139032359911659122268552148212314853518231679477196677844688222808633603 (93 digits)
Wed Oct 31 08:32:17 2007  commencing quadratic sieve (93-digit input)
Wed Oct 31 08:32:18 2007  using multiplier of 3
Wed Oct 31 08:32:18 2007  using 32kb Intel Core sieve core
Wed Oct 31 08:32:18 2007  sieve interval: 36 blocks of size 32768
Wed Oct 31 08:32:18 2007  processing polynomials in batches of 6
Wed Oct 31 08:32:18 2007  using a sieve bound of 1953863 (72941 primes)
Wed Oct 31 08:32:18 2007  using large prime bound of 244232875 (27 bits)
Wed Oct 31 08:32:18 2007  using double large prime bound of 1253277823035125 (42-51 bits)
Wed Oct 31 08:32:18 2007  using trial factoring cutoff of 51 bits
Wed Oct 31 08:32:18 2007  polynomial 'A' values have 12 factors
Wed Oct 31 09:57:24 2007  73505 relations (19333 full + 54172 combined from 979953 partial), need 73037
Wed Oct 31 09:57:24 2007  begin with 999286 relations
Wed Oct 31 09:57:24 2007  reduce to 184209 relations in 11 passes
Wed Oct 31 09:57:24 2007  attempting to read 184209 relations
Wed Oct 31 09:57:26 2007  recovered 184209 relations
Wed Oct 31 09:57:26 2007  recovered 160186 polynomials
Wed Oct 31 09:57:26 2007  attempting to build 73505 cycles
Wed Oct 31 09:57:26 2007  found 73505 cycles in 6 passes
Wed Oct 31 09:57:26 2007  distribution of cycle lengths:
Wed Oct 31 09:57:26 2007     length 1 : 19333
Wed Oct 31 09:57:26 2007     length 2 : 13661
Wed Oct 31 09:57:26 2007     length 3 : 12554
Wed Oct 31 09:57:26 2007     length 4 : 9800
Wed Oct 31 09:57:26 2007     length 5 : 7114
Wed Oct 31 09:57:26 2007     length 6 : 4591
Wed Oct 31 09:57:26 2007     length 7 : 2825
Wed Oct 31 09:57:26 2007     length 9+: 3627
Wed Oct 31 09:57:26 2007  largest cycle: 18 relations
Wed Oct 31 09:57:26 2007  matrix is 72941 x 73505 with weight 4546757 (avg 61.86/col)
Wed Oct 31 09:57:27 2007  filtering completed in 3 passes
Wed Oct 31 09:57:27 2007  matrix is 68316 x 68380 with weight 4231949 (avg 61.89/col)
Wed Oct 31 09:57:28 2007  saving the first 48 matrix rows for later
Wed Oct 31 09:57:28 2007  matrix is 68268 x 68380 with weight 3299116 (avg 48.25/col)
Wed Oct 31 09:57:28 2007  matrix includes 64 packed rows
Wed Oct 31 09:57:28 2007  using block size 27352 for processor cache size 4096 kB
Wed Oct 31 09:57:29 2007  commencing Lanczos iteration
Wed Oct 31 09:57:50 2007  lanczos halted after 1081 iterations
Wed Oct 31 09:57:50 2007  recovered 15 nontrivial dependencies
Wed Oct 31 09:57:50 2007  prp35 factor: 29916323560200857306637278521712341
Wed Oct 31 09:57:50 2007  prp59 factor: 32803016936544339453376593485631195739277624165372655627383
Wed Oct 31 09:57:50 2007  elapsed time 01:25:33

Oct 31, 2007 (3rd)

By Sinkiti Sibata / GGNFS

9·10¹⁴⁸-7 = 8(9)₁₄₇3_<149> = 53 · 839 · 3833 · 5333122741489_<13> · 380397540317863012963011373_<27> · C102

C102 = P48 · P55

P48 = 185048077381378285528736195447051909587258335893_<48>

P55 = 1406572115111896750750738223467919885903244947129739803_<55>

Number: 89993_148
N=260283465599715195282875769247700889484368036515112348257395053869878284353005891464605690479865649079
  ( 102 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=185048077381378285528736195447051909587258335893 (pp48)
 r2=1406572115111896750750738223467919885903244947129739803 (pp55)
Version: GGNFS-0.77.1-20060513-k8
Total time: 30.10 hours.
Scaled time: 59.93 units (timescale=1.991).
Factorization parameters were as follows:
name: 89993_148
n: 260283465599715195282875769247700889484368036515112348257395053869878284353005891464605690479865649079
m: 100000000000000000000000000000
c5: 9000
c0: -7
skew: 0.24
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 4250001)
Primes: RFBsize:114155, AFBsize:114082, largePrimes:3049998 encountered
Relations: rels:3108836, finalFF:263510
Max relations in full relation-set: 28
Initial matrix: 228304 x 263510 with sparse part having weight 32994625.
Pruned matrix : 218898 x 220103 with weight 26198623.
Total sieving time: 29.21 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.62 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 30.10 hours.
 --------- CPU info (if available) ----------

Oct 31, 2007 (2nd)

By matsui / GMP-ECM, Msieve

(5·10¹⁹⁸+7)/3 = 1(6)₁₉₇9_<199> = 2671 · 2222089 · 43446912661062564370891697_<26> · 151432609261393100562428907767_<30> · C134

C134 = P38 · P43 · P53

P38 = 78356711420850326025452572618724188949_<38>

P43 = 5527668366912659164266442169275274462403349_<43>

P53 = 98540986433720343595658132228977073747961703420580549_<53>

(5·10¹⁷³+7)/3 = 1(6)₁₇₂9_<174> = 79 · 141073 · 154543 · 165887 · 63473899 · 133660440077_<12> · C137

C137 = P34 · C104

P34 = 1862230537518772176753410725489813_<34>

C104 = [36921943839998587914228808236155511843378747795412617433005313650028624835179704262350945849262592485273_<104>]

Oct 31, 2007

By Womack

(10³⁰⁹-1)/9 is divisible by 5294796903161592416528456780680376286484870226446771978908657527791_<67> and the cofactor is prime.

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 30, 2007 (5th)

By Tyler Cadigan / Msieve, GGNFS

(64·10¹⁶³-1)/9 = 7(1)₁₆₃_<164> = 637330387763_<12> · 10957735036324101653_<20> · C134

C134 = P61 · P73

P61 = 5153208161696653721426359516088698419315495201808470280932923_<61>

P73 = 1975942751788253995617036939102852461531533982770011785041254696010379563_<73>

Mon Oct 29 19:58:09 2007  
Mon Oct 29 19:58:09 2007  
Mon Oct 29 19:58:09 2007  Msieve v. 1.29
Mon Oct 29 19:58:09 2007  random seeds: 79db1e80 385338a0
Mon Oct 29 19:58:09 2007  factoring 10182444315560575705513301530834416904561566048028307675788338594283441380448622210798637965512347107701350195485846065970978973052649 (134 digits)
Mon Oct 29 19:58:10 2007  commencing number field sieve (133-digit input)
Mon Oct 29 19:58:10 2007  R0: -400000000000000000000000000000000
Mon Oct 29 19:58:10 2007  R1:  1
Mon Oct 29 19:58:10 2007  A0: -2
Mon Oct 29 19:58:10 2007  A1:  0
Mon Oct 29 19:58:10 2007  A2:  0
Mon Oct 29 19:58:10 2007  A3:  0
Mon Oct 29 19:58:10 2007  A4:  0
Mon Oct 29 19:58:10 2007  A5:  125
Mon Oct 29 19:58:10 2007  size score = 2.442337e-011, Murphy alpha = 0.284179, combined = 2.221603e-011
Mon Oct 29 20:01:42 2007  restarting with 5837456 relations
Mon Oct 29 20:01:48 2007  factor base loaded:
Mon Oct 29 20:01:48 2007  348513 rational ideals (max prime = 4999999)
Mon Oct 29 20:01:48 2007  316326 algebraic ideals (max prime = 4499969)
Mon Oct 29 20:01:48 2007  added 15854 free relations
Mon Oct 29 20:01:48 2007  
Mon Oct 29 20:01:48 2007  commencing relation filtering
Mon Oct 29 20:01:48 2007  commencing duplicate removal, pass 1
Mon Oct 29 20:01:52 2007  error -14 reading relation 62058
Mon Oct 29 20:06:03 2007  found 79763 hash collisions in 5853309 relations
Mon Oct 29 20:06:03 2007  commencing duplicate removal, pass 2
Mon Oct 29 20:09:59 2007  found 17169 duplicates and 5836140 unique relations
Mon Oct 29 20:09:59 2007  memory use: 37.8 MB
Mon Oct 29 20:10:05 2007  ignoring smallest 282973 rational and 283029 algebraic ideals
Mon Oct 29 20:10:05 2007  filtering ideals above 3997355
Mon Oct 29 20:10:05 2007  need 962203 more relations than ideals
Mon Oct 29 20:10:05 2007  commencing singleton removal, pass 1
Mon Oct 29 20:14:14 2007  relations with 0 large ideals: 103993
Mon Oct 29 20:14:14 2007  relations with 1 large ideals: 760328
Mon Oct 29 20:14:14 2007  relations with 2 large ideals: 2000058
Mon Oct 29 20:14:14 2007  relations with 3 large ideals: 1934872
Mon Oct 29 20:14:14 2007  relations with 4 large ideals: 844689
Mon Oct 29 20:14:14 2007  relations with 5 large ideals: 173568
Mon Oct 29 20:14:14 2007  relations with 6 large ideals: 17913
Mon Oct 29 20:14:14 2007  relations with 7+ large ideals: 719
Mon Oct 29 20:14:14 2007  5836140 relations and about 5716455 large ideals
Mon Oct 29 20:14:14 2007  commencing singleton removal, pass 2
Mon Oct 29 20:18:32 2007  found 3032525 singletons
Mon Oct 29 20:18:32 2007  current dataset: 2803615 relations and about 2113481 large ideals
Mon Oct 29 20:18:32 2007  commencing singleton removal, pass 3
Mon Oct 29 20:22:13 2007  found 448303 singletons
Mon Oct 29 20:22:13 2007  current dataset: 2355312 relations and about 1639581 large ideals
Mon Oct 29 20:22:13 2007  commencing singleton removal, final pass
Mon Oct 29 20:26:10 2007  memory use: 77.5 MB
Mon Oct 29 20:26:10 2007  commencing in-memory singleton removal
Mon Oct 29 20:26:11 2007  begin with 2355312 relations and 1708927 unique ideals
Mon Oct 29 20:26:17 2007  reduce to 2069330 relations and 1416639 ideals in 11 passes
Mon Oct 29 20:26:17 2007  max relations containing the same ideal: 35
Mon Oct 29 20:26:18 2007  dataset has 15.3% excess relations
Mon Oct 29 20:26:22 2007  ignoring smallest 256574 rational and 256498 algebraic ideals
Mon Oct 29 20:26:22 2007  filtering ideals above 3597619
Mon Oct 29 20:26:22 2007  need 611282 more relations than ideals
Mon Oct 29 20:26:22 2007  commencing singleton removal, final pass
Mon Oct 29 20:29:45 2007  memory use: 93.6 MB
Mon Oct 29 20:29:45 2007  commencing in-memory singleton removal
Mon Oct 29 20:29:46 2007  begin with 2355312 relations and 1761848 unique ideals
Mon Oct 29 20:29:53 2007  reduce to 2068928 relations and 1469137 ideals in 11 passes
Mon Oct 29 20:29:53 2007  max relations containing the same ideal: 35
Mon Oct 29 20:29:54 2007  dataset has 6.0% excess relations
Mon Oct 29 20:29:54 2007  relations with 0 large ideals: 68851
Mon Oct 29 20:29:54 2007  relations with 1 large ideals: 298085
Mon Oct 29 20:29:54 2007  relations with 2 large ideals: 616837
Mon Oct 29 20:29:54 2007  relations with 3 large ideals: 631687
Mon Oct 29 20:29:54 2007  relations with 4 large ideals: 341963
Mon Oct 29 20:29:54 2007  relations with 5 large ideals: 94801
Mon Oct 29 20:29:54 2007  relations with 6 large ideals: 15793
Mon Oct 29 20:29:54 2007  relations with 7+ large ideals: 911
Mon Oct 29 20:29:54 2007  commencing 2-way merge
Mon Oct 29 20:30:00 2007  reduce to 1298002 relation sets and 698213 unique ideals
Mon Oct 29 20:30:00 2007  ignored 2 oversize relation sets
Mon Oct 29 20:30:00 2007  commencing full merge
Mon Oct 29 20:30:59 2007  found 664054 cycles, need 590413
Mon Oct 29 20:31:00 2007  weight of 590413 cycles is about 38798316 (65.71/cycle)
Mon Oct 29 20:31:00 2007  distribution of cycle lengths:
Mon Oct 29 20:31:00 2007  1 relations: 100601
Mon Oct 29 20:31:00 2007  2 relations: 68982
Mon Oct 29 20:31:00 2007  3 relations: 62992
Mon Oct 29 20:31:00 2007  4 relations: 55520
Mon Oct 29 20:31:00 2007  5 relations: 50346
Mon Oct 29 20:31:00 2007  6 relations: 44152
Mon Oct 29 20:31:00 2007  7 relations: 39232
Mon Oct 29 20:31:00 2007  8 relations: 34235
Mon Oct 29 20:31:00 2007  9 relations: 30168
Mon Oct 29 20:31:00 2007  10+ relations: 104185
Mon Oct 29 20:31:00 2007  heaviest cycle: 17 relations
Mon Oct 29 20:31:00 2007  commencing cycle optimization
Mon Oct 29 20:31:02 2007  start with 3228434 relations
Mon Oct 29 20:31:22 2007  pruned 92753 relations
Mon Oct 29 20:31:22 2007  distribution of cycle lengths:
Mon Oct 29 20:31:22 2007  1 relations: 100601
Mon Oct 29 20:31:22 2007  2 relations: 70333
Mon Oct 29 20:31:22 2007  3 relations: 65309
Mon Oct 29 20:31:22 2007  4 relations: 56690
Mon Oct 29 20:31:22 2007  5 relations: 52216
Mon Oct 29 20:31:22 2007  6 relations: 45474
Mon Oct 29 20:31:22 2007  7 relations: 40433
Mon Oct 29 20:31:22 2007  8 relations: 35072
Mon Oct 29 20:31:22 2007  9 relations: 30464
Mon Oct 29 20:31:22 2007  10+ relations: 93821
Mon Oct 29 20:31:22 2007  heaviest cycle: 17 relations
Mon Oct 29 20:31:25 2007  
Mon Oct 29 20:31:25 2007  commencing linear algebra
Mon Oct 29 20:31:27 2007  read 590413 cycles
Mon Oct 29 20:31:31 2007  cycles contain 1626805 unique relations
Mon Oct 29 20:35:42 2007  read 1626805 relations
Mon Oct 29 20:35:52 2007  using 32 quadratic characters above 134216228
Mon Oct 29 20:38:40 2007  read 590413 cycles
Mon Oct 29 20:40:52 2007  filtering completed in 3 passes
Mon Oct 29 20:40:53 2007  matrix is 585116 x 585316 with weight 52706044 (avg 90.05/col)
Mon Oct 29 20:42:11 2007  read 585316 cycles
Mon Oct 29 20:44:43 2007  matrix is 585116 x 585316 with weight 52706044 (avg 90.05/col)
Mon Oct 29 20:44:43 2007  saving the first 48 matrix rows for later
Mon Oct 29 20:44:44 2007  matrix is 585068 x 585316 with weight 39821171 (avg 68.03/col)
Mon Oct 29 20:44:44 2007  matrix includes 64 packed rows
Mon Oct 29 20:44:44 2007  using block size 21845 for processor cache size 512 kB
Mon Oct 29 20:44:55 2007  commencing Lanczos iteration
Mon Oct 29 23:39:22 2007  lanczos halted after 9254 iterations (dim = 585068)
Mon Oct 29 23:39:40 2007  recovered 51 nontrivial dependencies
Mon Oct 29 23:39:49 2007  
Mon Oct 29 23:39:49 2007  commencing square root phase
Mon Oct 29 23:39:49 2007  reading relations for dependency 1
Mon Oct 29 23:40:38 2007  read 292046 cycles
Mon Oct 29 23:40:40 2007  cycles contain 983974 unique relations
Mon Oct 29 23:45:16 2007  read 983974 relations
Mon Oct 29 23:45:37 2007  multiplying 1554024 relations
Mon Oct 29 23:58:13 2007  multiply complete, coefficients have about 43.64 million bits
Mon Oct 29 23:58:15 2007  initial square root is modulo 1843111
Tue Oct 30 00:16:39 2007  prp61 factor: 5153208161696653721426359516088698419315495201808470280932923
Tue Oct 30 00:16:39 2007  prp73 factor: 1975942751788253995617036939102852461531533982770011785041254696010379563
Tue Oct 30 00:16:39 2007  elapsed time 04:18:30

Oct 30, 2007 (4th)

By Sinkiti Sibata / GGNFS

(8·10¹⁶⁹+7)/3 = 2(6)₁₆₈9_<170> = 29 · 2731 · 3853 · 6101 · C158

C158 = P39 · P119

P39 = 662045957785193703483721009542997210001_<39>

P119 = 21635197395131458368660666363246008064391683714979718942359200843611409545192525720721351020928312546549349492289471827_<119>

Number: 26669_169
N=14323494981331534264770233164626933360731902226623376107836718853298476108817106742366885509525113696497209270753439876022351249265426627408162506926892141827
  ( 158 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=662045957785193703483721009542997210001 (pp39)
 r2=21635197395131458368660666363246008064391683714979718942359200843611409545192525720721351020928312546549349492289471827 (pp119)
Version: GGNFS-0.77.1-20060513-k8
Total time: 139.76 hours.
Scaled time: 279.94 units (timescale=2.003).
Factorization parameters were as follows:
name: 26669_169
n: 14323494981331534264770233164626933360731902226623376107836718853298476108817106742366885509525113696497209270753439876022351249265426627408162506926892141827
m: 10000000000000000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 7100001)
Primes: RFBsize:412849, AFBsize:412831, largePrimes:6055936 encountered
Relations: rels:6345700, finalFF:951274
Max relations in full relation-set: 28
Initial matrix: 825744 x 951274 with sparse part having weight 56560583.
Pruned matrix : 721298 x 725490 with weight 40805496.
Total sieving time: 133.63 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 5.58 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 139.76 hours.
 --------- CPU info (if available) ----------

Oct 30, 2007 (3rd)

By Jo Yeong Uk / GGNFS

9·10¹⁴³-7 = 8(9)₁₄₂3_<144> = 1777 · 1725179 · 133421887 · C127

C127 = P39 · P89

P39 = 156872632499525723095280260098133461577_<39>

P89 = 14026414070177028542787457357907396822775755157120560213926799915579235133672913797156429_<89>

Number: 89993_143
N=2200360499717057804285186354000826515700652096122032856111785933419856092599249419038475136935920236563158160790423597130028533
  ( 127 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=156872632499525723095280260098133461577 (pp39)
 r2=14026414070177028542787457357907396822775755157120560213926799915579235133672913797156429 (pp89)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 9.59 hours.
Scaled time: 20.58 units (timescale=2.146).
Factorization parameters were as follows:
n: 2200360499717057804285186354000826515700652096122032856111785933419856092599249419038475136935920236563158160790423597130028533
m: 100000000000000000000000000000
c5: 9
c0: -700
skew: 2.39
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1400001)
Primes: RFBsize:114155, AFBsize:114082, largePrimes:3411338 encountered
Relations: rels:3448077, finalFF:323928
Max relations in full relation-set: 28
Initial matrix: 228301 x 323928 with sparse part having weight 30228512.
Pruned matrix : 199683 x 200888 with weight 15655341.
Total sieving time: 9.35 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 9.59 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹⁴⁴-7 = 8(9)₁₄₃3_<145> = 30380069764762946805547503800941_<32> · C114

C114 = P40 · P74

P40 = 5793759319832245415885975057146558926953_<40>

P74 = 51132060310818176689028811056072205332653270314035794978186101297841513141_<74>

Number: 89993_144
N=296246850968027270505132871619611111688006744457888000889843536883278888233053939988057668145613936858002808589373
  ( 114 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=5793759319832245415885975057146558926953 (pp40)
 r2=51132060310818176689028811056072205332653270314035794978186101297841513141 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.87 hours.
Scaled time: 19.03 units (timescale=2.146).
Factorization parameters were as follows:
n: 296246850968027270505132871619611111688006744457888000889843536883278888233053939988057668145613936858002808589373
m: 100000000000000000000000000000
c5: 9
c0: -70
skew: 1.51
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1350001)
Primes: RFBsize:114155, AFBsize:114417, largePrimes:3343512 encountered
Relations: rels:3328593, finalFF:281277
Max relations in full relation-set: 28
Initial matrix: 228636 x 281277 with sparse part having weight 25879845.
Pruned matrix : 211599 x 212806 with weight 16431801.
Total sieving time: 8.61 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 8.87 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹⁵³-7 = 8(9)₁₅₂3_<154> = 235483 · 15771126802857831503737789_<26> · C124

C124 = P31 · C93

P31 = 2469438507084583723424410362013_<31>

C93 = [981345668424409173005139032359911659122268552148212314853518231679477196677844688222808633603_<93>]

9·10¹⁴⁶-7 = 8(9)₁₄₅3_<147> = 19 · 307 · 2243 · 17371526793899_<14> · 28598478520519_<14> · C114

C114 = P44 · P70

P44 = 64299853807288749095977974116352073454267827_<44>

P70 = 2153427995281495420234041605616327252058426335937525315582533212837981_<70>

Number: 89993_146
N=138465105281123041720280097879537854129018147941456341438827168511391802940627666355587781402709904235851131937287
  ( 114 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=64299853807288749095977974116352073454267827 (pp44)
 r2=2153427995281495420234041605616327252058426335937525315582533212837981 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.37 hours.
Scaled time: 22.21 units (timescale=2.143).
Factorization parameters were as follows:
n: 138465105281123041720280097879537854129018147941456341438827168511391802940627666355587781402709904235851131937287
m: 100000000000000000000000000000
c5: 90
c0: -7
skew: 0.6
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1575001)
Primes: RFBsize:135072, AFBsize:135493, largePrimes:3715295 encountered
Relations: rels:3729829, finalFF:320257
Max relations in full relation-set: 28
Initial matrix: 270632 x 320257 with sparse part having weight 29075311.
Pruned matrix : 251639 x 253056 with weight 19777051.
Total sieving time: 10.00 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 10.37 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 30, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

8·10¹⁶⁷-7 = 7(9)₁₆₆3_<168> = 15137 · C164

C164 = P41 · P123

P41 = 70835644003123593484318087394932806885707_<41>

P123 = 746102215179633311919695276118227149695996068322953673178010306203699906940184998267472539948678240767141330911324215957227_<123>

Number: n
N=52850630904406421351654885380194226068573693598467331703772213780802008323974367444011362885644447380590605800356741758604743344123670476316311025962872431789654489
  ( 164 digits)
SNFS difficulty: 167 digits.
Divisors found:

Tue Oct 30 07:24:05 2007  prp41 factor: 70835644003123593484318087394932806885707
Tue Oct 30 07:24:05 2007  prp123 factor: 746102215179633311919695276118227149695996068322953673178010306203699906940184998267472539948678240767141330911324215957227
Tue Oct 30 07:24:05 2007  elapsed time 02:09:23 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 78.72 hours.
Scaled time: 102.80 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_7_9_166_3
n: 52850630904406421351654885380194226068573693598467331703772213780802008323974367444011362885644447380590605800356741758604743344123670476316311025962872431789654489
skew: 0.78
deg: 5
c5: 25
c0: -7
m: 2000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3100001)
Primes: RFBsize:216816, AFBsize:216906, largePrimes:7450046 encountered
Relations: rels:6889776, finalFF:446877
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 78.46 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 78.72 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

9·10¹⁴¹-7 = 8(9)₁₄₀3_<142> = 2467639565737_<13> · C130

C130 = P62 · P68

P62 = 53727058137272382231521263461791395461691665958866250660772681_<62>

P68 = 67884046657300958448660911774042029705347021611364740350454114167369_<68>

Number: n
N=3647210121350119518190235337345061800537587608749415529958760713265023919457085448117350162821494933357724078360429982102496846289
  ( 130 digits)
SNFS difficulty: 141 digits.
Divisors found:

Tue Oct 30 09:24:32 2007  prp62 factor: 53727058137272382231521263461791395461691665958866250660772681
Tue Oct 30 09:24:32 2007  prp68 factor: 67884046657300958448660911774042029705347021611364740350454114167369
Tue Oct 30 09:24:32 2007  elapsed time 00:50:42 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.66 hours.
Scaled time: 9.64 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_8_9_140_3
n: 3647210121350119518190235337345061800537587608749415529958760713265023919457085448117350162821494933357724078360429982102496846289
skew: 0.60
deg: 5
c5: 90
c0: -7
m: 10000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 9500000)
Primes: RFBsize:148933, AFBsize:149225, largePrimes:6523890 encountered
Relations: rels:5928439, finalFF:382643
Max relations in full relation-set: 28
Initial matrix: 298225 x 382643 with sparse part having weight 26922338.
Pruned matrix : 236427 x 237982 with weight 14528939.
Total sieving time: 6.49 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 6.66 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Oct 30, 2007

By matsui / GMP-ECM

(5·10¹⁸¹+7)/3 = 1(6)₁₈₀9_<182> = 19 · 167393 · C175

C175 = P38 · P138

P38 = 15723245803923831841763637804116393807_<38>

P138 = 333284910953414496865344254925662573105861000375900329621890909608385992777196180707248922993978075855583628204941899412869920935091825201_<138>

Oct 29, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve 1.28, GMP-ECM

9·10¹⁸⁴-7 = 8(9)₁₈₃3_<185> = 31 · 311 · 22091 · 37100458201_<11> · 1275537910469_<13> · 282209150413571_<15> · 480434327015263_<15> · 14873984820428774119490711269_<29> · C97

C97 = P39 · P58

P39 = 593474640229445793717454630072648349617_<39>

P58 = 7461012807353624814862644671648910980191120545663272451503_<58>

Number: n
N=4427921891591479845215021556692579780756319432292202349671112615670635805041615039103114621124351
  ( 97 digits)
Divisors found:
 r1=593474640229445793717454630072648349617 (pp39)
 r2=7461012807353624814862644671648910980191120545663272451503 (pp58)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.00 hours.
Scaled time: 11.63 units (timescale=1.453).
Factorization parameters were as follows:
name: n
n:  4427921891591479845215021556692579780756319432292202349671112615670635805041615039103114621124351
m:  13069795307958322129988
deg: 4
c4: 151748640
c3: 1255715867918
c2: -263120823138764827
c1: -4731771597968022768
c0: 240860015889048958069487
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.565
# E(F1,F2) = 2.428134e-05
# GGNFS version 0.77.1-20051202-athlon polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1193586766.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [100000, 1180001)
Primes: RFBsize:92938, AFBsize:92740, largePrimes:1863035 encountered
Relations: rels:1930390, finalFF:234741
Max relations in full relation-set: 28
Initial matrix: 185753 x 234741 with sparse part having weight 16859853.
Pruned matrix : 163671 x 164663 with weight 9437558.
Polynomial selection time: 0.17 hours.
Total sieving time: 7.24 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.44 hours.
Total square root time: 0.06 hours, sqrts: 2.
Prototype def-par.txt line would be:
gnfs,96,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 8.00 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

9·10¹⁴⁰-7 = 8(9)₁₃₉3_<141> = 47 · 109 · 167 · 617 · C133

C133 = P33 · P101

P33 = 153337616869490449763658859895879_<33>

P101 = 11119053224090329768606633153477332542273472771580149117582678104067239138069306589653736225297573611_<101>

(89·10¹⁶⁴+1)/9 = 9(8)₁₆₃9_<165> = 17 · 19597 · 7888299157_<10> · C150

C150 = P42 · P109

P42 = 270666531521708051044165587427652002648199_<42>

P109 = 1390244075564748945696789150673380726874059327867465501106095914306348058416858266414264460951086291348664927_<109>

Number: n
N=376292541901713990156240140280107136920403712406844501532612508891705603189038511185276004611331447762586551055990351376936771061312168024647111016473
  ( 150 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Oct 29 21:17:16 2007  prp42 factor: 270666531521708051044165587427652002648199
Mon Oct 29 21:17:16 2007  prp109 factor: 1390244075564748945696789150673380726874059327867465501106095914306348058416858266414264460951086291348664927
Mon Oct 29 21:17:16 2007  elapsed time 02:10:55 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 74.57 hours.
Scaled time: 98.88 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_9_8_163_9
n: 376292541901713990156240140280107136920403712406844501532612508891705603189038511185276004611331447762586551055990351376936771061312168024647111016473
skew: 0.65
deg: 5
c5: 89
c0: 10
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3500000)
Primes: RFBsize:250150, AFBsize:249266, largePrimes:7709961 encountered
Relations: rels:7186570, finalFF:561747
Max relations in full relation-set: 28
Initial matrix: 499481 x 561747 with sparse part having weight 51822639.
Pruned matrix : 473183 x 475744 with weight 37331802.
Total sieving time: 74.27 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 74.57 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

9·10¹⁴⁵-7 = 8(9)₁₄₄3_<146> = 97 · 3307 · 3767 · C137

C137 = P29 · P108

P29 = 88689612345000909646591931059_<29>

P108 = 839785174596700619416492075514766572936766799231731694119293012984478206119418982501449042954689673043155839_<108>

Oct 29, 2007 (2nd)

By Jo Yeong Uk / GGNFS, GMP-ECM

9·10¹³⁸-7 = 8(9)₁₃₇3_<139> = 113 · 1039 · 21012038995387387919_<20> · C115

C115 = P55 · P60

P55 = 8324111480329451493669984302302012442668075809611357389_<55>

P60 = 438270694932342412379485394874876095508458992349269934992589_<60>

Number: 89993_138
N=3648214123178278233256210719479595987622179900672256982789110923572726048983147685427800495148109948692769945390121
  ( 115 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=8324111480329451493669984302302012442668075809611357389 (pp55)
 r2=438270694932342412379485394874876095508458992349269934992589 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.25 hours.
Scaled time: 13.42 units (timescale=2.146).
Factorization parameters were as follows:
n: 3648214123178278233256210719479595987622179900672256982789110923572726048983147685427800495148109948692769945390121
m: 10000000000000000000000000000
c5: 9
c0: -700
skew: 2.39
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:114082, largePrimes:3249074 encountered
Relations: rels:3266483, finalFF:322988
Max relations in full relation-set: 28
Initial matrix: 228301 x 322988 with sparse part having weight 26878127.
Pruned matrix : 191188 x 192393 with weight 12738220.
Total sieving time: 6.06 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.25 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹⁴⁹-7 = 8(9)₁₄₈3_<150> = C150

C150 = P38 · P42 · P72

P38 = 35794409962129142828512220689799871821_<38>

P42 = 123028439265110134626156384131454479013793_<42>

P72 = 204372184460583650412981392697490828081020379007054396748321776875537981_<72>

Number: 89993_149
N=899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 150 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=35794409962129142828512220689799871821 (pp38)
 r2=123028439265110134626156384131454479013793 (pp42)
 r3=204372184460583650412981392697490828081020379007054396748321776875537981 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 12.84 hours.
Scaled time: 27.54 units (timescale=2.146).
Factorization parameters were as follows:
n: 899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
m: 1000000000000000000000000000000
c5: 9
c0: -70
skew: 1.51
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:176833, largePrimes:5402800 encountered
Relations: rels:5281314, finalFF:455491
Max relations in full relation-set: 28
Initial matrix: 353199 x 455491 with sparse part having weight 38566153.
Pruned matrix : 301756 x 303585 with weight 22658433.
Total sieving time: 12.29 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.44 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 12.84 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹³⁹-7 = 8(9)₁₃₈3_<140> = 31 · 34319 · C134

C134 = P41 · P93

P41 = 95880034599375142177521603584056943225357_<41>

P93 = 882303513756038409718500891576339947944242061119473046440639355414422699311396515924957852941_<93>

Number: 89993_139
N=84595291426079224430368205705670422384290090413567580828451088412418964760421434942931076456284443207891048784224670054864746228224937
  ( 134 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=95880034599375142177521603584056943225357 (pp41)
 r2=882303513756038409718500891576339947944242061119473046440639355414422699311396515924957852941 (pp93)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.16 hours.
Scaled time: 13.12 units (timescale=2.129).
Factorization parameters were as follows:
n: 84595291426079224430368205705670422384290090413567580828451088412418964760421434942931076456284443207891048784224670054864746228224937
m: 10000000000000000000000000000
c5: 9
c0: -70
skew: 1.51
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:114417, largePrimes:3350084 encountered
Relations: rels:3437732, finalFF:383556
Max relations in full relation-set: 28
Initial matrix: 228636 x 383556 with sparse part having weight 32672853.
Pruned matrix : 174534 x 175741 with weight 12890921.
Total sieving time: 5.98 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.16 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10¹⁹⁷-7 = 8(9)₁₉₆3_<198> = C198

C198 = P33 · C166

P33 = 104572749495411191273052631155941_<33>

C166 = [8606448662225270711938618675616267002791985751466136050473524371365139986511632740091624538638242280156899111248894398265050813422371895877062117828590480106511274373_<166>]

Oct 29, 2007

By Sinkiti Sibata / GGNFS

9·10¹³⁷-7 = 8(9)₁₃₆3_<138> = 227 · 2521 · C133

C133 = P39 · P94

P39 = 221091843902924979644001926922716807503_<39>

P94 = 7113299338479217992920918313593338363891253403625902931023690166695268837106428754985186805093_<94>

Number: 89993_137
N=1572692466977826783651687062158048603186973912526844986693274293293165602769336690740510985256881840120083807034129173969493261012779
  ( 133 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=221091843902924979644001926922716807503 (pp39)
 r2=7113299338479217992920918313593338363891253403625902931023690166695268837106428754985186805093 (pp94)
Version: GGNFS-0.77.1-20060513-k8
Total time: 13.09 hours.
Scaled time: 26.31 units (timescale=2.010).
Factorization parameters were as follows:
name: 89993_137
n: 1572692466977826783651687062158048603186973912526844986693274293293165602769336690740510985256881840120083807034129173969493261012779
m: 1000000000000000000000000000
c5: 900
c0: -7
skew: 0.38
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 2125001)
Primes: RFBsize:78498, AFBsize:63823, largePrimes:1683910 encountered
Relations: rels:1718050, finalFF:173211
Max relations in full relation-set: 28
Initial matrix: 142385 x 173211 with sparse part having weight 19269917.
Pruned matrix : 135154 x 135929 with weight 13734266.
Total sieving time: 12.78 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 13.09 hours.
 --------- CPU info (if available) ----------

Oct 28, 2007 (5th)

By JMB / GMP-ECM

(2·10¹⁶⁴+43)/9 = (2)₁₆₃7_<164> = 3³ · 17² · 2309 · 631311078642593_<15> · C142

C142 = P36 · P106

P36 = 212146409889374522698249183584805409_<36>

P106 = 9209220022038251514752208083059669039690403032046144718649809261395595313649005423325208968370329688568373_<106>

Oct 28, 2007 (4th)

By Robert Backstrom / GGNFS, GMP-ECM

9·10¹²⁰-7 = 8(9)₁₁₉3_<121> = C121

C121 = P56 · P66

P56 = 20354029401725849662526304753223971301497103511422609997_<56>

P66 = 442172889817918611600780346173978409068598975005735222119428696669_<66>

Number: n
N=8999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 121 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=20354029401725849662526304753223971301497103511422609997 (pp56)
 r2=442172889817918611600780346173978409068598975005735222119428696669 (pp66)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.55 hours.
Scaled time: 2.24 units (timescale=1.442).
Factorization parameters were as follows:
name: KA_8_9_119_3
n: 8999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
skew: 0.95
deg: 5
c5: 9
c0: -7
m: 1000000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 250001)
Primes: RFBsize:78498, AFBsize:78361, largePrimes:4232731 encountered
Relations: rels:3638568, finalFF:200786
Max relations in full relation-set: 28
Initial matrix: 156923 x 200786 with sparse part having weight 10194178.
Pruned matrix : 122805 x 123653 with weight 4620848.
Total sieving time: 1.31 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.13 hours.
Total square root time: 0.05 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000
total time: 1.55 hours.
 --------- CPU info (if available) ----------

9·10¹²⁴-7 = 8(9)₁₂₃3_<125> = 31 · 83 · 859 · C119

C119 = P39 · P80

P39 = 514997239710717504843060243797163586321_<39>

P80 = 79068710858248681348102914984733040362741538735234491408794076224567905858038519_<80>

Number: n
N=40720167839482908161995686376886870777262039256956475117488995374641379744069220665756646323172444933890807512599498599
  ( 119 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=514997239710717504843060243797163586321 (pp39)
 r2=79068710858248681348102914984733040362741538735234491408794076224567905858038519 (pp80)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.17 hours.
Scaled time: 3.15 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_8_9_123_3
n: 40720167839482908161995686376886870777262039256956475117488995374641379744069220665756646323172444933890807512599498599
skew: 1.51
deg: 5
c5: 9
c0: -70
m: 10000000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 350001)
Primes: RFBsize:78498, AFBsize:78806, largePrimes:4616754 encountered
Relations: rels:3996538, finalFF:211076
Max relations in full relation-set: 28
Initial matrix: 157368 x 211076 with sparse part having weight 12304449.
Pruned matrix : 125655 x 126505 with weight 5315318.
Total sieving time: 1.90 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.16 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000
total time: 2.17 hours.
 --------- CPU info (if available) ----------

9·10¹²³-7 = 8(9)₁₂₂3_<124> = 283 · 449 · 18553 · C115

C115 = P33 · P83

P33 = 335087805245091568482853093222231_<33>

P83 = 11392970303565490307790042441076114728020253883982388272289002974166360045042039653_<83>

Oct 28, 2007 (3rd)

By Sinkiti Sibata / GGNFS

9·10¹⁰³-7 = 8(9)₁₀₂3_<104> = 8969263 · 22129553 · C90

C90 = P34 · P57

P34 = 3138341068996635669510657500009591_<34>

P57 = 144481741911394492878214372456463812416287949515103488657_<57>

Number: 89993_103
N=453432984360701811730662361842066998814076709622439235119159164702296684015661335059709287
  ( 90 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=3138341068996635669510657500009591 (pp34)
 r2=144481741911394492878214372456463812416287949515103488657 (pp57)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.16 hours.
Scaled time: 2.33 units (timescale=2.010).
Factorization parameters were as follows:
name: 89993_103
n: 453432984360701811730662361842066998814076709622439235119159164702296684015661335059709287
m: 100000000000000000000
c5: 9000
c0: -7
skew: 0.24
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [250000, 350001)
Primes: RFBsize:37706, AFBsize:41552, largePrimes:1383872 encountered
Relations: rels:1489916, finalFF:267931
Max relations in full relation-set: 28
Initial matrix: 79325 x 267931 with sparse part having weight 10896930.
Pruned matrix : 39729 x 40189 with weight 1773397.
Total sieving time: 1.10 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,103,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 1.16 hours.
 --------- CPU info (if available) ----------

9·10¹¹⁰-7 = 8(9)₁₀₉3_<111> = 19 · 41551595117_<11> · C100

C100 = P29 · P71

P29 = 41281949109330068117018801413_<29>

P71 = 27614743514922133541815936402538216668321370424896711617313719193012707_<71>

Number: 89993_110
N=1139990436450218045364874916232246048513796723724260459114263780638570351214091539941676577618554991
  ( 100 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=41281949109330068117018801413 (pp29)
 r2=27614743514922133541815936402538216668321370424896711617313719193012707 (pp71)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.60 hours.
Scaled time: 3.20 units (timescale=2.003).
Factorization parameters were as follows:
name: 89993_110
n: 1139990436450218045364874916232246048513796723724260459114263780638570351214091539941676577618554991
m: 10000000000000000000000
c5: 9
c0: -7
skew: 0.95
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:63908, largePrimes:2384591 encountered
Relations: rels:2925739, finalFF:659504
Max relations in full relation-set: 28
Initial matrix: 113070 x 659504 with sparse part having weight 48577546.
Pruned matrix : 58429 x 59058 with weight 4920438.
Total sieving time: 1.50 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.60 hours.
 --------- CPU info (if available) ----------

9·10¹³³-7 = 8(9)₁₃₂3_<134> = 264101 · 534617 · C123

C123 = P39 · P85

P39 = 182955127132944612210518087078849494903_<39>

P85 = 3484055901363921062151806188107621607898929991774539197434850631713521731052250641243_<85>

Number: 89993_133
N=637425890372322111870552134461924960577827615567570996460983077035726280509113823885139408501711796643783835904368410084429
  ( 123 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=182955127132944612210518087078849494903 (pp39)
 r2=3484055901363921062151806188107621607898929991774539197434850631713521731052250641243 (pp85)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.85 hours.
Scaled time: 13.77 units (timescale=2.010).
Factorization parameters were as follows:
name: 89993_133
n: 637425890372322111870552134461924960577827615567570996460983077035726280509113823885139408501711796643783835904368410084429
m: 100000000000000000000000000
c5: 9000
c0: -7
skew: 0.24
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1225001)
Primes: RFBsize:78498, AFBsize:63803, largePrimes:1569153 encountered
Relations: rels:1588445, finalFF:190481
Max relations in full relation-set: 28
Initial matrix: 142368 x 190481 with sparse part having weight 15782385.
Pruned matrix : 127348 x 128123 with weight 8890552.
Total sieving time: 6.62 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.85 hours.
 --------- CPU info (if available) ----------

9·10¹²²-7 = 8(9)₁₂₁3_<123> = 53 · 4483 · 916879 · 2468335253078521_<16> · C97

C97 = P38 · P59

P38 = 21496643135387952418448986201888231937_<38>

P59 = 77859405334185056592558073314508609031087592802266287870129_<59>

Number: 89993_122
N=1673715851202497322218396988251980025978426972094963254178577242866898726074527843954613286109873
  ( 97 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=21496643135387952418448986201888231937 (pp38)
 r2=77859405334185056592558073314508609031087592802266287870129 (pp59)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.78 hours.
Scaled time: 5.54 units (timescale=1.991).
Factorization parameters were as follows:
name: 89993_122
n: 1673715851202497322218396988251980025978426972094963254178577242866898726074527843954613286109873
m: 1000000000000000000000000
c5: 900
c0: -7
skew: 0.38
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63823, largePrimes:2113012 encountered
Relations: rels:2116801, finalFF:142981
Max relations in full relation-set: 28
Initial matrix: 112985 x 142981 with sparse part having weight 12791337.
Pruned matrix : 105117 x 105745 with weight 7557577.
Total sieving time: 2.61 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.78 hours.
 --------- CPU info (if available) ----------

9·10¹²⁷-7 = 8(9)₁₂₆3_<128> = 16927 · 2815289 · 34549727 · C110

C110 = P53 · P58

P53 = 18928495665651195086151678397725759673977330546366127_<53>

P58 = 2887877797068484257309586094965034801453924030197429437839_<58>

Number: 89993_127
N=54663182364741125803462775792405445851485144937413141458737770402786616920134187641356901510330757177881679553
  ( 110 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=18928495665651195086151678397725759673977330546366127 (pp53)
 r2=2887877797068484257309586094965034801453924030197429437839 (pp58)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.41 hours.
Scaled time: 8.86 units (timescale=2.010).
Factorization parameters were as follows:
name: 89993_127
n: 54663182364741125803462775792405445851485144937413141458737770402786616920134187641356901510330757177881679553
m: 10000000000000000000000000
c5: 900
c0: -7
skew: 0.38
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:63823, largePrimes:1546280 encountered
Relations: rels:1577253, finalFF:198015
Max relations in full relation-set: 28
Initial matrix: 127838 x 198015 with sparse part having weight 14562521.
Pruned matrix : 108690 x 109393 with weight 6383787.
Total sieving time: 4.25 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.41 hours.
 --------- CPU info (if available) ----------

9·10¹¹⁹-7 = 8(9)₁₁₈3_<120> = 61 · 823 · 1004981 · 1446682233738538319_<19> · C92

C92 = P41 · P51

P41 = 45567990874948473844291875103339917072403_<41>

P51 = 270596365668481699029128282701225154281973286874043_<51>

Number: 89993_119
N=12330532721575594545992327055219422353381614259277089538199489555365772207883504963972335329
  ( 92 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=45567990874948473844291875103339917072403 (pp41)
 r2=270596365668481699029128282701225154281973286874043 (pp51)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.11 hours.
Scaled time: 4.20 units (timescale=1.991).
Factorization parameters were as follows:
name: 89993_119
n: 12330532721575594545992327055219422353381614259277089538199489555365772207883504963972335329
m: 1000000000000000000000000
c5: 9
c0: -70
skew: 1.51
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64228, largePrimes:1981105 encountered
Relations: rels:1934715, finalFF:128846
Max relations in full relation-set: 28
Initial matrix: 113390 x 128846 with sparse part having weight 9933260.
Pruned matrix : 107064 x 107694 with weight 6957791.
Total sieving time: 1.96 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.11 hours.
 --------- CPU info (if available) ----------

Oct 28, 2007 (2nd)

By Sinkiti Sibata / PRIMO

(5·10²⁸⁴⁷+1)/3 is prime.

Oct 28, 2007

The factor table of 899...993 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Oct 27, 2007

By Yousuke Koide

10¹¹²¹+1 is divisible by 162578197086018239450239785966343_<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 26, 2007 (3rd)

By Sinkiti Sibata / GGNFS

(8·10¹⁶³+7)/3 = 2(6)₁₆₂9_<164> = 17 · 9672675193889_<13> · 2132690377238720580097964644733_<31> · C119

C119 = P32 · P88

P32 = 16241366780245493793149978382913_<32>

P88 = 4681907431777497416749516436722604837221873429043948077027598629819267084782903500320897_<88>

Number: 26669_163
N=76040575830655542110535543314902372731075646666123180911982484874925096768258162409352851616275001258339376508641632961
  ( 119 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=16241366780245493793149978382913 (pp32)
 r2=4681907431777497416749516436722604837221873429043948077027598629819267084782903500320897 (pp88)
Version: GGNFS-0.77.1-20060513-k8
Total time: 89.67 hours.
Scaled time: 179.08 units (timescale=1.997).
Factorization parameters were as follows:
name: 26669_163
n: 76040575830655542110535543314902372731075646666123180911982484874925096768258162409352851616275001258339376508641632961
m: 200000000000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 5150001)
Primes: RFBsize:315948, AFBsize:316791, largePrimes:5926048 encountered
Relations: rels:6075527, finalFF:765961
Max relations in full relation-set: 28
Initial matrix: 632805 x 765961 with sparse part having weight 56904865.
Pruned matrix : 534793 x 538021 with weight 40888773.
Total sieving time: 85.28 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 3.92 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 89.67 hours.
 --------- CPU info (if available) ----------

Oct 26, 2007 (2nd)

By Jo Yeong Uk / Msieve, GGNFS

(82·10¹⁶¹+71)/9 = 9(1)₁₆₀9_<162> = 11 · 23 · 3748991 · 2671832954149_<13> · 5966029856099_<13> · 302592140766530934908888222616061079_<36> · C93

C93 = P40 · P53

P40 = 3850694069121437110112555389391787483611_<40>

P53 = 51718395086698620503380784735167544390948057134540087_<53>

Fri Oct 26 00:04:24 2007  
Fri Oct 26 00:04:24 2007  
Fri Oct 26 00:04:24 2007  Msieve v. 1.28
Fri Oct 26 00:04:24 2007  random seeds: bb05f469 520cf979
Fri Oct 26 00:04:24 2007  factoring 199151717224829651201838246240894378459227321597236742980797132267408631739729758957535014157 (93 digits)
Fri Oct 26 00:04:24 2007  commencing quadratic sieve (92-digit input)
Fri Oct 26 00:04:24 2007  using multiplier of 53
Fri Oct 26 00:04:24 2007  using 32kb Intel Core sieve core
Fri Oct 26 00:04:24 2007  sieve interval: 36 blocks of size 32768
Fri Oct 26 00:04:24 2007  processing polynomials in batches of 6
Fri Oct 26 00:04:24 2007  using a sieve bound of 1879931 (70588 primes)
Fri Oct 26 00:04:24 2007  using large prime bound of 219951927 (27 bits)
Fri Oct 26 00:04:24 2007  using double large prime bound of 1037982177167364 (42-50 bits)
Fri Oct 26 00:04:24 2007  using trial factoring cutoff of 50 bits
Fri Oct 26 00:04:24 2007  polynomial 'A' values have 12 factors
Fri Oct 26 01:38:35 2007  70852 relations (18438 full + 52414 combined from 913373 partial), need 70684
Fri Oct 26 01:38:35 2007  begin with 931811 relations
Fri Oct 26 01:38:36 2007  reduce to 176982 relations in 10 passes
Fri Oct 26 01:38:36 2007  attempting to read 176982 relations
Fri Oct 26 01:38:37 2007  recovered 176982 relations
Fri Oct 26 01:38:37 2007  recovered 157867 polynomials
Fri Oct 26 01:38:38 2007  attempting to build 70852 cycles
Fri Oct 26 01:38:38 2007  found 70852 cycles in 5 passes
Fri Oct 26 01:38:38 2007  distribution of cycle lengths:
Fri Oct 26 01:38:38 2007     length 1 : 18438
Fri Oct 26 01:38:38 2007     length 2 : 13138
Fri Oct 26 01:38:38 2007     length 3 : 12424
Fri Oct 26 01:38:38 2007     length 4 : 9444
Fri Oct 26 01:38:38 2007     length 5 : 6893
Fri Oct 26 01:38:38 2007     length 6 : 4449
Fri Oct 26 01:38:38 2007     length 7 : 2721
Fri Oct 26 01:38:38 2007     length 9+: 3345
Fri Oct 26 01:38:38 2007  largest cycle: 17 relations
Fri Oct 26 01:38:38 2007  matrix is 70588 x 70852 with weight 4361172 (avg 61.55/col)
Fri Oct 26 01:38:38 2007  filtering completed in 3 passes
Fri Oct 26 01:38:38 2007  matrix is 66408 x 66472 with weight 4123761 (avg 62.04/col)
Fri Oct 26 01:38:39 2007  saving the first 48 matrix rows for later
Fri Oct 26 01:38:39 2007  matrix is 66360 x 66472 with weight 3167656 (avg 47.65/col)
Fri Oct 26 01:38:39 2007  matrix includes 64 packed rows
Fri Oct 26 01:38:39 2007  using block size 26588 for processor cache size 4096 kB
Fri Oct 26 01:38:41 2007  commencing Lanczos iteration
Fri Oct 26 01:39:01 2007  lanczos halted after 1051 iterations
Fri Oct 26 01:39:01 2007  recovered 17 nontrivial dependencies
Fri Oct 26 01:39:01 2007  prp40 factor: 3850694069121437110112555389391787483611
Fri Oct 26 01:39:01 2007  prp53 factor: 51718395086698620503380784735167544390948057134540087
Fri Oct 26 01:39:01 2007  elapsed time 01:34:37

10¹⁶⁰-3 = (9)₁₅₉7_<160> = 13 · 383 · 52771123082243438120761219452533939_<35> · C122

C122 = P55 · P68

P55 = 3104829324566476660204837376960208819056316254480075411_<55>

P68 = 12258118210972106300910696745912453876036288591144435630300652094167_<68>

Number: 99997_160
N=38059364885428552053660274073288904257094149099533297652419641952424130876827819709343439432012909374053370298093233227637
  ( 122 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=3104829324566476660204837376960208819056316254480075411 (pp55)
 r2=12258118210972106300910696745912453876036288591144435630300652094167 (pp68)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.28 hours.
Scaled time: 51.72 units (timescale=2.130).
Factorization parameters were as follows:
n: 38059364885428552053660274073288904257094149099533297652419641952424130876827819709343439432012909374053370298093233227637
m: 100000000000000000000000000000000
c5: 1
c0: -3
skew: 1.25
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3400001)
Primes: RFBsize:283146, AFBsize:282992, largePrimes:5668831 encountered
Relations: rels:5757196, finalFF:705905
Max relations in full relation-set: 28
Initial matrix: 566202 x 705905 with sparse part having weight 43019303.
Pruned matrix : 449468 x 452363 with weight 26383924.
Total sieving time: 23.17 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.99 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 24.28 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 26, 2007

By Robert Backstrom / GGNFS, Msieve

(68·10¹⁵⁹+13)/9 = 7(5)₁₅₈7_<160> = 3 · 11 · 4815673 · 4744027650700422249483517_<25> · C128

C128 = P43 · P85

P43 = 1817556499049832315979311388016701905830557_<43>

P85 = 5513918500405508167982559945335390530223566166104141567423964571081382710408776663717_<85>

Number: n
N=10021858405643136835110663638106493348996711376408485617314301858636084358685512690994172006148128480343234388008600600371800369
  ( 128 digits)
SNFS difficulty: 161 digits.
Divisors found:

Fri Oct 26 04:07:36 2007  prp43 factor: 1817556499049832315979311388016701905830557
Fri Oct 26 04:07:36 2007  prp85 factor: 5513918500405508167982559945335390530223566166104141567423964571081382710408776663717
Fri Oct 26 04:07:36 2007  elapsed time 01:12:41 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 35.05 hours.
Scaled time: 45.84 units (timescale=1.308).
Factorization parameters were as follows:
name: KA_7_5_158_7
n: 10021858405643136835110663638106493348996711376408485617314301858636084358685512690994172006148128480343234388008600600371800369
skew: 1.14
deg: 5
c5: 34
c0: 65
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700001)
Primes: RFBsize:216816, AFBsize:216756, largePrimes:7052915 encountered
Relations: rels:6510490, finalFF:471406
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 34.83 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 35.05 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 25, 2007 (4th)

By Robert Backstrom / GGNFS, Msieve

(8·10¹⁶⁷+7)/3 = 2(6)₁₆₆9_<168> = 13 · C167

C167 = P41 · P127

P41 = 13118854935330807737302880871625861715191_<41>

P127 = 1563613639600265717122264555652120246875230542463041437585843162802180545583168901897596747095254252168082117302855188658610343_<127>

Number: n
N=20512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820513
  ( 167 digits)
SNFS difficulty: 167 digits.
Divisors found:

Fri Oct 26 00:52:24 2007  prp41 factor: 13118854935330807737302880871625861715191
Fri Oct 26 00:52:24 2007  prp127 factor: 1563613639600265717122264555652120246875230542463041437585843162802180545583168901897596747095254252168082117302855188658610343
Fri Oct 26 00:52:24 2007  elapsed time 02:20:14 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 68.58 hours.
Scaled time: 82.23 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_2_6_166_9
n: 20512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820513
type: snfs
skew: 0.78
deg: 5
c5: 25
c0: 7
m: 2000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2800001)
Primes: RFBsize:250150, AFBsize:250196, largePrimes:7501352 encountered
Relations: rels:7006091, finalFF:549114
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 68.27 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.6,2.6,100000
total time: 68.58 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Oct 25, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(26·10²⁶⁸⁸-11)/3 is prime.

Oct 25, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM

(46·10¹⁶¹-1)/9 = 5(1)₁₆₁_<162> = 17 · 29 · 47 · 724447 · 855857254801063_<15> · 3172216729960337_<16> · C122

C122 = P31 · P91

P31 = 8979918563026048055214325630447_<31>

P91 = 1248899066404055568679090185969582597135314562972683825422549780576518206214842043840714379_<91>

(82·10¹⁶¹+71)/9 = 9(1)₁₆₀9_<162> = 11 · 23 · 3748991 · 2671832954149_<13> · 5966029856099_<13> · C128

C128 = P36 · C93

P36 = 302592140766530934908888222616061079_<36>

C93 = [199151717224829651201838246240894378459227321597236742980797132267408631739729758957535014157_<93>]

Oct 25, 2007

By Robert Backstrom / GGNFS, Msieve

10¹⁶⁶+9 = 1(0)₁₆₅9_<167> = 6841 · 3298055297_<10> · C153

C153 = P47 · P106

P47 = 96175707342105206747325741564689382490429756801_<47>

P106 = 4608473425480966721109597553701118029210118730372926247354918207318621993190226935764939329385047887076817_<106>

Number: n
N=443223191462926543459909958595746661943719852080722467101166627816472353539797980148447621698392127726651524401212365554604364053039646401916272115182417
  ( 153 digits)
SNFS difficulty: 166 digits.
Divisors found:

Thu Oct 25 15:40:05 2007  prp47 factor: 96175707342105206747325741564689382490429756801
Thu Oct 25 15:40:05 2007  prp106 factor: 4608473425480966721109597553701118029210118730372926247354918207318621993190226935764939329385047887076817
Thu Oct 25 15:40:05 2007  elapsed time 01:54:23 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 62.44 hours.
Scaled time: 82.79 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_1_0_165_9
n: 443223191462926543459909958595746661943719852080722467101166627816472353539797980148447621698392127726651524401212365554604364053039646401916272115182417
skew: 0.98
deg: 5
c5: 10
c0: 9
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2900000)
Primes: RFBsize:250150, AFBsize:250021, largePrimes:7553576 encountered
Relations: rels:7043754, finalFF:563405
Max relations in full relation-set: 28
Initial matrix: 500238 x 563405 with sparse part having weight 49550458.
Pruned matrix : 457419 x 459984 with weight 35024031.
Total sieving time: 62.12 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 62.44 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 24, 2007 (5th)

By Jo Yeong Uk / GGNFS, GMP-ECM

(10¹⁶⁰+11)/3 = (3)₁₅₉7_<160> = 2357 · 3547 · 6483784428566166293003_<22> · C131

C131 = P65 · P66

P65 = 98546042989459507145454598033560826513496496641717463749658701161_<65>

P66 = 624008085251487858816186117499534910163524917199921025095545919941_<66>

Number: 33337_160
N=61493527594963435585105940425622344176908261835783977623937353322902951931684135308791965353024017933025951725442269952202949751501
  ( 131 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=98546042989459507145454598033560826513496496641717463749658701161 (pp65)
 r2=624008085251487858816186117499534910163524917199921025095545919941 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.41 hours.
Scaled time: 51.96 units (timescale=2.129).
Factorization parameters were as follows:
n: 61493527594963435585105940425622344176908261835783977623937353322902951931684135308791965353024017933025951725442269952202949751501
m: 100000000000000000000000000000000
c5: 1
c0: 11
skew: 1.62
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3400001)
Primes: RFBsize:283146, AFBsize:283048, largePrimes:5715875 encountered
Relations: rels:5844133, finalFF:739067
Max relations in full relation-set: 28
Initial matrix: 566258 x 739067 with sparse part having weight 45560931.
Pruned matrix : 423383 x 426278 with weight 27548907.
Total sieving time: 23.43 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.85 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 24.41 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(28·10¹⁵⁹-1)/9 = 3(1)₁₅₉_<160> = 3³ · 97 · 717667 · 31119047 · 4319493713_<10> · C134

C134 = P51 · P83

P51 = 691407189640250229701631872793975317289967702892453_<51>

P83 = 17810004148297787657731990085303963501623195591076357396769870762158063825273702029_<83>

Number: 31111_159
N=12313964915655771746286044453350809950290851202515862861599384612499767983759056219534341024515693473314812267723013626438858554887137
  ( 134 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=691407189640250229701631872793975317289967702892453 (pp51)
 r2=17810004148297787657731990085303963501623195591076357396769870762158063825273702029 (pp83)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 31.18 hours.
Scaled time: 66.89 units (timescale=2.145).
Factorization parameters were as follows:
n: 12313964915655771746286044453350809950290851202515862861599384612499767983759056219534341024515693473314812267723013626438858554887137
m: 100000000000000000000000000000000
c5: 14
c0: -5
skew: 0.81
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3800001)
Primes: RFBsize:283146, AFBsize:284317, largePrimes:5680047 encountered
Relations: rels:5727480, finalFF:670051
Max relations in full relation-set: 28
Initial matrix: 567529 x 670051 with sparse part having weight 43786702.
Pruned matrix : 489700 x 492601 with weight 29899843.
Total sieving time: 29.75 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.29 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 31.18 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(2·10¹⁶²+43)/9 = (2)₁₆₁7_<162> = 79 · 3074539183721_<13> · 92026938157876922867_<20> · C127

C127 = P31 · P97

P31 = 7374950638373593966200740279443_<31>

P97 = 1348050841856743517595672702299157137569123136816328878609841055467622001119053294651183847225613_<97>

(4·10¹⁶²-13)/9 = (4)₁₆₁3_<162> = 4795407827859115566133901_<25> · C137

C137 = P30 · P108

P30 = 732132950352080637131122456739_<30>

P108 = 126590752328295613964062194725925454032813432338962666501971716450553063422318328708874925852644810865626637_<108>

(5·10¹⁶²-41)/9 = (5)₁₆₁1_<162> = 17 · 7802477 · 1221834755184846949_<19> · C136

C136 = P29 · P107

P29 = 74150969555284684198040824859_<29>

P107 = 46229241501927787031803827366761897615314009076339630433468603502437500587889723061122144734719131912055229_<107>

3·10¹⁶³-7 = 2(9)₁₆₂3_<164> = 41 · 43 · 73 · 433163734125755498123_<21> · C138

C138 = P33 · P105

P33 = 984803325251956195887249668731139_<33>

P105 = 546442521935781460110773913223987286991730594097092602213887622250012599971203648826978554376441175284731_<105>

Oct 24, 2007 (4th)

By Sinkiti Sibata / GGNFS

(8·10¹⁵⁸+7)/3 = 2(6)₁₅₇9_<159> = 453968096244493_<15> · C144

C144 = P56 · P88

P56 = 77025991204399032295102167879033530984020107406191788251_<56>

P88 = 7626163354920877208117873161490105884353828530163763489424107667430447229492870343004083_<88>

Number: 26669_158
N=587412791499445703414789501643028537938176365461039166386707531445737063824203352653873977007985725071863227998012464875392047576593221164428833
  ( 144 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=77025991204399032295102167879033530984020107406191788251 (pp56)
 r2=7626163354920877208117873161490105884353828530163763489424107667430447229492870343004083 (pp88)
Version: GGNFS-0.77.1-20060513-k8
Total time: 59.71 hours.
Scaled time: 118.95 units (timescale=1.992).
Factorization parameters were as follows:
name: 26669_158
n: 587412791499445703414789501643028537938176365461039166386707531445737063824203352653873977007985725071863227998012464875392047576593221164428833
m: 20000000000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3900001)
Primes: RFBsize:283146, AFBsize:284107, largePrimes:5971981 encountered
Relations: rels:6202849, finalFF:822675
Max relations in full relation-set: 28
Initial matrix: 567319 x 822675 with sparse part having weight 58139262.
Pruned matrix : 388038 x 390938 with weight 44121525.
Total sieving time: 56.94 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 2.38 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 59.71 hours.
 --------- CPU info (if available) ----------

Oct 24, 2007 (3rd)

By Robert Backstrom / GGNFS

(8·10¹⁵²+7)/3 = 2(6)₁₅₁9_<153> = 61 · C151

C151 = P39 · P113

P39 = 421869844046731851658147807645650077819_<39>

P113 = 10362401487434351205807812414291785916154078462280535061673815273435490140412383670255796593884378838685001402691_<113>

Number: n
N=4371584699453551912568306010928961748633879781420765027322404371584699453551912568306010928961748633879781420765027322404371584699453551912568306010929
  ( 151 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=421869844046731851658147807645650077819 (pp39)
 r2=10362401487434351205807812414291785916154078462280535061673815273435490140412383670255796593884378838685001402691 (pp113)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 16.95 hours.
Scaled time: 22.10 units (timescale=1.304).
Factorization parameters were as follows:
name: KA_2_6_151_9
n: 4371584699453551912568306010928961748633879781420765027322404371584699453551912568306010928961748633879781420765027322404371584699453551912568306010929
skew: 0.78
deg: 5
c5: 25
c0: 7
m: 2000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 750001)
Primes: RFBsize:203362, AFBsize:203182, largePrimes:6399966 encountered
Relations: rels:5939023, finalFF:511751
Max relations in full relation-set: 28
Initial matrix: 406608 x 511751 with sparse part having weight 27504928.
Pruned matrix : 311614 x 313711 with weight 13508229.
Total sieving time: 15.13 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.56 hours.
Total square root time: 0.09 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 16.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 24, 2007 (2nd)

By Kurt Beschorner

10⁷⁵³+1 is divisible by 1756473376297178637489284481878718601_<37>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 24, 2007

By Yousuke Koide

10¹³⁷¹+1 is divisible by 127539278618607069275328998039143_<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 23, 2007

By Sinkiti Sibata / GGNFS

(8·10¹⁴⁶+7)/3 = 2(6)₁₄₅9_<147> = 2167165829_<10> · C138

C138 = P64 · P74

P64 = 4143397241869544226241437570296544113990642586158773224155313511_<64>

P74 = 29697508503653602939343659106341885529158177653874575739404674525553127951_<74>

Number: 26669_146
N=123048574824435673891693992129047484472249246906461197560099895182809596923866349254192982509723148032649543343582622844440699543102045961
  ( 138 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=4143397241869544226241437570296544113990642586158773224155313511 (pp64)
 r2=29697508503653602939343659106341885529158177653874575739404674525553127951 (pp74)
Version: GGNFS-0.77.1-20060513-k8
Total time: 19.70 hours.
Scaled time: 39.37 units (timescale=1.998).
Factorization parameters were as follows:
name: 26669_146
n: 123048574824435673891693992129047484472249246906461197560099895182809596923866349254192982509723148032649543343582622844440699543102045961
m: 200000000000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2850001)
Primes: RFBsize:114155, AFBsize:114392, largePrimes:2877121 encountered
Relations: rels:2886374, finalFF:288594
Max relations in full relation-set: 28
Initial matrix: 228612 x 288594 with sparse part having weight 30123579.
Pruned matrix : 210472 x 211679 with weight 20270448.
Total sieving time: 18.98 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.51 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 19.70 hours.
 --------- CPU info (if available) ----------

Oct 23, 2007 (2nd)

By Jo Yeong Uk / GGNFS

(8·10¹⁶⁵+7)/3 = 2(6)₁₆₄9_<166> = 73 · 9803 · 19961 · 3844331 · 12325751 · 106692540971_<12> · 5524900734469672569379_<22> · C109

C109 = P33 · P36 · P42

P33 = 161800001655869356136898432615667_<33>

P36 = 226209579099872731684276944664364189_<36>

P42 = 182609076402191723318653867302508477992533_<42>

Number: 26669_165
N=6683621898604490720408773048442746311375034340493821379268599844292684440397247763706382879797337575415946579
  ( 109 digits)
Divisors found:
 r1=161800001655869356136898432615667 (pp33)
 r2=226209579099872731684276944664364189 (pp36)
 r3=182609076402191723318653867302508477992533 (pp42)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 14.55 hours.
Scaled time: 30.77 units (timescale=2.114).
Factorization parameters were as follows:
name: 26669_165
n: 6683621898604490720408773048442746311375034340493821379268599844292684440397247763706382879797337575415946579
skew: 30844.34
# norm 3.88e+15
c5: 32640
c4: -6377134016
c3: 10966983900756
c2: 6023277967525827220
c1: 20338186144994372135593
c0: -322736910701913843682752030
# alpha -6.58
Y1: 391238345143
Y0: -728218088733067565453
# Murphy_E 1.05e-09
# M 2458195276530130644457672644483945265068481024582090432931298737948038172243268879673145326804447368387365992
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1200000, 1920001)
Primes: RFBsize:176302, AFBsize:175803, largePrimes:7512919 encountered
Relations: rels:7327983, finalFF:490794
Max relations in full relation-set: 28
Initial matrix: 352190 x 490794 with sparse part having weight 47989971.
Pruned matrix : 258659 x 260483 with weight 27043110.
Polynomial selection time: 0.68 hours.
Total sieving time: 13.24 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000
total time: 14.55 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 23, 2007

By Robert Backstrom / GGNFS, Msieve

(64·10¹⁶⁰+53)/9 = 7(1)₁₅₉7_<161> = 23 · 191 · 114769 · 748180586440778137_<18> · C135

C135 = P43 · P92

P43 = 2272678914182122391159400004256881975433059_<43>

P92 = 82948234356112188698160244749473598135682577177508948629769483777144299322248884566566919647_<92>

Number: n
N=188514703189773269056083345014625106760612761414432617373683190484568696824418797686302626998621689259459609264199987578100566480410173
  ( 135 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Oct 23 03:14:29 2007  prp43 factor: 2272678914182122391159400004256881975433059
Tue Oct 23 03:14:29 2007  prp92 factor: 82948234356112188698160244749473598135682577177508948629769483777144299322248884566566919647
Tue Oct 23 03:14:29 2007  elapsed time 01:10:32 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 38.03 hours.
Scaled time: 49.78 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_7_1_159_7
n: 188514703189773269056083345014625106760612761414432617373683190484568696824418797686302626998621689259459609264199987578100566480410173
skew: 1.93
deg: 5
c5: 2
c0: 53
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:216816, AFBsize:216946, largePrimes:7083358 encountered
Relations: rels:6573818, finalFF:499435
Max relations in full relation-set: 28
Initial matrix: 433827 x 499435 with sparse part having weight 36087703.
Pruned matrix : 381360 x 383593 with weight 23854377.
Total sieving time: 37.83 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 38.03 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(8·10¹⁶⁰+7)/3 = 2(6)₁₅₉9_<161> = 49843 · C156

C156 = P70 · P86

P70 = 8206529381083043352109674031409945933677801693490815409442456291123149_<70>

P86 = 65193609889480326298653585942015762338033823753726962763716880835878142163048859303067_<86>

Number: n
N=535013275016886356492720475626801490011970922028502832226524620642149683339017849380387750871068488386868099164710524379886175925740157427656173718810397983
  ( 156 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Oct 23 23:09:38 2007  prp70 factor: 8206529381083043352109674031409945933677801693490815409442456291123149
Tue Oct 23 23:09:38 2007  prp86 factor: 65193609889480326298653585942015762338033823753726962763716880835878142163048859303067
Tue Oct 23 23:09:38 2007  elapsed time 01:04:53 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 36.34 hours.
Scaled time: 52.83 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_2_6_159_9
n: 535013275016886356492720475626801490011970922028502832226524620642149683339017849380387750871068488386868099164710524379886175925740157427656173718810397983
skew: 1.95
deg: 5
c5: 1
c0: 28
m: 200000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1800000)
Primes: RFBsize:203362, AFBsize:203227, largePrimes:7259162 encountered
Relations: rels:6779635, finalFF:504684
Max relations in full relation-set: 28
Initial matrix: 406653 x 504684 with sparse part having weight 41751576.
Pruned matrix : 337714 x 339811 with weight 26445618.
Total sieving time: 36.12 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 36.34 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Oct 22, 2007 (4th)

By Sinkiti Sibata / PRIMO

(85·10²⁵⁸⁰-13)/9 is prime.

Oct 22, 2007 (3rd)

By Jo Yeong Uk / GGNFS

(8·10¹⁵⁴+7)/3 = 2(6)₁₅₃9_<155> = 17224619 · 55682718131_<11> · 46415095754141034190321569677_<29> · C108

C108 = P35 · P73

P35 = 63976167233321490585818587278762619_<35>

P73 = 9363133420441845598841194850047950471022696892436041111098985547200676067_<73>

Number: 26669_154
N=599017389534088974031064754543587991849505713299448734373260781981910865693172098475924868395465908007539473
  ( 108 digits)
Divisors found:
 r1=63976167233321490585818587278762619 (pp35)
 r2=9363133420441845598841194850047950471022696892436041111098985547200676067 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.65 hours.
Scaled time: 22.83 units (timescale=2.144).
Factorization parameters were as follows:
name: 26669_154
n: 599017389534088974031064754543587991849505713299448734373260781981910865693172098475924868395465908007539473
skew: 21354.62
# norm 6.78e+14
c5: 32400
c4: 104238510
c3: -63159803819065
c2: 42231149150739894
c1: 10386860579266260178521
c0: 1573011234854712440644311
# alpha -5.93
Y1: 268163654693
Y0: -450172247251438281950
# Murphy_E 1.31e-09
# M 353372238522770296188352642033280019967747150736232710020604793608863613888916745569090484185353683588909139
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1440001)
Primes: RFBsize:135072, AFBsize:135004, largePrimes:4543413 encountered
Relations: rels:4565506, finalFF:355041
Max relations in full relation-set: 28
Initial matrix: 270157 x 355041 with sparse part having weight 33355043.
Pruned matrix : 221309 x 222723 with weight 18208925.
Polynomial selection time: 0.60 hours.
Total sieving time: 9.69 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 10.65 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹⁵⁷+7)/3 = 2(6)₁₅₆9_<158>= 71 · 73 · 4423 · 17761 · 463849 · 131698991 · C133

C133 = P48 · P85

P48 = 272730925941823417805548362043843409679870198107_<48>

P85 = 3931060343889521523931450002903303012283257053146040409429479768292617881055891882137_<85>

Number: 26669_157
N=1072121727522171991711117449162947893294510889614725272405934873471024006838246193709580176818241416588454805181432061281055284514659
  ( 133 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=272730925941823417805548362043843409679870198107 (pp48)
 r2=3931060343889521523931450002903303012283257053146040409429479768292617881055891882137 (pp85)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 19.84 hours.
Scaled time: 42.45 units (timescale=2.140).
Factorization parameters were as follows:
n: 1072121727522171991711117449162947893294510889614725272405934873471024006838246193709580176818241416588454805181432061281055284514659
m: 20000000000000000000000000000000
c5: 25
c0: 7
skew: 0.78
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2700001)
Primes: RFBsize:216816, AFBsize:216906, largePrimes:5656803 encountered
Relations: rels:5671985, finalFF:600758
Max relations in full relation-set: 28
Initial matrix: 433786 x 600758 with sparse part having weight 46380712.
Pruned matrix : 331528 x 333760 with weight 28777533.
Total sieving time: 19.11 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.61 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 19.84 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 22, 2007 (2nd)

By Sinkiti Sibata / GGNFS

(8·10¹⁵⁰+7)/3 = 2(6)₁₄₉9_<151> = 19 · 19173023 · 221211127 · C134

C134 = P52 · P83

P52 = 3153611510488812690844381411841100171038865591531757_<52>

P83 = 10493234479791580568317662070396265616908097303633122206670593944661297064473922083_<83>

Number: 26669_150
N=33091585037728817063066885723269305783539863851825906597312108108442540229578000079303679297783978010391230631520577621957205438089831
  ( 134 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=3153611510488812690844381411841100171038865591531757 (pp52)
 r2=10493234479791580568317662070396265616908097303633122206670593944661297064473922083 (pp83)
Version: GGNFS-0.77.1-20060513-k8
Total time: 21.11 hours.
Scaled time: 42.22 units (timescale=2.000).
Factorization parameters were as follows:
name: 26669_150
n: 33091585037728817063066885723269305783539863851825906597312108108442540229578000079303679297783978010391230631520577621957205438089831
m: 1000000000000000000000000000000
c5: 8
c0: 7
skew: 0.97
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:176343, largePrimes:5664697 encountered
Relations: rels:5756890, finalFF:642726
Max relations in full relation-set: 28
Initial matrix: 352710 x 642726 with sparse part having weight 56826393.
Pruned matrix : 241016 x 242843 with weight 25378288.
Total sieving time: 20.10 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.75 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 21.11 hours.
 --------- CPU info (if available) ----------

(8·10¹⁴³+7)/3 = 2(6)₁₄₂9_<144> = 13² · 3517 · 62776679931694823_<17> · C121

C121 = P47 · P75

P47 = 20021116406067209554446200468334668005750140859_<47>

P75 = 356962853960238997946851914156890231498548267914175830313090442617598040829_<75>

Number: 26669_143
N=7146794851779914387843228963979571845388741890295760803609820465560862056129003230767892770563281325758005179009183132111
  ( 121 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=20021116406067209554446200468334668005750140859 (pp47)
 r2=356962853960238997946851914156890231498548267914175830313090442617598040829 (pp75)
Version: GGNFS-0.77.1-20060513-k8
Total time: 17.14 hours.
Scaled time: 34.23 units (timescale=1.997).
Factorization parameters were as follows:
nama: 26669_143
n: 7146794851779914387843228963979571845388741890295760803609820465560862056129003230767892770563281325758005179009183132111
m: 20000000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2550001)
Primes: RFBsize:100021, AFBsize:100373, largePrimes:2900939 encountered
Relations: rels:2943333, finalFF:278741
Max relations in full relation-set: 28
Initial matrix: 200460 x 278741 with sparse part having weight 32014645.
Pruned matrix : 180795 x 181861 with weight 19476116.
Total sieving time: 16.50 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.43 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 17.14 hours.
 --------- CPU info (if available) ----------

Oct 22, 2007

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(13·10¹⁶⁵-1)/3 = 4(3)₁₆₅_<166> = 7 · 801331 · C159

C159 = P77 · P83

P77 = 20581230672475861430727158263255086663302501457153191742856250309416063163917_<77>

P83 = 37535376232092446430954426168419670162044288493908322073297750728833564783295676597_<83>

Number: n
N=772524236610862487060961848534025324889524577294050832451318642418200528394692853574389419127735753449721834821125875633937845433469588781189106148455031750449
  ( 159 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Oct 22 02:26:02 2007  prp77 factor: 20581230672475861430727158263255086663302501457153191742856250309416063163917
Mon Oct 22 02:26:02 2007  prp83 factor: 37535376232092446430954426168419670162044288493908322073297750728833564783295676597
Mon Oct 22 02:26:02 2007  elapsed time 02:07:00 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 54.52 hours.
Scaled time: 65.37 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_4_3_165
n: 772524236610862487060961848534025324889524577294050832451318642418200528394692853574389419127735753449721834821125875633937845433469588781189106148455031750449
type: snfs
skew: 0.60
deg: 5
c5: 13
c0: -1
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300001)
Primes: RFBsize:250150, AFBsize:249271, largePrimes:7324010 encountered
Relations: rels:6828395, finalFF:550183
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 54.23 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 54.52 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(8·10¹⁶²+7)/3 = 2(6)₁₆₁9_<163> = 23 · 2417 · C158

C158 = P38 · P121

P38 = 13758431094795674099921153836784941879_<38>

P121 = 3486545464024582803252161746345501308393073883180459970373351716778246003294776444321266822336985947908508412928696412621_<121>

Oct 21, 2007 (5th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(2·10¹⁶⁵+1)/3 = (6)₁₆₄7_<165> = 1907 · 25763 · 1950089 · C151

C151 = P38 · P54 · P61

P38 = 11159480313913593484408359509139419441_<38>

P54 = 145144015245287700460200196670856548838130894793891909_<54>

P61 = 4295998076553065365533511361350566844970496455322403010819807_<61>

prp38 factor: 11159480313913593484408359509139419441
prp54 factor: 145144015245287700460200196670856548838130894793891909
prp61 factor: 4295998076553065365533511361350566844970496455322403010819807

GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM]
Input number is 6958364614900921735999678821358908199403904875839651413675026093315854699909592774863910249349186886963352504343210374853320078119407677971416772426283 (151 digits)
Using B1=1361500, B2=1303162716, polynomial Dickson(6), sigma=52991453
Step 1 took 19547ms
Step 2 took 9719ms
********** Factor found in step 2: 11159480313913593484408359509139419441
Found probable prime factor of 38 digits: 11159480313913593484408359509139419441
Composite cofactor 623538410316944757090120947223253498225421302104017860093686064012093871425660741494485547326568250544542234241563 has 114 digits

Number: n
N=623538410316944757090120947223253498225421302104017860093686064012093871425660741494485547326568250544542234241563
  ( 114 digits)
SNFS difficulty: 165 digits.
Divisors found:

Sun Oct 21 14:25:53 2007  prp54 factor: 145144015245287700460200196670856548838130894793891909
Sun Oct 21 14:25:53 2007  prp61 factor: 4295998076553065365533511361350566844970496455322403010819807
Sun Oct 21 14:25:53 2007  elapsed time 01:41:00 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 43.08 hours.
Scaled time: 62.64 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_6_164_7

n: 623538410316944757090120947223253498225421302104017860093686064012093871425660741494485547326568250544542234241563

# n: 6958364614900921735999678821358908199403904875839651413675026093315854699909592774863910249349186886963352504343210374853320078119407677971416772426283

skew: 0.87
deg: 5
c5: 2
c0: 1
m: 1000000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300001)
Primes: RFBsize:203362, AFBsize:203032, largePrimes:7214058 encountered
Relations: rels:6650540, finalFF:426929
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 42.87 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 43.08 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(8·10¹⁶⁵-53)/9 = (8)₁₆₄3_<165> = 6403993 · C159

C159 = P45 · P114

P45 = 350982021485651168585060151283338980210340619_<45>

P114 = 395468373808917744465660761189260784883193175621159446317143996419722368165129799067011823208112320581081097991649_<114>

Number: n
N=138802289273097095654053477086700264801802389366897947716196580616013928948530844566645979920479127458273125671575357575951268043061397613783914018783107490731
  ( 159 digits)
SNFS difficulty: 165 digits.
Divisors found:

Sun Oct 21 20:17:38 2007  prp45 factor: 350982021485651168585060151283338980210340619
Sun Oct 21 20:17:38 2007  prp114 factor: 395468373808917744465660761189260784883193175621159446317143996419722368165129799067011823208112320581081097991649
Sun Oct 21 20:17:38 2007  elapsed time 01:35:15 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 47.74 hours.
Scaled time: 63.31 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_8_164_3
n: 138802289273097095654053477086700264801802389366897947716196580616013928948530844566645979920479127458273125671575357575951268043061397613783914018783107490731
skew: 1.46
deg: 5
c5: 8
c0: -53
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2200000)
Primes: RFBsize:250150, AFBsize:250051, largePrimes:7311231 encountered
Relations: rels:6818524, finalFF:565781
Max relations in full relation-set: 28
Initial matrix: 500266 x 565781 with sparse part having weight 42203089.
Pruned matrix : 447352 x 449917 with weight 27775961.
Total sieving time: 47.50 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 47.74 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 21, 2007 (4th)

By anonymous / GMP-ECM

(5·10¹⁹⁰+7)/3 = 1(6)₁₈₉9_<191> = 983 · 3110537 · 4168826771_<10> · 54213944958939972267302651_<26> · C146

C146 = P29 · P117

P29 = 95241712200343898401070633893_<29>

P117 = 253225715089880357003437152506851618536597279889801230013665252373632182359449182088181293413579341092522759275175463_<117>

Oct 21, 2007 (3rd)

By Sinkiti Sibata / GGNFS

(8·10¹³⁰+7)/3 = 2(6)₁₂₉9_<131> = 359 · C128

C128 = P33 · P96

P33 = 682633639211723545834566164085833_<33>

P96 = 108814456650602300245382079887888010720933070751698732192617045113744525935607329203942293274227_<96>

Number: 26669_130
N=74280408542246982358402971216341689879294336118848653667595171773444753946146703806870937790157845868152274837511606313834726091
  ( 128 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=682633639211723545834566164085833 (pp33)
 r2=108814456650602300245382079887888010720933070751698732192617045113744525935607329203942293274227 (pp96)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.74 hours.
Scaled time: 7.43 units (timescale=1.987).
Factorization parameters were as follows:
name: 26669_130
n: 74280408542246982358402971216341689879294336118848653667595171773444753946146703806870937790157845868152274837511606313834726091
m: 100000000000000000000000000
c5: 8
c0: 7
skew: 0.97
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:63951, AFBsize:64073, largePrimes:1455357 encountered
Relations: rels:1452260, finalFF:170662
Max relations in full relation-set: 28
Initial matrix: 128089 x 170662 with sparse part having weight 10762332.
Pruned matrix : 114592 x 115296 with weight 5636879.
Total sieving time: 3.59 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 3.74 hours.
 --------- CPU info (if available) ----------

(8·10¹³³+7)/3 = 2(6)₁₃₂9_<134> = 73 · 523 · 30253 · 694831 · 1145213 · C113

C113 = P42 · P72

P42 = 133271547249140168413145147446888048704353_<42>

P72 = 217707224173432323868406589757746873580273750494054826756936569259268393_<72>

Number: 26669_133
N=29014178612908736597074844178599916279879417120217498603765526981626610191279580281530698625258572423340334414729
  ( 113 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=133271547249140168413145147446888048704353 (pp42)
 r2=217707224173432323868406589757746873580273750494054826756936569259268393 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.92 hours.
Scaled time: 13.77 units (timescale=1.988).
Factorization parameters were as follows:
name: 26669_133
n: 29014178612908736597074844178599916279879417120217498603765526981626610191279580281530698625258572423340334414729
m: 200000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1225001)
Primes: RFBsize:78498, AFBsize:64168, largePrimes:1593511 encountered
Relations: rels:1626248, finalFF:203055
Max relations in full relation-set: 28
Initial matrix: 142732 x 203055 with sparse part having weight 17060245.
Pruned matrix : 124557 x 125334 with weight 8832672.
Total sieving time: 6.72 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.92 hours.
 --------- CPU info (if available) ----------

(8·10¹⁰³+7)/3 = 2(6)₁₀₂9_<104> = 6641346161_<10> · C94

C94 = P44 · P50

P44 = 50628118279694776375171982905395943152916717_<44>

P50 = 79308699618830633011348707020263138933756280563537_<50>

Number: 26669_103
N=4015250224910941314607779057861800657715583674522859533065478269484027075195044432297987948029
  ( 94 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=50628118279694776375171982905395943152916717 (pp44)
 r2=79308699618830633011348707020263138933756280563537 (pp50)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.18 hours.
Scaled time: 2.36 units (timescale=1.995).
Factorization parameters were as follows:
name: 26669_103
n: 4015250224910941314607779057861800657715583674522859533065478269484027075195044432297987948029
m: 200000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [250000, 350001)
Primes: RFBsize:37706, AFBsize:41542, largePrimes:1391765 encountered
Relations: rels:1503988, finalFF:273193
Max relations in full relation-set: 28
Initial matrix: 79314 x 273193 with sparse part having weight 11183859.
Pruned matrix : 40266 x 40726 with weight 1829275.
Total sieving time: 1.13 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,103,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 1.18 hours.
 --------- CPU info (if available) ----------

(8·10¹⁰⁴+7)/3 = 2(6)₁₀₃9_<105> = 76561 · C100

C100 = P33 · P67

P33 = 733945223005884153559250475665329_<33>

P67 = 4745669469153279016048570235521763800475125498182552663288629329901_<67>

Number: 26669_104
N=3483061436849919236512933042497703356365077084503424284775103076849396777297405554612226416408702429
  ( 100 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=733945223005884153559250475665329 (pp33)
 r2=4745669469153279016048570235521763800475125498182552663288629329901 (pp67)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.96 hours.
Scaled time: 3.87 units (timescale=1.977).
Factorization parameters were as follows:
name: 26669_104
n: 3483061436849919236512933042497703356365077084503424284775103076849396777297405554612226416408702429
m: 1000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:64193, largePrimes:2081424 encountered
Relations: rels:2253638, finalFF:328853
Max relations in full relation-set: 28
Initial matrix: 113355 x 328853 with sparse part having weight 22829670.
Pruned matrix : 62492 x 63122 with weight 3004338.
Total sieving time: 1.88 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,105,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.96 hours.
 --------- CPU info (if available) ----------

(8·10¹³⁴+7)/3 = 2(6)₁₃₃9_<135> = 148654243 · 1262823917_<10> · C118

C118 = P41 · P77

P41 = 37620956682884538589371868827603031738343_<41>

P77 = 37758852612331776616795032844299692308607656131997210191374930427924942519293_<77>

Number: 26669_134
N=1420524158523955469338558698249232537056327868898328355704847871904688048016727899141317771917491175737048611605351499
  ( 118 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=37620956682884538589371868827603031738343 (pp41)
 r2=37758852612331776616795032844299692308607656131997210191374930427924942519293 (pp77)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.82 hours.
Scaled time: 11.68 units (timescale=2.007).
Factorization parameters were as follows:
name: 26669_134
n: 1420524158523955469338558698249232537056327868898328355704847871904688048016727899141317771917491175737048611605351499
m: 1000000000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:64193, largePrimes:1541556 encountered
Relations: rels:1560889, finalFF:192289
Max relations in full relation-set: 28
Initial matrix: 142755 x 192289 with sparse part having weight 14621950.
Pruned matrix : 126409 x 127186 with weight 7901050.
Total sieving time: 5.64 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.82 hours.
 --------- CPU info (if available) ----------

(8·10¹⁴²+7)/3 = 2(6)₁₄₁9_<143> = 3064708476607_<13> · 4187678852923_<13> · C118

C118 = P40 · P78

P40 = 9788973638568650061780766529522450169529_<40>

P78 = 212260427653808834797575069001986356489959724932965465429439372027648665816401_<78>

Number: 26669_142
N=2077811730814442779423909735030670832942412279493881032584070517296902178699768133028182972994685705973158369638645129
  ( 118 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=9788973638568650061780766529522450169529 (pp40)
 r2=212260427653808834797575069001986356489959724932965465429439372027648665816401 (pp78)
Version: GGNFS-0.77.1-20060513-k8
Total time: 10.11 hours.
Scaled time: 20.14 units (timescale=1.992).
Factorization parameters were as follows:
name: 26669_142
n: 2077811730814442779423909735030670832942412279493881032584070517296902178699768133028182972994685705973158369638645129
m: 20000000000000000000000000000
c5: 25
c0: 7
skew: 0.78
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1750001)
Primes: RFBsize:100021, AFBsize:99418, largePrimes:2798512 encountered
Relations: rels:2847765, finalFF:330698
Max relations in full relation-set: 28
Initial matrix: 199503 x 330698 with sparse part having weight 30315932.
Pruned matrix : 162985 x 164046 with weight 13847017.
Total sieving time: 9.75 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 10.11 hours.
 --------- CPU info (if available) ----------

Oct 21, 2007 (2nd)

By Jo Yeong Uk / GGNFS

(8·10¹³⁹+7)/3 = 2(6)₁₃₈9_<140> = 1768103158425827_<16> · 27452760668249467_<17> · C108

C108 = P40 · P69

P40 = 1241873230306512944129120625376444423573_<40>

P69 = 442382402449578672496474001239726150208458221956431612701743308645417_<69>

Number: 26669_139
N=549382863160814110758042194456932311882676877376245309068323886591250711707365842143014691420858830013214941
  ( 108 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=1241873230306512944129120625376444423573 (pp40)
 r2=442382402449578672496474001239726150208458221956431612701743308645417 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.56 hours.
Scaled time: 11.90 units (timescale=2.140).
Factorization parameters were as follows:
n: 549382863160814110758042194456932311882676877376245309068323886591250711707365842143014691420858830013214941
m: 10000000000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1100001)
Primes: RFBsize:114155, AFBsize:114442, largePrimes:3315311 encountered
Relations: rels:3411950, finalFF:393858
Max relations in full relation-set: 28
Initial matrix: 228661 x 393858 with sparse part having weight 33230335.
Pruned matrix : 169036 x 170243 with weight 12385404.
Total sieving time: 5.40 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 5.56 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹⁴¹+7)/3 = 2(6)₁₄₀9_<142> = 29 · 73 · 1339806917806153_<16> · 92415619460291259403_<20> · C104

C104 = P39 · P65

P39 = 502212812269744236328154953897511547463_<39>

P65 = 20256877015611825323436706422598519488570631957881652952297498821_<65>

Number: 26669_141
N=10173263173812758517105524274113209930018018460702750505221307224574470950799246504255661100980128041123
  ( 104 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=502212812269744236328154953897511547463 (pp39)
 r2=20256877015611825323436706422598519488570631957881652952297498821 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.21 hours.
Scaled time: 13.22 units (timescale=2.127).
Factorization parameters were as follows:
n: 10173263173812758517105524274113209930018018460702750505221307224574470950799246504255661100980128041123
m: 20000000000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:114392, largePrimes:3261056 encountered
Relations: rels:3266559, finalFF:311634
Max relations in full relation-set: 28
Initial matrix: 228612 x 311634 with sparse part having weight 26294993.
Pruned matrix : 196110 x 197317 with weight 13252279.
Total sieving time: 6.01 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.21 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹⁵¹+7)/3 = 2(6)₁₅₀9_<152> = 83 · 191 · 222531925376261959597_<21> · 87151965549522581150273_<23> · C104

C104 = P37 · P68

P37 = 2151824979439633304570135127360335431_<37>

P68 = 40307031630293129082698941368209006104445744505208908458146567077043_<68>

Number: 26669_151
N=86733677509128161765261668212148242470942103656896529718188268435982587405152137619461718298337699610533
  ( 104 digits)
Divisors found:
 r1=2151824979439633304570135127360335431 (pp37)
 r2=40307031630293129082698941368209006104445744505208908458146567077043 (pp68)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.74 hours.
Scaled time: 12.28 units (timescale=2.138).
Factorization parameters were as follows:
name: 26669_151
n: 86733677509128161765261668212148242470942103656896529718188268435982587405152137619461718298337699610533
skew: 11778.21
# norm 6.95e+14
c5: 62160
c4: 1496130332
c3: -45556222412128
c2: -74626143902162469
c1: 113505084408824096690
c0: -1919290235623806504596725
# alpha -6.68
Y1: 4648483103
Y0: -67442740130436131592
# Murphy_E 2.11e-09
# M 56184838726415761082613399246235419642783909465629485767916514734753284656665661743230574578593360749961
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1620001)
Primes: RFBsize:135072, AFBsize:135343, largePrimes:4346551 encountered
Relations: rels:4257071, finalFF:317428
Max relations in full relation-set: 28
Initial matrix: 270499 x 317428 with sparse part having weight 25317400.
Pruned matrix : 238627 x 240043 with weight 16192467.
Polynomial selection time: 0.39 hours.
Total sieving time: 5.00 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 5.74 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 21, 2007

By Yousuke Koide

10¹⁰⁷³+1 is divisible by 588831771788611721102815421599303_<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 20, 2007 (5th)

By Jo Yeong Uk / GGNFS

(8·10¹³⁷+7)/3 = 2(6)₁₃₆9_<138> = 13 · 773 · 56401 · 23192382931_<11> · 887752643993_<12> · C107

C107 = P36 · P72

P36 = 225827415705440762247969188163076931_<36>

P72 = 101191741405873712462631199841067741763362688081142783407044807587961997_<72>

Number: 26669_137
N=22851869452421705492448224919086710644084493570019228618031253647076457659430866698743479971878791015391207
  ( 107 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=225827415705440762247969188163076931 (pp36)
 r2=101191741405873712462631199841067741763362688081142783407044807587961997 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.05 hours.
Scaled time: 6.48 units (timescale=2.122).
Factorization parameters were as follows:
n: 22851869452421705492448224919086710644084493570019228618031253647076457659430866698743479971878791015391207
m: 2000000000000000000000000000
c5: 25
c0: 7
skew: 0.78
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1250001)
Primes: RFBsize:107126, AFBsize:106423, largePrimes:2289110 encountered
Relations: rels:2432530, finalFF:305349
Max relations in full relation-set: 28
Initial matrix: 213613 x 305349 with sparse part having weight 22381011.
Pruned matrix : 177541 x 178673 with weight 10158100.
Total sieving time: 2.91 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 3.05 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 20, 2007 (4th)

By Sinkiti Sibata / GGNFS

8·10¹⁶²-7 = 7(9)₁₆₁3_<163> = 494213 · 388509891553534266757079_<24> · C134

C134 = P59 · P76

P59 = 16147676136454049333700128338546853224145331776821755134693_<59>

P76 = 2580261432154997404112328929704725753375527855692727120431726388111826233063_<76>

Number: 79993_162
N=41665225953822000619568717595040558356062958012654461159308411510245494930736049031230987938063485411773501288539791869984896374954659
  ( 134 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=16147676136454049333700128338546853224145331776821755134693 (pp59)
 r2=2580261432154997404112328929704725753375527855692727120431726388111826233063 (pp76)
Version: GGNFS-0.77.1-20060513-k8
Total time: 61.95 hours.
Scaled time: 124.03 units (timescale=2.002).
Factorization parameters were as follows:
name: 79993_162
n: 41665225953822000619568717595040558356062958012654461159308411510245494930736049031230987938063485411773501288539791869984896374954659
m: 200000000000000000000000000000000
c5: 25
c0: -7
skew: 0.78
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4150001)
Primes: RFBsize:315948, AFBsize:315706, largePrimes:5839925 encountered
Relations: rels:6045274, finalFF:823077
Max relations in full relation-set: 28
Initial matrix: 631718 x 823077 with sparse part having weight 47717456.
Pruned matrix : 473657 x 476879 with weight 31143738.
Total sieving time: 59.04 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 2.51 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 61.95 hours.
 --------- CPU info (if available) ----------

(8·10¹¹¹+7)/3 = 2(6)₁₁₀9_<112> = 2145389 · 1377179399_<10> · C96

C96 = P35 · P62

P35 = 18106717789925267749261242702101927_<35>

P62 = 49846243240205443718855673321344571054539531011124970246880177_<62>

Number: 26669_111
N=902551859238370029090835659332155419008692464984287175991403902356426578709847092352072009801079
  ( 96 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=18106717789925267749261242702101927 (pp35)
 r2=49846243240205443718855673321344571054539531011124970246880177 (pp62)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.44 hours.
Scaled time: 2.88 units (timescale=2.004).
Factorization parameters were as follows:
name: 26669_111
n: 902551859238370029090835659332155419008692464984287175991403902356426578709847092352072009801079
m: 20000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:63943, largePrimes:2241963 encountered
Relations: rels:2551561, finalFF:441249
Max relations in full relation-set: 28
Initial matrix: 113106 x 441249 with sparse part having weight 35014615.
Pruned matrix : 62074 x 62703 with weight 4765126.
Total sieving time: 1.35 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,112,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.44 hours.
 --------- CPU info (if available) ----------

(8·10¹²³+7)/3 = 2(6)₁₂₂9_<124> = 1229019557_<10> · 379092951201193_<15> · C100

C100 = P49 · P52

P49 = 2898545393005568842248882069535618909163031509171_<49>

P52 = 1974622690311058776335153117537051940589078496100539_<52>

Number: 26669_123
N=5723533501925381515361880891681341029181435487375163222371432533464834744116374151471404911716543169
  ( 100 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=2898545393005568842248882069535618909163031509171 (pp49)
 r2=1974622690311058776335153117537051940589078496100539 (pp52)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.84 hours.
Scaled time: 5.61 units (timescale=1.980).
Factorization parameters were as follows:
name: 26669_123
n: 5723533501925381515361880891681341029181435487375163222371432533464834744116374151471404911716543169
m: 2000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:64168, largePrimes:2114570 encountered
Relations: rels:2123330, finalFF:147078
Max relations in full relation-set: 28
Initial matrix: 113332 x 147078 with sparse part having weight 13374411.
Pruned matrix : 104524 x 105154 with weight 7551198.
Total sieving time: 2.67 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.84 hours.
 --------- CPU info (if available) ----------

(8·10¹²⁸+7)/3 = 2(6)₁₂₇9_<129> = 419 · 16311689 · 7428034067_<10> · C109

C109 = P45 · P65

P45 = 351941064731415296526137239470932854807364819_<45>

P65 = 14924917745215309816252937894497602188907340265178654448165423583_<65>

Number: 26669_128
N=5252691442279870184066566890500076729558621086294228055364583650241045931829029287346821680267717975147126477
  ( 109 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=351941064731415296526137239470932854807364819 (pp45)
 r2=14924917745215309816252937894497602188907340265178654448165423583 (pp65)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.50 hours.
Scaled time: 8.89 units (timescale=1.977).
Factorization parameters were as follows:
name: 26669_128
n: 5252691442279870184066566890500076729558621086294228055364583650241045931829029287346821680267717975147126477
m: 20000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64168, largePrimes:1486278 encountered
Relations: rels:1489312, finalFF:175012
Max relations in full relation-set: 28
Initial matrix: 128185 x 175012 with sparse part having weight 12253287.
Pruned matrix : 114089 x 114793 with weight 6318497.
Total sieving time: 4.34 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.50 hours.
 --------- CPU info (if available) ----------

Oct 20, 2007 (3rd)

By Jo Yeong Uk / GGNFS

6·10¹⁵⁷+7 = 6(0)₁₅₆7_<158> = 29575545858739133328361799_<26> · C133

C133 = P54 · P79

P54 = 909973554507637615273149646490856241896005712528152743_<54>

P79 = 2229408796486527839879415799102804165173602971152320543487096830961582839982551_<79>

Number: 60007_157
N=2028703046989440216492418523064717588124374356914471327996618052411940079032641598918868315472019544767523143015305980889826382787393
  ( 133 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=909973554507637615273149646490856241896005712528152743 (pp54)
 r2=2229408796486527839879415799102804165173602971152320543487096830961582839982551 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 31.18 hours.
Scaled time: 66.81 units (timescale=2.143).
Factorization parameters were as follows:
n: 2028703046989440216492418523064717588124374356914471327996618052411940079032641598918868315472019544767523143015305980889826382787393
m: 20000000000000000000000000000000
c5: 75
c0: 28
skew: 0.82
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3800001)
Primes: RFBsize:283146, AFBsize:283092, largePrimes:5685473 encountered
Relations: rels:5694522, finalFF:634310
Max relations in full relation-set: 28
Initial matrix: 566304 x 634310 with sparse part having weight 42093593.
Pruned matrix : 518113 x 521008 with weight 30976126.
Total sieving time: 29.55 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.48 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 31.18 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹²⁰+7)/3 = 2(6)₁₁₉9_<121> = C121

C121 = P61 · P61

P61 = 1060471105842071452080239329331029536565351505210275149416401_<61>

P61 = 2514605680415204721631917533968366670395835407292136222935069_<61>

Number: 26669_120
N=2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 121 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=1060471105842071452080239329331029536565351505210275149416401 (pp61)
 r2=2514605680415204721631917533968366670395835407292136222935069 (pp61)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.89 hours.
Scaled time: 1.88 units (timescale=2.115).
Factorization parameters were as follows:
n: 2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
m: 2000000000000000000000000
c5: 1
c0: 28
skew: 1.95
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 450001)
Primes: RFBsize:49098, AFBsize:49156, largePrimes:1800198 encountered
Relations: rels:1786914, finalFF:141902
Max relations in full relation-set: 28
Initial matrix: 98318 x 141902 with sparse part having weight 11624596.
Pruned matrix : 86828 x 87383 with weight 5098835.
Total sieving time: 0.84 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.89 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹²⁹+7)/3 = 2(6)₁₂₈9_<130> = C130

C130 = P34 · P97

P34 = 1638212584355948805449002823879881_<34>

P97 = 1627790368681026216200316702373859265165289584295147399375933455475170245176591783551889658852549_<97>

Number: 26669_129
N=2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 130 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=1638212584355948805449002823879881 (pp34)
 r2=1627790368681026216200316702373859265165289584295147399375933455475170245176591783551889658852549 (pp97)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.97 hours.
Scaled time: 4.23 units (timescale=2.142).
Factorization parameters were as follows:
n: 2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
m: 100000000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 900001)
Primes: RFBsize:78498, AFBsize:78746, largePrimes:1495528 encountered
Relations: rels:1503818, finalFF:187166
Max relations in full relation-set: 28
Initial matrix: 157308 x 187166 with sparse part having weight 9227172.
Pruned matrix : 142970 x 143820 with weight 5564851.
Total sieving time: 1.90 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.97 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(16·10¹⁵⁹-61)/9 = 1(7)₁₅₈1_<160> = 7 · 11 · 139 · 283 · 1123 · 5563 · 11321 · 1123247 · 11160628967_<11> · C126

C126 = P48 · P79

P48 = 188771796820566483431209728112718047569192774367_<48>

P79 = 3506798873133264834251861643109592173565728384191166286258478470759285819773297_<79>

Number: 17771_159
N=661984724369704169532858342692717943247722809774460911744787521251800997758672407790754400607584194600473401375243866412677999
  ( 126 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=188771796820566483431209728112718047569192774367 (pp48)
 r2=3506798873133264834251861643109592173565728384191166286258478470759285819773297 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 29.47 hours.
Scaled time: 63.21 units (timescale=2.145).
Factorization parameters were as follows:
n: 661984724369704169532858342692717943247722809774460911744787521251800997758672407790754400607584194600473401375243866412677999
m: 200000000000000000000000000000000
c5: 1
c0: -1220
skew: 4.14
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3700001)
Primes: RFBsize:283146, AFBsize:282548, largePrimes:5712059 encountered
Relations: rels:5803604, finalFF:708737
Max relations in full relation-set: 28
Initial matrix: 565758 x 708737 with sparse part having weight 44615649.
Pruned matrix : 451837 x 454729 with weight 28540403.
Total sieving time: 28.30 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 1.04 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 29.47 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹⁰⁶+7)/3 = 2(6)₁₀₅9_<107> = 38933 · C102

C102 = P31 · P72

P31 = 4246217137079532440315775172579_<31>

P72 = 161305309862279566253022081601447659781689908478972816016415808296252467_<72>

Number: 26669_106
N=684937371039135609037748610861394361253092920316098596734561083570920983912533497718302382725879502393
  ( 102 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=4246217137079532440315775172579 (pp31)
 r2=161305309862279566253022081601447659781689908478972816016415808296252467 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.46 hours.
Scaled time: 0.97 units (timescale=2.131).
Factorization parameters were as follows:
n: 684937371039135609037748610861394361253092920316098596734561083570920983912533497718302382725879502393
m: 2000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 260001)
Primes: RFBsize:30757, AFBsize:30719, largePrimes:1032267 encountered
Relations: rels:965725, finalFF:100183
Max relations in full relation-set: 28
Initial matrix: 61541 x 100183 with sparse part having weight 4259001.
Pruned matrix : 47943 x 48314 with weight 1440203.
Total sieving time: 0.43 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,107,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.46 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹¹⁴+7)/3 = 2(6)₁₁₃9_<115> = 19 · 59 · 131 · 1613 · 172841183 · C98

C98 = P38 · P61

P38 = 15049466556427553742046054404910545751_<38>

P61 = 4328018617649452918247261765466850080785970021940189130656211_<61>

Number: 26669_114
N=65134371441911253580479783239297921264158773495625664468264260314515100006542227915558640767809461
  ( 98 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=15049466556427553742046054404910545751 (pp38)
 r2=4328018617649452918247261765466850080785970021940189130656211 (pp61)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.67 hours.
Scaled time: 1.44 units (timescale=2.143).
Factorization parameters were as follows:
n: 65134371441911253580479783239297921264158773495625664468264260314515100006542227915558640767809461
m: 100000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 390001)
Primes: RFBsize:49098, AFBsize:49236, largePrimes:1810475 encountered
Relations: rels:1862920, finalFF:208249
Max relations in full relation-set: 28
Initial matrix: 98398 x 208249 with sparse part having weight 15809065.
Pruned matrix : 71479 x 72034 with weight 3436955.
Total sieving time: 0.63 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.67 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹²¹+7)/3 = 2(6)₁₂₀9_<122> = 1201 · 130987 · 356098343 · C105

C105 = P34 · P72

P34 = 2613842632420286549810407132723579_<34>

P72 = 182116015280402325835265886158642537928794970041065896876634298939239171_<72>

Number: 26669_121
N=476022604786419945107592660920030371584869577656015528481440710159671902378490644477488507224323312113009
  ( 105 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=2613842632420286549810407132723579 (pp34)
 r2=182116015280402325835265886158642537928794970041065896876634298939239171 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.03 hours.
Scaled time: 2.21 units (timescale=2.145).
Factorization parameters were as follows:
n: 476022604786419945107592660920030371584869577656015528481440710159671902378490644477488507224323312113009
m: 2000000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 480001)
Primes: RFBsize:49098, AFBsize:49101, largePrimes:1853503 encountered
Relations: rels:1867932, finalFF:158603
Max relations in full relation-set: 28
Initial matrix: 98264 x 158603 with sparse part having weight 13988463.
Pruned matrix : 85087 x 85642 with weight 5253077.
Total sieving time: 0.97 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 1.03 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹²²+7)/3 = 2(6)₁₂₁9_<123> = 71 · C121

C121 = P32 · P89

P32 = 41145387625225226433684691675373_<32>

P89 = 91282857238129608087362318513711416984201527885327331838828175050639169331657601989276343_<89>

Number: 26669_122
N=3755868544600938967136150234741784037558685446009389671361502347417840375586854460093896713615023474178403755868544600939
  ( 121 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=41145387625225226433684691675373 (pp32)
 r2=91282857238129608087362318513711416984201527885327331838828175050639169331657601989276343 (pp89)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.01 hours.
Scaled time: 2.16 units (timescale=2.140).
Factorization parameters were as follows:
n: 3755868544600938967136150234741784037558685446009389671361502347417840375586854460093896713615023474178403755868544600939
m: 2000000000000000000000000
c5: 25
c0: 7
skew: 0.78
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:63951, AFBsize:63568, largePrimes:1347942 encountered
Relations: rels:1344158, finalFF:170026
Max relations in full relation-set: 28
Initial matrix: 127582 x 170026 with sparse part having weight 7333871.
Pruned matrix : 103697 x 104398 with weight 3449577.
Total sieving time: 0.96 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000
total time: 1.01 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10¹³⁶+7)/3 = 2(6)₁₃₅9_<137> = C137

C137 = P58 · P79

P58 = 5964796989232317289442216128587619639536748687234582636411_<58>

P79 = 4470674645726497105263584854203238916337233478995531171674915681021609495628279_<79>

Number: 26669_136
N=26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 137 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=5964796989232317289442216128587619639536748687234582636411 (pp58)
 r2=4470674645726497105263584854203238916337233478995531171674915681021609495628279 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.34 hours.
Scaled time: 7.05 units (timescale=2.115).
Factorization parameters were as follows:
n: 26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
m: 2000000000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1300001)
Primes: RFBsize:107126, AFBsize:107483, largePrimes:2282771 encountered
Relations: rels:2388130, finalFF:269548
Max relations in full relation-set: 28
Initial matrix: 214674 x 269548 with sparse part having weight 20402502.
Pruned matrix : 193656 x 194793 with weight 11687881.
Total sieving time: 3.16 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 3.34 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 20, 2007 (2nd)

By Sinkiti Sibata / PRIMO

(19·10²⁴⁵⁰-1)/9 is prime.

Oct 20, 2007

The factor table of 266...669 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Oct 19, 2007 (4th)

By anonymous / GMP-ECM

(5·10¹⁹⁷+7)/3 = 1(6)₁₉₆9_<198> = 83 · C196

C196 = P32 · P165

P32 = 15064399083367851403807447165139_<32>

P165 = 133296530276542123994572514856391958946944378887295148756651456417065116602615650106241786028692598529148978098311741021285646641176103363192439421156437978817430437_<165>

Oct 19, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

(7·10¹⁶⁵-61)/9 = (7)₁₆₄1_<165> = 3 · 24320321 · C158

C158 = P43 · P56 · P60

P43 = 2761925283898534955675154755036172189749839_<43>

P56 = 31324884696363766525451707222706492435165921240617655521_<56>

P60 = 123214995686345230412614529840111656059539641564894743216343_<60>

Number: n
N=10660190680018543310314829284500778557127566665722021483978737750182625437355833389668633866274185248593522234318340586839263316436459011345255650994872117817
  ( 158 digits)
SNFS difficulty: 165 digits.
Divisors found:

Fri Oct 19 11:07:36 2007  prp43 factor: 2761925283898534955675154755036172189749839
Fri Oct 19 11:07:36 2007  prp56 factor: 31324884696363766525451707222706492435165921240617655521
Fri Oct 19 11:07:36 2007  prp60 factor: 123214995686345230412614529840111656059539641564894743216343
Fri Oct 19 11:07:36 2007  elapsed time 01:47:49 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 68.73 hours.
Scaled time: 89.90 units (timescale=1.308).
Factorization parameters were as follows:
name: KA_7_164_1
n: 10660190680018543310314829284500778557127566665722021483978737750182625437355833389668633866274185248593522234318340586839263316436459011345255650994872117817
skew: 1.54
deg: 5
c5: 7
c0: -61
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2700000)
Primes: RFBsize:216816, AFBsize:217077, largePrimes:7393191 encountered
Relations: rels:6842637, finalFF:458263
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 68.48 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 68.73 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 19, 2007 (2nd)

By Sinkiti Sibata / GGNFS

8·10¹⁵⁷-7 = 7(9)₁₅₆3_<158> = 857 · 3270705001345087307_<19> · C137

C137 = P45 · P92

P45 = 578713235026034382304696193140789480917763057_<45>

P92 = 49317877250812105191907662188584024853530218296906864974832385857053714133780682125502798451_<92>

Number: 79993_157
N=28540908288434340243572900615340141426849017077515115869543700976161255377143717419668797504442722574263007547983496570507801448444624707
  ( 137 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=578713235026034382304696193140789480917763057 (pp45)
 r2=49317877250812105191907662188584024853530218296906864974832385857053714133780682125502798451 (pp92)
Version: GGNFS-0.77.1-20060513-k8
Total time: 32.59 hours.
Scaled time: 64.80 units (timescale=1.988).
Factorization parameters were as follows:
name: 79993_157
n: 28540908288434340243572900615340141426849017077515115869543700976161255377143717419668797504442722574263007547983496570507801448444624707
m: 20000000000000000000000000000000
c5: 25
c0: -7
skew: 0.78
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216906, largePrimes:5533011 encountered
Relations: rels:5442369, finalFF:511459
Max relations in full relation-set: 28
Initial matrix: 433786 x 511459 with sparse part having weight 38990519.
Pruned matrix : 385864 x 388096 with weight 26569740.
Total sieving time: 30.52 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 1.78 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.59 hours.
 --------- CPU info (if available) ----------

Oct 19, 2007

By Yousuke Koide

10¹²⁴⁰+1 is divisible by 15595203791066837732161767737921_<32>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 17, 2007 (5th)

By suberi / PRIMO

(49·10²³⁴⁰+23)/9 is prime.

(49·10²⁴⁵⁴+23)/9 is prime.

Oct 17, 2007 (4th)

By Jo Yeong Uk / GGNFS

6·10¹⁴⁷+7 = 6(0)₁₄₆7_<148> = 31 · 74460874157397706814885857_<26> · C121

C121 = P34 · P87

P34 = 3757810852757300286714196049398151_<34>

P87 = 691713910870677076891814665811219671401933953308716939722566516154829814248796350852671_<87>

Number: 60007_147
N=2599330041273026231158261182959552205625966726296449796273234752243784692588394514029060595219631994321473925185220811321
  ( 121 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=3757810852757300286714196049398151 (pp34)
 r2=691713910870677076891814665811219671401933953308716939722566516154829814248796350852671 (pp87)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 13.31 hours.
Scaled time: 28.42 units (timescale=2.135).
Factorization parameters were as follows:
n: 2599330041273026231158261182959552205625966726296449796273234752243784692588394514029060595219631994321473925185220811321
m: 200000000000000000000000000000
c5: 75
c0: 28
skew: 0.82
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1800001)
Primes: RFBsize:135072, AFBsize:134748, largePrimes:3940451 encountered
Relations: rels:4092560, finalFF:408421
Max relations in full relation-set: 28
Initial matrix: 269886 x 408421 with sparse part having weight 41102101.
Pruned matrix : 230332 x 231745 with weight 21474737.
Total sieving time: 12.95 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 13.31 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

6·10¹⁴⁹+7 = 6(0)₁₄₈7_<150> = 25747 · 436150417 · 2488433141_<10> · 314768938357_<12> · C116

C116 = P45 · P72

P45 = 288204824127944521231161772400113432086544229_<45>

P72 = 236684181525452140035337569045008331845614114346156387833169766487401841_<72>

Number: 60007_149
N=68213522910409429827571176132944362685370905642562309751882399036574081305064117581575728647981845432390542542525589
  ( 116 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=288204824127944521231161772400113432086544229 (pp45)
 r2=236684181525452140035337569045008331845614114346156387833169766487401841 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.33 hours.
Scaled time: 24.17 units (timescale=2.133).
Factorization parameters were as follows:
n: 68213522910409429827571176132944362685370905642562309751882399036574081305064117581575728647981845432390542542525589
m: 1000000000000000000000000000000
c5: 3
c0: 35
skew: 1.63
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1650001)
Primes: RFBsize:135072, AFBsize:135283, largePrimes:3745970 encountered
Relations: rels:3742941, finalFF:304925
Max relations in full relation-set: 28
Initial matrix: 270420 x 304925 with sparse part having weight 27971216.
Pruned matrix : 258210 x 259626 with weight 21031729.
Total sieving time: 10.95 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 11.33 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 17, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

8·10¹⁶⁰-7 = 7(9)₁₅₉3_<161> = 179 · 2341 · C156

C156 = P74 · P83

P74 = 16454596943744503209146711864636020997566170732129357607128813577870908913_<74>

P83 = 11602412280012005744956049762841701654854199246869403531853864740606458920710587799_<83>

Number: n
N=190913017642749242910564410472533582793009719859010736470829684110548182866033949107362321884120571116292278284360166953433928584212925288576958230618152487
  ( 156 digits)
SNFS difficulty: 160 digits.
Divisors found:

Thu Oct 18 14:19:06 2007  prp74 factor: 16454596943744503209146711864636020997566170732129357607128813577870908913
Thu Oct 18 14:19:06 2007  prp83 factor: 11602412280012005744956049762841701654854199246869403531853864740606458920710587799
Thu Oct 18 14:19:06 2007  elapsed time 01:30:26 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 44.43 hours.
Scaled time: 53.27 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_7_9_159_3
n: 190913017642749242910564410472533582793009719859010736470829684110548182866033949107362321884120571116292278284360166953433928584212925288576958230618152487
type: snfs
skew: 0.97
deg: 5
c5: 8
c0: -7
m: 100000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1900000)
Primes: RFBsize:230209, AFBsize:229842, largePrimes:6910058 encountered
Relations: rels:6394628, finalFF:542880
Max relations in full relation-set: 28
Initial matrix: 460116 x 542880 with sparse part having weight 33147572.
Pruned matrix : 389747 x 392111 with weight 20148312.
Total sieving time: 44.19 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 44.43 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Oct 17, 2007 (2nd)

By Sinkiti Sibata / GGNFS

8·10¹⁵⁶-7 = 7(9)₁₅₅3_<157> = 181 · 909281 · C149

C149 = P41 · P49 · P61

P41 = 10904285406759073728471842840772332558593_<41>

P49 = 1088070887339914750056094304772577853777226365141_<49>

P61 = 4096933317053668078876000501612735226248308616390449901334401_<61>

Number: 79993_156
N=48608620467846913541870107667669010851819834748797120444766932935980545031569810354864742533717415158103700184799645686904547817062501954598199593813
  ( 149 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=10904285406759073728471842840772332558593 (pp41)
 r2=1088070887339914750056094304772577853777226365141 (pp49)
 r3=4096933317053668078876000501612735226248308616390449901334401 (pp61)
Version: GGNFS-0.77.1-20060513-k8
Total time: 40.39 hours.
Scaled time: 80.67 units (timescale=1.997).
Factorization parameters were as follows:
name: 79993_156
n: 48608620467846913541870107667669010851819834748797120444766932935980545031569810354864742533717415158103700184799645686904547817062501954598199593813
m: 20000000000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:217381, largePrimes:5747043 encountered
Relations: rels:5780210, finalFF:606107
Max relations in full relation-set: 28
Initial matrix: 434262 x 606107 with sparse part having weight 50764657.
Pruned matrix : 345539 x 347774 with weight 31579083.
Total sieving time: 38.37 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.68 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 40.39 hours.
 --------- CPU info (if available) ----------

Oct 18, 2007

By Sinkiti Sibata / PRIMO

(8·10²³⁰⁸+7)/3 is prime.

Oct 17, 2007 (3rd)

By Jo Yeong Uk / GGNFS

(4·10¹⁸⁸-31)/9 = (4)₁₈₇1_<188> = C188

C188 = P89 · P100

P89 = 13495944323227175196168775505661471275310792953928331944840120875227820565323694150016861_<89>

P100 = 3293170405864330551260159426012918407131606691963604942513292260623991525800017750997167920521516781_<100>

Number: 44441_188
N=44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
  ( 188 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=13495944323227175196168775505661471275310792953928331944840120875227820565323694150016861 (pp89)
 r2=3293170405864330551260159426012918407131606691963604942513292260623991525800017750997167920521516781 (pp100)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 506.97 hours.
Scaled time: 1079.34 units (timescale=2.129).
Factorization parameters were as follows:
n: 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
m: 100000000000000000000000000000000000000
c5: 1
c0: -775
skew: 3.78
type: snfs
Factor base limits: 13000000/13000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 51/51
Sieved algebraic special-q in [6500000, 14600001)
Primes: RFBsize:849252, AFBsize:849399, largePrimes:12866508 encountered
Relations: rels:13641443, finalFF:1950967
Max relations in full relation-set: 28
Initial matrix: 1698715 x 1950967 with sparse part having weight 145829012.
Pruned matrix : 1480381 x 1488938 with weight 111459556.
Total sieving time: 484.73 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 21.67 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,13000000,13000000,28,28,51,51,2.6,2.6,100000
total time: 506.97 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

P89 is the largest factor found by GGNFS in our tables so far. Congratulations!

Oct 17, 2007 (2nd)

By Robert Backstrom / GGNFS

8·10¹⁵⁸-7 = 7(9)₁₅₇3_<159> = 13 · 67 · C156

C156 = P75 · P82

P75 = 346176468096559273822741304052813207109273708583996031665987163333529663757_<75>

P82 = 2653226273941471985206044635089360508906271929143252016829426314360757542050928219_<82>

Number: n
N=918484500574052812858783008036739380022962112514351320321469575200918484500574052812858783008036739380022962112514351320321469575200918484500574052812858783
  ( 156 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=346176468096559273822741304052813207109273708583996031665987163333529663757 (pp75)
 r2=2653226273941471985206044635089360508906271929143252016829426314360757542050928219 (pp82)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 41.09 hours.
Scaled time: 53.30 units (timescale=1.297).
Factorization parameters were as follows:
name: KA_7_9_157_3
n: 918484500574052812858783008036739380022962112514351320321469575200918484500574052812858783008036739380022962112514351320321469575200918484500574052812858783
skew: 0.49
deg: 5
c5: 250
c0: -7
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:216816, AFBsize:217701, largePrimes:7120715 encountered
Relations: rels:6580353, finalFF:493138
Max relations in full relation-set: 48
Initial matrix: 434583 x 493138 with sparse part having weight 42370582.
Pruned matrix : 389862 x 392098 with weight 27989624.
Total sieving time: 36.05 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 4.66 hours.
Total square root time: 0.16 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 41.09 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 17, 2007

By Sinkiti Sibata / GGNFS

8·10¹⁵⁵-7 = 7(9)₁₅₄3_<156> = 17 · 29 · 43 · 671189 · 25898947 · C139

C139 = P33 · P107

P33 = 152487428057225842444645257923753_<33>

P107 = 14236841024808958548325101138045141061138828604047990755202358992513725161786539507007143495539941593140193_<107>

Number: 79993_155
N=2170939271532717501787887771947025467482753556964582820892856569651806507508303518706699363818037448964912725918478477349824220002633704329
  ( 139 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=152487428057225842444645257923753 (pp33)
 r2=14236841024808958548325101138045141061138828604047990755202358992513725161786539507007143495539941593140193 (pp107)
Version: GGNFS-0.77.1-20060513-k8
Total time: 32.46 hours.
Scaled time: 64.57 units (timescale=1.989).
Factorization parameters were as follows:
name: 79993_155
n: 2170939271532717501787887771947025467482753556964582820892856569651806507508303518706699363818037448964912725918478477349824220002633704329
m: 10000000000000000000000000000000
c5: 8
c0: -7
skew: 0.97
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216531, largePrimes:5864311 encountered
Relations: rels:6046107, finalFF:741412
Max relations in full relation-set: 28
Initial matrix: 433412 x 741412 with sparse part having weight 59974965.
Pruned matrix : 286069 x 288300 with weight 35055031.
Total sieving time: 30.74 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.41 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.46 hours.
 --------- CPU info (if available) ----------

Oct 16, 2007 (5th)

By Sinkiti Sibata / PRIMO

(13·10²²¹⁵+23)/9 is prime.

Oct 16, 2007 (4th)

By suberi / PRIMO

(32·10²⁴⁸⁸-41)/9 is prime.

6·10²⁷⁴⁹+7 is prime.

(55·10²⁶⁸⁴+17)/9 is prime.

Oct 16, 2007 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

8·10¹⁵⁴-7 = 7(9)₁₅₃3_<155> = 2356867 · 603555989507_<12> · C137

C137 = P33 · P105

P33 = 113351694760778508277044308809837_<33>

P105 = 496145811653311910056803679142753059087314051602854121158090203147254006251607995277425635648201231426581_<105>

Number: 79993_154
N=56238968599364916192824354906296195040092106248699331349662875284930630365782995510575903116148472404164256027791590822905326605756077297
  ( 137 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=113351694760778508277044308809837 (pp33)
 r2=496145811653311910056803679142753059087314051602854121158090203147254006251607995277425635648201231426581 (pp105)
Version: GGNFS-0.77.1-20060513-k8
Total time: 32.35 hours.
Scaled time: 64.79 units (timescale=2.003).
Factorization parameters were as follows:
name: 79993_154
n: 56238968599364916192824354906296195040092106248699331349662875284930630365782995510575903116148472404164256027791590822905326605756077297
m: 10000000000000000000000000000000
c5: 4
c0: -35
skew: 1.54
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216906, largePrimes:5878753 encountered
Relations: rels:6079432, finalFF:757874
Max relations in full relation-set: 28
Initial matrix: 433786 x 757874 with sparse part having weight 61304584.
Pruned matrix : 284596 x 286828 with weight 35456047.
Total sieving time: 30.84 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.20 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.35 hours.
 --------- CPU info (if available) ----------

8·10¹⁵¹-7 = 7(9)₁₅₀3_<152> = 23 · 107 · 5569 · 6029 · 5676941659286357_<16> · 21788576409750498214905595223_<29> · C97

C97 = P31 · P67

P31 = 5423671886025109442120246388749_<31>

P67 = 1443175595670302296287530288340641513337370692964945259930652789367_<67>

Sun Oct 14 13:22:15 2007  Msieve v. 1.28
Sun Oct 14 13:22:15 2007  random seeds: bb320d00 c465a215
Sun Oct 14 13:22:15 2007  factoring 7827310904834559223584755757587750335344461821449169367211160089090463613553875031305565495631883 (97 digits)
Sun Oct 14 13:22:16 2007  commencing quadratic sieve (97-digit input)
Sun Oct 14 13:22:17 2007  using multiplier of 2
Sun Oct 14 13:22:17 2007  using 64kb Pentium 2 sieve core
Sun Oct 14 13:22:17 2007  sieve interval: 18 blocks of size 65536
Sun Oct 14 13:22:17 2007  processing polynomials in batches of 6
Sun Oct 14 13:22:17 2007  using a sieve bound of 2395621 (88235 primes)
Sun Oct 14 13:22:17 2007  using large prime bound of 359343150 (28 bits)
Sun Oct 14 13:22:17 2007  using double large prime bound of 2511405435485700 (43-52 bits)
Sun Oct 14 13:22:17 2007  using trial factoring cutoff of 52 bits
Sun Oct 14 13:22:17 2007  polynomial 'A' values have 13 factors
Tue Oct 16 05:45:50 2007  88486 relations (21837 full + 66649 combined from 1318373 partial), need 88331
Tue Oct 16 05:46:24 2007  begin with 1340210 relations
Tue Oct 16 05:49:03 2007  reduce to 229420 relations in 11 passes
Tue Oct 16 05:49:04 2007  attempting to read 229420 relations
Tue Oct 16 05:49:50 2007  recovered 229420 relations
Tue Oct 16 05:49:51 2007  recovered 215053 polynomials
Tue Oct 16 05:51:40 2007  attempting to build 88486 cycles
Tue Oct 16 05:51:49 2007  found 88486 cycles in 6 passes
Tue Oct 16 05:51:55 2007  distribution of cycle lengths:
Tue Oct 16 05:51:55 2007     length 1 : 21837
Tue Oct 16 05:51:55 2007     length 2 : 15474
Tue Oct 16 05:51:55 2007     length 3 : 15081
Tue Oct 16 05:51:55 2007     length 4 : 12029
Tue Oct 16 05:51:55 2007     length 5 : 8894
Tue Oct 16 05:51:55 2007     length 6 : 6072
Tue Oct 16 05:51:55 2007     length 7 : 3868
Tue Oct 16 05:51:55 2007     length 9+: 5231
Tue Oct 16 05:51:55 2007  largest cycle: 19 relations
Tue Oct 16 05:52:26 2007  matrix is 88235 x 88486 with weight 5849695 (avg 66.11/col)
Tue Oct 16 05:53:30 2007  filtering completed in 3 passes
Tue Oct 16 05:53:30 2007  matrix is 83979 x 84043 with weight 5585692 (avg 66.46/col)
Tue Oct 16 05:53:34 2007  saving the first 48 matrix rows for later
Tue Oct 16 05:53:35 2007  matrix is 83931 x 84043 with weight 4343397 (avg 51.68/col)
Tue Oct 16 05:53:35 2007  matrix includes 64 packed rows
Tue Oct 16 05:53:35 2007  using block size 10922 for processor cache size 256 kB
Tue Oct 16 05:53:38 2007  commencing Lanczos iteration
Tue Oct 16 05:59:52 2007  lanczos halted after 1329 iterations
Tue Oct 16 05:59:53 2007  recovered 18 nontrivial dependencies
Tue Oct 16 06:24:18 2007  prp31 factor: 5423671886025109442120246388749
Tue Oct 16 06:24:18 2007  prp67 factor: 1443175595670302296287530288340641513337370692964945259930652789367
Tue Oct 16 06:24:18 2007  elapsed time 41:02:03

8·10¹⁵²-7 = 7(9)₁₅₁3_<153> = 13 · 18307 · 4639298979169_<13> · 238372349228810543_<18> · C118

C118 = P33 · P86

P33 = 132196018950577432404812799228403_<33>

P86 = 22993381145741293920904930229003616713749210764279783545611429634014833752788402278923_<86>

Number: 79993_152
N=3039633449680265926335230629866243286215279582467641725078699207006615408808046094193646027979410320642927781189849969
  ( 118 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=132196018950577432404812799228403 (pp33)
 r2=22993381145741293920904930229003616713749210764279783545611429634014833752788402278923 (pp86)
Version: GGNFS-0.77.1-20060513-k8
Total time: 21.25 hours.
Scaled time: 42.02 units (timescale=1.978).
Factorization parameters were as follows:
name: 79993_152
n: 3039633449680265926335230629866243286215279582467641725078699207006615408808046094193646027979410320642927781189849969
m: 2000000000000000000000000000000
c5: 25
c0: -7
skew: 0.78
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:175903, largePrimes:5420804 encountered
Relations: rels:5333741, finalFF:489141
Max relations in full relation-set: 28
Initial matrix: 352269 x 489141 with sparse part having weight 41279494.
Pruned matrix : 285474 x 287299 with weight 22202017.
Total sieving time: 20.13 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.86 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 21.25 hours.
 --------- CPU info (if available) ----------

Oct 16, 2007 (2nd)

By Bryan Koen / GGNFS

(23·10¹⁷⁰+1)/3 = 7(6)₁₆₉7_<171> = 13 · 461 · 1289 · 10909069 · 3428780111_<10> · 5783988689_<10> · 1475103520971674381_<19> · C120

C120 = P50 · P71

P50 = 28622256358095202962667644344453285032065134088263_<50>

P71 = 10864963237661550249466184242559236733294008124794269198135353057048507_<71>

Number: 76667_170
N=310979763109628948369420398838169134459778745943966806045542931361213579741500676681882065931657868642085688329210373341
  ( 120 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=28622256358095202962667644344453285032065134088263 (pp50)
 r2=10864963237661550249466184242559236733294008124794269198135353057048507 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 96.07 hours.
Scaled time: 214.23 units (timescale=2.230).
Factorization parameters were as follows:
n: 310979763109628948369420398838169134459778745943966806045542931361213579741500676681882065931657868642085688329210373341
m: 10000000000000000000000000000000000
c5: 23
c0: 1
skew: 0.53
type: snfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 6700001)
Primes: RFBsize:412849, AFBsize:412891, largePrimes:5994447 encountered
Relations: rels:6291016, finalFF:958381
Max relations in full relation-set: 28
Initial matrix: 825805 x 958381 with sparse part having weight 51452736.
Pruned matrix : 711926 x 716119 with weight 36381718.
Total sieving time: 83.92 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 11.78 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 96.07 hours.
 --------- CPU info (if available) ----------

Oct 16, 2007

By Robert Backstrom / GGNFS, Msieve

6·10¹⁶⁴+7 = 6(0)₁₆₃7_<165> = 29 · 127031 · C159

C159 = P61 · P98

P61 = 1770843922137685855971883220866292296403759900031873711559753_<61>

P98 = 91973613665363851062774584215016713526677170996970636469854370682108828520625054063548519257625981_<98>

Number: n
N=162870914756349183297370530516716120610255601470072876590807728442066408443879704628167058868877784108630556918091402614458213973835873350490879364499406742693
  ( 159 digits)
SNFS difficulty: 165 digits.
Divisors found:

Tue Oct 16 01:56:00 2007  prp61 factor: 1770843922137685855971883220866292296403759900031873711559753
Tue Oct 16 01:56:00 2007  prp98 factor: 91973613665363851062774584215016713526677170996970636469854370682108828520625054063548519257625981
Tue Oct 16 01:56:00 2007  elapsed time 01:28:26 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 53.90 hours.
Scaled time: 70.50 units (timescale=1.308).
Factorization parameters were as follows:
name: KA_6_0_163_7
n: 162870914756349183297370530516716120610255601470072876590807728442066408443879704628167058868877784108630556918091402614458213973835873350490879364499406742693
skew: 1.63
deg: 5
c5: 3
c0: 35
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2700001)
Primes: RFBsize:216816, AFBsize:216606, largePrimes:7411428 encountered
Relations: rels:6890615, finalFF:484135
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 53.63 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 53.90 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

6·10¹⁸⁵+7 = 6(0)₁₈₄7_<186> = 9109 · 486119 · 10533650783_<11> · 7198232528923_<13> · 6020878659975871147_<19> · 57715737637649789572192595701_<29> · C106

C106 = P44 · P63

P44 = 15856940822896359383771402356889784989979289_<44>

P63 = 324309472250677628769264887001027044666888119049640084725461111_<63>

Number: n
N=5142556109783744147491364117529179269926062940937525300905943350583234457373321719669183987601774864930079
  ( 106 digits)
Divisors found:

Wed Oct 17 00:32:49 2007  prp44 factor: 15856940822896359383771402356889784989979289
Wed Oct 17 00:32:49 2007  prp63 factor: 324309472250677628769264887001027044666888119049640084725461111
Wed Oct 17 00:32:49 2007  elapsed time 00:52:18 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.70 hours.
Scaled time: 12.65 units (timescale=1.454).
Factorization parameters were as follows:
name: n
n: 5142556109783744147491364117529179269926062940937525300905943350583234457373321719669183987601774864930079
skew: 21313.42
# norm 5.43e+14
c5: 9000
c4: -76048988
c3: 12119061025586
c2: -340898511045832731
c1: -5046737451005388060230
c0: -9154601256957836199856000
# alpha -6.42
Y1: 5525266307
Y0: -224588401435796917287
# Murphy_E 1.76e-09
# M 241119437529606858479298978826451053129591147004948447723988093141534466268833497155997142159084665980338
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved  special-q in [100000, 1300000)
Primes: RFBsize:183072, AFBsize:182920, largePrimes:4087871 encountered
Relations: rels:4028528, finalFF:410738
Max relations in full relation-set: 28
Initial matrix: 366075 x 410738 with sparse part having weight 23343007.
Pruned matrix : 317878 x 319772 with weight 13914370.
Total sieving time: 8.54 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 8.70 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Oct 15, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(86·10²¹⁰⁷+13)/9 is prime.

Oct 15, 2007 (2nd)

By Sinkiti Sibata / GGNFS

8·10¹⁴⁶-7 = 7(9)₁₄₅3_<147> = 13 · 1046365087_<10> · 19154907071_<11> · C127

C127 = P52 · P76

P52 = 1580183000642280038370796123881094831961607470495009_<52>

P76 = 1943014132025684712297993803987711508705879519397502794606730636362479155677_<76>

Number: 79993_146
N=3070317901434701737005636645958802200607040503016177760156771811800164613700248026172643912484812419742745714980450551562516093
  ( 127 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=1580183000642280038370796123881094831961607470495009 (pp52)
 r2=1943014132025684712297993803987711508705879519397502794606730636362479155677 (pp76)
Version: GGNFS-0.77.1-20060513-k8
Total time: 19.55 hours.
Scaled time: 39.02 units (timescale=1.996).
Factorization parameters were as follows:
name: 79993_146
n: 3070317901434701737005636645958802200607040503016177760156771811800164613700248026172643912484812419742745714980450551562516093
m: 200000000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2850001)
Primes: RFBsize:114155, AFBsize:114392, largePrimes:2881812 encountered
Relations: rels:2895290, finalFF:293370
Max relations in full relation-set: 28
Initial matrix: 228612 x 293370 with sparse part having weight 30568649.
Pruned matrix : 209081 x 210288 with weight 20114196.
Total sieving time: 18.83 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.52 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 19.55 hours.
 --------- CPU info (if available) ----------

Oct 15, 2007

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

6·10¹⁸⁸+7 = 6(0)₁₈₇7_<189> = 17 · 199 · 257 · 3463 · 16649 · 96059 · 61883693 · 90624285000529213_<17> · 454041790607190733_<18> · 517371257791985827755390629_<27> · C101

C101 = P49 · P53

P49 = 3525119596170058088736272803183372325772469391249_<49>

P53 = 26831479803562967544394299568098567920660248574603957_<53>

Number: n
N=94584175249780957684016168054931694295712083157601963382080588311931355733585636495867363625056572293
  ( 101 digits)
Divisors found:
 r1=3525119596170058088736272803183372325772469391249 (pp49)
 r2=26831479803562967544394299568098567920660248574603957 (pp53)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.98 hours.
Scaled time: 9.14 units (timescale=1.309).
Factorization parameters were as follows:
name: n
n: 94584175249780957684016168054931694295712083157601963382080588311931355733585636495867363625056572293
skew: 7737.01
# norm 9.79e+13
c5: 78000
c4: -297470066
c3: -15863340244548
c2: 7080761517578508
c1: 414301049080350364575
c0: -367453236957540790697550
# alpha -5.80
Y1: 14831016739
Y0: -16471952224750940243
# Murphy_E 2.86e-09
# M 1155531281704554954285740779202815785221773336456573589977276941683087980735395064780088119878136440
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:135072, AFBsize:135064, largePrimes:3586849 encountered
Relations: rels:3583146, finalFF:407778
Max relations in full relation-set: 48
Initial matrix: 270216 x 407778 with sparse part having weight 25913894.
Pruned matrix : 153604 x 155019 with weight 8586650.
Total sieving time: 6.41 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.35 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 6.98 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10¹⁴²-7 = 7(9)₁₄₁3_<143> = 2857 · C140

C140 = P66 · P75

P66 = 170295424162300840230361627660073534692518109605861209895558110069_<66>

P75 = 164428376204146486985826323441216525770957734599964780155385367813374589421_<75>

Number: n
N=28001400070003500175008750437521876093804690234511725586279313965698284914245712285614280714035701785089254462723136156807840392019600980049
  ( 140 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=170295424162300840230361627660073534692518109605861209895558110069 (pp66)
 r2=164428376204146486985826323441216525770957734599964780155385367813374589421 (pp75)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.72 hours.
Scaled time: 9.22 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_7_9_141_3
n: 28001400070003500175008750437521876093804690234511725586279313965698284914245712285614280714035701785089254462723136156807840392019600980049
type: snfs
skew: 0.65
deg: 5
c5: 25
c0: -7
m: 20000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 850001)
Primes: RFBsize:148933, AFBsize:148500, largePrimes:5611558 encountered
Relations: rels:4989427, finalFF:361392
Max relations in full relation-set: 28
Initial matrix: 297497 x 361392 with sparse part having weight 17904087.
Pruned matrix : 240103 x 241654 with weight 9277622.
Total sieving time: 6.20 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.13 hours.
Total square root time: 0.19 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 7.72 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

5·10¹⁶⁵-1 = 4(9)₁₆₅_<166> = 428440364567_<12> · C155

C155 = P67 · P88

P67 = 4418255297469253568147847349351285035723609901981851222353873612047_<67>

P88 = 2641367423527036890767831864312306241956122491114136519637229891724953923688971860336151_<88>

Number: n
N=11670235611561044253628931909394969161619544523964876135974702959832102611543850287772225137109509941642444928668610984199652981246175861323416965983211097
  ( 155 digits)
SNFS difficulty: 165 digits.
Divisors found:

Mon Oct 15 22:21:57 2007  prp67 factor: 4418255297469253568147847349351285035723609901981851222353873612047
Mon Oct 15 22:21:57 2007  prp88 factor: 2641367423527036890767831864312306241956122491114136519637229891724953923688971860336151
Mon Oct 15 22:21:57 2007  elapsed time 01:18:34 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 44.16 hours.
Scaled time: 64.21 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_4_9_165
n: 11670235611561044253628931909394969161619544523964876135974702959832102611543850287772225137109509941642444928668610984199652981246175861323416965983211097
skew: 0.72
deg: 5
c5: 5
c0: -1
m: 1000000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2400000)
Primes: RFBsize:203362, AFBsize:203387, largePrimes:7325021 encountered
Relations: rels:6796373, finalFF:457305
Max relations in full relation-set: 28
Initial matrix: 406814 x 457305 with sparse part having weight 40727776.
Pruned matrix : 379736 x 381834 with weight 30695175.
Total sieving time: 43.93 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 44.16 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

8·10¹⁶⁸-7 = 7(9)₁₆₇3_<169> = 889051 · 3504811485997_<13> · 212811322817407_<15> · 15345355832599422733596083704019_<32> · C105

C105 = P33 · P73

P33 = 350969010395558715534644431751677_<33>

P73 = 2240052427411472440287076912394101922396296096003376631991190413937458559_<73>

Oct 14, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

6·10¹⁴⁶+7 = 6(0)₁₄₅7_<147> = 4357 · C144

C144 = P62 · P83

P62 = 11418173072097254220419104341228272288444055633023768296587371_<62>

P83 = 12060548760877474653322042621937488929340653264886088872424357570501388208759630481_<83>

Number: n
N=137709433096167087445490016066100527886160201973835207711728253385356896947440899701629561624971310534771631856782189579986229056690383291255451
  ( 144 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=11418173072097254220419104341228272288444055633023768296587371 (pp62)
 r2=12060548760877474653322042621937488929340653264886088872424357570501388208759630481 (pp83)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 14.29 hours.
Scaled time: 17.06 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_6_0_145_7
n: 137709433096167087445490016066100527886160201973835207711728253385356896947440899701629561624971310534771631856782189579986229056690383291255451
type: snfs
skew: 0.65
deg: 5
c5: 60
c0: 7
m: 100000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:148933, AFBsize:148615, largePrimes:6235655 encountered
Relations: rels:5562121, finalFF:337505
Max relations in full relation-set: 28
Initial matrix: 297615 x 337505 with sparse part having weight 22977078.
Pruned matrix : 271076 x 272628 with weight 15819578.
Total sieving time: 11.99 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 1.85 hours.
Total square root time: 0.22 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 14.29 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

6·10¹⁴⁸+7 = 6(0)₁₄₇7_<149> = 4549 · 787609 · 12956873023_<11> · C130

C130 = P40 · P90

P40 = 9540749344069170990484839035782631826167_<40>

P90 = 135469633078895411887709169907086398273346654936908113597527218378494142638547322866052347_<90>

Number: n
N=1292481812938762669912955974480348284084579994249280402316109378518340638209958112361129835839479159506743055281672649662826363949
  ( 130 digits)
SNFS difficulty: 149 digits.
Divisors found:

Sun Oct 14 07:28:32 2007  prp40 factor: 9540749344069170990484839035782631826167
Sun Oct 14 07:28:32 2007  prp90 factor: 135469633078895411887709169907086398273346654936908113597527218378494142638547322866052347
Sun Oct 14 07:28:32 2007  elapsed time 00:56:42 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 15.17 hours.
Scaled time: 17.95 units (timescale=1.183).
Factorization parameters were as follows:
name: KA_6_0_147_7
n: 1292481812938762669912955974480348284084579994249280402316109378518340638209958112361129835839479159506743055281672649662826363949
skew: 0.52
deg: 5
c5: 375
c0: 14
m: 200000000000000000000000000000
type: snfs
rlim: 1800000
alim: 1800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1850000)
Primes: RFBsize:135072, AFBsize:135288, largePrimes:6951878 encountered
Relations: rels:6272499, finalFF:315014
Max relations in full relation-set: 28
Initial matrix: 270426 x 315014 with sparse part having weight 39437700.
Pruned matrix : 259998 x 261414 with weight 27086460.
Total sieving time: 14.94 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.5,2.5,100000
total time: 15.17 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10¹⁵³-7 = 7(9)₁₅₂3_<154> = 73 · 246833 · 540901 · C141

C141 = P38 · P104

P38 = 45503821118476645834178831665898714663_<38>

P104 = 18038409980107755666629933064361219737535695629711907649346771548449394176944215804284623352754129419979_<104>

Oct 14, 2007

By Sinkiti Sibata / GGNFS, Msieve

8·10¹³⁷-7 = 7(9)₁₃₆3_<138> = 73 · 9964781 · C130

C130 = P48 · P82

P48 = 141316153943199860951746141560760739245162925887_<48>

P82 = 7782292667443130880016248231198064453618474981570509859512503079754219269452839403_<82>

Number: 79993_137
N=1099763668623428964057555400254567520253691063597981621885075953108843075523576896430442484976881173696051081207012566599402325461
  ( 130 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=141316153943199860951746141560760739245162925887 (pp48)
 r2=7782292667443130880016248231198064453618474981570509859512503079754219269452839403 (pp82)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.78 hours.
Scaled time: 13.49 units (timescale=1.990).
Factorization parameters were as follows:
name: 79993_137
n: 1099763668623428964057555400254567520253691063597981621885075953108843075523576896430442484976881173696051081207012566599402325461
m: 2000000000000000000000000000
c5: 25
c0: -7
skew: 0.78
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1225001)
Primes: RFBsize:78498, AFBsize:63568, largePrimes:1548308 encountered
Relations: rels:1559004, finalFF:182026
Max relations in full relation-set: 28
Initial matrix: 142130 x 182026 with sparse part having weight 14809823.
Pruned matrix : 129678 x 130452 with weight 8882231.
Total sieving time: 6.56 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.78 hours.
 --------- CPU info (if available) ----------

8·10¹⁶⁵-7 = 7(9)₁₆₄3_<166> = 2381 · 5443 · 9170957 · 1193913161057723_<16> · 18720100338778545677_<20> · 221092714624829016465471979_<27> · C92

C92 = P38 · P54

P38 = 14107017695779960660551276385083916411_<38>

P54 = 965577295039246891714130651139286441420217189730013597_<54>

Sat Oct 13 14:10:21 2007  Msieve v. 1.28
Sat Oct 13 14:10:21 2007  random seeds: d891a068 1d65775f
Sat Oct 13 14:10:21 2007  factoring 13621415987762003925737115669456429853506846533116955465249119119459261411157655645041440367 (92 digits)
Sat Oct 13 14:10:22 2007  commencing quadratic sieve (91-digit input)
Sat Oct 13 14:10:22 2007  using multiplier of 7
Sat Oct 13 14:10:22 2007  using 64kb Pentium 2 sieve core
Sat Oct 13 14:10:22 2007  sieve interval: 18 blocks of size 65536
Sat Oct 13 14:10:22 2007  processing polynomials in batches of 6
Sat Oct 13 14:10:22 2007  using a sieve bound of 1753547 (65651 primes)
Sat Oct 13 14:10:22 2007  using large prime bound of 177108247 (27 bits)
Sat Oct 13 14:10:22 2007  using double large prime bound of 702796695147472 (42-50 bits)
Sat Oct 13 14:10:22 2007  using trial factoring cutoff of 50 bits
Sat Oct 13 14:10:22 2007  polynomial 'A' values have 12 factors
Sun Oct 14 04:42:53 2007  66323 relations (17390 full + 48933 combined from 797713 partial), need 65747
Sun Oct 14 04:43:12 2007  begin with 815103 relations
Sun Oct 14 04:43:18 2007  reduce to 165651 relations in 10 passes
Sun Oct 14 04:43:18 2007  attempting to read 165651 relations
Sun Oct 14 04:43:40 2007  recovered 165651 relations
Sun Oct 14 04:43:40 2007  recovered 143802 polynomials
Sun Oct 14 04:44:26 2007  attempting to build 66323 cycles
Sun Oct 14 04:44:27 2007  found 66323 cycles in 5 passes
Sun Oct 14 04:44:31 2007  distribution of cycle lengths:
Sun Oct 14 04:44:31 2007     length 1 : 17390
Sun Oct 14 04:44:31 2007     length 2 : 12238
Sun Oct 14 04:44:31 2007     length 3 : 11622
Sun Oct 14 04:44:31 2007     length 4 : 8894
Sun Oct 14 04:44:31 2007     length 5 : 6300
Sun Oct 14 04:44:31 2007     length 6 : 4157
Sun Oct 14 04:44:31 2007     length 7 : 2532
Sun Oct 14 04:44:31 2007     length 9+: 3190
Sun Oct 14 04:44:32 2007  largest cycle: 19 relations
Sun Oct 14 04:44:33 2007  matrix is 65651 x 66323 with weight 3988888 (avg 60.14/col)
Sun Oct 14 04:44:40 2007  filtering completed in 4 passes
Sun Oct 14 04:44:40 2007  matrix is 61409 x 61473 with weight 3690038 (avg 60.03/col)
Sun Oct 14 04:44:44 2007  saving the first 48 matrix rows for later
Sun Oct 14 04:44:44 2007  matrix is 61361 x 61473 with weight 2824181 (avg 45.94/col)
Sun Oct 14 04:44:44 2007  matrix includes 64 packed rows
Sun Oct 14 04:44:44 2007  using block size 10922 for processor cache size 256 kB
Sun Oct 14 04:44:47 2007  commencing Lanczos iteration
Sun Oct 14 04:49:15 2007  lanczos halted after 972 iterations
Sun Oct 14 04:49:16 2007  recovered 17 nontrivial dependencies
Sun Oct 14 04:50:10 2007  prp38 factor: 14107017695779960660551276385083916411
Sun Oct 14 04:50:10 2007  prp54 factor: 965577295039246891714130651139286441420217189730013597
Sun Oct 14 04:50:10 2007  elapsed time 14:39:49

8·10¹³¹-7 = 7(9)₁₃₀3_<132> = 149 · 281 · 376313501619021334931_<21> · C107

C107 = P44 · P64

P44 = 37274544353516647698335148848851846484864657_<44>

P64 = 1362182369130717145175925548652388406862572932354777517395196191_<64>

Number: 79993_131
N=50774727135741302668281681978154025666220800077589563173122909846534600529922377074914069545651920596921487
  ( 107 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=37274544353516647698335148848851846484864657 (pp44)
 r2=1362182369130717145175925548652388406862572932354777517395196191 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.40 hours.
Scaled time: 8.79 units (timescale=1.999).
Factorization parameters were as follows:
name: 79993_131
n: 50774727135741302668281681978154025666220800077589563173122909846534600529922377074914069545651920596921487
m: 200000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:63943, largePrimes:1469981 encountered
Relations: rels:1455868, finalFF:158326
Max relations in full relation-set: 28
Initial matrix: 127959 x 158326 with sparse part having weight 11756685.
Pruned matrix : 119410 x 120113 with weight 7188237.
Total sieving time: 4.24 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.40 hours.
 --------- CPU info (if available) ----------

6·10¹⁵⁰+7 = 6(0)₁₄₉7_<151> = 13 · 1021 · 51377866217_<11> · 38690659722181_<14> · 13553397374370467_<17> · C107

C107 = P44 · P63

P44 = 75896163172818350563639937211446513525782697_<44>

P63 = 221071096062905112755419151133504653865878416206951105384644033_<63>

Number: 60007_150
N=16778447979584046870105927524867093522623211025234406911205125926978020882062201070003687860376291055697001
  ( 107 digits)
Divisors found:
 r1=75896163172818350563639937211446513525782697 (pp44)
 r2=221071096062905112755419151133504653865878416206951105384644033 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 19.13 hours.
Scaled time: 12.93 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_150
n: 16778447979584046870105927524867093522623211025234406911205125926978020882062201070003687860376291055697001
skew: 36403.92
# norm 2.09e+14
c5: 2100
c4: -112214840
c3: -13116197646990
c2: 123037965666033289
c1: 5760329507112287712094
c0: 1238462310613528311780792
# alpha -5.17
Y1: 120696764773
Y0: -380634342801918434537
# Murphy_E 1.56e-09
# M 13741135059811030920870521422422840200370178162132655706061264578222105542413703524686047496399343377873432
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2300001)
Primes: RFBsize:183072, AFBsize:183420, largePrimes:4395571 encountered
Relations: rels:4422833, finalFF:421465
Max relations in full relation-set: 28
Initial matrix: 366571 x 421465 with sparse part having weight 30675596.
Pruned matrix : 323362 x 325258 with weight 19810409.
Total sieving time: 15.47 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.20 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 19.13 hours.
 --------- CPU info (if available) ----------

8·10¹³⁴-7 = 7(9)₁₃₃3_<135> = 13 · 31 · 43 · 379 · 398471 · 16515812627621261_<17> · C107

C107 = P41 · P66

P41 = 48003731369287073342189922196135629754309_<41>

P66 = 385572109653783210030204978859579938448033879962204411809558451037_<66>

Number: 79993_134
N=18508899975309508283025996892062552559124843281306774880121900716696676128531676413045071788063922916268433
  ( 107 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=48003731369287073342189922196135629754309 (pp41)
 r2=385572109653783210030204978859579938448033879962204411809558451037 (pp66)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.87 hours.
Scaled time: 11.71 units (timescale=1.996).
Factorization parameters were as follows:
name: 79993_134
n: 18508899975309508283025996892062552559124843281306774880121900716696676128531676413045071788063922916268433
m: 1000000000000000000000000000
c5: 4
c0: -35
skew: 1.54
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:64193, largePrimes:1523402 encountered
Relations: rels:1537466, finalFF:188576
Max relations in full relation-set: 28
Initial matrix: 142755 x 188576 with sparse part having weight 13498820.
Pruned matrix : 126954 x 127731 with weight 7386006.
Total sieving time: 5.68 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.87 hours.
 --------- CPU info (if available) ----------

8·10¹³⁶-7 = 7(9)₁₃₅3_<137> = 163 · 269 · 22407799279_<11> · 81876428270723_<14> · C108

C108 = P42 · P67

P42 = 110918576820312746668279691257635716599183_<42>

P67 = 8965772596523034939022478706473281787255547555025279231551238868629_<67>

Number: 79993_136
N=994470736500895131291624755886395172525421692165650373010779297212968520824895570611922816043828312385730107
  ( 108 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=110918576820312746668279691257635716599183 (pp42)
 r2=8965772596523034939022478706473281787255547555025279231551238868629 (pp67)
Version: GGNFS-0.77.1-20060513-k8
Total time: 7.91 hours.
Scaled time: 15.72 units (timescale=1.988).
Factorization parameters were as follows:
name: 79993_136
n: 994470736500895131291624755886395172525421692165650373010779297212968520824895570611922816043828312385730107
m: 2000000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1375001)
Primes: RFBsize:78498, AFBsize:63943, largePrimes:1589559 encountered
Relations: rels:1610836, finalFF:189841
Max relations in full relation-set: 28
Initial matrix: 142506 x 189841 with sparse part having weight 16890095.
Pruned matrix : 128981 x 129757 with weight 9843551.
Total sieving time: 7.67 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 7.91 hours.
 --------- CPU info (if available) ----------

Oct 13, 2007 (6th)

By Robert Backstrom / Msieve, GGNFS

8·10¹¹⁰-7 = 7(9)₁₀₉3_<111> = 13 · 30197 · 69511273067394199277_<20> · C86

C86 = P43 · P43

P43 = 3412752588243064179197971634430268240789861_<43>

P43 = 8590585972779452282610598329176427275489929_<43>

Sat Oct 13 14:21:54 2007  Msieve v. 1.28
Sat Oct 13 14:21:54 2007  random seeds: 71c0a470 a1018f8f
Sat Oct 13 14:21:54 2007  factoring 29317544513127637059005073107012633156477405810349541305000972214868654912800710809869 (86 digits)
Sat Oct 13 14:21:54 2007  commencing quadratic sieve (85-digit input)
Sat Oct 13 14:21:54 2007  using multiplier of 1
Sat Oct 13 14:21:54 2007  using 64kb Opteron sieve core
Sat Oct 13 14:21:54 2007  sieve interval: 7 blocks of size 65536
Sat Oct 13 14:21:54 2007  processing polynomials in batches of 15
Sat Oct 13 14:21:54 2007  using a sieve bound of 1442579 (55333 primes)
Sat Oct 13 14:21:54 2007  using large prime bound of 115406320 (26 bits)
Sat Oct 13 14:21:54 2007  using double large prime bound of 325097179907280 (41-49 bits)
Sat Oct 13 14:21:54 2007  using trial factoring cutoff of 49 bits
Sat Oct 13 14:21:54 2007  polynomial 'A' values have 11 factors
Sat Oct 13 14:54:41 2007  55598 relations (16566 full + 39032 combined from 566706 partial), need 55429
Sat Oct 13 14:54:42 2007  begin with 583272 relations
Sat Oct 13 14:54:43 2007  reduce to 129047 relations in 9 passes
Sat Oct 13 14:54:43 2007  attempting to read 129047 relations
Sat Oct 13 14:54:44 2007  recovered 129047 relations
Sat Oct 13 14:54:44 2007  recovered 103401 polynomials
Sat Oct 13 14:54:45 2007  attempting to build 55598 cycles
Sat Oct 13 14:54:45 2007  found 55598 cycles in 5 passes
Sat Oct 13 14:54:45 2007  distribution of cycle lengths:
Sat Oct 13 14:54:45 2007     length 1 : 16566
Sat Oct 13 14:54:46 2007     length 2 : 11426
Sat Oct 13 14:54:46 2007     length 3 : 9845
Sat Oct 13 14:54:46 2007     length 4 : 7055
Sat Oct 13 14:54:46 2007     length 5 : 4727
Sat Oct 13 14:54:46 2007     length 6 : 2766
Sat Oct 13 14:54:46 2007     length 7 : 1568
Sat Oct 13 14:54:46 2007     length 9+: 1645
Sat Oct 13 14:54:46 2007  largest cycle: 19 relations
Sat Oct 13 14:54:46 2007  matrix is 55333 x 55598 with weight 2843187 (avg 51.14/col)
Sat Oct 13 14:54:47 2007  filtering completed in 3 passes
Sat Oct 13 14:54:47 2007  matrix is 49684 x 49748 with weight 2566866 (avg 51.60/col)
Sat Oct 13 14:54:48 2007  saving the first 48 matrix rows for later
Sat Oct 13 14:54:48 2007  matrix is 49636 x 49748 with weight 1895227 (avg 38.10/col)
Sat Oct 13 14:54:48 2007  matrix includes 64 packed rows
Sat Oct 13 14:54:48 2007  commencing Lanczos iteration
Sat Oct 13 14:56:13 2007  lanczos halted after 786 iterations
Sat Oct 13 14:56:13 2007  recovered 16 nontrivial dependencies
Sat Oct 13 14:56:14 2007  prp43 factor: 3412752588243064179197971634430268240789861
Sat Oct 13 14:56:14 2007  prp43 factor: 8590585972779452282610598329176427275489929
Sat Oct 13 14:56:14 2007  elapsed time 00:34:20

8·10¹⁰³-7 = 7(9)₁₀₂3_<104> = 281 · 9903493 · 76751663 · C87

C87 = P35 · P53

P35 = 11645958539351398837968999925860551_<35>

P53 = 32161199219947116795810535309580815458905862060506117_<53>

Sat Oct 13 14:18:15 2007  Msieve v. 1.28
Sat Oct 13 14:18:15 2007  random seeds: fd6310c0 0e9f8101
Sat Oct 13 14:18:15 2007  factoring 374547992691324672010178946818039861713393421705423703090741037387853600337071824490467 (87 digits)
Sat Oct 13 14:18:15 2007  commencing quadratic sieve (87-digit input)
Sat Oct 13 14:18:15 2007  using multiplier of 7
Sat Oct 13 14:18:15 2007  using 64kb Athlon XP sieve core
Sat Oct 13 14:18:15 2007  sieve interval: 10 blocks of size 65536
Sat Oct 13 14:18:15 2007  processing polynomials in batches of 11
Sat Oct 13 14:18:15 2007  using a sieve bound of 1483429 (56667 primes)
Sat Oct 13 14:18:15 2007  using large prime bound of 118674320 (26 bits)
Sat Oct 13 14:18:15 2007  using double large prime bound of 341855144981120 (42-49 bits)
Sat Oct 13 14:18:15 2007  using trial factoring cutoff of 49 bits
Sat Oct 13 14:18:15 2007  polynomial 'A' values have 11 factors
Sat Oct 13 15:27:24 2007  56771 relations (15604 full + 41167 combined from 595942 partial), need 56763
Sat Oct 13 15:27:25 2007  begin with 611546 relations
Sat Oct 13 15:27:25 2007  reduce to 136916 relations in 9 passes
Sat Oct 13 15:27:25 2007  attempting to read 136916 relations
Sat Oct 13 15:27:27 2007  recovered 136916 relations
Sat Oct 13 15:27:27 2007  recovered 116979 polynomials
Sat Oct 13 15:27:28 2007  attempting to build 56771 cycles
Sat Oct 13 15:27:28 2007  found 56771 cycles in 6 passes
Sat Oct 13 15:27:28 2007  distribution of cycle lengths:
Sat Oct 13 15:27:28 2007     length 1 : 15604
Sat Oct 13 15:27:28 2007     length 2 : 10981
Sat Oct 13 15:27:28 2007     length 3 : 9938
Sat Oct 13 15:27:28 2007     length 4 : 7431
Sat Oct 13 15:27:28 2007     length 5 : 5307
Sat Oct 13 15:27:28 2007     length 6 : 3290
Sat Oct 13 15:27:28 2007     length 7 : 1927
Sat Oct 13 15:27:28 2007     length 9+: 2293
Sat Oct 13 15:27:28 2007  largest cycle: 20 relations
Sat Oct 13 15:27:29 2007  matrix is 56667 x 56771 with weight 3278330 (avg 57.75/col)
Sat Oct 13 15:27:30 2007  filtering completed in 4 passes
Sat Oct 13 15:27:30 2007  matrix is 52445 x 52509 with weight 3068265 (avg 58.43/col)
Sat Oct 13 15:27:31 2007  saving the first 48 matrix rows for later
Sat Oct 13 15:27:31 2007  matrix is 52397 x 52509 with weight 2467820 (avg 47.00/col)
Sat Oct 13 15:27:31 2007  matrix includes 64 packed rows
Sat Oct 13 15:27:31 2007  using block size 10922 for processor cache size 256 kB
Sat Oct 13 15:27:32 2007  commencing Lanczos iteration
Sat Oct 13 15:28:04 2007  lanczos halted after 830 iterations
Sat Oct 13 15:28:04 2007  recovered 18 nontrivial dependencies
Sat Oct 13 15:28:05 2007  prp35 factor: 11645958539351398837968999925860551
Sat Oct 13 15:28:05 2007  prp53 factor: 32161199219947116795810535309580815458905862060506117
Sat Oct 13 15:28:05 2007  elapsed time 01:09:50

8·10¹¹⁹-7 = 7(9)₁₁₈3_<120> = 31 · C119

C119 = P41 · P78

P41 = 65850038351296212647890397578950381287521_<41>

P78 = 391897290556327270259798161999635360467060860906617319029511693859070848809543_<78>

Number: n
N=25806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903
  ( 119 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=65850038351296212647890397578950381287521 (pp41)
 r2=391897290556327270259798161999635360467060860906617319029511693859070848809543 (pp78)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.48 hours.
Scaled time: 1.94 units (timescale=1.313).
Factorization parameters were as follows:
name: KA_7_9_118_3
n: 25806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903
skew: 1.54
deg: 5
c5: 4
c0: -35
m: 1000000000000000000000000
type: snfs
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:63951, AFBsize:64193, largePrimes:4027991 encountered
Relations: rels:3391987, finalFF:155362
Max relations in full relation-set: 48
Initial matrix: 128208 x 155362 with sparse part having weight 9403022.
Pruned matrix : 112183 x 112888 with weight 4664374.
Total sieving time: 1.28 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.12 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000
total time: 1.48 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 13, 2007 (5th)

By Sinkiti Sibata / GGNFS

6·10¹³⁴+7 = 6(0)₁₃₃7_<135> = 193 · 863 · 23603 · 100586824269101_<15> · C112

C112 = P35 · P77

P35 = 16080745011300179212403283434151191_<35>

P77 = 94355816472667095064977591820097467102390568492729306979142286831385089101801_<77>

Number: 60007_134
N=1517311825029996661504435096321997519435645891033130360977335775340869413282472959239396871158506225871024394991
  ( 112 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=16080745011300179212403283434151191 (pp35)
 r2=94355816472667095064977591820097467102390568492729306979142286831385089101801 (pp77)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.83 hours.
Scaled time: 11.61 units (timescale=1.992).
Factorization parameters were as follows:
name: 60007_134
n: 1517311825029996661504435096321997519435645891033130360977335775340869413282472959239396871158506225871024394991
m: 1000000000000000000000000000
c5: 3
c0: 35
skew: 1.63
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:63993, largePrimes:1532434 encountered
Relations: rels:1543630, finalFF:184907
Max relations in full relation-set: 28
Initial matrix: 142556 x 184907 with sparse part having weight 13770867.
Pruned matrix : 128299 x 129075 with weight 7860258.
Total sieving time: 5.62 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.83 hours.
 --------- CPU info (if available) ----------

8·10¹⁰²-7 = 7(9)₁₀₁3_<103> = 2599231 · C97

C97 = P36 · P62

P36 = 123290814675728514277867589716453613_<36>

P62 = 24964012229434350382875423100742889170251821341837628816240131_<62>

Number: 79993_102
N=3077833405341810712476113127305730040923642415776050685760519168938813056630980470762313930543303
  ( 97 digits)
SNFS difficulty: 102 digits.
Divisors found:
 r1=123290814675728514277867589716453613 (pp36)
 r2=24964012229434350382875423100742889170251821341837628816240131 (pp62)
Version: GGNFS-0.77.1-20060513-k8
Total time: 0.89 hours.
Scaled time: 1.79 units (timescale=1.999).
Factorization parameters were as follows:
name: 79993_102
n: 3077833405341810712476113127305730040923642415776050685760519168938813056630980470762313930543303
m: 200000000000000000000
c5: 25
c0: -7
skew: 0.78
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [250000, 310001)
Primes: RFBsize:37706, AFBsize:41317, largePrimes:1576393 encountered
Relations: rels:1849951, finalFF:427438
Max relations in full relation-set: 28
Initial matrix: 79087 x 427438 with sparse part having weight 15779526.
Pruned matrix : 37970 x 38429 with weight 2534723.
Total sieving time: 0.84 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,102,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 0.89 hours.
 --------- CPU info (if available) ----------

8·10¹¹³-7 = 7(9)₁₁₂3_<114> = 43 · 73 · 947 · 138185209 · C100

C100 = P34 · P67

P34 = 1766907794190056087078782907983423_<34>

P67 = 1102232585621228023273179280338960623464028098584925315433259382103_<67>

Number: 79993_113
N=1947543346544406138446494012197593494161099060936009527105845848444968706122941158047420354746878569
  ( 100 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=1766907794190056087078782907983423 (pp34)
 r2=1102232585621228023273179280338960623464028098584925315433259382103 (pp67)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.01 hours.
Scaled time: 7.94 units (timescale=1.983).
Factorization parameters were as follows:
name: 79993_113
n: 1947543346544406138446494012197593494161099060936009527105845848444968706122941158047420354746878569
m: 20000000000000000000000
c5: 250
c0: -7
skew: 0.49
type: snfs
n: 1947543346544406138446494012197593494161099060936009527105845848444968706122941158047420354746878569
m: 20000000000000000000000
c5: 250
c0: -7
skew: 0.49
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64168, largePrimes:2727503 encountered
Relations: rels:3846323, finalFF:1205129
Max relations in full relation-set: 28
Initial matrix: 113332 x 1205129 with sparse part having weight 90876931.
Pruned matrix : 49293 x 49923 with weight 10051860.
Total sieving time: 3.88 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 4.01 hours.
 --------- CPU info (if available) ----------

8·10¹²⁸-7 = 7(9)₁₂₇3_<129> = 13 · 4458931 · 28353751 · 344697087446640263047_<21> · C94

C94 = P39 · P55

P39 = 212705206095827642161365792695450030873_<39>

P55 = 6638800655743115255251905310435410068403132728886029351_<55>

Number: 79993_128
N=1412107461708955027069290923954737312907713787250726572515699054670309444073066843051334153423
  ( 94 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=212705206095827642161365792695450030873 (pp39)
 r2=6638800655743115255251905310435410068403132728886029351 (pp55)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 5.28 hours.
Scaled time: 3.57 units (timescale=0.676).
Factorization parameters were as follows:
name: 79993_128
n: 1412107461708955027069290923954737312907713787250726572515699054670309444073066843051334153423
m: 20000000000000000000000000
c5: 250
c0: -7
skew: 0.49
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64168, largePrimes:1487851 encountered
Relations: rels:1489577, finalFF:174328
Max relations in full relation-set: 28
Initial matrix: 128185 x 174328 with sparse part having weight 12264098.
Pruned matrix : 114449 x 115153 with weight 6368258.
Total sieving time: 4.96 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.28 hours.
 --------- CPU info (if available) ----------

8·10¹¹⁴-7 = 7(9)₁₁₃3_<115> = 230904677 · C107

C107 = P48 · P59

P48 = 587132704218609332602624273840988912804671457773_<48>

P59 = 59009370997911180303851532975515874983963222792974758349433_<59>

Number: 79993_114
N=34646331568242768854785908039446078435215064959468101202644760634276801591160494336803753871126655437992709
  ( 107 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=587132704218609332602624273840988912804671457773 (pp48)
 r2=59009370997911180303851532975515874983963222792974758349433 (pp59)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.32 hours.
Scaled time: 6.61 units (timescale=1.994).
Factorization parameters were as follows:
name: 79993_114
n: 34646331568242768854785908039446078435215064959468101202644760634276801591160494336803753871126655437992709
m: 100000000000000000000000
c5: 4
c0: -35
skew: 1.54
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64193, largePrimes:2486912 encountered
Relations: rels:3148089, finalFF:767372
Max relations in full relation-set: 28
Initial matrix: 113355 x 767372 with sparse part having weight 60310023.
Pruned matrix : 62081 x 62711 with weight 6647029.
Total sieving time: 3.20 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.32 hours.
 --------- CPU info (if available) ----------

Oct 13, 2007 (4th)

The factor table of 799...993 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Oct 13, 2007 (3rd)

By Robert Backstrom / GGNFS

6·10¹⁴⁴+7 = 6(0)₁₄₃7_<145> = 13 · 61 · 6217 · C139

C139 = P47 · P92

P47 = 17996214744046724344420417956846958165765495333_<47>

P92 = 67626362611447967176376164281940047499923797596474846813424537050089499416597128887441863259_<92>

Number: n
N=1217018543914390047546886146495361840910930266662961521321860634744135035509558565062115612299270539368420113178667855558559788368588670247
  ( 139 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=17996214744046724344420417956846958165765495333 (pp47)
 r2=67626362611447967176376164281940047499923797596474846813424537050089499416597128887441863259 (pp92)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.95 hours.
Scaled time: 11.51 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_6_0_143_7
n: 1217018543914390047546886146495361840910930266662961521321860634744135035509558565062115612299270539368420113178667855558559788368588670247
skew: 1.63
deg: 5
c5: 3
c0: 35
m: 100000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:148933, AFBsize:148840, largePrimes:6333809 encountered
Relations: rels:5693227, finalFF:347656
Max relations in full relation-set: 28
Initial matrix: 297838 x 347656 with sparse part having weight 22955213.
Pruned matrix : 259683 x 261236 with weight 14197561.
Total sieving time: 6.15 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.51 hours.
Total square root time: 0.13 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 7.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Oct 13, 2007 (2nd)

By Sinkiti Sibata / GGNFS

6·10¹³²+7 = 6(0)₁₃₁7_<133> = 13 · 31 · 59 · 2090009 · 148913261947_<12> · C111

C111 = P55 · P57

P55 = 1983329501828473727548585254782922572449329984672734213_<55>

P57 = 408806495210391060163003461145989705978462625906890077609_<57>

Number: 60007_132
N=810797982489869232300976179328579352721883380713949594003733868807533449400899968769781243999195835893799536717
  ( 111 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=1983329501828473727548585254782922572449329984672734213 (pp55)
 r2=408806495210391060163003461145989705978462625906890077609 (pp57)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 7.78 hours.
Scaled time: 5.26 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_132
n: 810797982489869232300976179328579352721883380713949594003733868807533449400899968769781243999195835893799536717
m: 100000000000000000000000000
c5: 600
c0: 7
skew: 0.41
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1250001)
Primes: RFBsize:63951, AFBsize:63523, largePrimes:1533110 encountered
Relations: rels:1528629, finalFF:158241
Max relations in full relation-set: 28
Initial matrix: 127540 x 158241 with sparse part having weight 14199593.
Pruned matrix : 119830 x 120531 with weight 9182188.
Total sieving time: 7.35 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 7.78 hours.
 --------- CPU info (if available) ----------

6·10¹⁶⁷-7 = 5(9)₁₆₆3_<168> = 86004929922823687_<17> · 117124643630091042473553137641_<30> · C122

C122 = P55 · P68

P55 = 1422924018199617086667469983408773956446337923324187259_<55>

P68 = 41859873490837916408900575837828799444368507615420908476733092182981_<68>

Number: 59993_167
N=59563419388910720197810859969956349938363680093704772757910598946408447555545711050233081537114891883517241917857936839079
  ( 122 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=1422924018199617086667469983408773956446337923324187259 (pp55)
 r2=41859873490837916408900575837828799444368507615420908476733092182981 (pp68)
Version: GGNFS-0.77.1-20060513-k8
Total time: 154.80 hours.
Scaled time: 308.82 units (timescale=1.995).
Factorization parameters were as follows:
name: 59993_167
n: 59563419388910720197810859969956349938363680093704772757910598946408447555545711050233081537114891883517241917857936839079
m: 1000000000000000000000000000000000
c5: 600
c0: -7
skew: 0.41
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 7450001)
Primes: RFBsize:380800, AFBsize:380567, largePrimes:6136257 encountered
Relations: rels:6361592, finalFF:867619
Max relations in full relation-set: 28
Initial matrix: 761433 x 867619 with sparse part having weight 66909828.
Pruned matrix : 680057 x 683928 with weight 51296332.
Total sieving time: 147.94 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 6.30 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 154.80 hours.
 --------- CPU info (if available) ----------

Oct 13, 2007

By Jo Yeong Uk / GMP-ECM, GGNFS

6·10¹⁹³+7 = 6(0)₁₉₂7_<194> = C194

C194 = P37 · C157

P37 = 9431867921209970677263227064224760463_<37>

C157 = [6361412235753920282712594389572541485300199982510262458997768914548898435588007324833733189857362507423842664895526461468007039663923961796686299905053607689_<157>]

6·10¹⁴⁰+7 = 6(0)₁₃₉7_<141> = 17 · 25765322537_<11> · 29151135776457323_<17> · C113

C113 = P52 · P61

P52 = 6123908191785128062611453979386707666992816396823857_<52>

P61 = 7673307351852464227438937019759901799643665911557369118867853_<61>

Number: 60007_140
N=46990629750094353640929945031801720386834025557110371526615491443551271997160943220584424618795094865880900769021
  ( 113 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=6123908191785128062611453979386707666992816396823857 (pp52)
 r2=7673307351852464227438937019759901799643665911557369118867853 (pp61)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.19 hours.
Scaled time: 13.10 units (timescale=2.117).
Factorization parameters were as follows:
n: 46990629750094353640929945031801720386834025557110371526615491443551271997160943220584424618795094865880900769021
m: 10000000000000000000000000000
c5: 6
c0: 7
skew: 1.03
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:114412, largePrimes:3206977 encountered
Relations: rels:3155190, finalFF:262058
Max relations in full relation-set: 28
Initial matrix: 228633 x 262058 with sparse part having weight 22384343.
Pruned matrix : 214081 x 215288 with weight 15710541.
Total sieving time: 5.95 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.19 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

6·10¹⁸³+7 = 6(0)₁₈₂7_<184> = C184

C184 = P37 · P148

P37 = 4646109535270935651861373920553944113_<37>

P148 = 1291403044730436574664225203953221354301912479271324672689780038042977651172600578097674193944368819808698887156719580132180993397271065994090189239_<148>

6·10¹⁶⁰+7 = 6(0)₁₅₉7_<161> = 4229 · 482513 · 19099104039013_<14> · C139

C139 = P34 · P105

P34 = 2891475901086594031773677024975431_<34>

P105 = 532441594081401683367165802963920698884830621397625778059323292338660459693626121501287829706854904467897_<105>

Oct 12, 2007 (3rd)

By Jo Yeong Uk / GGNFS

6·10¹⁵²+7 = 6(0)₁₅₁7_<153> = C153

C153 = P43 · P111

P43 = 1840685266806508095129806305318544351784701_<43>

P111 = 325965557947322722135583311765356705447166321685192963549916970963466614546316438202055770474848508291355137107_<111>

Number: 60007_152
N=600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
  ( 153 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=1840685266806508095129806305318544351784701 (pp43)
 r2=325965557947322722135583311765356705447166321685192963549916970963466614546316438202055770474848508291355137107 (pp111)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 20.05 hours.
Scaled time: 42.60 units (timescale=2.125).
Factorization parameters were as follows:
n: 600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
m: 2000000000000000000000000000000
c5: 75
c0: 28
skew: 0.82
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2500001)
Primes: RFBsize:176302, AFBsize:175743, largePrimes:5716294 encountered
Relations: rels:5680786, finalFF:487419
Max relations in full relation-set: 28
Initial matrix: 352111 x 487419 with sparse part having weight 48790712.
Pruned matrix : 305178 x 307002 with weight 29072127.
Total sieving time: 19.36 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.56 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 20.05 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 12, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

(89·10¹⁶³+1)/9 = 9(8)₁₆₂9_<164> = 3² · 11 · 191 · 44453 · 169823791 · C147

C147 = P71 · P77

P71 = 53555495404586983124284868689499027110767249977749056417262621184569457_<71>

P77 = 12935263718227109600388586097547759844207588321745878007455274683392359947511_<77>

Number: n
N=692754456618632700742588855519739501284878125239435320459568642724351039203120317771928341708484604722354579869380134021593082789437079791653771527
  ( 147 digits)
SNFS difficulty: 164 digits.
Divisors found:

Fri Oct 12 07:40:24 2007  prp71 factor: 53555495404586983124284868689499027110767249977749056417262621184569457
Fri Oct 12 07:40:24 2007  prp77 factor: 12935263718227109600388586097547759844207588321745878007455274683392359947511
Fri Oct 12 07:40:24 2007  elapsed time 01:36:36 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 40.85 hours.
Scaled time: 58.50 units (timescale=1.432).
Factorization parameters were as follows:
name: KA_9_8_162_9
n: 692754456618632700742588855519739501284878125239435320459568642724351039203120317771928341708484604722354579869380134021593082789437079791653771527
skew: 0.10
deg: 5
c5: 89000
c0: 1
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100001)
Primes: RFBsize:203362, AFBsize:202807, largePrimes:7209972 encountered
Relations: rels:6664266, finalFF:448066
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 40.59 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 40.85 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

6·10¹⁴⁵+7 = 6(0)₁₄₄7_<146> = 163 · C144

C144 = P64 · P80

P64 = 3919572055477532086753025839329335485817252963822084748594102007_<64>

P80 = 93912844131744392068992466757974562467028071947951869170587151041083038337579227_<80>

Number: n
N=368098159509202453987730061349693251533742331288343558282208588957055214723926380368098159509202453987730061349693251533742331288343558282208589
  ( 144 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=3919572055477532086753025839329335485817252963822084748594102007 (pp64)
 r2=93912844131744392068992466757974562467028071947951869170587151041083038337579227 (pp80)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 11.95 hours.
Scaled time: 14.29 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_6_0_144_7
n: 368098159509202453987730061349693251533742331288343558282208588957055214723926380368098159509202453987730061349693251533742331288343558282208589
type: snfs
skew: 1.03
deg: 5
c5: 6
c0: 7
m: 100000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:148933, AFBsize:149160, largePrimes:6126432 encountered
Relations: rels:5452417, finalFF:336584
Max relations in full relation-set: 28
Initial matrix: 298159 x 336584 with sparse part having weight 21730162.
Pruned matrix : 270315 x 271869 with weight 14890622.
Total sieving time: 9.92 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 1.75 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 11.95 hours.
 --------- CPU info (if available) ----------

6·10¹³⁸+7 = 6(0)₁₃₇7_<139> = 13 · C138

C138 = P52 · P86

P52 = 8786475728072227386487041599685529123701731718444931_<52>

P86 = 52528280487235138475680678891847720293425922478509734700005290994634833797311729822369_<86>

Number: n
N=461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461539
  ( 138 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=8786475728072227386487041599685529123701731718444931 (pp52)
 r2=52528280487235138475680678891847720293425922478509734700005290994634833797311729822369 (pp86)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.79 hours.
Scaled time: 8.84 units (timescale=1.302).
Factorization parameters were as follows:
name: KA_6_0_137_3
n: 461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461539
skew: 0.26
deg: 5
c5: 6000
c0: 7
m: 1000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 750001)
Primes: RFBsize:114155, AFBsize:114432, largePrimes:6211466 encountered
Relations: rels:5545647, finalFF:312486
Max relations in full relation-set: 48
Initial matrix: 228654 x 312486 with sparse part having weight 29654727.
Pruned matrix : 190499 x 191706 with weight 12900013.
Total sieving time: 5.71 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.83 hours.
Total square root time: 0.08 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,75000
total time: 6.79 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(25·10¹⁶⁴-7)/9 = 2(7)₁₆₄_<165> = 109 · 233 · 98429 · 3605093 · C149

C149 = P69 · P81

P69 = 202665523211650989063300380086943340369476928178393708116016987186139_<69>

P81 = 152088249235178053009249905689353519859990659090201830262384603581442406000454727_<81>

Number: n
N=30823044605591338486772528468080215864221880056493623390494021588481356096730350429012600680064293390882554678466909555819589219907302066966191429053
  ( 149 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=202665523211650989063300380086943340369476928178393708116016987186139 (pp69)
 r2=152088249235178053009249905689353519859990659090201830262384603581442406000454727 (pp81)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 63.84 hours.
Scaled time: 83.38 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_2_7_164
n: 30823044605591338486772528468080215864221880056493623390494021588481356096730350429012600680064293390882554678466909555819589219907302066966191429053
skew: 1.23
deg: 5
c5: 5
c0: -14
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2800001)
Primes: RFBsize:216816, AFBsize:217381, largePrimes:7523615 encountered
Relations: rels:7019729, finalFF:495769
Max relations in full relation-set: 28
Initial matrix: 434262 x 495769 with sparse part having weight 44468095.
Pruned matrix : 406710 x 408945 with weight 32940913.
Total sieving time: 58.95 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 4.48 hours.
Total square root time: 0.14 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 63.84 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 12, 2007

By Sinkiti Sibata / GGNFS

6·10¹¹⁴+7 = 6(0)₁₁₃7_<115> = 13 · 23 · 294199 · 314707 · 2354837 · C95

C95 = P32 · P64

P32 = 13963735493801662655038504422019_<32>

P64 = 6591283660858015718799436869882276779748116589270476529805242367_<64>

Number: 60007_114
N=92038941604838034885826953995277077283508823907453477048445035739217774475488560068977546478973
  ( 95 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=13963735493801662655038504422019 (pp32)
 r2=6591283660858015718799436869882276779748116589270476529805242367 (pp64)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.60 hours.
Scaled time: 1.08 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_114
n: 92038941604838034885826953995277077283508823907453477048445035739217774475488560068977546478973
m: 100000000000000000000000
c5: 3
c0: 35
skew: 1.63
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:63993, largePrimes:2069865 encountered
Relations: rels:2160911, finalFF:246690
Max relations in full relation-set: 28
Initial matrix: 113156 x 246690 with sparse part having weight 18938825.
Pruned matrix : 79136 x 79765 with weight 3921681.
Total sieving time: 1.41 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.60 hours.
 --------- CPU info (if available) ----------

6·10¹¹⁶+7 = 6(0)₁₁₅7_<117> = 1433 · C114

C114 = P46 · P68

P46 = 4260569836341526184189932091009434032922764443_<46>

P68 = 98273714505283129560284285927238795172266087521311216860992588389453_<68>

Number: 60007_116
N=418702023726448011165387299371946964410327983251919050942079553384508025122121423586880669923237962316817864619679
  ( 114 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=4260569836341526184189932091009434032922764443 (pp46)
 r2=98273714505283129560284285927238795172266087521311216860992588389453 (pp68)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.17 hours.
Scaled time: 1.47 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_116
n: 418702023726448011165387299371946964410327983251919050942079553384508025122121423586880669923237962316817864619679
m: 100000000000000000000000
c5: 60
c0: 7
skew: 0.65
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63883, largePrimes:2216313 encountered
Relations: rels:2423409, finalFF:333688
Max relations in full relation-set: 28
Initial matrix: 113048 x 333688 with sparse part having weight 30159400.
Pruned matrix : 73820 x 74449 with weight 5302920.
Total sieving time: 1.96 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.17 hours.
 --------- CPU info (if available) ----------

6·10¹¹⁷+7 = 6(0)₁₁₆7_<118> = 31 · 2602909783189_<13> · C104

C104 = P39 · P65

P39 = 761007481197519851161967935908199514911_<39>

P65 = 97710562768479463816800500502385687103003804418987111582005841643_<65>

Number: 60007_117
N=74358469258832718774436183724553279940996020408249446899718017650687200724318637458592452381540883238773
  ( 104 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=761007481197519851161967935908199514911 (pp39)
 r2=97710562768479463816800500502385687103003804418987111582005841643 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.20 hours.
Scaled time: 1.49 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_117
n: 74358469258832718774436183724553279940996020408249446899718017650687200724318637458592452381540883238773
m: 100000000000000000000000
c5: 600
c0: 7
skew: 0.41
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63523, largePrimes:1980594 encountered
Relations: rels:1938172, finalFF:128803
Max relations in full relation-set: 28
Initial matrix: 112687 x 128803 with sparse part having weight 10218920.
Pruned matrix : 106545 x 107172 with weight 7132342.
Total sieving time: 1.89 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.20 hours.
 --------- CPU info (if available) ----------

6·10¹²⁷+7 = 6(0)₁₂₆7_<128> = 197 · 9720031 · 266168660299_<12> · C108

C108 = P43 · P65

P43 = 3583617409332378966987419272264607655669797_<43>

P65 = 32850260496263134596383389203484134247046587543608521946389524867_<65>

Number: 60007_127
N=117722765415512284233525269842016058687696108332067481812522215595485313176760239621795561889746921472341999
  ( 108 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=3583617409332378966987419272264607655669797 (pp43)
 r2=32850260496263134596383389203484134247046587543608521946389524867 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 5.28 hours.
Scaled time: 3.57 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_127
n: 117722765415512284233525269842016058687696108332067481812522215595485313176760239621795561889746921472341999
m: 10000000000000000000000000
c5: 600
c0: 7
skew: 0.41
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:63523, largePrimes:1506649 encountered
Relations: rels:1516333, finalFF:181202
Max relations in full relation-set: 28
Initial matrix: 127540 x 181202 with sparse part having weight 12751877.
Pruned matrix : 111515 x 112216 with weight 6223089.
Total sieving time: 4.97 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.28 hours.
 --------- CPU info (if available) ----------

Oct 11, 2007 (4th)

By Sinkiti Sibata / Msieve

6·10¹⁵⁵+7 = 6(0)₁₅₄7_<156> = 30253 · 8290186057_<10> · 93174093649657_<14> · 47369174977499761_<17> · 7846580404504329797862521_<25> · C86

C86 = P41 · P46

P41 = 11519704348754539604022205034624081555611_<41>

P46 = 5996609457515185443760101854342559834794121041_<46>

Thu Oct 11 07:46:13 2007  Msieve v. 1.28
Thu Oct 11 07:46:13 2007  random seeds: a4efa528 11c3b45d
Thu Oct 11 07:46:13 2007  factoring 69079168045520282358058872569745380341436008514853935086936756082097682617184706711051 (86 digits)
Thu Oct 11 07:46:14 2007  commencing quadratic sieve (86-digit input)
Thu Oct 11 07:46:14 2007  using multiplier of 11
Thu Oct 11 07:46:14 2007  using 64kb Pentium 2 sieve core
Thu Oct 11 07:46:14 2007  sieve interval: 9 blocks of size 65536
Thu Oct 11 07:46:14 2007  processing polynomials in batches of 12
Thu Oct 11 07:46:14 2007  using a sieve bound of 1470947 (55891 primes)
Thu Oct 11 07:46:14 2007  using large prime bound of 117675760 (26 bits)
Thu Oct 11 07:46:14 2007  using double large prime bound of 336694943593840 (41-49 bits)
Thu Oct 11 07:46:14 2007  using trial factoring cutoff of 49 bits
Thu Oct 11 07:46:14 2007  polynomial 'A' values have 11 factors
Thu Oct 11 13:23:21 2007  56030 relations (15871 full + 40159 combined from 586780 partial), need 55987
Thu Oct 11 13:23:28 2007  begin with 602651 relations
Thu Oct 11 13:23:29 2007  reduce to 133601 relations in 10 passes
Thu Oct 11 13:23:29 2007  attempting to read 133601 relations
Thu Oct 11 13:23:38 2007  recovered 133601 relations
Thu Oct 11 13:23:38 2007  recovered 112180 polynomials
Thu Oct 11 13:23:39 2007  attempting to build 56030 cycles
Thu Oct 11 13:23:39 2007  found 56030 cycles in 6 passes
Thu Oct 11 13:23:42 2007  distribution of cycle lengths:
Thu Oct 11 13:23:42 2007     length 1 : 15871
Thu Oct 11 13:23:42 2007     length 2 : 11072
Thu Oct 11 13:23:42 2007     length 3 : 9884
Thu Oct 11 13:23:42 2007     length 4 : 7361
Thu Oct 11 13:23:42 2007     length 5 : 4850
Thu Oct 11 13:23:42 2007     length 6 : 3171
Thu Oct 11 13:23:42 2007     length 7 : 1783
Thu Oct 11 13:23:42 2007     length 9+: 2038
Thu Oct 11 13:23:42 2007  largest cycle: 20 relations
Thu Oct 11 13:23:42 2007  matrix is 55891 x 56030 with weight 3116041 (avg 55.61/col)
Thu Oct 11 13:23:47 2007  filtering completed in 3 passes
Thu Oct 11 13:23:47 2007  matrix is 51400 x 51464 with weight 2897239 (avg 56.30/col)
Thu Oct 11 13:23:49 2007  saving the first 48 matrix rows for later
Thu Oct 11 13:23:49 2007  matrix is 51352 x 51464 with weight 2270531 (avg 44.12/col)
Thu Oct 11 13:23:49 2007  matrix includes 64 packed rows
Thu Oct 11 13:23:49 2007  using block size 5461 for processor cache size 128 kB
Thu Oct 11 13:23:51 2007  commencing Lanczos iteration
Thu Oct 11 13:26:11 2007  lanczos halted after 814 iterations
Thu Oct 11 13:26:12 2007  recovered 16 nontrivial dependencies
Thu Oct 11 13:26:13 2007  prp41 factor: 11519704348754539604022205034624081555611
Thu Oct 11 13:26:13 2007  prp46 factor: 5996609457515185443760101854342559834794121041
Thu Oct 11 13:26:13 2007  elapsed time 05:40:00

6·10¹⁰⁴+7 = 6(0)₁₀₃7_<105> = 8629566092175419113_<19> · C86

C86 = P39 · P48

P39 = 312703414298744945585964596618843105759_<39>

P48 = 222346177668355476515021026054869613681073668721_<48>

Thu Oct 11 08:00:35 2007  Msieve v. 1.26
Thu Oct 11 08:00:35 2007  random seeds: 35251e1c b1bd4346
Thu Oct 11 08:00:35 2007  factoring 69528408913170114020623970508248965547977728760224458789292141359530747384979933264239 (86 digits)
Thu Oct 11 08:00:36 2007  commencing quadratic sieve (86-digit input)
Thu Oct 11 08:00:36 2007  using multiplier of 31
Thu Oct 11 08:00:36 2007  using 64kb Pentium 2 sieve core
Thu Oct 11 08:00:36 2007  sieve interval: 9 blocks of size 65536
Thu Oct 11 08:00:36 2007  processing polynomials in batches of 12
Thu Oct 11 08:00:36 2007  using a sieve bound of 1470947 (55662 primes)
Thu Oct 11 08:00:36 2007  using large prime bound of 117675760 (26 bits)
Thu Oct 11 08:00:36 2007  using double large prime bound of 336694943593840 (41-49 bits)
Thu Oct 11 08:00:36 2007  using trial factoring cutoff of 49 bits
Thu Oct 11 08:00:36 2007  polynomial 'A' values have 11 factors
Thu Oct 11 13:29:42 2007  55839 relations (15809 full + 40030 combined from 583377 partial), need 55758
Thu Oct 11 13:29:51 2007  begin with 599186 relations
Thu Oct 11 13:29:54 2007  reduce to 132538 relations in 10 passes
Thu Oct 11 13:29:54 2007  attempting to read 132538 relations
Thu Oct 11 13:30:03 2007  recovered 132538 relations
Thu Oct 11 13:30:03 2007  recovered 110467 polynomials
Thu Oct 11 13:30:16 2007  attempting to build 55839 cycles
Thu Oct 11 13:30:16 2007  found 55838 cycles in 5 passes
Thu Oct 11 13:30:18 2007  distribution of cycle lengths:
Thu Oct 11 13:30:18 2007     length 1 : 15809
Thu Oct 11 13:30:18 2007     length 2 : 11217
Thu Oct 11 13:30:18 2007     length 3 : 9985
Thu Oct 11 13:30:18 2007     length 4 : 7192
Thu Oct 11 13:30:18 2007     length 5 : 4922
Thu Oct 11 13:30:18 2007     length 6 : 3106
Thu Oct 11 13:30:18 2007     length 7 : 1762
Thu Oct 11 13:30:18 2007     length 9+: 1845
Thu Oct 11 13:30:18 2007  largest cycle: 18 relations
Thu Oct 11 13:30:19 2007  matrix is 55662 x 55838 with weight 3139688 (avg 56.23/col)
Thu Oct 11 13:30:22 2007  filtering completed in 3 passes
Thu Oct 11 13:30:22 2007  matrix is 50880 x 50944 with weight 2899893 (avg 56.92/col)
Thu Oct 11 13:30:24 2007  saving the first 48 matrix rows for later
Thu Oct 11 13:30:24 2007  matrix is 50832 x 50944 with weight 2295297 (avg 45.06/col)
Thu Oct 11 13:30:24 2007  matrix includes 64 packed rows
Thu Oct 11 13:30:24 2007  using block size 10922 for processor cache size 256 kB
Thu Oct 11 13:30:25 2007  commencing Lanczos iteration
Thu Oct 11 13:33:05 2007  lanczos halted after 805 iterations
Thu Oct 11 13:33:06 2007  recovered 17 nontrivial dependencies
Thu Oct 11 13:33:21 2007  prp39 factor: 312703414298744945585964596618843105759
Thu Oct 11 13:33:21 2007  prp48 factor: 222346177668355476515021026054869613681073668721
Thu Oct 11 13:33:21 2007  elapsed time 05:32:46

Oct 11, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(4·10¹⁶²+23)/9 = (4)₁₆₁7_<162> = 3 · 191537 · 36201871247_<11> · C146

C146 = P68 · P79

P68 = 14267717847005813507700165288034158445726684150241889062913896709923_<68>

P79 = 1497469599792136047698907928447361359099204601762726546842329109356470216353817_<79>

Number: n
N=21365473734302912529054906948237323508436428295729914712019667578602171034133803699777503768069330971332086852316622127836560860767947345582826091
  ( 146 digits)
SNFS difficulty: 162 digits.
Divisors found:

Thu Oct 11 07:49:06 2007  prp68 factor: 14267717847005813507700165288034158445726684150241889062913896709923
Thu Oct 11 07:49:06 2007  prp79 factor: 1497469599792136047698907928447361359099204601762726546842329109356470216353817
Thu Oct 11 07:49:06 2007  elapsed time 02:07:31 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 67.17 hours.
Scaled time: 80.33 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_4_161_7
n: 21365473734302912529054906948237323508436428295729914712019667578602171034133803699777503768069330971332086852316622127836560860767947345582826091
type: snfs
skew: 1.13
deg: 5
c5: 25
c0: 46
m: 200000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2900000)
Primes: RFBsize:230209, AFBsize:229862, largePrimes:7394863 encountered
Relations: rels:6833492, finalFF:510861
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 66.85 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 67.17 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

6·10¹⁰⁶+7 = 6(0)₁₀₅7_<107> = C107

C107 = P33 · P74

P33 = 660354883413107731466749453206421_<33>

P74 = 90860235166103760559298389079671871752970399872818769276787670766575373867_<74>

Number: n
N=60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
  ( 107 digits)
SNFS difficulty: 106 digits.
Divisors found:
 r1=660354883413107731466749453206421 (pp33)
 r2=90860235166103760559298389079671871752970399872818769276787670766575373867 (pp74)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.81 hours.
Scaled time: 0.97 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_6_0_105_7
n: 60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
type: snfs
skew: 0.65
deg: 5
c5: 60
c0: 7
m: 1000000000000000000000
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:41538, AFBsize:41547, largePrimes:2680462 encountered
Relations: rels:2220524, finalFF:111084
Max relations in full relation-set: 28
Initial matrix: 83152 x 111084 with sparse part having weight 5499964.
Pruned matrix : 67479 x 67958 with weight 2313666.
Total sieving time: 0.68 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.04 hours.
Total square root time: 0.04 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,106,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.4,2.4,50000
total time: 0.81 hours.
 --------- CPU info (if available) ----------

6·10¹¹²+7 = 6(0)₁₁₁7_<113> = 43 · C112

C112 = P29 · P32 · P52

P29 = 42037675529382231904791550999_<29>

P32 = 14936485810428385363892834492251_<32>

P52 = 2222264100043128899370105966054617650050692155163401_<52>

N = 6*10^112+7 : c112

prp29 factor: 42037675529382231904791550999
prp32 factor: 14936485810428385363892834492251
prp52 factor: 2222264100043128899370105966054617650050692155163401

GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM]
Input number is 1395348837209302325581395348837209302325581395348837209302325581395348837209302325581395348837209302325581395349 (112 digits)
Using B1=87500, B2=26096911, polynomial x^2, sigma=730686625
Step 1 took 1203ms
Step 2 took 953ms
********** Factor found in step 2: 42037675529382231904791550999
Found probable prime factor of 29 digits: 42037675529382231904791550999
Composite cofactor 33192816197318600608605463828793223988644935250050070386447688396465987039773305651 has 83 digits

Thu Oct 11 14:51:32 2007  
Thu Oct 11 14:51:32 2007  
Thu Oct 11 14:51:32 2007  Msieve v. 1.28
Thu Oct 11 14:51:32 2007  random seeds: 409cfc00 e37a735e
Thu Oct 11 14:51:32 2007  factoring 33192816197318600608605463828793223988644935250050070386447688396465987039773305651 (83 digits)
Thu Oct 11 14:51:32 2007  commencing quadratic sieve (83-digit input)
Thu Oct 11 14:51:33 2007  using multiplier of 1
Thu Oct 11 14:51:33 2007  using 64kb Athlon XP sieve core
Thu Oct 11 14:51:33 2007  sieve interval: 6 blocks of size 65536
Thu Oct 11 14:51:33 2007  processing polynomials in batches of 17
Thu Oct 11 14:51:33 2007  using a sieve bound of 1369321 (52647 primes)
Thu Oct 11 14:51:33 2007  using large prime bound of 121869569 (26 bits)
Thu Oct 11 14:51:33 2007  using trial factoring cutoff of 27 bits
Thu Oct 11 14:51:33 2007  polynomial 'A' values have 10 factors
Thu Oct 11 15:25:57 2007  52751 relations (26020 full + 26731 combined from 283185 partial), need 52743
Thu Oct 11 15:25:58 2007  begin with 309205 relations
Thu Oct 11 15:25:58 2007  reduce to 76065 relations in 2 passes
Thu Oct 11 15:25:58 2007  attempting to read 76065 relations
Thu Oct 11 15:25:59 2007  recovered 76065 relations
Thu Oct 11 15:25:59 2007  recovered 69714 polynomials
Thu Oct 11 15:25:59 2007  attempting to build 52751 cycles
Thu Oct 11 15:25:59 2007  found 52751 cycles in 1 passes
Thu Oct 11 15:25:59 2007  distribution of cycle lengths:
Thu Oct 11 15:25:59 2007     length 1 : 26020
Thu Oct 11 15:25:59 2007     length 2 : 26731
Thu Oct 11 15:25:59 2007  largest cycle: 2 relations
Thu Oct 11 15:25:59 2007  matrix is 52647 x 52751 with weight 1646722 (avg 31.22/col)
Thu Oct 11 15:26:00 2007  filtering completed in 4 passes
Thu Oct 11 15:26:00 2007  matrix is 46089 x 46153 with weight 1415834 (avg 30.68/col)
Thu Oct 11 15:26:00 2007  saving the first 48 matrix rows for later
Thu Oct 11 15:26:01 2007  matrix is 46041 x 46153 with weight 1132687 (avg 24.54/col)
Thu Oct 11 15:26:01 2007  matrix includes 64 packed rows
Thu Oct 11 15:26:01 2007  commencing Lanczos iteration
Thu Oct 11 15:27:17 2007  lanczos halted after 730 iterations
Thu Oct 11 15:27:18 2007  recovered 10 nontrivial dependencies
Thu Oct 11 15:27:18 2007  prp32 factor: 14936485810428385363892834492251
Thu Oct 11 15:27:18 2007  prp52 factor: 2222264100043128899370105966054617650050692155163401
Thu Oct 11 15:27:18 2007  elapsed time 00:35:46

(55·10¹⁶⁴-1)/9 = 6(1)₁₆₄_<165> = 13 · 863 · 19751 · C157

C157 = P46 · P112

P46 = 2039347963490980778560349082035680167389362879_<46>

P112 = 1352339114250697693044223701395926133298449563024538791688249501380572686573552852589778414243811182815085121861_<112>

Number: n
N=2757890018596357122830957296003083613878567247312881325398578877625921784561272606907739980779742968471198081644196023138538802706004178942492698464864797819
  ( 157 digits)
SNFS difficulty: 166 digits.
Divisors found:

Thu Oct 11 23:37:55 2007  prp46 factor: 2039347963490980778560349082035680167389362879
Thu Oct 11 23:37:55 2007  prp112 factor: 1352339114250697693044223701395926133298449563024538791688249501380572686573552852589778414243811182815085121861
Thu Oct 11 23:37:55 2007  elapsed time 01:27:35 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 46.45 hours.
Scaled time: 61.40 units (timescale=1.322).
Factorization parameters were as follows:
name: KA_6_1_164
n: 2757890018596357122830957296003083613878567247312881325398578877625921784561272606907739980779742968471198081644196023138538802706004178942492698464864797819
skew: 0.71
deg: 5
c5: 11
c0: -2
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2200000)
Primes: RFBsize:250150, AFBsize:250187, largePrimes:7389826 encountered
Relations: rels:6945502, finalFF:606876
Max relations in full relation-set: 28
Initial matrix: 500404 x 606876 with sparse part having weight 45655180.
Pruned matrix : 414282 x 416848 with weight 26923583.
Total sieving time: 46.18 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 46.45 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 11, 2007 (2nd)

By Yousuke Koide

10¹⁰⁰⁹+1 is divisible by 873234964696345278371172272680705837_<36>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 11, 2007

The factor table of 600...007 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Oct 10, 2007 (2nd)

By Sinkiti Sibata / PRIMO

(28·10²²⁰⁷+53)/9 is prime.

Oct 10, 2007

By Jo Yeong Uk / GGNFS

(8·10¹⁵⁹-53)/9 = (8)₁₅₈3_<159> = 480451 · 4208429 · 104033087 · 13728238483_<11> · C129

C129 = P42 · P87

P42 = 316712295015730221860570435349138324870013_<42>

P87 = 971912454296354051931961805793739631984439234627451326067513307017004518364331228609949_<87>

Number: 88883_159
N=307816623954569300455053980011477723245374843831649497265306543156045707790951139583730144537538886277612234831260348782103559337
  ( 129 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=316712295015730221860570435349138324870013 (pp42)
 r2=971912454296354051931961805793739631984439234627451326067513307017004518364331228609949 (pp87)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 36.09 hours.
Scaled time: 76.93 units (timescale=2.132).
Factorization parameters were as follows:
n: 307816623954569300455053980011477723245374843831649497265306543156045707790951139583730144537538886277612234831260348782103559337
m: 100000000000000000000000000000000
c5: 4
c0: -265
skew: 2.31
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4100001)
Primes: RFBsize:283146, AFBsize:282842, largePrimes:5712676 encountered
Relations: rels:5728756, finalFF:637907
Max relations in full relation-set: 28
Initial matrix: 566052 x 637907 with sparse part having weight 44270840.
Pruned matrix : 519131 x 522025 with weight 33004800.
Total sieving time: 34.34 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.60 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 36.09 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 9, 2007 (5th)

By Sinkiti Sibata / GGNFS

6·10¹⁶³-7 = 5(9)₁₆₂3_<164> = 30339296027748931253_<20> · C145

C145 = P50 · P96

P50 = 15909833358959093262353180001154624082529476187767_<50>

P96 = 124302573471643865966793637908816400185876720580733444177989495780776161055978026073936417281843_<96>

Number: 59993_163
N=1977633230023623206564389103658481345270454210925237336059189627833971133619728015943405220774679827442341511985530665001766489444666368027814581
  ( 145 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=15909833358959093262353180001154624082529476187767 (pp50)
 r2=124302573471643865966793637908816400185876720580733444177989495780776161055978026073936417281843 (pp96)
Version: GGNFS-0.77.1-20060513-k8
Total time: 95.21 hours.
Scaled time: 190.23 units (timescale=1.998).
Factorization parameters were as follows:
name: 59993_163
n: 1977633230023623206564389103658481345270454210925237336059189627833971133619728015943405220774679827442341511985530665001766489444666368027814581
m: 200000000000000000000000000000000
c5: 375
c0: -14
skew: 0.52
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 5350001)
Primes: RFBsize:315948, AFBsize:315866, largePrimes:5944123 encountered
Relations: rels:6092944, finalFF:763528
Max relations in full relation-set: 28
Initial matrix: 631880 x 763528 with sparse part having weight 59643557.
Pruned matrix : 535995 x 539218 with weight 43398744.
Total sieving time: 90.70 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 4.03 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 95.21 hours.
 --------- CPU info (if available) ----------

Oct 9, 2007 (4th)

By Sinkiti Sibata / PRIMO

(8·10²⁰⁷³-11)/3 is prime.

Oct 9, 2007 (3rd)

By suberi / PRIMO

5·10²⁷³³+9 is prime.

Oct 9, 2007 (2nd)

By Jo Yeong Uk / GGNFS

(8·10¹⁵⁹-17)/9 = (8)₁₅₈7_<159> = 229 · 800509 · 4884721 · 262148354051_<12> · C133

C133 = P41 · P93

P41 = 31689588497279916590736503849012575753313_<41>

P93 = 119492948637304780639682337876688171145045603197808488844094715899024113564434226339292816029_<93>

Number: 88887_159
N=3786682370642793460441992233699759761247607307411975413165317553691947475895090384189590618511490509963186182014264349114253796254077
  ( 133 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=31689588497279916590736503849012575753313 (pp41)
 r2=119492948637304780639682337876688171145045603197808488844094715899024113564434226339292816029 (pp93)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 31.11 hours.
Scaled time: 66.71 units (timescale=2.144).
Factorization parameters were as follows:
n: 3786682370642793460441992233699759761247607307411975413165317553691947475895090384189590618511490509963186182014264349114253796254077
m: 100000000000000000000000000000000
c5: 4
c0: -85
skew: 1.84
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3800001)
Primes: RFBsize:283146, AFBsize:283447, largePrimes:5649191 encountered
Relations: rels:5661375, finalFF:639116
Max relations in full relation-set: 28
Initial matrix: 566657 x 639116 with sparse part having weight 40954229.
Pruned matrix : 512428 x 515325 with weight 29660434.
Total sieving time: 29.57 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.40 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 31.11 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 9, 2007

By Robert Backstrom / GGNFS, Msieve

4·10¹⁶²+3 = 4(0)₁₆₁3_<163> = 7 · 16111 · 898857769272037_<15> · C143

C143 = P47 · P96

P47 = 52633384675921297349532423419308829377260438229_<47>

P96 = 749699425654555588156813979006319175064153379838686656191939648186729452596767342041598941114643_<96>

Number: n
N=39459218261793484031429986564259843918054327571537121376310544925094790528770124732699157255927616425625128819829539343779063155819583908887247
  ( 143 digits)
SNFS difficulty: 162 digits.
Divisors found:

Tue Oct 09 03:46:58 2007  prp47 factor: 52633384675921297349532423419308829377260438229
Tue Oct 09 03:46:58 2007  prp96 factor: 749699425654555588156813979006319175064153379838686656191939648186729452596767342041598941114643
Tue Oct 09 03:46:58 2007  elapsed time 01:16:25 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 36.15 hours.
Scaled time: 52.53 units (timescale=1.453).
Factorization parameters were as follows:
name: KA_4_0_161_3
n: 39459218261793484031429986564259843918054327571537121376310544925094790528770124732699157255927616425625128819829539343779063155819583908887247
skew: 0.75
deg: 5
c5: 25
c0: 6
m: 200000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1900000)
Primes: RFBsize:203362, AFBsize:202562, largePrimes:7139160 encountered
Relations: rels:6577562, finalFF:434257
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 35.92 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 36.15 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Oct 8, 2007 (4th)

By Bryan Koen / GMP-ECM

(23·10¹⁷³+1)/3 = 7(6)₁₇₂7_<174> = 11 · 19 · 41 · C170

C170 = P30 · P141

P30 = 357911945978650040346202809163_<30>

P141 = 249977110919930838083661846538618118461822803550100409862996457896163981755684629971850878837293997356705743192000800069352481784564014480361_<141>

Oct 8, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(31·10²¹⁷⁷+23)/9 is prime.

Oct 8, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

(73·10¹⁵⁹-1)/9 = 8(1)₁₅₉_<160> = 2657 · 105091757 · 340002075499_<12> · C137

C137 = P68 · P69

P68 = 85748085121300963152030695599342054561573492952495448497507158243159_<68>

P69 = 996355092269813964638397829269428609707014906515819237429532829639679_<69>

Number: n
N=85435541262993683107759178811222508432637694938946198668249661730703724787996850375797180518678700584591827296195920977054636644636705961
  ( 137 digits)
SNFS difficulty: 161 digits.
Divisors found:

Mon Oct 08 11:11:00 2007  prp68 factor: 85748085121300963152030695599342054561573492952495448497507158243159
Mon Oct 08 11:11:00 2007  prp69 factor: 996355092269813964638397829269428609707014906515819237429532829639679
Mon Oct 08 11:11:01 2007  elapsed time 01:25:31 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 45.89 hours.
Scaled time: 60.85 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_8_1_159
n: 85435541262993683107759178811222508432637694938946198668249661730703724787996850375797180518678700584591827296195920977054636644636705961
skew: 0.67
deg: 5
c5: 73
c0: -10
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100000)
Primes: RFBsize:250150, AFBsize:250101, largePrimes:7499050 encountered
Relations: rels:7084336, finalFF:634136
Max relations in full relation-set: 28
Initial matrix: 500316 x 634136 with sparse part having weight 48027068.
Pruned matrix : 392586 x 395151 with weight 27479275.
Total sieving time: 45.64 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 45.89 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

6·10¹⁶⁴-7 = 5(9)₁₆₃3_<165> = 17 · 302404974167609_<15> · C150

C150 = P51 · P99

P51 = 604857162810389628774661784293336029351376392407791_<51>

P99 = 192957014318376632131120220747611805227589329088927241976832631934622388748514730334494973730320991_<99>

Number: n
N=116711432224977017360883726082633787948846053120532190717761735193932640441906310777526105200497999505680676600497638929152987804613749651905799240881
  ( 150 digits)
SNFS difficulty: 165 digits.
Divisors found:

Mon Oct 08 17:31:28 2007  prp51 factor: 604857162810389628774661784293336029351376392407791
Mon Oct 08 17:31:28 2007  prp99 factor: 192957014318376632131120220747611805227589329088927241976832631934622388748514730334494973730320991
Mon Oct 08 17:31:28 2007  elapsed time 01:42:50 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 53.19 hours.
Scaled time: 63.34 units (timescale=1.191).
Factorization parameters were as follows:
name: KA_5_9_163_3
n: 116711432224977017360883726082633787948846053120532190717761735193932640441906310777526105200497999505680676600497638929152987804613749651905799240881
skew: 1.63
deg: 5
c5: 3
c0: -35
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2600000)
Primes: RFBsize:216816, AFBsize:216606, largePrimes:7376363 encountered
Relations: rels:6846162, finalFF:475104
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 52.94 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 53.19 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 8, 2007

By Jo Yeong Uk / GGNFS

(5·10¹⁵⁹-41)/9 = (5)₁₅₈1_<159> = 203232471011_<12> · 30634761442301959_<17> · C131

C131 = P66 · P66

P66 = 140302918730839359783997803266247889954113331203299846460516096197_<66>

P66 = 635994249340914371879827621457572197377938193794948288296614712167_<66>

Number: 55551_159
N=89231849478559493177495087019280828859221907790013794337807829144866668300309536154113542379040143520122806007729736339743638328899
  ( 131 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=140302918730839359783997803266247889954113331203299846460516096197 (pp66)
 r2=635994249340914371879827621457572197377938193794948288296614712167 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 27.76 hours.
Scaled time: 59.39 units (timescale=2.139).
Factorization parameters were as follows:
n: 89231849478559493177495087019280828859221907790013794337807829144866668300309536154113542379040143520122806007729736339743638328899
m: 100000000000000000000000000000000
c5: 1
c0: -82
skew: 2.41
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:282833, largePrimes:5618340 encountered
Relations: rels:5637592, finalFF:646613
Max relations in full relation-set: 28
Initial matrix: 566045 x 646613 with sparse part having weight 40570327.
Pruned matrix : 501999 x 504893 with weight 27943297.
Total sieving time: 26.39 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.23 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 27.76 hours.
 --------- CPU info (if available) ----------

Oct 7, 2007 (5th)

By Sinkiti Sibata / PRIMO

(17·10²⁰⁶⁸-53)/9 is prime.

Oct 7, 2007 (4th)

By Yousuke Koide

10¹⁰⁰⁷+1 is divisible by 80130271534233515728987750894609_<32>

10¹⁰⁵⁴+1 is divisible by 111276132074930025328712302045364981_<36>

10¹⁶⁰⁵+1 is divisible by 4298338634928851216299618775086771_<34>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 7, 2007 (3rd)

By Sinkiti Sibata / GGNFS

6·10¹⁶¹-7 = 5(9)₁₆₀3_<162> = 59 · 4889 · 22063 · 61949 · 56338169 · 5137570679_<10> · C130

C130 = P32 · P99

P32 = 25632208522320555148392302355173_<32>

P99 = 205132168410612051871480238620927190554253620898540807301677670565578241342961193951890988344739443_<99>

Number: 59993_161
N=5257990515336585603900960324981397066212063936330995720178877708548412575128763722465208456773985220196118351156898540333928188639
  ( 130 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=25632208522320555148392302355173 (pp32)
 r2=205132168410612051871480238620927190554253620898540807301677670565578241342961193951890988344739443 (pp99)
Version: GGNFS-0.77.1-20060513-k8
Total time: 67.83 hours.
Scaled time: 134.98 units (timescale=1.990).
Factorization parameters were as follows:
name: 59993_161
n: 5257990515336585603900960324981397066212063936330995720178877708548412575128763722465208456773985220196118351156898540333928188639
m: 100000000000000000000000000000000
c5: 60
c0: -7
skew: 0.65
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4350001)
Primes: RFBsize:315948, AFBsize:316366, largePrimes:5776158 encountered
Relations: rels:5879966, finalFF:735887
Max relations in full relation-set: 28
Initial matrix: 632381 x 735887 with sparse part having weight 44476895.
Pruned matrix : 553498 x 556723 with weight 31162467.
Total sieving time: 64.08 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.36 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 67.83 hours.
 --------- CPU info (if available) ----------

Oct 7, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM

10¹⁹²+9 = 1(0)₁₉₁9_<193> = C193

C193 = P48 · P145

P48 = 325208379747671632800443572929049811907718391209_<48>

P145 = 3074951515012920315894112276452006313835272802228418099697777887803931547784516799444634005241238767287033369894773351997005678938044816110863201_<145>

Oct 7, 2007

By suberi / PRIMO

(13·10²⁰⁷⁹-7)/3 is prime.

(13·10²¹²⁰-7)/3 is prime.

(13·10²²⁶⁰-7)/3 is prime.

(13·10²⁴²³-7)/3 is prime.

Oct 6, 2007 (4th)

By Jo Yeong Uk / GGNFS

(4·10¹⁵⁹+41)/9 = (4)₁₅₈9_<159> = 3709 · 3456197 · 40995079027450649_<17> · C132

C132 = P48 · P85

P48 = 218551920024031168927773697661809538745109102567_<48>

P85 = 3869686706115428835860198962763376764473465747888783930870949253002451781545174371711_<85>

Number: 44449_159
N=845727459512995808632831376766004857195411667709864917200855795181161872981252627569069291871505578807711339836312388193111282282137
  ( 132 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=218551920024031168927773697661809538745109102567 (pp48)
 r2=3869686706115428835860198962763376764473465747888783930870949253002451781545174371711 (pp85)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 27.95 hours.
Scaled time: 59.92 units (timescale=2.144).
Factorization parameters were as follows:
n: 845727459512995808632831376766004857195411667709864917200855795181161872981252627569069291871505578807711339836312388193111282282137
m: 100000000000000000000000000000000
c5: 2
c0: 205
skew: 2.52
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:283793, largePrimes:5629726 encountered
Relations: rels:5660465, finalFF:657003
Max relations in full relation-set: 28
Initial matrix: 567004 x 657003 with sparse part having weight 41479342.
Pruned matrix : 495662 x 498561 with weight 28049677.
Total sieving time: 26.61 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 27.95 hours.
 --------- CPU info (if available) ----------

Oct 6, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

2·10¹⁶¹+3 = 2(0)₁₆₀3_<162> = 1645747984609139286241_<22> · C141

C141 = P44 · P97

P44 = 23143371269685496536153160328427093498540901_<44>

P97 = 5250976096680145607463471043357442149484478476541758912748098433643075952275139383190561991897383_<97>

Number: n
N=121525289333712574060203929849274253650679147008067862136662858454750139437642287196603579159652285468795971038414619211834083134495020362083
  ( 141 digits)
SNFS difficulty: 161 digits.
Divisors found:

Sat Oct 06 11:57:55 2007  prp44 factor: 23143371269685496536153160328427093498540901
Sat Oct 06 11:57:55 2007  prp97 factor: 5250976096680145607463471043357442149484478476541758912748098433643075952275139383190561991897383
Sat Oct 06 11:57:55 2007  elapsed time 01:40:44 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 43.82 hours.
Scaled time: 63.63 units (timescale=1.452).
Factorization parameters were as follows:
name: KA_2_0_160_3
n: 121525289333712574060203929849274253650679147008067862136662858454750139437642287196603579159652285468795971038414619211834083134495020362083
skew: 0.68
deg: 5
c5: 20
c0: 3
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300000)
Primes: RFBsize:203362, AFBsize:203062, largePrimes:7438144 encountered
Relations: rels:6924431, finalFF:458969
Max relations in full relation-set: 28
Initial matrix: 406490 x 458969 with sparse part having weight 41917861.
Pruned matrix : 379962 x 382058 with weight 31649775.
Total sieving time: 43.56 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 43.82 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

2·10¹⁶⁰-9 = 1(9)₁₅₉1_<161> = 158642813009799873789292199_<27> · C135

C135 = P48 · P87

P48 = 514829968216555250825419476063055331353216130401_<48>

P87 = 244875747315362559771904473968778705005860870814895857896156971504755878896463497536209_<87>

Number: n
N=126069373207373321436708046654043582257956838503880528523913166513739523221993375991519276144852178818516438085011957703665140363189809
  ( 135 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=514829968216555250825419476063055331353216130401 (pp48)
 r2=244875747315362559771904473968778705005860870814895857896156971504755878896463497536209 (pp87)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 39.32 hours.
Scaled time: 46.99 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_1_9_159_1
n: 126069373207373321436708046654043582257956838503880528523913166513739523221993375991519276144852178818516438085011957703665140363189809
type: snfs
skew: 1.35
deg: 5
c5: 2
c0: -9
m: 100000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1600001)
Primes: RFBsize:230209, AFBsize:230337, largePrimes:6544960 encountered
Relations: rels:6024747, finalFF:519640
Max relations in full relation-set: 28
Initial matrix: 460611 x 519640 with sparse part having weight 28682777.
Pruned matrix : 405415 x 407782 with weight 18445497.
Total sieving time: 35.33 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.68 hours.
Total square root time: 0.09 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 39.32 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Oct 6, 2007 (2nd)

By Sinkiti Sibata / GGNFS

6·10¹⁶⁰-7 = 5(9)₁₅₉3_<161> = 110893837864780114169227_<24> · 53482456690377432712639319435401_<32> · C107

C107 = P51 · P56

P51 = 125543951754463483312651367167081146619879782542807_<51>

P56 = 80581749745901679359607613279455998414547734638470247237_<56>

Number: 59993_160
N=10116551302389730489061629792753496443305947169260756466085450095805957750759395081955491468661781825974259
  ( 107 digits)
Divisors found:
 r1=125543951754463483312651367167081146619879782542807 (pp51)
 r2=80581749745901679359607613279455998414547734638470247237 (pp56)
Version: GGNFS-0.77.1-20060513-k8
Total time: 16.09 hours.
Scaled time: 31.66 units (timescale=1.968).
Factorization parameters were as follows:
name: 59993_160
n: 10116551302389730489061629792753496443305947169260756466085450095805957750759395081955491468661781825974259
skew: 8717.48
# norm 7.18e+14
c5: 34200
c4: 3446830450
c3: -49450344917839
c2: -282207816974048745
c1: 293743109705688382953
c0: -105852972657943776101076
# alpha -6.04
Y1: 1982489113
Y0: -196879813041941649923
# Murphy_E 1.63e-09
# M 8200850302644055184453131829831345367830490194178486463399401491964831823878780279463907218481306105711361
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2300001)
Primes: RFBsize:183072, AFBsize:182207, largePrimes:4770558 encountered
Relations: rels:5287342, finalFF:797494
Max relations in full relation-set: 28
Initial matrix: 365359 x 797494 with sparse part having weight 66842766.
Pruned matrix : 198399 x 200289 with weight 27225588.
Total sieving time: 15.17 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.58 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 16.09 hours.
 --------- CPU info (if available) ----------

6·10¹⁴⁸-7 = 5(9)₁₄₇3_<149> = 17 · 5261 · 7069 · 20877877 · 4124979457_<10> · C124

C124 = P46 · P78

P46 = 2202754157836179317307651152968047629805882079_<46>

P78 = 500267040879752050179524392513061490125276212618093746534715313369595549802451_<78>

Number: 59993_148
N=1101965304326275718376569832258079442992217073921951287705392731002575698336321117095630581548488817660192266002626251175629
  ( 124 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=2202754157836179317307651152968047629805882079 (pp46)
 r2=500267040879752050179524392513061490125276212618093746534715313369595549802451 (pp78)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 38.13 hours.
Scaled time: 25.82 units (timescale=0.677).
Factorization parameters were as follows:
name: 59993_148
n: 1101965304326275718376569832258079442992217073921951287705392731002575698336321117095630581548488817660192266002626251175629
m: 200000000000000000000000000000
c5: 375
c0: -14
skew: 0.52
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 4550001)
Primes: RFBsize:114155, AFBsize:114432, largePrimes:3074783 encountered
Relations: rels:3142613, finalFF:260671
Max relations in full relation-set: 28
Initial matrix: 228653 x 260671 with sparse part having weight 33256669.
Pruned matrix : 220290 x 221497 with weight 26947508.
Total sieving time: 35.67 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 2.06 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 38.13 hours.
 --------- CPU info (if available) ----------

Oct 6, 2007

By Bryan Koen / GGNFS

(61·10¹⁶⁹-7)/9 = 6(7)₁₆₉_<170> = 679517 · 2099650316119_<13> · 462133680259364512974037301324911_<33> · C120

C120 = P38 · P82

P38 = 56540095809527061398275309610361450221_<38>

P82 = 1818092044741429958746153841013907596909769895723120119363711217697392274661650529_<82>

Number: 67777_169
N=102795098400219410634465090516194534805474053557213593780153631997610268197607479386423556429973192979895429973931816909
  ( 120 digits)
Divisors found:
 r1=56540095809527061398275309610361450221 (pp38)
 r2=1818092044741429958746153841013907596909769895723120119363711217697392274661650529 (pp82)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 57.70 hours.
Scaled time: 129.60 units (timescale=2.246).
Factorization parameters were as follows:
name: 67777_169
n: 102795098400219410634465090516194534805474053557213593780153631997610268197607479386423556429973192979895429973931816909
skew: 105558.47
# norm 5.86e+015
c5: 3420
c4: -855817826
c3: -172975041238792
c2: 10097144255620342185
c1: 454824918396171751978112
c0: 4817673992078805183239899869
# alpha -4.79
Y1: 1203809206333
Y0: -124620494456053891335838
# Murphy_E 3.13e-010
# M 19860790920966959294374370574608201829699352757127470678651745225926909610626249915480516469649586859101696560082650191
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4350001)
Primes: RFBsize:315948, AFBsize:316478, largePrimes:7651281 encountered
Relations: rels:7683310, finalFF:711142
Max relations in full relation-set: 28
Initial matrix: 632504 x 711142 with sparse part having weight 59334766.
Pruned matrix : 568876 x 572102 with weight 42656010.
Total sieving time: 48.21 hours.
Total relation processing time: 0.50 hours.
Matrix solve time: 8.60 hours.
Time per square root: 0.39 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 57.70 hours.
 --------- CPU info (if available) ----------

Oct 5, 2007 (4th)

By Jo Yeong Uk / PRIMO

(55·10²⁰¹⁵+17)/9 is prime.

Oct 5, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

6·10¹⁵¹-7 = 5(9)₁₅₀3_<152> = 38049083 · C145

C145 = P45 · P100

P45 = 163890451242523530323685961374784914589069397_<45>

P100 = 9621735296463067319406359609200658570446718765888423723850749029550679811036943776234172558145948143_<100>

Number: n
N=1576910539473448019759109569079496607053578663117847018809888269843454571559582658010444036193986593579666558586970413978176556843695812590279771
  ( 145 digits)
SNFS difficulty: 151 digits.
Divisors found:

Fri Oct 05 09:28:44 2007  prp45 factor: 163890451242523530323685961374784914589069397
Fri Oct 05 09:28:44 2007  prp100 factor: 9621735296463067319406359609200658570446718765888423723850749029550679811036943776234172558145948143
Fri Oct 05 09:28:44 2007  elapsed time 00:54:09 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.99 hours.
Scaled time: 26.51 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_5_9_150_3
n: 1576910539473448019759109569079496607053578663117847018809888269843454571559582658010444036193986593579666558586970413978176556843695812590279771
skew: 0.65
deg: 5
c5: 60
c0: -7
m: 1000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 900000)
Primes: RFBsize:216816, AFBsize:216901, largePrimes:6806958 encountered
Relations: rels:6383461, finalFF:576223
Max relations in full relation-set: 28
Initial matrix: 433784 x 576223 with sparse part having weight 36816750.
Pruned matrix : 309229 x 311461 with weight 17215851.
Total sieving time: 19.80 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 19.99 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 5, 2007 (2nd)

By Jo Yeong Uk / Msieve, GGNFS, GMP-ECM

6·10¹⁵⁹-7 = 5(9)₁₅₈3_<160> = 13 · 46099251251888935727327_<23> · 24879066220185916328457524320554279793687_<41> · C96

C96 = P41 · P56

P41 = 17014311483120697384989356382969398497597_<41>

P56 = 23651874787979709585009977994193399030605069949949286937_<56>

Thu Oct  4 21:37:14 2007  
Thu Oct  4 21:37:14 2007  
Thu Oct  4 21:37:14 2007  Msieve v. 1.28
Thu Oct  4 21:37:14 2007  random seeds: 1a77d3d5 9d0329b9
Thu Oct  4 21:37:14 2007  factoring 402420364802456082600245272138853200856277707189366407172983739323623291446802112677069257990389 (96 digits)
Thu Oct  4 21:37:14 2007  commencing quadratic sieve (96-digit input)
Thu Oct  4 21:37:14 2007  using multiplier of 1
Thu Oct  4 21:37:14 2007  using 32kb Intel Core sieve core
Thu Oct  4 21:37:14 2007  sieve interval: 36 blocks of size 32768
Thu Oct  4 21:37:14 2007  processing polynomials in batches of 6
Thu Oct  4 21:37:14 2007  using a sieve bound of 2248781 (83529 primes)
Thu Oct  4 21:37:14 2007  using large prime bound of 337317150 (28 bits)
Thu Oct  4 21:37:14 2007  using double large prime bound of 2241140878991550 (43-51 bits)
Thu Oct  4 21:37:14 2007  using trial factoring cutoff of 51 bits
Thu Oct  4 21:37:14 2007  polynomial 'A' values have 12 factors
Fri Oct  5 02:05:05 2007  83793 relations (19127 full + 64666 combined from 1276886 partial), need 83625
Fri Oct  5 02:05:06 2007  begin with 1296013 relations
Fri Oct  5 02:05:07 2007  reduce to 225145 relations in 12 passes
Fri Oct  5 02:05:07 2007  attempting to read 225145 relations
Fri Oct  5 02:05:08 2007  recovered 225145 relations
Fri Oct  5 02:05:08 2007  recovered 213597 polynomials
Fri Oct  5 02:05:09 2007  attempting to build 83793 cycles
Fri Oct  5 02:05:09 2007  found 83793 cycles in 6 passes
Fri Oct  5 02:05:09 2007  distribution of cycle lengths:
Fri Oct  5 02:05:09 2007     length 1 : 19127
Fri Oct  5 02:05:09 2007     length 2 : 13665
Fri Oct  5 02:05:09 2007     length 3 : 13753
Fri Oct  5 02:05:09 2007     length 4 : 11694
Fri Oct  5 02:05:09 2007     length 5 : 8929
Fri Oct  5 02:05:09 2007     length 6 : 6357
Fri Oct  5 02:05:09 2007     length 7 : 4300
Fri Oct  5 02:05:09 2007     length 9+: 5968
Fri Oct  5 02:05:09 2007  largest cycle: 20 relations
Fri Oct  5 02:05:09 2007  matrix is 83529 x 83793 with weight 5817253 (avg 69.42/col)
Fri Oct  5 02:05:10 2007  filtering completed in 4 passes
Fri Oct  5 02:05:10 2007  matrix is 80599 x 80663 with weight 5617583 (avg 69.64/col)
Fri Oct  5 02:05:11 2007  saving the first 48 matrix rows for later
Fri Oct  5 02:05:11 2007  matrix is 80551 x 80663 with weight 4705622 (avg 58.34/col)
Fri Oct  5 02:05:11 2007  matrix includes 64 packed rows
Fri Oct  5 02:05:11 2007  using block size 32265 for processor cache size 4096 kB
Fri Oct  5 02:05:14 2007  commencing Lanczos iteration
Fri Oct  5 02:05:49 2007  lanczos halted after 1276 iterations
Fri Oct  5 02:05:49 2007  recovered 17 nontrivial dependencies
Fri Oct  5 02:05:50 2007  prp41 factor: 17014311483120697384989356382969398497597
Fri Oct  5 02:05:50 2007  prp56 factor: 23651874787979709585009977994193399030605069949949286937
Fri Oct  5 02:05:50 2007  elapsed time 04:28:36

(5·10¹⁶¹-23)/9 = (5)₁₆₀3_<161> = 181 · 9377 · 59980747 · 1556391950309252260727_<22> · C126

C126 = P30 · P97

P30 = 204200339305081254682089876323_<30>

P97 = 1717108343637436044836379289726170911481645229487158423846189656851215623920488863042590355402187_<97>

6·10¹⁸⁵-7 = 5(9)₁₈₄3_<186> = 1259 · 105094819 · 18234595094684519_<17> · 496645177774564607081_<21> · 91097916289552225379407273_<26> · C112

C112 = P43 · P70

P43 = 1567828725851495950483147060696472797473131_<43>

P70 = 3505861909643653215337674382799814173297028903124851463841838321295469_<70>

Number: 59993_185
N=5496591010807901243959700004966756355343953965432332097077840850790392390952200017975624837864532764649639543439
  ( 112 digits)
Divisors found:
 r1=1567828725851495950483147060696472797473131 (pp43)
 r2=3505861909643653215337674382799814173297028903124851463841838321295469 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 17.45 hours.
Scaled time: 37.14 units (timescale=2.129).
Factorization parameters were as follows:
name: 59993_185
n: 5496591010807901243959700004966756355343953965432332097077840850790392390952200017975624837864532764649639543439
skew: 31918.14
# norm 4.35e+15
c5: 49500
c4: 1148015948
c3: -102222124732255
c2: -6099585714717477637
c1: 33741417547897847981555
c0: 598316031826581667570223049
# alpha -6.53
Y1: 598253464301
Y0: -2565057913790794214018
# Murphy_E 7.81e-10
# M 3628664822376311219602672466853507363069765951502221673628741042021637214537904922189021557595578069943077896990
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1400000, 2240001)
Primes: RFBsize:203362, AFBsize:203437, largePrimes:7582629 encountered
Relations: rels:7467623, finalFF:565840
Max relations in full relation-set: 28
Initial matrix: 406880 x 565840 with sparse part having weight 52660477.
Pruned matrix : 291699 x 293797 with weight 29738311.
Polynomial selection time: 0.94 hours.
Total sieving time: 15.79 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.47 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000
total time: 17.45 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Oct 5, 2007

By Sinkiti Sibata / GGNFS

6·10¹⁴²-7 = 5(9)₁₄₁3_<143> = 353 · 85223 · 1064743 · 17170804432778660568577_<23> · C108

C108 = P32 · P76

P32 = 42191759522915775604583057626823_<32>

P76 = 2585572109501371476246882696300039865583164290410873961325438433783561473999_<76>

Number: 59993_142
N=109089836673239920516770319965068209364823641145718230527163887975622905277416393899382401902254788759475177
  ( 108 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=42191759522915775604583057626823 (pp32)
 r2=2585572109501371476246882696300039865583164290410873961325438433783561473999 (pp76)
Version: GGNFS-0.77.1-20060513-k8
Total time: 17.01 hours.
Scaled time: 34.09 units (timescale=2.004).
Factorization parameters were as follows:
name: 59993_142
n: 109089836673239920516770319965068209364823641145718230527163887975622905277416393899382401902254788759475177
m: 10000000000000000000000000000
c5: 600
c0: -7
skew: 0.41
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2550001)
Primes: RFBsize:100021, AFBsize:99733, largePrimes:2907987 encountered
Relations: rels:2943976, finalFF:268434
Max relations in full relation-set: 28
Initial matrix: 199820 x 268434 with sparse part having weight 31091401.
Pruned matrix : 182446 x 183509 with weight 19802614.
Total sieving time: 16.40 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 17.01 hours.
 --------- CPU info (if available) ----------

6·10¹⁵²-7 = 5(9)₁₅₁3_<153> = 19 · 79 · 317 · 683 · 194723 · C139

C139 = P61 · P79

P61 = 2422519199645591483038400362598333261141854085321449290981587_<61>

P79 = 3913867442685506786621678329983313608259562954908441460080566565534765765237163_<79>

Number: 59993_152
N=9481419024773431796374859861929423222068324195372690108617292629460624268055670298332904077189122625243218702260577584276221851166121117681
  ( 139 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=2422519199645591483038400362598333261141854085321449290981587 (pp61)
 r2=3913867442685506786621678329983313608259562954908441460080566565534765765237163 (pp79)
Version: GGNFS-0.77.1-20060513-k8
Total time: 30.48 hours.
Scaled time: 59.79 units (timescale=1.962).
Factorization parameters were as follows:
name: 59993_152
n: 9481419024773431796374859861929423222068324195372690108617292629460624268055670298332904077189122625243218702260577584276221851166121117681
m: 1000000000000000000000000000000
c5: 600
c0: -7
skew: 0.41
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2300001)
Primes: RFBsize:176302, AFBsize:175743, largePrimes:5726784 encountered
Relations: rels:5711566, finalFF:522112
Max relations in full relation-set: 28
Initial matrix: 352111 x 522112 with sparse part having weight 50262752.
Pruned matrix : 292470 x 294294 with weight 27860308.
Total sieving time: 28.94 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.25 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 30.48 hours.
 --------- CPU info (if available) ----------

Oct 4, 2007 (10th)

By Jo Yeong Uk / GGNFS

6·10¹⁴⁵-7 = 5(9)₁₄₄3_<146> = 1766550377_<10> · 157012037513_<12> · 4348276733443_<13> · C113

C113 = P36 · P78

P36 = 208622310195879907337278472254444759_<36>

P78 = 238459345830976112102219160803088310324167412809493635059788300420093626611189_<78>

Number: 59993_145
N=49747939615056500626663559867471926285149195969519260672945306537946404080535869032470347651193685603727971808451
  ( 113 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=208622310195879907337278472254444759 (pp36)
 r2=238459345830976112102219160803088310324167412809493635059788300420093626611189 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.31 hours.
Scaled time: 21.94 units (timescale=2.128).
Factorization parameters were as follows:
n: 49747939615056500626663559867471926285149195969519260672945306537946404080535869032470347651193685603727971808451
m: 100000000000000000000000000000
c5: 6
c0: -7
skew: 1.03
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1450001)
Primes: RFBsize:114155, AFBsize:114412, largePrimes:3499162 encountered
Relations: rels:3558668, finalFF:328093
Max relations in full relation-set: 28
Initial matrix: 228633 x 328093 with sparse part having weight 33496163.
Pruned matrix : 202020 x 203227 with weight 17855809.
Total sieving time: 10.03 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 10.31 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Oct 4, 2007 (9th)

By Robert Backstrom / GGNFS, Msieve

(17·10¹⁶¹-71)/9 = 1(8)₁₆₀1_<162> = 7 · 11 · 523 · 12553 · 892039002817_<12> · C141

C141 = P70 · P71

P70 = 5517382888130356012700422947230695246102802588279510829603153154612691_<70>

P71 = 75918829205014441614543498027493064480460216213141344861042989326442621_<71>

Number: n
N=418873249142637799821007491061910714467071107673848593381389819578321584166718844538758955967710943384855248756160831082732301629584089903111
  ( 141 digits)
SNFS difficulty: 162 digits.
Divisors found:

Thu Oct 04 19:17:06 2007  prp70 factor: 5517382888130356012700422947230695246102802588279510829603153154612691
Thu Oct 04 19:17:06 2007  prp71 factor: 75918829205014441614543498027493064480460216213141344861042989326442621
Thu Oct 04 19:17:06 2007  elapsed time 01:24:27 (Msieve 1.26)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 56.52 hours.
Scaled time: 73.71 units (timescale=1.304).
Factorization parameters were as follows:
name: KA_1_8_160_1
n: 418873249142637799821007491061910714467071107673848593381389819578321584166718844538758955967710943384855248756160831082732301629584089903111
skew: 0.84
deg: 5
c5: 170
c0: -71
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300000)
Primes: RFBsize:216816, AFBsize:216842, largePrimes:7378545 encountered
Relations: rels:6867652, finalFF:491420
Max relations in full relation-set: 28
Initial matrix: 433725 x 491420 with sparse part having weight 41722542.
Pruned matrix : 394644 x 396876 with weight 30589920.
Total sieving time: 55.53 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.74 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 56.52 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 4, 2007 (8th)

By Sinkiti Sibata / GGNFS

6·10¹³²-7 = 5(9)₁₃₁3_<133> = 17 · 31397 · 60607 · 17658261422573_<14> · C110

C110 = P45 · P65

P45 = 157220545256202605499721340161299887750890477_<45>

P65 = 66808873437291415726408144788722762650560407722248850407211168531_<65>

Number: 59993_132
N=10503727509763587149462644038115572609411003558019047308296016303974338616397089884714139804160694574969979287
  ( 110 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=157220545256202605499721340161299887750890477 (pp45)
 r2=66808873437291415726408144788722762650560407722248850407211168531 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 8.23 hours.
Scaled time: 5.57 units (timescale=0.677).
Factorization parameters were as follows:
name: 59993_132
n: 10503727509763587149462644038115572609411003558019047308296016303974338616397089884714139804160694574969979287
m: 100000000000000000000000000
c5: 600
c0: -7
skew: 0.41
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1300001)
Primes: RFBsize:63951, AFBsize:63523, largePrimes:1546399 encountered
Relations: rels:1543966, finalFF:157068
Max relations in full relation-set: 28
Initial matrix: 127540 x 157068 with sparse part having weight 14736218.
Pruned matrix : 120366 x 121067 with weight 9730311.
Total sieving time: 7.77 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 8.23 hours.
 --------- CPU info (if available) ----------

Oct 4, 2007 (7th)

By Jo Yeong Uk / GMP-ECM

6·10¹⁵⁹-7 = 5(9)₁₅₈3_<160> = 13 · 46099251251888935727327_<23> · C137

C137 = P41 · C96

P41 = 24879066220185916328457524320554279793687_<41>

C96 = [402420364802456082600245272138853200856277707189366407172983739323623291446802112677069257990389_<96>]

Oct 4, 2007 (6th)

By Sinkiti Sibata / GGNFS

6·10¹³⁵-7 = 5(9)₁₃₄3_<136> = 13 · 414413481743_<12> · 36564792200396563_<17> · C107

C107 = P43 · P65

P43 = 1126059761985818701739729351936313997694323_<43>

P65 = 27048891575232108774848633209666793723302095208678124558846257723_<65>

Number: 59993_135
N=30458668409186085102726075004708104994463090774955003534458454777954452719667825900945750528186059032006529
  ( 107 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=1126059761985818701739729351936313997694323 (pp43)
 r2=27048891575232108774848633209666793723302095208678124558846257723 (pp65)
Version: GGNFS-0.77.1-20060513-k8
Total time: 7.79 hours.
Scaled time: 15.48 units (timescale=1.986).
Factorization parameters were as follows:
name: 59993_135
n: 30458668409186085102726075004708104994463090774955003534458454777954452719667825900945750528186059032006529
m: 1000000000000000000000000000
c5: 6
c0: -7
skew: 1.03
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1375001)
Primes: RFBsize:78498, AFBsize:63888, largePrimes:1589402 encountered
Relations: rels:1605693, finalFF:183280
Max relations in full relation-set: 28
Initial matrix: 142452 x 183280 with sparse part having weight 16657071.
Pruned matrix : 130634 x 131410 with weight 10249543.
Total sieving time: 7.56 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 7.79 hours.
 --------- CPU info (if available) ----------

Oct 4, 2007 (5th)

By Robert Backstrom / GGNFS, Msieve

(73·10¹⁵⁸-1)/9 = 8(1)₁₅₈_<159> = 26530558669965200379377507_<26> · C134

C134 = P54 · P81

P54 = 212107814191998704725420221052699981457889085100997601_<54>

P81 = 144137600146936537044461384043301075248536512091523845543692062426638973343118573_<81>

Number: n
N=30572711310047020199673079420220032560072723217483618025140594148989783940701088253778438397676150664410526395099842238233630731543373
  ( 134 digits)
SNFS difficulty: 159 digits.
Divisors found:

Thu Oct 04 16:13:30 2007  prp54 factor: 212107814191998704725420221052699981457889085100997601
Thu Oct 04 16:13:30 2007  prp81 factor: 144137600146936537044461384043301075248536512091523845543692062426638973343118573
Thu Oct 04 16:13:30 2007  elapsed time 01:50:08 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 50.48 hours.
Scaled time: 60.38 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_8_1_158
n: 30572711310047020199673079420220032560072723217483618025140594148989783940701088253778438397676150664410526395099842238233630731543373
type: snfs
skew: 0.11
deg: 5
c5: 73000
c0: -1
m: 10000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100000)
Primes: RFBsize:230209, AFBsize:230497, largePrimes:7060727 encountered
Relations: rels:6539168, finalFF:541829
Max relations in full relation-set: 28
Initial matrix: 460773 x 541829 with sparse part having weight 34927383.
Pruned matrix : 393656 x 396023 with weight 22051476.
Total sieving time: 50.21 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 50.48 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Oct 4, 2007 (4th)

By Jo Yeong Uk / PRIMO

(38·10²⁰⁴³+61)/9 is prime.

Oct 4, 2007 (3rd)

By Jo Yeong Uk / GGNFS, GMP-ECM

6·10¹³¹-7 = 5(9)₁₃₀3_<132> = 53 · 169607 · C125

C125 = P59 · P67

P59 = 12872498163753083570298872692434111691304047437203023579603_<59>

P67 = 5185238891853061753866196726218370889062130742679403097113868915761_<67>

Number: 59993_131
N=66746978113999611310097449475596804199185887107943546740850741408746145779182529734944412560401843507037523259931310684822883
  ( 125 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=12872498163753083570298872692434111691304047437203023579603 (pp59)
 r2=5185238891853061753866196726218370889062130742679403097113868915761 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.84 hours.
Scaled time: 6.06 units (timescale=2.135).
Factorization parameters were as follows:
n: 66746978113999611310097449475596804199185887107943546740850741408746145779182529734944412560401843507037523259931310684822883
m: 100000000000000000000000000
c5: 60
c0: -7
skew: 0.65
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 1100001)
Primes: RFBsize:78498, AFBsize:78436, largePrimes:1617139 encountered
Relations: rels:1662134, finalFF:216620
Max relations in full relation-set: 28
Initial matrix: 157001 x 216620 with sparse part having weight 13625699.
Pruned matrix : 135783 x 136632 with weight 6867620.
Total sieving time: 2.75 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 2.84 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

(86·10¹⁵⁸+31)/9 = 9(5)₁₅₇9_<159> = 7² · 1657 · 48530561 · 369122094120620012071_<21> · C126

C126 = P49 · P78

P49 = 3016236812826278990601156748919149544847529142617_<49>

P78 = 217814388128186210847141219564082430746842862444289701637257172552121621783169_<78>

Number: 95559_158
N=656979775835466476708907333677417137270421517155228763448205475015038680910810608163311078289165054665585517079132773251213273
  ( 126 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=3016236812826278990601156748919149544847529142617 (pp49)
 r2=217814388128186210847141219564082430746842862444289701637257172552121621783169 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 36.34 hours.
Scaled time: 76.82 units (timescale=2.114).
Factorization parameters were as follows:
n: 656979775835466476708907333677417137270421517155228763448205475015038680910810608163311078289165054665585517079132773251213273
m: 100000000000000000000000000000000
c5: 43
c0: 1550
skew: 2.05
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4100001)
Primes: RFBsize:283146, AFBsize:282493, largePrimes:5699146 encountered
Relations: rels:5718310, finalFF:642706
Max relations in full relation-set: 28
Initial matrix: 565705 x 642706 with sparse part having weight 43053754.
Pruned matrix : 513370 x 516262 with weight 31561464.
Total sieving time: 34.80 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.38 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 36.34 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

6·10¹⁴¹-7 = 5(9)₁₄₀3_<142> = 13 · 1447583 · 84331879 · C127

C127 = P37 · P90

P37 = 6476031936152650611823116269070611627_<37>

P90 = 583799427952449996104077409330623614593075799711097271574870756751412606331718775669681999_<90>

Oct 4, 2007 (2nd)

By Sinkiti Sibata / Msieve, GGNFS

6·10¹²⁷-7 = 5(9)₁₂₆3_<128> = 343127 · 582525896334758811474813322548179_<33> · C90

C90 = P42 · P48

P42 = 538379064288744086953750328027856177081161_<42>

P48 = 557561730154771569560097260837268094018249256461_<48>

Wed Oct 03 15:19:24 2007  Msieve v. 1.26
Wed Oct 03 15:19:24 2007  random seeds: ee28c423 6aa74c56
Wed Oct 03 15:19:24 2007  factoring 300179562563939145447468893460840371948057004209201877467016267991673377504711137500631221 (90 digits)
Wed Oct 03 15:19:25 2007  commencing quadratic sieve (90-digit input)
Wed Oct 03 15:19:26 2007  using multiplier of 5
Wed Oct 03 15:19:26 2007  using 64kb Pentium 2 sieve core
Wed Oct 03 15:19:26 2007  sieve interval: 18 blocks of size 65536
Wed Oct 03 15:19:26 2007  processing polynomials in batches of 6
Wed Oct 03 15:19:26 2007  using a sieve bound of 1579619 (60000 primes)
Wed Oct 03 15:19:26 2007  using large prime bound of 126369520 (26 bits)
Wed Oct 03 15:19:26 2007  using double large prime bound of 382786039401520 (42-49 bits)
Wed Oct 03 15:19:26 2007  using trial factoring cutoff of 49 bits
Wed Oct 03 15:19:26 2007  polynomial 'A' values have 12 factors
Thu Oct 04 01:00:41 2007  60563 relations (16228 full + 44335 combined from 633835 partial), need 60096
Thu Oct 04 01:00:52 2007  begin with 650063 relations
Thu Oct 04 01:01:24 2007  reduce to 146669 relations in 10 passes
Thu Oct 04 01:01:24 2007  attempting to read 146669 relations
Thu Oct 04 01:01:38 2007  recovered 146669 relations
Thu Oct 04 01:01:38 2007  recovered 124245 polynomials
Thu Oct 04 01:02:13 2007  attempting to build 60563 cycles
Thu Oct 04 01:02:14 2007  found 60563 cycles in 6 passes
Thu Oct 04 01:02:17 2007  distribution of cycle lengths:
Thu Oct 04 01:02:17 2007     length 1 : 16228
Thu Oct 04 01:02:17 2007     length 2 : 11907
Thu Oct 04 01:02:17 2007     length 3 : 10599
Thu Oct 04 01:02:17 2007     length 4 : 8065
Thu Oct 04 01:02:17 2007     length 5 : 5670
Thu Oct 04 01:02:17 2007     length 6 : 3510
Thu Oct 04 01:02:18 2007     length 7 : 2163
Thu Oct 04 01:02:18 2007     length 9+: 2421
Thu Oct 04 01:02:18 2007  largest cycle: 19 relations
Thu Oct 04 01:02:20 2007  matrix is 60000 x 60563 with weight 3581602 (avg 59.14/col)
Thu Oct 04 01:02:25 2007  filtering completed in 3 passes
Thu Oct 04 01:02:25 2007  matrix is 55899 x 55963 with weight 3306276 (avg 59.08/col)
Thu Oct 04 01:02:28 2007  saving the first 48 matrix rows for later
Thu Oct 04 01:02:28 2007  matrix is 55851 x 55963 with weight 2583325 (avg 46.16/col)
Thu Oct 04 01:02:28 2007  matrix includes 64 packed rows
Thu Oct 04 01:02:28 2007  using block size 10922 for processor cache size 256 kB
Thu Oct 04 01:02:29 2007  commencing Lanczos iteration
Thu Oct 04 01:06:36 2007  lanczos halted after 885 iterations
Thu Oct 04 01:06:37 2007  recovered 17 nontrivial dependencies
Thu Oct 04 01:07:05 2007  prp42 factor: 538379064288744086953750328027856177081161
Thu Oct 04 01:07:05 2007  prp48 factor: 557561730154771569560097260837268094018249256461
Thu Oct 04 01:07:05 2007  elapsed time 09:47:41

6·10¹²³-7 = 5(9)₁₂₂3_<124> = 13² · 1660493 · C116

C116 = P45 · P71

P45 = 419726743015322283340796841866026105998611897_<45>

P71 = 50940224585810878707118381444742680923300871417714179798205170107648957_<71>

Number: 59993_123
N=21380974553871444688254468890053067115588260258501612679604952428097769224215962068469171433819236054429504159841429
  ( 116 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=419726743015322283340796841866026105998611897 (pp45)
 r2=50940224585810878707118381444742680923300871417714179798205170107648957 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 3.06 hours.
Scaled time: 2.07 units (timescale=0.677).
Factorization parameters were as follows:
name: 59993_123
n: 21380974553871444688254468890053067115588260258501612679604952428097769224215962068469171433819236054429504159841429
m: 2000000000000000000000000
c5: 375
c0: -14
skew: 0.52
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:64283, largePrimes:2107214 encountered
Relations: rels:2116210, finalFF:152007
Max relations in full relation-set: 28
Initial matrix: 113447 x 152007 with sparse part having weight 13697410.
Pruned matrix : 103414 x 104045 with weight 7180122.
Total sieving time: 2.74 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.06 hours.
 --------- CPU info (if available) ----------

6·10¹²⁸-7 = 5(9)₁₂₇3_<129> = 47 · 157 · 8893 · C121

C121 = P35 · P42 · P46

P35 = 45062760365254252417196977668457049_<35>

P42 = 107331866482129355939909099089742932497167_<42>

P46 = 1890422922086710862023492300837255153472513593_<46>

Number: 59993_128
N=9143352172651724671661080561054985575066639417445336126160095189610799042575211729177505031243824903769647139905342227519
  ( 121 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=45062760365254252417196977668457049 (pp35)
 r2=107331866482129355939909099089742932497167 (pp42)
 r3=1890422922086710862023492300837255153472513593 (pp46)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 5.27 hours.
Scaled time: 3.57 units (timescale=0.677).
Factorization parameters were as follows:
name: 59993_128
n: 9143352172651724671661080561054985575066639417445336126160095189610799042575211729177505031243824903769647139905342227519
m: 20000000000000000000000000
c5: 375
c0: -14
skew: 0.52
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64283, largePrimes:1484571 encountered
Relations: rels:1488026, finalFF:176006
Max relations in full relation-set: 28
Initial matrix: 128300 x 176006 with sparse part having weight 12189392.
Pruned matrix : 113811 x 114516 with weight 6184426.
Total sieving time: 4.96 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.27 hours.
 --------- CPU info (if available) ----------

(37·10¹⁶¹-1)/9 = 4(1)₁₆₁_<162> = 3 · 41 · 1307 · 2075820356295079_<16> · 1262790142328673659357_<22> · C120

C120 = P38 · P83

P38 = 37343365815058483964552266720070550859_<38>

P83 = 26124266598228484286956693574306899716358742145356317706463821362063741663610307863_<83>

Number: 41111_161
N=975568044227759770362488001375467674400042183142302355527744077810832923409238855463500596189094164000811015620989104317
  ( 120 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=37343365815058483964552266720070550859 (pp38)
 r2=26124266598228484286956693574306899716358742145356317706463821362063741663610307863 (pp83)
Version: GGNFS-0.77.1-20060513-k8
Total time: 73.17 hours.
Scaled time: 146.20 units (timescale=1.998).
Factorization parameters were as follows:
name: 41111_161
n: 975568044227759770362488001375467674400042183142302355527744077810832923409238855463500596189094164000811015620989104317
m: 100000000000000000000000000000000
c5: 370
c0: -1
skew: 0.31
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4550001)
Primes: RFBsize:315948, AFBsize:315496, largePrimes:5801398 encountered
Relations: rels:5906549, finalFF:737188
Max relations in full relation-set: 28
Initial matrix: 631511 x 737188 with sparse part having weight 47432370.
Pruned matrix : 551065 x 554286 with weight 33711664.
Total sieving time: 69.23 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.52 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 73.17 hours.
 --------- CPU info (if available) ----------

Oct 4, 2007

By Robert Backstrom / Msieve, GGNFS

6·10¹⁵⁵-7 = 5(9)₁₅₄3_<156> = 9151759 · 44509450084691841113_<20> · 1276610766484719268151_<22> · 1340426558177838497399939_<25> · C84

C84 = P36 · P49

P36 = 217264834889735630458321389261532721_<36>

P49 = 3961899731258636703690742682913482426977474823891_<49>

Wed Oct 03 15:36:33 2007  Msieve v. 1.26
Wed Oct 03 15:36:33 2007  random seeds: 965c87cc d2ef83b1
Wed Oct 03 15:36:33 2007  factoring 860781490961595669697733605784670171336258336753794416470408536041356301000209037411 (84 digits)
Wed Oct 03 15:36:34 2007  commencing quadratic sieve (84-digit input)
Wed Oct 03 15:36:34 2007  using multiplier of 1
Wed Oct 03 15:36:34 2007  using 64kb Opteron sieve core
Wed Oct 03 15:36:34 2007  sieve interval: 6 blocks of size 65536
Wed Oct 03 15:36:34 2007  processing polynomials in batches of 17
Wed Oct 03 15:36:34 2007  using a sieve bound of 1409117 (53799 primes)
Wed Oct 03 15:36:34 2007  using large prime bound of 119774945 (26 bits)
Wed Oct 03 15:36:34 2007  using trial factoring cutoff of 27 bits
Wed Oct 03 15:36:34 2007  polynomial 'A' values have 11 factors
Wed Oct 03 16:07:49 2007  54021 relations (27210 full + 26811 combined from 284568 partial), need 53895
Wed Oct 03 16:07:50 2007  begin with 311778 relations
Wed Oct 03 16:07:50 2007  reduce to 77387 relations in 2 passes
Wed Oct 03 16:07:50 2007  attempting to read 77387 relations
Wed Oct 03 16:07:51 2007  recovered 77387 relations
Wed Oct 03 16:07:51 2007  recovered 71517 polynomials
Wed Oct 03 16:07:51 2007  attempting to build 54021 cycles
Wed Oct 03 16:07:51 2007  found 54021 cycles in 1 passes
Wed Oct 03 16:07:51 2007  distribution of cycle lengths:
Wed Oct 03 16:07:51 2007     length 1 : 27210
Wed Oct 03 16:07:51 2007     length 2 : 26811
Wed Oct 03 16:07:51 2007  largest cycle: 2 relations
Wed Oct 03 16:07:51 2007  matrix is 53799 x 54021 with weight 1755888 (avg 32.50/col)
Wed Oct 03 16:07:51 2007  filtering completed in 4 passes
Wed Oct 03 16:07:51 2007  matrix is 46702 x 46766 with weight 1491481 (avg 31.89/col)
Wed Oct 03 16:07:52 2007  saving the first 48 matrix rows for later
Wed Oct 03 16:07:52 2007  matrix is 46654 x 46766 with weight 1088600 (avg 23.28/col)
Wed Oct 03 16:07:52 2007  matrix includes 64 packed rows
Wed Oct 03 16:07:52 2007  commencing Lanczos iteration
Wed Oct 03 16:08:46 2007  lanczos halted after 739 iterations
Wed Oct 03 16:08:47 2007  recovered 6 nontrivial dependencies
Wed Oct 03 16:08:47 2007  prp36 factor: 217264834889735630458321389261532721
Wed Oct 03 16:08:47 2007  prp49 factor: 3961899731258636703690742682913482426977474823891
Wed Oct 03 16:08:47 2007  elapsed time 00:32:14

(31·10¹⁵⁸-13)/9 = 3(4)₁₅₇3_<159> = 7 · 127 · 78148787 · 4740691519332947_<16> · C133

C133 = P41 · P92

P41 = 58339351804238222158586791687727596860143_<41>

P92 = 17926350607259622695271137524190494788700231091726771361636249626207975716925845807554474581_<92>

Number: n
N=1045811674643038618720970610503378607430945162952929917680418191298320275906164719144573731068294405811697968071724804081565705525083
  ( 133 digits)
SNFS difficulty: 159 digits.
Divisors found:

Thu Oct 04 02:14:25 2007  prp41 factor: 58339351804238222158586791687727596860143
Thu Oct 04 02:14:25 2007  prp92 factor: 17926350607259622695271137524190494788700231091726771361636249626207975716925845807554474581
Thu Oct 04 02:14:25 2007  elapsed time 01:06:27 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 42.50 hours.
Scaled time: 61.62 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_3_4_157_3
n: 1045811674643038618720970610503378607430945162952929917680418191298320275906164719144573731068294405811697968071724804081565705525083
skew: 0.21
deg: 5
c5: 31000
c0: -13
m: 10000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1800000)
Primes: RFBsize:183072, AFBsize:182522, largePrimes:7262660 encountered
Relations: rels:6751741, finalFF:444988
Max relations in full relation-set: 28
Initial matrix: 365661 x 444988 with sparse part having weight 40908464.
Pruned matrix : 320686 x 322578 with weight 26986987.
Total sieving time: 42.25 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 42.50 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(82·10¹⁶⁰-1)/9 = 9(1)₁₆₀_<161> = 1183282325293_<13> · 1398206145473_<13> · C137

C137 = P59 · P79

P59 = 22056688036771319510990392077888123590637483193298813665679_<59>

P79 = 2496729301249539633152615904948407043950273202114296465618776682890249002888781_<79>

Number: n
N=55069579309927136700780310410936392743026521929117229883721627958613372143091384300827504395420854995614166408956523800756004310953847299
  ( 137 digits)
SNFS difficulty: 161 digits.
Divisors found:

Thu Oct 04 02:36:45 2007  prp59 factor: 22056688036771319510990392077888123590637483193298813665679
Thu Oct 04 02:36:45 2007  prp79 factor: 2496729301249539633152615904948407043950273202114296465618776682890249002888781
Thu Oct 04 02:36:45 2007  elapsed time 01:27:51 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 36.40 hours.
Scaled time: 48.16 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_9_1_160
n: 55069579309927136700780310410936392743026521929117229883721627958613372143091384300827504395420854995614166408956523800756004310953847299
skew: 0.41
deg: 5
c5: 82
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:250150, AFBsize:250142, largePrimes:7161867 encountered
Relations: rels:6671064, finalFF:562452
Max relations in full relation-set: 28
Initial matrix: 500360 x 562452 with sparse part having weight 39726103.
Pruned matrix : 448099 x 450664 with weight 25765807.
Total sieving time: 36.16 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 36.40 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

6·10¹³³-7 = 5(9)₁₃₂3_<134> = 419 · C132

C132 = P39 · P40 · P53

P39 = 803784771613572434432727851402219930947_<39>

P40 = 8211994164161688590117664996602372379877_<40>

P53 = 21694458850171435203820744840123411555745339465862013_<53>

Number: n
N=143198090692124105011933174224343675417661097852028639618138424821002386634844868735083532219570405727923627684964200477326968973747
  ( 132 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=803784771613572434432727851402219930947 (pp39)
 r2=8211994164161688590117664996602372379877 (pp40)
 r3=21694458850171435203820744840123411555745339465862013 (pp53)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.50 hours.
Scaled time: 6.52 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_5_9_132_3
n: 143198090692124105011933174224343675417661097852028639618138424821002386634844868735083532219570405727923627684964200477326968973747
skew: 0.52
deg: 5
c5: 375
c0: -14
m: 200000000000000000000000000
type: snfs
rlim: 1200000
alim: 1200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 550001)
Primes: RFBsize:92938, AFBsize:93099, largePrimes:5807271 encountered
Relations: rels:5166926, finalFF:262402
Max relations in full relation-set: 28
Initial matrix: 186103 x 262402 with sparse part having weight 21646923.
Pruned matrix : 153360 x 154354 with weight 9710538.
Total sieving time: 3.84 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.40 hours.
Total square root time: 0.12 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,48,48,2.5,2.5,75000
total time: 4.50 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

6·10¹⁴⁰-7 = 5(9)₁₃₉3_<141> = 118447393 · C133

C133 = P39 · P95

P39 = 488302592269751645844131141513207371459_<39>

P95 = 10373772369705551105830529941865993946904275182321723727108870993322153016866124697921503890739_<95>

Number: n
N=5065539939743545052105958972013845842938898621432723301896564325396338609157906919910005955133178828173955673300466815677403723018201
  ( 133 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=488302592269751645844131141513207371459 (pp39)
 r2=10373772369705551105830529941865993946904275182321723727108870993322153016866124697921503890739 (pp95)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.15 hours.
Scaled time: 9.46 units (timescale=1.322).
Factorization parameters were as follows:
name: KA_5_9_139_3
n: 5065539939743545052105958972013845842938898621432723301896564325396338609157906919910005955133178828173955673300466815677403723018201
skew: 1.03
deg: 5
c5: 6
c0: -7
m: 10000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 850001)
Primes: RFBsize:114155, AFBsize:114412, largePrimes:6395094 encountered
Relations: rels:5722594, finalFF:311875
Max relations in full relation-set: 48
Initial matrix: 228633 x 311875 with sparse part having weight 33205990.
Pruned matrix : 195644 x 196851 with weight 15042093.
Total sieving time: 5.86 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 1.01 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000
total time: 7.15 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 3, 2007 (5th)

By suberi / PRIMO

(13·10²⁵⁶³+41)/9 is prime.

(13·10²⁶⁴¹+41)/9 is prime.

Oct 3, 2007 (4th)

By Robert Backstrom / GMP-ECM, Msieve

6·10¹²⁵-7 = 5(9)₁₂₄3_<126> = 23 · 3623 · 10966621 · C114

C114 = P38 · P77

P38 = 50636596327829583320839536142290785563_<38>

P77 = 12966349985343467300064590701602747532440337222241547532187032604088384653879_<77>

6·10¹⁵⁷-7 = 5(9)₁₅₆3_<158> = 53 · 97 · 739 · 1091 · 519487 · 709369890512947561_<18> · 1398747574182377711176049107_<28> · C98

C98 = P35 · P64

P35 = 22320341571287862440791180961911537_<35>

P64 = 1258191770139023959637271001787399781177095229292345787867966729_<64>

Wed Oct 03 16:19:38 2007  Msieve v. 1.26
Wed Oct 03 16:19:38 2007  random seeds: b8709f30 80cbbce4
Wed Oct 03 16:19:38 2007  factoring 28083270071686319089592401973395533416884243987372294079591744321397845903861895820202049357252473 (98 digits)
Wed Oct 03 16:19:38 2007  commencing quadratic sieve (98-digit input)
Wed Oct 03 16:19:38 2007  using multiplier of 1
Wed Oct 03 16:19:38 2007  using 64kb Opteron sieve core
Wed Oct 03 16:19:38 2007  sieve interval: 18 blocks of size 65536
Wed Oct 03 16:19:38 2007  processing polynomials in batches of 6
Wed Oct 03 16:19:38 2007  using a sieve bound of 2473301 (90543 primes)
Wed Oct 03 16:19:38 2007  using large prime bound of 370995150 (28 bits)
Wed Oct 03 16:19:38 2007  using double large prime bound of 2659884601469100 (43-52 bits)
Wed Oct 03 16:19:38 2007  using trial factoring cutoff of 52 bits
Wed Oct 03 16:19:38 2007  polynomial 'A' values have 13 factors
Wed Oct 03 23:18:45 2007  90718 relations (21893 full + 68825 combined from 1364772 partial), need 90639
Wed Oct 03 23:18:47 2007  begin with 1386665 relations
Wed Oct 03 23:18:48 2007  reduce to 237587 relations in 12 passes
Wed Oct 03 23:18:48 2007  attempting to read 237587 relations
Wed Oct 03 23:18:52 2007  recovered 237587 relations
Wed Oct 03 23:18:52 2007  recovered 225257 polynomials
Wed Oct 03 23:18:52 2007  attempting to build 90718 cycles
Wed Oct 03 23:18:53 2007  found 90718 cycles in 6 passes
Wed Oct 03 23:18:53 2007  distribution of cycle lengths:
Wed Oct 03 23:18:53 2007     length 1 : 21893
Wed Oct 03 23:18:53 2007     length 2 : 15660
Wed Oct 03 23:18:53 2007     length 3 : 15243
Wed Oct 03 23:18:53 2007     length 4 : 12310
Wed Oct 03 23:18:53 2007     length 5 : 9641
Wed Oct 03 23:18:53 2007     length 6 : 6118
Wed Oct 03 23:18:53 2007     length 7 : 4176
Wed Oct 03 23:18:53 2007     length 9+: 5677
Wed Oct 03 23:18:53 2007  largest cycle: 19 relations
Wed Oct 03 23:18:53 2007  matrix is 90543 x 90718 with weight 6047781 (avg 66.67/col)
Wed Oct 03 23:18:54 2007  filtering completed in 3 passes
Wed Oct 03 23:18:54 2007  matrix is 86539 x 86603 with weight 5807038 (avg 67.05/col)
Wed Oct 03 23:18:55 2007  saving the first 48 matrix rows for later
Wed Oct 03 23:18:55 2007  matrix is 86491 x 86603 with weight 4591383 (avg 53.02/col)
Wed Oct 03 23:18:55 2007  matrix includes 64 packed rows
Wed Oct 03 23:18:55 2007  using block size 21845 for processor cache size 512 kB
Wed Oct 03 23:18:55 2007  commencing Lanczos iteration
Wed Oct 03 23:20:21 2007  lanczos halted after 1370 iterations
Wed Oct 03 23:20:21 2007  recovered 17 nontrivial dependencies
Wed Oct 03 23:20:22 2007  prp35 factor: 22320341571287862440791180961911537
Wed Oct 03 23:20:22 2007  prp64 factor: 1258191770139023959637271001787399781177095229292345787867966729
Wed Oct 03 23:20:22 2007  elapsed time 07:00:44

Oct 3, 2007 (3rd)

By Sinkiti Sibata / Msieve v. 1.26, GGNFS

6·10¹⁵³-7 = 5(9)₁₅₂3_<154> = 13 · 139747 · 41191413729044567_<17> · 28576336929599376517741_<23> · 1025244729230700913218569_<25> · C85

C85 = P42 · P43

P42 = 356746994819799697074718391780142365509993_<42>

P43 = 7671217220429161293573234558957602035904237_<43>

Wed Oct 03 14:47:30 2007  Msieve v. 1.26
Wed Oct 03 14:47:30 2007  random seeds: 460178a0 145787d5
Wed Oct 03 14:47:30 2007  factoring 2736683689998000234925592599907106848522357423838373040075488018168277701797414540341 (85 digits)
Wed Oct 03 14:47:30 2007  commencing quadratic sieve (85-digit input)
Wed Oct 03 14:47:31 2007  using multiplier of 21
Wed Oct 03 14:47:31 2007  using 64kb Pentium 2 sieve core
Wed Oct 03 14:47:31 2007  sieve interval: 6 blocks of size 65536
Wed Oct 03 14:47:31 2007  processing polynomials in batches of 17
Wed Oct 03 14:47:31 2007  using a sieve bound of 1425547 (54412 primes)
Wed Oct 03 14:47:31 2007  using large prime bound of 116894854 (26 bits)
Wed Oct 03 14:47:31 2007  using double large prime bound of 332683806537686 (41-49 bits)
Wed Oct 03 14:47:31 2007  using trial factoring cutoff of 49 bits
Wed Oct 03 14:47:31 2007  polynomial 'A' values have 11 factors
Wed Oct 03 19:20:05 2007  54584 relations (15772 full + 38812 combined from 574026 partial), need 54508
Wed Oct 03 19:20:07 2007  begin with 589798 relations
Wed Oct 03 19:20:09 2007  reduce to 128585 relations in 11 passes
Wed Oct 03 19:20:09 2007  attempting to read 128585 relations
Wed Oct 03 19:20:14 2007  recovered 128585 relations
Wed Oct 03 19:20:14 2007  recovered 109292 polynomials
Wed Oct 03 19:20:15 2007  attempting to build 54584 cycles
Wed Oct 03 19:20:15 2007  found 54584 cycles in 5 passes
Wed Oct 03 19:20:19 2007  distribution of cycle lengths:
Wed Oct 03 19:20:19 2007     length 1 : 15772
Wed Oct 03 19:20:19 2007     length 2 : 11077
Wed Oct 03 19:20:19 2007     length 3 : 9717
Wed Oct 03 19:20:19 2007     length 4 : 6987
Wed Oct 03 19:20:19 2007     length 5 : 4720
Wed Oct 03 19:20:19 2007     length 6 : 2838
Wed Oct 03 19:20:19 2007     length 7 : 1656
Wed Oct 03 19:20:19 2007     length 9+: 1817
Wed Oct 03 19:20:19 2007  largest cycle: 17 relations
Wed Oct 03 19:20:20 2007  matrix is 54412 x 54584 with weight 2905977 (avg 53.24/col)
Wed Oct 03 19:20:22 2007  filtering completed in 3 passes
Wed Oct 03 19:20:22 2007  matrix is 49748 x 49812 with weight 2673600 (avg 53.67/col)
Wed Oct 03 19:20:24 2007  saving the first 48 matrix rows for later
Wed Oct 03 19:20:24 2007  matrix is 49700 x 49812 with weight 1993341 (avg 40.02/col)
Wed Oct 03 19:20:24 2007  matrix includes 64 packed rows
Wed Oct 03 19:20:24 2007  commencing Lanczos iteration
Wed Oct 03 19:25:55 2007  lanczos halted after 787 iterations
Wed Oct 03 19:25:56 2007  recovered 19 nontrivial dependencies
Wed Oct 03 19:25:59 2007  prp42 factor: 356746994819799697074718391780142365509993
Wed Oct 03 19:25:59 2007  prp43 factor: 7671217220429161293573234558957602035904237
Wed Oct 03 19:25:59 2007  elapsed time 04:38:29

8·10¹⁶⁰-3 = 7(9)₁₅₉7_<161> = 43² · 431 · 48859 · 4647456722639_<13> · 626627965062020591_<18> · C120

C120 = P47 · P74

P47 = 14692417462058974457446490078935236626410262041_<47>

P74 = 48018970537507694295810504240418883922125431142142818767721221650978656473_<74>

Number: 79997_160
N=705514761235373466365712554295053490555390684232165126019501416207453667149193594120119006252562816485365473350050841393
  ( 120 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=14692417462058974457446490078935236626410262041 (pp47)
 r2=48018970537507694295810504240418883922125431142142818767721221650978656473 (pp74)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 60.89 hours.
Scaled time: 41.22 units (timescale=0.677).
Factorization parameters were as follows:
name: 79997_160
n: 705514761235373466365712554295053490555390684232165126019501416207453667149193594120119006252562816485365473350050841393
m: 100000000000000000000000000000000
c5: 8
c0: -3
skew: 0.82
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3500001)
Primes: RFBsize:283146, AFBsize:283367, largePrimes:5694153 encountered
Relations: rels:5794190, finalFF:713570
Max relations in full relation-set: 28
Initial matrix: 566578 x 713570 with sparse part having weight 44691099.
Pruned matrix : 447630 x 450526 with weight 27726964.
Total sieving time: 52.59 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 7.83 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 60.89 hours.
 --------- CPU info (if available) ----------

Oct 3, 2007 (2nd)

By Jo Yeong Uk / GGNFS

6·10¹¹¹-7 = 5(9)₁₁₀3_<112> = 13 · 2423 · C108

C108 = P51 · P57

P51 = 360964079692659801539218828060656161476910423250161_<51>

P57 = 527704135252280213728502010679882140961843051369612566587_<57>

Number: 59993_111
N=190482237531350201593701387345630020000634940791771167338645671291152100066668783135972570557795485570970507
  ( 108 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=360964079692659801539218828060656161476910423250161 (pp51)
 r2=527704135252280213728502010679882140961843051369612566587 (pp57)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.71 hours.
Scaled time: 1.53 units (timescale=2.145).
Factorization parameters were as follows:
n: 190482237531350201593701387345630020000634940791771167338645671291152100066668783135972570557795485570970507
m: 10000000000000000000000
c5: 60
c0: -7
skew: 0.65
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 320001)
Primes: RFBsize:30757, AFBsize:30694, largePrimes:1074870 encountered
Relations: rels:1007128, finalFF:101389
Max relations in full relation-set: 28
Initial matrix: 61518 x 101389 with sparse part having weight 4955758.
Pruned matrix : 50735 x 51106 with weight 1760939.
Total sieving time: 0.68 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.71 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

6·10¹²²-7 = 5(9)₁₂₁3_<123> = 29 · C122

C122 = P38 · P84

P38 = 68004493287578401111324018574258290351_<38>

P84 = 304239531422152873078652750157120871113171209374964566110469309352350285844274312067_<84>

Number: 59993_122
N=20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517
  ( 122 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=68004493287578401111324018574258290351 (pp38)
 r2=304239531422152873078652750157120871113171209374964566110469309352350285844274312067 (pp84)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.52 hours.
Scaled time: 3.26 units (timescale=2.144).
Factorization parameters were as follows:
n: 20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517
m: 2000000000000000000000000
c5: 75
c0: -28
skew: 0.82
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [400000, 720001)
Primes: RFBsize:63951, AFBsize:63523, largePrimes:1389910 encountered
Relations: rels:1372098, finalFF:158574
Max relations in full relation-set: 28
Initial matrix: 127540 x 158574 with sparse part having weight 7799698.
Pruned matrix : 114540 x 115241 with weight 4337757.
Total sieving time: 1.46 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000
total time: 1.52 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

6·10¹³⁷-7 = 5(9)₁₃₆3_<138> = C138

C138 = P44 · P95

P44 = 11930304707794017951010060929038611787637529_<44>

P95 = 50292093512751817677191069598755399434481984540235534607565516222232375080068547729293970178017_<95>

Number: 59993_137
N=599999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 138 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=11930304707794017951010060929038611787637529 (pp44)
 r2=50292093512751817677191069598755399434481984540235534607565516222232375080068547729293970178017 (pp95)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.81 hours.
Scaled time: 10.24 units (timescale=2.129).
Factorization parameters were as follows:
n: 599999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
m: 2000000000000000000000000000
c5: 75
c0: -28
skew: 0.82
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1600001)
Primes: RFBsize:107126, AFBsize:106878, largePrimes:2399412 encountered
Relations: rels:2552130, finalFF:267534
Max relations in full relation-set: 28
Initial matrix: 214070 x 267534 with sparse part having weight 24798377.
Pruned matrix : 197717 x 198851 with weight 15730218.
Total sieving time: 4.58 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 4.81 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

6·10¹³⁰-7 = 5(9)₁₂₉3_<131> = 3581 · 11927683 · 77492399487775327777_<20> · C101

C101 = P41 · P60

P41 = 41741913374238084153759348799228096820219_<41>

P60 = 434269551129510598310111242531747787622152307167204480286557_<60>

Number: 59993_130
N=18127241984317287948259696060358425132269108005734409737154495900535745003233991139307777121631495983
  ( 101 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=41741913374238084153759348799228096820219 (pp41)
 r2=434269551129510598310111242531747787622152307167204480286557 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.61 hours.
Scaled time: 5.60 units (timescale=2.145).
Factorization parameters were as follows:
n: 18127241984317287948259696060358425132269108005734409737154495900535745003233991139307777121631495983
m: 100000000000000000000000000
c5: 6
c0: -7
skew: 1.03
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 1050001)
Primes: RFBsize:78498, AFBsize:78516, largePrimes:1562106 encountered
Relations: rels:1575211, finalFF:190100
Max relations in full relation-set: 28
Initial matrix: 157080 x 190100 with sparse part having weight 11252053.
Pruned matrix : 145006 x 145855 with weight 6877487.
Total sieving time: 2.51 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 2.61 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Oct 3, 2007

The factor table of 599...993 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Oct 2, 2007 (3rd)

By Jo Yeong Uk / GGNFS

4·10¹⁵⁸+7 = 4(0)₁₅₇7_<159> = 11 · 37 · 12007 · 64184521 · 801992267819_<12> · C133

C133 = P47 · P86

P47 = 40168232933255472863199410867005086259141899511_<47>

P86 = 39586568659768781756154959633375249919813838935426658359620291935490219828230564916987_<86>

Number: 40007_158
N=1590122510953903345542624420568097263521630484531474875782839648114082015795534996005269615326322770371113782601521530538607210893357
  ( 133 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=40168232933255472863199410867005086259141899511 (pp47)
 r2=39586568659768781756154959633375249919813838935426658359620291935490219828230564916987 (pp86)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.50 hours.
Scaled time: 52.33 units (timescale=2.136).
Factorization parameters were as follows:
n: 1590122510953903345542624420568097263521630484531474875782839648114082015795534996005269615326322770371113782601521530538607210893357
m: 100000000000000000000000000000000
c5: 1
c0: 175
skew: 2.81
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3400001)
Primes: RFBsize:283146, AFBsize:283052, largePrimes:5731305 encountered
Relations: rels:5871089, finalFF:749665
Max relations in full relation-set: 28
Initial matrix: 566262 x 749665 with sparse part having weight 45967150.
Pruned matrix : 415205 x 418100 with weight 27576167.
Total sieving time: 23.50 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.87 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 24.50 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Oct 2, 2007 (2nd)

By Sinkiti Sibata / GGNFS

(5·10¹⁶¹+7)/3 = 1(6)₁₆₀9_<162> = 570049 · 111524293 · 148946655411315836615893811933_<30> · C119

C119 = P59 · P60

P59 = 19431998449239836919883891499392364284154878753810288198627_<59>

P60 = 905771934729220258028194158863173230204066471520265077490687_<60>

Number: 16669_161
N=17600958831023174839925978092753242124486597026417452012549969280102392991960434543098921399672637559438776334598686749
  ( 119 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=19431998449239836919883891499392364284154878753810288198627 (pp59)
 r2=905771934729220258028194158863173230204066471520265077490687 (pp60)
Version: GGNFS-0.77.1-20060513-k8
Total time: 73.18 hours.
Scaled time: 146.44 units (timescale=2.001).
Factorization parameters were as follows:
name: 16669_161
n: 17600958831023174839925978092753242124486597026417452012549969280102392991960434543098921399672637559438776334598686749
m: 100000000000000000000000000000000
c5: 50
c0: 7
skew: 0.67
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4550001)
Primes: RFBsize:315948, AFBsize:316881, largePrimes:5795306 encountered
Relations: rels:5901400, finalFF:737692
Max relations in full relation-set: 28
Initial matrix: 632894 x 737692 with sparse part having weight 45414630.
Pruned matrix : 553191 x 556419 with weight 32190862.
Total sieving time: 69.32 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.47 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 73.18 hours.
 --------- CPU info (if available) ----------

Oct 2, 2007

By Robert Backstrom / GGNFS, Msieve

(4·10¹⁶¹-7)/3 = 1(3)₁₆₀1_<162> = 11 · 11124606089_<11> · 100299923063_<12> · C140

C140 = P45 · P95

P45 = 866216913035861859660556067350054626872174933_<45>

P95 = 12541057250108172132778787912475915358164724857304431753382275697071209996577378790384734808091_<95>

Number: n
N=10863275897394715416026646238743388383563411275697039333548489540819916417179198180218113482105248693668875830361857053271903904435535782903
  ( 140 digits)
SNFS difficulty: 161 digits.
Divisors found:

prp45 factor: 866216913035861859660556067350054626872174933
prp95 factor: 12541057250108172132778787912475915358164724857304431753382275697071209996577378790384734808091
elapsed time 02:26:08 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 40.30 hours.
Scaled time: 48.24 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_1_3_160_1
n: 10863275897394715416026646238743388383563411275697039333548489540819916417179198180218113482105248693668875830361857053271903904435535782903
type: snfs
skew: 0.71
deg: 5
c5: 40
c0: -7
m: 100000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:250150, AFBsize:249831, largePrimes:6771115 encountered
Relations: rels:6304352, finalFF:590349
Max relations in full relation-set: 28
Initial matrix: 500047 x 590349 with sparse part having weight 31375036.
Pruned matrix : 415114 x 417678 with weight 17906321.
Total sieving time: 40.07 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.3,2.3,100000
total time: 40.30 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

5·10¹⁶¹-1 = 4(9)₁₆₁_<162> = 23 · 5039 · 5503 · 121219311137_<12> · C142

C142 = P69 · P74

P69 = 205172085665013628136788854347422145538579372307983152097920947502671_<69>

P74 = 31521596990625887572504276079879084677165618298704568194646451128941172807_<74>

Number: n
N=6467351798058730387628097619584464793561004208531537922182496075642274563849187638841619505437822847268801141316782851382812647988076505067497
  ( 142 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Oct 02 05:21:23 2007  prp69 factor: 205172085665013628136788854347422145538579372307983152097920947502671
Tue Oct 02 05:21:23 2007  prp74 factor: 31521596990625887572504276079879084677165618298704568194646451128941172807
Tue Oct 02 05:21:23 2007  elapsed time 01:18:32 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 29.84 hours.
Scaled time: 43.39 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_4_9_161
n: 6467351798058730387628097619584464793561004208531537922182496075642274563849187638841619505437822847268801141316782851382812647988076505067497
skew: 0.46
deg: 5
c5: 50
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1600000)
Primes: RFBsize:203362, AFBsize:203587, largePrimes:7032000 encountered
Relations: rels:6494307, finalFF:456833
Max relations in full relation-set: 28
Initial matrix: 407014 x 456833 with sparse part having weight 35481673.
Pruned matrix : 369264 x 371363 with weight 25332214.
Total sieving time: 29.63 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 29.84 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(28·10¹⁶⁰-1)/9 = 3(1)₁₆₀_<161> = 53 · 113 · 367 · 10608547 · 331545143 · C139

C139 = P51 · P88

P51 = 633091035242735539801967600647466189684568802167457_<51>

P88 = 6356680828325396531036158080960100862662205508268214943170736874990151494680541613194001_<88>

Number: n
N=4024357646312174958831474608222302299118450594684435034315875112537932079099180653597254994891579763036098222505425488832273115077429825457
  ( 139 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Oct 02 06:04:18 2007  prp51 factor: 633091035242735539801967600647466189684568802167457
Tue Oct 02 06:04:18 2007  prp88 factor: 6356680828325396531036158080960100862662205508268214943170736874990151494680541613194001
Tue Oct 02 06:04:18 2007  elapsed time 01:22:53 (Msieve 1.26)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 34.41 hours.
Scaled time: 44.59 units (timescale=1.296).
Factorization parameters were as follows:
name: KA_3_1_160
n: 4024357646312174958831474608222302299118450594684435034315875112537932079099180653597254994891579763036098222505425488832273115077429825457
skew: 0.51
deg: 5
c5: 28
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:216816, AFBsize:216531, largePrimes:7070916 encountered
Relations: rels:6546532, finalFF:488128
Max relations in full relation-set: 28
Initial matrix: 433413 x 488128 with sparse part having weight 35567073.
Pruned matrix : 391277 x 393508 with weight 24641110.
Total sieving time: 33.14 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 1.06 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 34.41 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁶¹-3 = 6(9)₁₆₀7_<162> = 11759927 · 890858477521139_<15> · C140

C140 = P52 · P89

P52 = 5434034586523956104106766412088428719802308238404951_<52>

P89 = 12295955952110120403085408303775786006169912054674465432621806697568821168788407881446399_<89>

Number: n
N=66816649918141495127926394200224912688873813650781970983701894207994243406438544537584681883365367975168764122211116754043488833134562721449
  ( 140 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Oct 02 11:41:36 2007  prp52 factor: 5434034586523956104106766412088428719802308238404951
Tue Oct 02 11:41:36 2007  prp89 factor: 12295955952110120403085408303775786006169912054674465432621806697568821168788407881446399
Tue Oct 02 11:41:36 2007  elapsed time 02:02:16 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 53.37 hours.
Scaled time: 70.61 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_6_9_160_7
n: 66816649918141495127926394200224912688873813650781970983701894207994243406438544537584681883365367975168764122211116754043488833134562721449
skew: 0.53
deg: 5
c5: 70
c0: -3
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2500000)
Primes: RFBsize:250150, AFBsize:249361, largePrimes:7482224 encountered
Relations: rels:6975734, finalFF:559949
Max relations in full relation-set: 28
Initial matrix: 499578 x 559949 with sparse part having weight 47483613.
Pruned matrix : 454399 x 456960 with weight 33007219.
Total sieving time: 53.09 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 53.37 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 1, 2007 (3rd)

By Jo Yeong Uk / GGNFS

2·10¹⁵⁸-7 = 1(9)₁₅₇3_<159> = 953 · 25057 · 2414090848213589432916932990633_<31> · C121

C121 = P53 · P69

P53 = 31571248495465350553236417278124057355578453451578557_<53>

P69 = 109891134207565565423460471928953710097707635400211726467910976480493_<69>

Number: 19993_158
N=3469400305515585275088518477571852718127951025814114467282749380810057951257353312433363378995962611612031180850967588601
  ( 121 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=31571248495465350553236417278124057355578453451578557 (pp53)
 r2=109891134207565565423460471928953710097707635400211726467910976480493 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 34.21 hours.
Scaled time: 72.22 units (timescale=2.111).
Factorization parameters were as follows:
n: 3469400305515585275088518477571852718127951025814114467282749380810057951257353312433363378995962611612031180850967588601
m: 100000000000000000000000000000000
c5: 1
c0: -350
skew: 3.23
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4000001)
Primes: RFBsize:283146, AFBsize:283727, largePrimes:5808005 encountered
Relations: rels:5905005, finalFF:708062
Max relations in full relation-set: 28
Initial matrix: 566937 x 708062 with sparse part having weight 48034519.
Pruned matrix : 464821 x 467719 with weight 33043298.
Total sieving time: 32.81 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.26 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 34.21 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Oct 2, 2007 (2nd)

By Jo Yeong Uk / PRIMO

4·10²⁰³⁸+9 is prime!

Oct 1, 2007

By Sinkiti Sibata / GGNFS

(5·10¹⁵⁹+7)/3 = 1(6)₁₅₈9_<160> = 61 · 139 · 22354882834663_<14> · C142

C142 = P50 · P93

P50 = 20633650419206281386733031458970921470010125270621_<50>

P93 = 426143283646225856200448242499018567906598044643963243984154881765936470251951711802769440857_<93>

Number: 16669_159
N=8792891543248889413056523663055605397019366650336981625335329343284007000558823348485757194490519250667301471004607262229383740155945979162197
  ( 142 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=20633650419206281386733031458970921470010125270621 (pp50)
 r2=426143283646225856200448242499018567906598044643963243984154881765936470251951711802769440857 (pp93)
Version: GGNFS-0.77.1-20060513-k8
Total time: 40.03 hours.
Scaled time: 77.81 units (timescale=1.944).
Factorization parameters were as follows:
name: 16669_159
n: 8792891543248889413056523663055605397019366650336981625335329343284007000558823348485757194490519250667301471004607262229383740155945979162197
m: 100000000000000000000000000000000
c5: 1
c0: 14
skew: 1.7
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3300001)
Primes: RFBsize:283146, AFBsize:283092, largePrimes:5781861 encountered
Relations: rels:5963802, finalFF:786585
Max relations in full relation-set: 28
Initial matrix: 566302 x 786585 with sparse part having weight 46911389.
Pruned matrix : 388163 x 391058 with weight 28940900.
Total sieving time: 37.70 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 2.02 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 40.03 hours.
 --------- CPU info (if available) ----------

(5·10¹⁵⁴+7)/3 = 1(6)₁₅₃9_<155> = 17² · 211 · 89227 · 3642209 · 34988803 · C131

C131 = P64 · P67

P64 = 3039500772684756067905656547847651710767202885317667360748022141_<64>

P67 = 7908169219491322981400916567456394408788268380654149703529298881099_<67>

Number: 16669_154
N=24036886453165680508340850848781676496510660976142667106365241496273418489191071703314462061843335352040879870593174633908578412959
  ( 131 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=3039500772684756067905656547847651710767202885317667360748022141 (pp64)
 r2=7908169219491322981400916567456394408788268380654149703529298881099 (pp67)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 35.56 hours.
Scaled time: 24.07 units (timescale=0.677).
Factorization parameters were as follows:
name: 16669_154
n: 24036886453165680508340850848781676496510660976142667106365241496273418489191071703314462061843335352040879870593174633908578412959
m: 10000000000000000000000000000000
c5: 1
c0: 14
skew: 1.7
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2400001)
Primes: RFBsize:216816, AFBsize:216671, largePrimes:5670953 encountered
Relations: rels:5752856, finalFF:662121
Max relations in full relation-set: 28
Initial matrix: 433551 x 662121 with sparse part having weight 48626390.
Pruned matrix : 281115 x 283346 with weight 30459459.
Total sieving time: 31.66 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 3.54 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 35.56 hours.
 --------- CPU info (if available) ----------

September 2007

Sep 30, 2007 (4th)

By Jo Yeong Uk / GGNFS

(5·10¹⁶²+7)/3 = 1(6)₁₆₁9_<163> = 26605422918850732566241_<23> · 63779260936918673666795069_<26> · C114

C114 = P56 · P59

P56 = 12345841030073355518195566173708094971913700674342341749_<56>

P59 = 79557003995848246810709883183266502089230667106521497802989_<59>

Number: 16669_162
N=982198124161653180383430896087817726373941018203689950840839374285322703169061071123818762648082907378560911687761
  ( 114 digits)
Divisors found:
 r1=12345841030073355518195566173708094971913700674342341749 (pp56)
 r2=79557003995848246810709883183266502089230667106521497802989 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.98 hours.
Scaled time: 53.55 units (timescale=2.144).
Factorization parameters were as follows:
name: 16669_162
n: 982198124161653180383430896087817726373941018203689950840839374285322703169061071123818762648082907378560911687761
skew: 79581.38
# norm 1.52e+16
c5: 14400
c4: -5104766820
c3: -426663243207224
c2: 28085394149617420745
c1: 790358088000437855793756
c0: -30202005118332397627600032105
# alpha -6.65
Y1: 1156683005687
Y0: -9263415975208444237468
# Murphy_E 5.69e-10
# M 282687440591493322167609652050488048787882302796981977330370789227978501143302103505532468545998949397979264317724
type: gnfs
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1800000, 3075001)
Primes: RFBsize:256726, AFBsize:255796, largePrimes:7643428 encountered
Relations: rels:7673917, finalFF:699431
Max relations in full relation-set: 28
Initial matrix: 512600 x 699431 with sparse part having weight 61343989.
Pruned matrix : 366077 x 368704 with weight 35631843.
Polynomial selection time: 1.18 hours.
Total sieving time: 22.62 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.87 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000
total time: 24.98 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Sep 30, 2007 (3rd)

By Sinkiti Sibata / GGNFS

(5·10¹⁶⁰+7)/3 = 1(6)₁₅₉9_<161> = 79 · 22979881 · 8218427297_<10> · 120437201921_<12> · 576732416278247_<15> · C116

C116 = P55 · P61

P55 = 4977320437750921565229473834967340708864912661751976709_<55>

P61 = 3231130839822657913824785584822600613852060607675347893277881_<61>

Number: 16669_160
N=16082373566096614517840744716684819770544179685787058568186342091536319780818203204639102366383712317368525176873629
  ( 116 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=4977320437750921565229473834967340708864912661751976709 (pp55)
 r2=3231130839822657913824785584822600613852060607675347893277881 (pp61)
Version: GGNFS-0.77.1-20060513-k8
Total time: 48.41 hours.
Scaled time: 96.57 units (timescale=1.995).
Factorization parameters were as follows:
name: 16669_160
n: 16082373566096614517840744716684819770544179685787058568186342091536319780818203204639102366383712317368525176873629
m: 100000000000000000000000000000000
c5: 5
c0: 7
skew: 1.07
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3500001)
Primes: RFBsize:283146, AFBsize:282597, largePrimes:5621726 encountered
Relations: rels:5644743, finalFF:651649
Max relations in full relation-set: 28
Initial matrix: 565808 x 651649 with sparse part having weight 40725051.
Pruned matrix : 498172 x 501065 with weight 27770530.
Total sieving time: 45.45 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 2.62 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 48.41 hours.
 --------- CPU info (if available) ----------

Sep 30, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

(5·10¹⁶⁴+7)/3 = 1(6)₁₆₃9_<165> = 13 · 191 · 111667 · C156

C156 = P59 · P98

P59 = 26302708085062711351718348313317723934590092763062351780943_<59>

P98 = 22853183997916580633609069137995891297392038889869322628145873448439676832765537008398620936667403_<98>

Number: n
N=601100627511426222646761161680965546206801796708529971231335989315691212650463737172222577853390145565689747467684178070804876373058548212170868388304701029
  ( 156 digits)
SNFS difficulty: 165 digits.
Divisors found:

Linear algebra by Msieve 1.26:

Sun Sep 30 03:05:26 2007  commencing square root phase
Sun Sep 30 03:05:26 2007  reading relations for dependency 1
Sun Sep 30 03:05:27 2007  read 217366 cycles
Sun Sep 30 03:05:27 2007  cycles contain 795544 unique relations
Sun Sep 30 03:06:01 2007  read 795544 relations
Sun Sep 30 03:06:08 2007  multiplying 1142918 relations
Sun Sep 30 03:08:47 2007  multiply complete, coefficients have about 24.09 million bits
Sun Sep 30 03:08:48 2007  initial square root is modulo 8296751
Sun Sep 30 03:15:04 2007  prp59 factor: 26302708085062711351718348313317723934590092763062351780943
Sun Sep 30 03:15:04 2007  prp98 factor: 22853183997916580633609069137995891297392038889869322628145873448439676832765537008398620936667403
Sun Sep 30 03:15:04 2007  elapsed time 01:26:28

Version: GGNFS-0.77.1-20051202-athlon
Total time: 40.61 hours.
Scaled time: 53.77 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_1_6_163_9
n: 601100627511426222646761161680965546206801796708529971231335989315691212650463737172222577853390145565689747467684178070804876373058548212170868388304701029
skew: 1.70
deg: 5
c5: 1
c0: 14
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1900000)
Primes: RFBsize:250150, AFBsize:250091, largePrimes:7227599 encountered
Relations: rels:6752702, finalFF:576673
Max relations in full relation-set: 28
Initial matrix: 500305 x 576673 with sparse part having weight 39570403.
Pruned matrix : 436717 x 439282 with weight 24359944.
Total sieving time: 40.39 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 40.61 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(5·10¹⁶³+7)/3 = 1(6)₁₆₂9_<164> = 19 · 932483 · 3338407 · C150

C150 = P36 · P115

P36 = 179096204859467232396164279888334937_<36>

P115 = 1573361650372442894213033131277538811100419125034880034126626043409760465523866973561143332026778461515089011520283_<115>

Number: n
N=281783100453132491764192749729106318410556661674307444387519334626303961635821594561083163050656636337622215383852258673518554659375130169219873027171
  ( 150 digits)
SNFS difficulty: 164 digits.
Divisors found:

Linear algebra using Msieve 1.26:

Sun Sep 30 18:13:20 2007  commencing square root phase
Sun Sep 30 18:13:20 2007  reading relations for dependency 1
Sun Sep 30 18:13:21 2007  read 238377 cycles
Sun Sep 30 18:13:21 2007  cycles contain 836180 unique relations
Sun Sep 30 18:13:57 2007  read 836180 relations
Sun Sep 30 18:14:04 2007  multiplying 1175696 relations
Sun Sep 30 18:16:39 2007  multiply complete, coefficients have about 28.40 million bits
Sun Sep 30 18:16:40 2007  initial square root is modulo 143457841
Sun Sep 30 18:22:25 2007  prp36 factor: 179096204859467232396164279888334937
Sun Sep 30 18:22:25 2007  prp115 factor: 1573361650372442894213033131277538811100419125034880034126626043409760465523866973561143332026778461515089011520283
Sun Sep 30 18:22:25 2007  elapsed time 01:32:22

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 65.07 hours.
Scaled time: 79.39 units (timescale=1.220).
Factorization parameters were as follows:
name: KA_1_6_162_9
n: 281783100453132491764192749729106318410556661674307444387519334626303961635821594561083163050656636337622215383852258673518554659375130169219873027171
skew: 0.45
deg: 5
c5: 8
c0: 35
m: 500000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3100000)
Primes: RFBsize:216816, AFBsize:217636, largePrimes:7586330 encountered
Relations: rels:7073916, finalFF:488697
Max relations in full relation-set: 28
Initial matrix: 434517 x 488697 with sparse part having weight 43843717.
Pruned matrix : 412969 x 415205 with weight 33648580.
Total sieving time: 64.61 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.20 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 65.07 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(55·10¹⁵⁸-1)/9 = 6(1)₁₅₈_<159> = 13 · 23 · 5763827 · 1559789123863_<13> · C138

C138 = P59 · P80

P59 = 15010258650299280272276491101329623983515589707475827317847_<59>

P80 = 15145513101806035552114587951495643112100912817276775268355705388408504954678887_<80>

Number: n
N=227338069049605129053211193199122381737271351068558536526884137163254204545481577681925791011163714893896017433744000903964174094369196289
  ( 138 digits)
SNFS difficulty: 160 digits.
Divisors found:

Linear algebra using Msieve 1.26:

Sun Sep 30 21:00:47 2007  commencing square root phase
Sun Sep 30 21:00:47 2007  reading relations for dependency 1
Sun Sep 30 21:00:47 2007  read 187803 cycles
Sun Sep 30 21:00:48 2007  cycles contain 698085 unique relations
Sun Sep 30 21:01:15 2007  read 698085 relations
Sun Sep 30 21:01:20 2007  multiplying 993110 relations
Sun Sep 30 21:03:51 2007  multiply complete, coefficients have about 26.43 million bits
Sun Sep 30 21:03:52 2007  initial square root is modulo 38909441
Sun Sep 30 21:09:48 2007  prp59 factor: 15010258650299280272276491101329623983515589707475827317847
Sun Sep 30 21:09:48 2007  prp80 factor: 15145513101806035552114587951495643112100912817276775268355705388408504954678887
Sun Sep 30 21:09:48 2007  elapsed time 01:03:31

Version: GGNFS-0.77.1-20051202-athlon
Total time: 29.89 hours.
Scaled time: 43.28 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_6_1_158
n: 227338069049605129053211193199122381737271351068558536526884137163254204545481577681925791011163714893896017433744000903964174094369196289
skew: 0.56
deg: 5
c5: 88
c0: -5
m: 50000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1600000)
Primes: RFBsize:183072, AFBsize:183537, largePrimes:7075458 encountered
Relations: rels:6528000, finalFF:420262
Max relations in full relation-set: 28
Initial matrix: 366675 x 420262 with sparse part having weight 36710081.
Pruned matrix : 330856 x 332753 with weight 26194028.
Total sieving time: 29.67 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 29.89 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Sep 30, 2007

By Bruce Dodson

(10³³⁹-1)/9 is divisible by 777734075184513369134763199249605543798943174359980119_<54>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 29, 2007 (5th)

By Yousuke Koide

10¹⁰⁷⁵+1 is divisible by 17749774754658825560922224895404476651_<38>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 29, 2007 (4th)

By suberi / PRIMO

6·10²⁵⁹³+7 is prime!

(55·10²⁹⁶⁹+71)/9 is prime!

Sep 29, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

(2·10¹⁶⁵-17)/3 = (6)₁₆₄1_<165> = 24310071773347_<14> · C152

C152 = P50 · P102

P50 = 51734164323600805573653584774564809428106146895381_<50>

P102 = 530084446675280350994104791959744914314598013435184675057749458635575389733945696768078005752479641723_<102>

Number: n
N=27423475869683962390491718591322401700236139951798106363550172466967761626634044630890142340664811630560708218722793851241742987522268137155303643581463
  ( 152 digits)
SNFS difficulty: 165 digits.
Divisors found:

Linear algebra using Msieve 1.26:

...
Sat Sep 29 12:41:06 2007  commencing square root phase
Sat Sep 29 12:41:06 2007  reading relations for dependency 1
Sat Sep 29 12:41:06 2007  read 242194 cycles
Sat Sep 29 12:41:07 2007  cycles contain 838445 unique relations
Sat Sep 29 12:41:38 2007  read 838445 relations
Sat Sep 29 12:41:44 2007  multiplying 1189934 relations
Sat Sep 29 12:44:18 2007  multiply complete, coefficients have about 26.63 million bits
Sat Sep 29 12:44:18 2007  initial square root is modulo 44576321
Sat Sep 29 12:50:18 2007  prp50 factor: 51734164323600805573653584774564809428106146895381
Sat Sep 29 12:50:18 2007  prp102 factor: 530084446675280350994104791959744914314598013435184675057749458635575389733945696768078005752479641723
Sat Sep 29 12:50:18 2007  elapsed time 01:33:37

Version: GGNFS-0.77.1-20051202-athlon
Total time: 63.87 hours.
Scaled time: 92.54 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_6_164_1
n: 27423475869683962390491718591322401700236139951798106363550172466967761626634044630890142340664811630560708218722793851241742987522268137155303643581463
skew: 1.53
deg: 5
c5: 2
c0: -17
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3300000)
Primes: RFBsize:216816, AFBsize:216686, largePrimes:7771552 encountered
Relations: rels:7297268, finalFF:503771
Max relations in full relation-set: 28
Initial matrix: 433567 x 503771 with sparse part having weight 49944999.
Pruned matrix : 407928 x 410159 with weight 37183923.
Total sieving time: 63.60 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 63.87 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

5·10¹⁶⁷-7 = 4(9)₁₆₆3_<168> = 13 · C167

C167 = P47 · P121

P47 = 27166347444900583109731812696436491851217550133_<47>

P121 = 1415778788059272495359858060016860902525618476647398886043545011620987173109239480930954828521246215935467936088821001417_<121>

Number: n
N=38461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461
  ( 167 digits)
SNFS difficulty: 167 digits.
Divisors found:

Linear algebra by Msieve 1.26:

Sat Sep 29 23:21:09 2007  commencing square root phase
Sat Sep 29 23:21:09 2007  reading relations for dependency 1
Sat Sep 29 23:21:09 2007  read 257497 cycles
Sat Sep 29 23:21:10 2007  cycles contain 895173 unique relations
Sat Sep 29 23:22:06 2007  read 895173 relations
Sat Sep 29 23:22:16 2007  multiplying 1259610 relations
Sat Sep 29 23:29:41 2007  multiply complete, coefficients have about 37.13 milli on bits
Sat Sep 29 23:29:43 2007  initial square root is modulo 214451
Sat Sep 29 23:41:15 2007  prp47 factor: 27166347444900583109731812696436491851217550133
Sat Sep 29 23:41:15 2007  prp121 factor: 1415778788059272495359858060016860902525618476647398886043545011620987173109239480930954828521246215935467936088821001417
Sat Sep 29 23:41:15 2007  elapsed time 02:44:57

Version: GGNFS-0.77.1-20051202-athlon
Total time: 199.44 hours.
Scaled time: 238.33 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_4_9_166_3
n: 38461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461
type: snfs
skew: 1.00
deg: 5
c5: 500
c0: -7
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3300000)
Primes: RFBsize:250150, AFBsize:249951, largePrimes:7696642 encountered
Relations: rels:7217894, finalFF:566646
Max relations in full relation-set: 28
Initial matrix: 500167 x 566646 with sparse part having weight 45760093.
Pruned matrix : 461435 x 463999 with weight 34043459.
Total sieving time: 198.86 hours.
Total relation processing time: 0.58 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.6,2.6,100000
total time: 199.44 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Sep 29, 2007 (2nd)

By Jo Yeong Uk / GGNFS

(5·10¹⁵⁵+7)/3 = 1(6)₁₅₄9_<156> = 59 · 3975371759544157964120556169_<28> · C126

C126 = P50 · P77

P50 = 12183673828219514815541105378476410328653530357743_<50>

P77 = 58323116951920764556691672750208036680903493856562686440783028131664900724273_<77>

Number: 16669_155
N=710589833587302941718597558350764196066850853049176811985093853269458721857536326881047933687224985740262132968074713493595839
  ( 126 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=12183673828219514815541105378476410328653530357743 (pp50)
 r2=58323116951920764556691672750208036680903493856562686440783028131664900724273 (pp77)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 18.11 hours.
Scaled time: 38.82 units (timescale=2.143).
Factorization parameters were as follows:
n: 710589833587302941718597558350764196066850853049176811985093853269458721857536326881047933687224985740262132968074713493595839
m: 10000000000000000000000000000000
c5: 5
c0: 7
skew: 1.07
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216351, largePrimes:5702060 encountered
Relations: rels:5761249, finalFF:638372
Max relations in full relation-set: 28
Initial matrix: 433232 x 638372 with sparse part having weight 49932713.
Pruned matrix : 308816 x 311046 with weight 30557046.
Total sieving time: 17.42 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.57 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 18.11 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Sep 29, 2007

By Sinkiti Sibata / GGNFS

(5·10¹⁵²+7)/3 = 1(6)₁₅₁9_<153> = 13 · 4987 · 377579803 · 3436321013_<10> · 6969202531_<10> · 1361822893003_<13> · C108

C108 = P46 · P62

P46 = 2737389693912651920291775161351885326232522611_<46>

P62 = 76264635966685860724726069046227515943445121318873286926559367_<62>

Number: 16669_152
N=208766028505206032982047684947445945022194314191543387718652600248442907703745958949603148169464391261347237
  ( 108 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=2737389693912651920291775161351885326232522611 (pp46)
 r2=76264635966685860724726069046227515943445121318873286926559367 (pp62)
Version: GGNFS-0.77.1-20060513-k8
Total time: 26.20 hours.
Scaled time: 51.28 units (timescale=1.957).
Factorization parameters were as follows:
name: 16669_152
n: 208766028505206032982047684947445945022194314191543387718652600248442907703745958949603148169464391261347237
m: 1000000000000000000000000000000
c5: 500
c0: 7
skew: 0.43
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176133, largePrimes:5921246 encountered
Relations: rels:6179778, finalFF:785801
Max relations in full relation-set: 28
Initial matrix: 352501 x 785801 with sparse part having weight 71297699.
Pruned matrix : 226386 x 228212 with weight 33405143.
Total sieving time: 24.91 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.02 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 26.20 hours.
 --------- CPU info (if available) ----------

5·10¹⁶¹-7 = 4(9)₁₆₀3_<162> = 13 · 103 · 58693 · 85201 · 56518060850527_<14> · C136

C136 = P49 · P87

P49 = 4798551110626920975723815067816871876805464439071_<49>

P87 = 275334764005974011025338002993961748286200016743548777673724333243675964471822107503727_<87>

Number: 49993_161
N=1321207937615067776138099496089850613691726498550114845141787036218852281776516361293885682470727693894523974030933270087638528096917617
  ( 136 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=4798551110626920975723815067816871876805464439071 (pp49)
 r2=275334764005974011025338002993961748286200016743548777673724333243675964471822107503727 (pp87)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 94.90 hours.
Scaled time: 64.25 units (timescale=0.677).
Factorization parameters were as follows:
name: 49993_161
n: 1321207937615067776138099496089850613691726498550114845141787036218852281776516361293885682470727693894523974030933270087638528096917617
m: 100000000000000000000000000000000
c5: 50
c0: -7
skew: 0.67
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4550001)
Primes: RFBsize:315948, AFBsize:316881, largePrimes:5844440 encountered
Relations: rels:5989509, finalFF:769982
Max relations in full relation-set: 28
Initial matrix: 632894 x 769982 with sparse part having weight 47420540.
Pruned matrix : 526978 x 530206 with weight 32469606.
Total sieving time: 82.02 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 12.29 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 94.90 hours.
 --------- CPU info (if available) ----------

Sep 28, 2007 (5th)

By Bruce Dodson

10³⁵²+1 is divisible by 196492106862714324563103086902334481596741493532094589569_<57>, cofactor is prime.

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 28, 2007 (4th)

By Robert Backstrom / GGNFS

(14·10¹⁶⁴-41)/9 = 1(5)₁₆₃1_<165> = 7394276783_<10> · C155

C155 = P33 · P122

P33 = 241913548612846605274086927369517_<33>

P122 = 86962022362460490445785055865229214136443842893085986014021798676035510354833177041605490276301765124099002836589234876341_<122>

Number: n
N=21037291424252539446163109033236138674247346680037789377346270695525241546202958190719320217737047557792989848315711277798343615987894452010473997907897297
  ( 155 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=241913548612846605274086927369517 (pp33)
 r2=86962022362460490445785055865229214136443842893085986014021798676035510354833177041605490276301765124099002836589234876341 (pp122)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 74.48 hours.
Scaled time: 98.54 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_1_5_163_1
n: 21037291424252539446163109033236138674247346680037789377346270695525241546202958190719320217737047557792989848315711277798343615987894452010473997907897297
skew: 1.96
deg: 5
c5: 7
c0: -205
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2800001)
Primes: RFBsize:250150, AFBsize:250442, largePrimes:7581353 encountered
Relations: rels:7099178, finalFF:586042
Max relations in full relation-set: 48
Initial matrix: 500657 x 586042 with sparse part having weight 50177668.
Pruned matrix : 439767 x 442334 with weight 33392103.
Total sieving time: 60.70 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 13.32 hours.
Total square root time: 0.10 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 74.48 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Sep 28, 2007 (3rd)

By Sinkiti Sibata / GGNFS

(5·10¹³⁸+7)/3 = 1(6)₁₃₇9_<139> = 17 · 3307 · 111476834769978619_<18> · C117

C117 = P58 · P60

P58 = 2207115310302675107711411136506882374916425885644292317671_<58>

P60 = 120491380689937645366860425953951437824016468528431170048099_<60>

Number: 16669_138
N=265938371080269481663171733466742068358255746135570115355624735763817783285646181622002721514196167950503021257657429
  ( 117 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=2207115310302675107711411136506882374916425885644292317671 (pp58)
 r2=120491380689937645366860425953951437824016468528431170048099 (pp60)
Version: GGNFS-0.77.1-20060513-k8
Total time: 9.91 hours.
Scaled time: 19.51 units (timescale=1.969).
Factorization parameters were as follows:
name: 16669_138
n: 265938371080269481663171733466742068358255746135570115355624735763817783285646181622002721514196167950503021257657429
m: 5000000000000000000000000000
c5: 8
c0: 35
skew: 1.34
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1675001)
Primes: RFBsize:78498, AFBsize:63913, largePrimes:1600904 encountered
Relations: rels:1609087, finalFF:168926
Max relations in full relation-set: 28
Initial matrix: 142476 x 168926 with sparse part having weight 16797660.
Pruned matrix : 135545 x 136321 with weight 12105787.
Total sieving time: 9.60 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 9.91 hours.
 --------- CPU info (if available) ----------

(5·10¹³⁹+7)/3 = 1(6)₁₃₈9_<140> = 6871 · 89220757 · C128

C128 = P41 · P87

P41 = 68519056331623047707327877417940217357011_<41>

P87 = 396781599919562194526485294892308063321566863525043969970677953144473101558904885402357_<87>

Number: 16669_139
N=27187100796240000941757996128380631790386988553157290361212166281105529340875250396473903242091659504609700154156408933849874927
  ( 128 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=68519056331623047707327877417940217357011 (pp41)
 r2=396781599919562194526485294892308063321566863525043969970677953144473101558904885402357 (pp87)
Version: GGNFS-0.77.1-20060513-k8
Total time: 7.76 hours.
Scaled time: 15.49 units (timescale=1.996).
Factorization parameters were as follows:
name: 16669_139
n: 27187100796240000941757996128380631790386988553157290361212166281105529340875250396473903242091659504609700154156408933849874927
m: 10000000000000000000000000000
c5: 1
c0: 14
skew: 1.7
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1375001)
Primes: RFBsize:78498, AFBsize:63623, largePrimes:1550075 encountered
Relations: rels:1551224, finalFF:171077
Max relations in full relation-set: 28
Initial matrix: 142185 x 171077 with sparse part having weight 14886101.
Pruned matrix : 133835 x 134609 with weight 10106155.
Total sieving time: 7.52 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 7.76 hours.
 --------- CPU info (if available) ----------

Sep 28, 2007 (2nd)

By Jo Yeong Uk / GGNFS, GMP-ECM

(5·10¹⁴²+7)/3 = 1(6)₁₄₁9_<143> = 813978461 · C134

C134 = P40 · P94

P40 = 5800307603283903977690274884081525862077_<40>

P94 = 3530082139245880010115509104883085123122514153709233376692762673105064986713732631002976914277_<94>

Number: 16669_142
N=20475562272484586870004004524471890991064770529188077209658090285348062381550740648734029175578721691342968676743237148957761754173329
  ( 134 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=5800307603283903977690274884081525862077 (pp40)
 r2=3530082139245880010115509104883085123122514153709233376692762673105064986713732631002976914277 (pp94)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.83 hours.
Scaled time: 14.63 units (timescale=2.141).
Factorization parameters were as follows:
n: 20475562272484586870004004524471890991064770529188077209658090285348062381550740648734029175578721691342968676743237148957761754173329
m: 50000000000000000000000000000
c5: 4
c0: 175
skew: 2.13
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1200001)
Primes: RFBsize:114155, AFBsize:114067, largePrimes:3312011 encountered
Relations: rels:3363019, finalFF:351333
Max relations in full relation-set: 28
Initial matrix: 228286 x 351333 with sparse part having weight 30146662.
Pruned matrix : 184826 x 186031 with weight 13060822.
Total sieving time: 6.64 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.83 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

(5·10¹⁴³+7)/3 = 1(6)₁₄₂9_<144> = 2597673844567493_<16> · C128

C128 = P33 · P96

P33 = 434046091093577317652060703761719_<33>

P96 = 147818325628859156953088758822031349145171816910978388451598502100954879491436158318814376510207_<96>

Number: 16669_143
N=64159966431203876277211145259729258839851155070514316316238539204930112595630101081864207165422843650012653726820231156499365833
  ( 128 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=434046091093577317652060703761719 (pp33)
 r2=147818325628859156953088758822031349145171816910978388451598502100954879491436158318814376510207 (pp96)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.24 hours.
Scaled time: 17.65 units (timescale=2.141).
Factorization parameters were as follows:
n: 64159966431203876277211145259729258839851155070514316316238539204930112595630101081864207165422843650012653726820231156499365833
m: 100000000000000000000000000000
c5: 1
c0: 140
skew: 2.69
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1300001)
Primes: RFBsize:114155, AFBsize:114557, largePrimes:3356219 encountered
Relations: rels:3388872, finalFF:326333
Max relations in full relation-set: 28
Initial matrix: 228776 x 326333 with sparse part having weight 29776228.
Pruned matrix : 196932 x 198139 with weight 14882362.
Total sieving time: 8.02 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 8.24 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

(5·10¹⁵⁸+7)/3 = 1(6)₁₅₇9_<159> = 13² · 98960718128861_<14> · C142

C142 = P31 · P112

P31 = 2810189725402685724689364943993_<31>

P112 = 3546202774378704117363718958207959078238914256676956218627386149550232256336887900588798661867954338838309183537_<112>

Sep 28, 2007

By Sinkiti Sibata / GGNFS

5·10¹⁷⁹-7 = 4(9)₁₇₈3_<180> = 13 · 157 · 319001 · 740321 · 1275172341197_<13> · 3168934862695211_<16> · 185503352859609293_<18> · C121

C121 = P59 · P62

P59 = 20824276942434306550878491316554921169577070969181605095403_<59>

P62 = 66452449689374424275673726430638274402626958940230091126916841_<62>

Number: 49993_179
N=1383824215834715620070456110706078885338595809203545862722727074810567580733069553796012130255235581892164045691052381923
  ( 121 digits)
Divisors found:
 r1=20824276942434306550878491316554921169577070969181605095403 (pp59)
 r2=66452449689374424275673726430638274402626958940230091126916841 (pp62)
Version: GGNFS-0.77.1-20060513-k8
Total time: 84.55 hours.
Scaled time: 168.59 units (timescale=1.994).
Factorization parameters were as follows:
name: 49993_179
n: 1383824215834715620070456110706078885338595809203545862722727074810567580733069553796012130255235581892164045691052381923
skew: 50602.07
# norm 4.41e+16
c5: 37800
c4: 20128544688
c3: 731574065956501
c2: -49160751458878107328
c1: 392457585328640355756184
c0: -30872663122950055012866120
# alpha -5.82
Y1: 2624022091559
Y0: -129633393211373317821743
# Murphy_E 2.81e-10
# M 506787805364640852991178403337491309782409889508448185433954099888929241273787199158859515253510600449456791072798496402
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 4960001)
Primes: RFBsize:348513, AFBsize:348699, largePrimes:7743207 encountered
Relations: rels:7931207, finalFF:836390
Max relations in full relation-set: 28
Initial matrix: 697293 x 836390 with sparse part having weight 72523171.
Pruned matrix : 582401 x 585951 with weight 47666914.
Total sieving time: 78.91 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 4.74 hours.
Time per square root: 0.47 hours.
Prototype def-par.txt line would be:
gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 84.55 hours.
 --------- CPU info (if available) ----------

Sep 27, 2007 (5th)

By suberi / PRIMO

(17·10²⁴⁶⁵-11)/3 is prime!

Sep 27, 2007 (4th)

By Sinkiti Sibata / GGNFS

(5·10¹⁴¹+7)/3 = 1(6)₁₄₀9_<142> = 3643 · 25537 · 51757591 · 63071636252236439379138851123_<29> · C97 = P33 · P65

P33 = 391280500666926357614593359860867_<33>

P65 = 14025661202251856928100285392792838965856556326678840999770191689_<65>

Number: 16669_141
N=5487967737401790843509693098739988690283003641505514417737061993133022559891161126165558959734363
  ( 97 digits)
Divisors found:
 r1=391280500666926357614593359860867 (pp33)
 r2=14025661202251856928100285392792838965856556326678840999770191689 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 13.08 hours.
Scaled time: 8.86 units (timescale=0.677).
Factorization parameters were as follows:
name: 16669_141
n:  5487967737401790843509693098739988690283003641505514417737061993133022559891161126165558959734363
m:  14369675926318849190988
deg: 4
c4: 128713368
c3: 321000566584
c2: 421345394109067688
c1: -1579948430526136245
c0: -274075801134666159754345
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.486
# E(F1,F2) = 1.904845e-05
# GGNFS version 0.77.1-20060513-pentium4 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1190818402.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1680001)
Primes: RFBsize:92938, AFBsize:92333, largePrimes:1922598 encountered
Relations: rels:2011676, finalFF:220756
Max relations in full relation-set: 28
Initial matrix: 185350 x 220756 with sparse part having weight 21582414.
Pruned matrix : 170926 x 171916 with weight 14807077.
Polynomial selection time: 0.17 hours.
Total sieving time: 11.89 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.81 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,96,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 13.08 hours.
 --------- CPU info (if available) ----------

Sep 27, 2007 (3rd)

By Jo Yeong Uk / GMP-ECM, GGNFS

(5·10¹⁸⁷+7)/3 = 1(6)₁₈₆9_<188> = C188

C188 = P30 · P158

P30 = 809800994185580459461342700011_<30>

P158 = 20581188200970768756638678837132189543155931483203808645215586178063428078238759791181233823231551560665801684249575705334754779112834205568013634241048487879_<158>

(5·10¹³²+7)/3 = 1(6)₁₃₁9_<133> = 71 · C131

C131 = P34 · P97

P34 = 2485169554431976453434061661307773_<34>

P97 = 9445704966847322970558865702100853962207830112965205476236509054211032779897889569875889195527943_<97>

Number: 16669_132
N=23474178403755868544600938967136150234741784037558685446009389671361502347417840375586854460093896713615023474178403755868544600939
  ( 131 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=2485169554431976453434061661307773 (pp34)
 r2=9445704966847322970558865702100853962207830112965205476236509054211032779897889569875889195527943 (pp97)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.33 hours.
Scaled time: 4.95 units (timescale=2.128).
Factorization parameters were as follows:
n: 23474178403755868544600938967136150234741784037558685446009389671361502347417840375586854460093896713615023474178403755868544600939
m: 500000000000000000000000000
c5: 4
c0: 175
skew: 2.13
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1100001)
Primes: RFBsize:107126, AFBsize:106873, largePrimes:2226874 encountered
Relations: rels:2343305, finalFF:290382
Max relations in full relation-set: 28
Initial matrix: 214063 x 290382 with sparse part having weight 19190038.
Pruned matrix : 176356 x 177490 with weight 8874710.
Total sieving time: 2.19 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 2.33 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

(5·10¹³⁵+7)/3 = 1(6)₁₃₄9_<136> = 283 · 92553614341_<11> · C122

C122 = P49 · P74

P49 = 2576769183774005584057447380213481615877532498847_<49>

P74 = 24694111962373273863858692871467284566884745178594644170287579543940440309_<74>

Number: 16669_135
N=63631026725308488187427141159783305023986096327229654593888951415465371751129423611565979517723069748777754256294214823723
  ( 122 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=2576769183774005584057447380213481615877532498847 (pp49)
 r2=24694111962373273863858692871467284566884745178594644170287579543940440309 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.83 hours.
Scaled time: 6.02 units (timescale=2.129).
Factorization parameters were as follows:
n: 63631026725308488187427141159783305023986096327229654593888951415465371751129423611565979517723069748777754256294214823723
m: 1000000000000000000000000000
c5: 5
c0: 7
skew: 1.07
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1200001)
Primes: RFBsize:107126, AFBsize:107203, largePrimes:2285972 encountered
Relations: rels:2456639, finalFF:329462
Max relations in full relation-set: 28
Initial matrix: 214394 x 329462 with sparse part having weight 24010778.
Pruned matrix : 168264 x 169399 with weight 9837861.
Total sieving time: 2.69 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 2.83 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

(5·10¹⁵¹+7)/3 = 1(6)₁₅₀9_<152> = 17701418095831_<14> · 1812077986113440186399161321739_<31> · C108

C108 = P39 · P70

P39 = 194105463026917266409863270055667221771_<39>

P70 = 2676862394581312139459903416519678229802305636596524777765101615813171_<70>

(5·10¹³⁷+7)/3 = 1(6)₁₃₆9_<138> = 293 · 132893 · 1015853 · 512709215972310397_<18> · C106

C106 = P44 · P63

P44 = 33067855423525789757242415631561806102865053_<44>

P63 = 248525526252847290942368984924627161881822914913147146704360297_<63>

Number: 16669_137
N=8218206171184817335096503188675348229821826657900353296819064455753352874913254325905363890559179282000741
  ( 106 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=33067855423525789757242415631561806102865053 (pp44)
 r2=248525526252847290942368984924627161881822914913147146704360297 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.56 hours.
Scaled time: 7.54 units (timescale=2.118).
Factorization parameters were as follows:
n: 8218206171184817335096503188675348229821826657900353296819064455753352874913254325905363890559179282000741
m: 5000000000000000000000000000
c5: 4
c0: 175
skew: 2.13
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1350001)
Primes: RFBsize:107126, AFBsize:106873, largePrimes:2329174 encountered
Relations: rels:2479966, finalFF:306952
Max relations in full relation-set: 28
Initial matrix: 214063 x 306952 with sparse part having weight 23622463.
Pruned matrix : 181583 x 182717 with weight 11078387.
Total sieving time: 3.40 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 3.56 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Sep 27, 2007 (2nd)

By Robert Backstrom / GGNFS

2·10¹⁶⁷-7 = 1(9)₁₆₆3_<168> = 23 · C166

C166 = P33 · P134

P33 = 817671420061668453239381786225641_<33>

P134 = 10634653432374120218546314263462036182748850386624188463030773029103326239415114946154180410545538376172609896000131661254182519321751_<134>

Number: n
N=8695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391
  ( 166 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=817671420061668453239381786225641 (pp33)
 r2=10634653432374120218546314263462036182748850386624188463030773029103326239415114946154180410545538376172609896000131661254182519321751 (pp134)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 93.38 hours.
Scaled time: 121.68 units (timescale=1.303).
Factorization parameters were as follows:
name: KA_1_9_166_3
n: 8695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391
skew: 0.51
deg: 5
c5: 200
c0: -7
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 4100001)
Primes: RFBsize:216816, AFBsize:216921, largePrimes:7989364 encountered
Relations: rels:7543447, finalFF:491774
Max relations in full relation-set: 28
Initial matrix: 433802 x 491774 with sparse part having weight 54393195.
Pruned matrix : 412924 x 415157 with weight 43131647.
Total sieving time: 87.10 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 5.82 hours.
Total square root time: 0.15 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 93.38 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(5·10¹⁴⁸+7)/3 = 1(6)₁₄₇9_<149> = C149

C149 = P47 · P50 · P53

P47 = 18650313335606201329724729364112809673312876463_<47>

P50 = 84145670486626078050750612549722130221630831476553_<50>

P53 = 10620154668476690275768442467100096825061277196932171_<53>

Number: n
N=16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 149 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=18650313335606201329724729364112809673312876463 (pp47)
 r2=84145670486626078050750612549722130221630831476553 (pp50)
 r3=10620154668476690275768442467100096825061277196932171 (pp53)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 14.42 hours.
Scaled time: 18.77 units (timescale=1.302).
Factorization parameters were as follows:
name: KA_1_6_147_9
n: 16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
skew: 0.84
deg: 5
c5: 8
c0: 35
m: 500000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:148933, AFBsize:149505, largePrimes:6860845 encountered
Relations: rels:6228580, finalFF:338172
Max relations in full relation-set: 28
Initial matrix: 298503 x 338172 with sparse part having weight 28470354.
Pruned matrix : 279282 x 280838 with weight 20632016.
Total sieving time: 12.23 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.80 hours.
Total square root time: 0.19 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 14.42 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Sep 27, 2007

By Jo Yeong Uk / GGNFS

(5·10¹³¹+7)/3 = 1(6)₁₃₀9_<132> = 502809239 · 2578087651229_<13> · C111

C111 = P40 · P71

P40 = 1302814026384104145222921505524360161093_<40>

P71 = 98688238257748130465524894016056404057253771100584036810592603966756843_<71>

Number: 16669_131
N=128572421041330628945312107304054615470294816718767333011548094860238837956131360269939220155411684012240109399
  ( 111 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=1302814026384104145222921505524360161093 (pp40)
 r2=98688238257748130465524894016056404057253771100584036810592603966756843 (pp71)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.83 hours.
Scaled time: 6.05 units (timescale=2.139).
Factorization parameters were as follows:
n: 128572421041330628945312107304054615470294816718767333011548094860238837956131360269939220155411684012240109399
m: 100000000000000000000000000
c5: 50
c0: 7
skew: 0.67
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 1100001)
Primes: RFBsize:78498, AFBsize:78386, largePrimes:1577484 encountered
Relations: rels:1592551, finalFF:190981
Max relations in full relation-set: 28
Initial matrix: 156949 x 190981 with sparse part having weight 11746680.
Pruned matrix : 144889 x 145737 with weight 7156255.
Total sieving time: 2.73 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 2.83 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Sep 26, 2007 (5th)

By JMB / GGNFS

8·10¹⁸¹+3 = 8(0)₁₈₀3_<182> = 17 · 47 · 120077 · 766223541469_<12> · 752719880879203667_<18> · 148057738580234774662331071_<27> · C118

C118 = P45 · P74

P45 = 147863869707137044125193702898663252618158313_<45>

P74 = 66039126656639520936203017529360818061007971819918535640380875386612837009_<74>

Number: N
N=9764800819530466924518836952107346921926064836602594080779488507011172569982077589063765484307783295905707377627405817
  ( 118 digits)
Divisors found:
 r1=147863869707137044125193702898663252618158313 (pp45)
 r2=66039126656639520936203017529360818061007971819918535640380875386612837009 (pp74)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 72.97 hours.
Scaled time: 134.20 units (timescale=1.839).
Factorization parameters were as follows:
name: 8*10^181+3
n: 9764800819530466924518836952107346921926064836602594080779488507011172569982077589063765484307783295905707377627405817
skew: 67407.88
# norm 1.60e+16
c5: 12060
c4: 3987625233
c3: -501223287428036
c2: -13966524767850640108
c1: 532227260136176141487706
c0: 11552261902925874836942455365
# alpha -5.61
Y1: 2159113508321
Y0: -60487020326792030157938
# Murphy_E 3.57e-10
# M 5213949619208846846643369347895106390731876475313017475218358403523304199793861470938855378906618354132884471051345753
type: gnfs
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 25000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1500000, 1900001)
Primes: RFBsize:216816, AFBsize:216818, largePrimes:8168351 encountered
Relations: rels:8459764, finalFF:541290
Max relations in full relation-set: 28
Initial matrix: 433714 x 541290 with sparse part having weight 68304122.
Pruned matrix : 370334 x 372566 with weight 51046323.
Total sieving time: 68.03 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 4.39 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,50,50,2.4,2.4,60000
total time: 72.97 hours.
 --------- CPU info (if available) ----------

Sep 26, 2007 (4th)

By suberi / PRIMO

(52·10²⁴⁸²-43)/9 is prime!

Sep 26, 2007 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

(5·10¹⁰⁹+7)/3 = 1(6)₁₀₈9_<110> = 19² · C107

C107 = P42 · P66

P42 = 153946522305899923004676383646159813796121_<42>

P66 = 299896685009093874497686190587633018428192207232800575636015338349_<66>

Number: 16669_109
N=46168051708217913204062788550323176361957525392428439519852262234533702677746999076638965835641735918744229
  ( 107 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=153946522305899923004676383646159813796121 (pp42)
 r2=299896685009093874497686190587633018428192207232800575636015338349 (pp66)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.17 hours.
Scaled time: 0.79 units (timescale=0.677).
Factorization parameters were as follows:
name: 16669_109
n: 46168051708217913204062788550323176361957525392428439519852262234533702677746999076638965835641735918744229
m: 10000000000000000000000
c5: 1
c0: 14
skew: 1.7
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:63623, largePrimes:1899503 encountered
Relations: rels:1884233, finalFF:172922
Max relations in full relation-set: 28
Initial matrix: 112785 x 172922 with sparse part having weight 11280001.
Pruned matrix : 87896 x 88523 with weight 3680813.
Total sieving time: 1.01 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.17 hours.
 --------- CPU info (if available) ----------

(5·10¹¹⁵+7)/3 = 1(6)₁₁₄9_<116> = 83 · 1069 · 1180428929_<10> · C102

C102 = P39 · P63

P39 = 296398376609473226797596655124462993281_<39>

P63 = 536880075739627642112309347769656425847569291133442846496928603_<63>

Number: 16669_115
N=159130382883196664131166647978403378748111484644347405870264581612954267174235629404567704102325716443
  ( 102 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=296398376609473226797596655124462993281 (pp39)
 r2=536880075739627642112309347769656425847569291133442846496928603 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.63 hours.
Scaled time: 1.10 units (timescale=0.677).
Factorization parameters were as follows:
name: 16669_115
n: 159130382883196664131166647978403378748111484644347405870264581612954267174235629404567704102325716443
m: 100000000000000000000000
c5: 5
c0: 7
skew: 1.07
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:64228, largePrimes:2093547 encountered
Relations: rels:2213778, finalFF:271300
Max relations in full relation-set: 28
Initial matrix: 113391 x 271300 with sparse part having weight 21663794.
Pruned matrix : 76323 x 76953 with weight 4050572.
Total sieving time: 1.45 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.63 hours.
 --------- CPU info (if available) ----------

(5·10¹²⁰+7)/3 = 1(6)₁₁₉9_<121> = 210451967185245864060738227648101_<33> · C88

C88 = P34 · P55

P34 = 2003771457999863638436035664075387_<34>

P55 = 3952278809073709433995319843828553332517951348922169387_<55>

Wed Sep 26 14:24:28 2007  Msieve v. 1.26
Wed Sep 26 14:24:28 2007  random seeds: 5143490f 0701fb59
Wed Sep 26 14:24:28 2007  factoring 7919463471679591443105528414604368703900563230510077999800695379563554517322213551577769 (88 digits)
Wed Sep 26 14:24:29 2007  commencing quadratic sieve (88-digit input)
Wed Sep 26 14:24:30 2007  using multiplier of 1
Wed Sep 26 14:24:30 2007  using 64kb Pentium 2 sieve core
Wed Sep 26 14:24:30 2007  sieve interval: 14 blocks of size 65536
Wed Sep 26 14:24:30 2007  processing polynomials in batches of 8
Wed Sep 26 14:24:30 2007  using a sieve bound of 1527497 (57880 primes)
Wed Sep 26 14:24:30 2007  using large prime bound of 122199760 (26 bits)
Wed Sep 26 14:24:30 2007  using double large prime bound of 360351695070240 (42-49 bits)
Wed Sep 26 14:24:30 2007  using trial factoring cutoff of 49 bits
Wed Sep 26 14:24:30 2007  polynomial 'A' values have 11 factors
Wed Sep 26 19:19:22 2007  58229 relations (16203 full + 42026 combined from 608880 partial), need 57976
Wed Sep 26 19:19:29 2007  begin with 625083 relations
Wed Sep 26 19:19:47 2007  reduce to 139473 relations in 10 passes
Wed Sep 26 19:19:48 2007  attempting to read 139473 relations
Wed Sep 26 19:19:56 2007  recovered 139473 relations
Wed Sep 26 19:19:56 2007  recovered 112269 polynomials
Wed Sep 26 19:20:15 2007  attempting to build 58229 cycles
Wed Sep 26 19:20:15 2007  found 58229 cycles in 5 passes
Wed Sep 26 19:20:17 2007  distribution of cycle lengths:
Wed Sep 26 19:20:17 2007     length 1 : 16203
Wed Sep 26 19:20:17 2007     length 2 : 11462
Wed Sep 26 19:20:17 2007     length 3 : 10350
Wed Sep 26 19:20:17 2007     length 4 : 7641
Wed Sep 26 19:20:17 2007     length 5 : 5205
Wed Sep 26 19:20:17 2007     length 6 : 3172
Wed Sep 26 19:20:17 2007     length 7 : 1903
Wed Sep 26 19:20:17 2007     length 9+: 2293
Wed Sep 26 19:20:17 2007  largest cycle: 18 relations
Wed Sep 26 19:20:18 2007  matrix is 57880 x 58229 with weight 3346646 (avg 57.47/col)
Wed Sep 26 19:20:22 2007  filtering completed in 3 passes
Wed Sep 26 19:20:22 2007  matrix is 53415 x 53479 with weight 3096508 (avg 57.90/col)
Wed Sep 26 19:20:24 2007  saving the first 48 matrix rows for later
Wed Sep 26 19:20:24 2007  matrix is 53367 x 53479 with weight 2483927 (avg 46.45/col)
Wed Sep 26 19:20:24 2007  matrix includes 64 packed rows
Wed Sep 26 19:20:24 2007  using block size 10922 for processor cache size 256 kB
Wed Sep 26 19:20:24 2007  commencing Lanczos iteration
Wed Sep 26 19:23:14 2007  lanczos halted after 845 iterations
Wed Sep 26 19:23:15 2007  recovered 16 nontrivial dependencies
Wed Sep 26 19:23:35 2007  prp34 factor: 2003771457999863638436035664075387
Wed Sep 26 19:23:35 2007  prp55 factor: 3952278809073709433995319843828553332517951348922169387
Wed Sep 26 19:23:35 2007  elapsed time 04:59:07

(5·10¹²¹+7)/3 = 1(6)₁₂₀9_<122> = 79 · 2382356651_<10> · C110

C110 = P39 · P72

P39 = 275708725429269016809228525155998997753_<39>

P72 = 321191741127943587251282728962673310095889920760636481110578718074425937_<72>

Number: 16669_121
N=88555365564793051234214008584940727814733466817154162992301027014493685329128418132245529605674917232827919561
  ( 110 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=275708725429269016809228525155998997753 (pp39)
 r2=321191741127943587251282728962673310095889920760636481110578718074425937 (pp72)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.59 hours.
Scaled time: 1.75 units (timescale=0.677).
Factorization parameters were as follows:
name: 16669_121
n: 88555365564793051234214008584940727814733466817154162992301027014493685329128418132245529605674917232827919561
m: 1000000000000000000000000
c5: 50
c0: 7
skew: 0.67
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:63963, largePrimes:2104728 encountered
Relations: rels:2144770, finalFF:180084
Max relations in full relation-set: 28
Initial matrix: 113126 x 180084 with sparse part having weight 15976568.
Pruned matrix : 96531 x 97160 with weight 6113251.
Total sieving time: 2.32 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.59 hours.
 --------- CPU info (if available) ----------

(5·10¹²⁵+7)/3 = 1(6)₁₂₄9_<126> = 4105166921_<10> · 20017012591_<11> · C106

C106 = P33 · P74

P33 = 168513932435459060567620404345611_<33>

P74 = 12036018680677828464748171772279011079478949036231241898241956856646325889_<74>

Number: 16669_125
N=2028236838747666687478534951496303214000516428894914134664497036559678113327291556491062877412232492823179
  ( 106 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=168513932435459060567620404345611 (pp33)
 r2=12036018680677828464748171772279011079478949036231241898241956856646325889 (pp74)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 3.06 hours.
Scaled time: 2.07 units (timescale=0.677).
Factorization parameters were as follows:
name: 16669_125
n: 2028236838747666687478534951496303214000516428894914134664497036559678113327291556491062877412232492823179
m: 10000000000000000000000000
c5: 5
c0: 7
skew: 1.07
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:64228, largePrimes:2213124 encountered
Relations: rels:2360223, finalFF:266542
Max relations in full relation-set: 28
Initial matrix: 113391 x 266542 with sparse part having weight 25504051.
Pruned matrix : 85873 x 86503 with weight 6283883.
Total sieving time: 2.80 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.06 hours.
 --------- CPU info (if available) ----------

Sep 26, 2007 (2nd)

By Jo Yeong Uk / GGNFS

(5·10¹¹³+7)/3 = 1(6)₁₁₂9_<114> = 139 · C112

C112 = P56 · P56

P56 = 33323707073076001771345428051913373104674894761352370801_<56>

P56 = 35981614073029109077263780581405124329331786404763064471_<56>

Number: 16669_113
N=1199040767386091127098321342925659472422062350119904076738609112709832134292565947242206235011990407673860911271
  ( 112 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=33323707073076001771345428051913373104674894761352370801 (pp56)
 r2=35981614073029109077263780581405124329331786404763064471 (pp56)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.70 hours.
Scaled time: 1.50 units (timescale=2.143).
Factorization parameters were as follows:
n: 1199040767386091127098321342925659472422062350119904076738609112709832134292565947242206235011990407673860911271
m: 100000000000000000000000
c5: 1
c0: 140
skew: 2.69
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 340001)
Primes: RFBsize:30757, AFBsize:30764, largePrimes:1046995 encountered
Relations: rels:964799, finalFF:87555
Max relations in full relation-set: 28
Initial matrix: 61585 x 87555 with sparse part having weight 4230236.
Pruned matrix : 54927 x 55298 with weight 1881639.
Total sieving time: 0.67 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.70 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

(5·10¹¹⁶+7)/3 = 1(6)₁₁₅9_<117> = 13 · C116

C116 = P32 · P84

P32 = 31003216721782548975602081797253_<32>

P84 = 413522020491030430690268175769186538084881606692266956654906116015314098195825309421_<84>

Number: 16669_116
N=12820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820513
  ( 116 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=31003216721782548975602081797253 (pp32)
 r2=413522020491030430690268175769186538084881606692266956654906116015314098195825309421 (pp84)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.84 hours.
Scaled time: 1.79 units (timescale=2.139).
Factorization parameters were as follows:
n: 12820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820513
m: 100000000000000000000000
c5: 50
c0: 7
skew: 0.67
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 420001)
Primes: RFBsize:49098, AFBsize:49041, largePrimes:1943562 encountered
Relations: rels:1936531, finalFF:147809
Max relations in full relation-set: 28
Initial matrix: 98204 x 147809 with sparse part having weight 12274062.
Pruned matrix : 85193 x 85748 with weight 4983589.
Total sieving time: 0.78 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 0.84 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

(5·10¹¹⁷+7)/3 = 1(6)₁₁₆9_<118> = 337 · 509 · 23677 · C108

C108 = P48 · P60

P48 = 516041832369522017710254534990233044032515687357_<48>

P60 = 795224009016448425092100987054725056223874009925853849747737_<60>

Number: 16669_117
N=410368854757085343761438229042281635409146357321018036623580685567761868529348166730485220151100269610261109
  ( 108 digits)
SNFS difficulty: 119 digits.
Divisors found:
 r1=516041832369522017710254534990233044032515687357 (pp48)
 r2=795224009016448425092100987054725056223874009925853849747737 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.79 hours.
Scaled time: 1.67 units (timescale=2.113).
Factorization parameters were as follows:
n: 410368854757085343761438229042281635409146357321018036623580685567761868529348166730485220151100269610261109
m: 500000000000000000000000
c5: 4
c0: 175
skew: 2.13
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 420001)
Primes: RFBsize:49098, AFBsize:49096, largePrimes:1978458 encountered
Relations: rels:2032316, finalFF:203074
Max relations in full relation-set: 28
Initial matrix: 98258 x 203074 with sparse part having weight 16906655.
Pruned matrix : 75540 x 76095 with weight 4051422.
Total sieving time: 0.74 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,119,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 0.79 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

(5·10¹¹⁹+7)/3 = 1(6)₁₁₈9_<120> = 179449580749_<12> · C108

C108 = P50 · P59

P50 = 25753449757830406639991914695740623420290006566179_<50>

P59 = 36063750448248243471048952703868375635140956097798086208939_<59>

Number: 16669_119
N=928765985247894944730399218898130893992433011358033499769124983962581877754703244378693651035712215324874081
  ( 108 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=25753449757830406639991914695740623420290006566179 (pp50)
 r2=36063750448248243471048952703868375635140956097798086208939 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.78 hours.
Scaled time: 1.67 units (timescale=2.129).
Factorization parameters were as follows:
n: 928765985247894944730399218898130893992433011358033499769124983962581877754703244378693651035712215324874081
m: 1000000000000000000000000
c5: 1
c0: 14
skew: 1.7
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 420001)
Primes: RFBsize:49098, AFBsize:48926, largePrimes:1974603 encountered
Relations: rels:2025360, finalFF:198858
Max relations in full relation-set: 28
Initial matrix: 98088 x 198858 with sparse part having weight 16755508.
Pruned matrix : 76604 x 77158 with weight 4195384.
Total sieving time: 0.73 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 0.78 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

(5·10¹²⁸+7)/3 = 1(6)₁₂₇9_<129> = 13 · 29 · 41491 · C122

C122 = P33 · P89

P33 = 349983130933154147542494609343249_<33>

P89 = 30444327507033853270702399006913464736680064207497013075681509886136946770149506545458183_<89>

Number: 16669_128
N=10655001060066055465971858309540183216152828175044875135214627202503260377049374912642310058783427748363226684657422856567
  ( 122 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=349983130933154147542494609343249 (pp33)
 r2=30444327507033853270702399006913464736680064207497013075681509886136946770149506545458183 (pp89)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.94 hours.
Scaled time: 4.16 units (timescale=2.145).
Factorization parameters were as follows:
n: 10655001060066055465971858309540183216152828175044875135214627202503260377049374912642310058783427748363226684657422856567
m: 100000000000000000000000000
c5: 1
c0: 140
skew: 2.69
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 900001)
Primes: RFBsize:78498, AFBsize:78641, largePrimes:1495828 encountered
Relations: rels:1503438, finalFF:186230
Max relations in full relation-set: 28
Initial matrix: 157203 x 186230 with sparse part having weight 9104275.
Pruned matrix : 143047 x 143897 with weight 5517984.
Total sieving time: 1.86 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.94 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Sep 26, 2007

The factor table of 166...669 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Sep 25, 2007 (3rd)

By Robert Backstrom / GGNFS

3·10¹⁵⁸+7 = 3(0)₁₅₇7_<159> = 89 · 2076619 · 259656955391_<12> · C139

C139 = P45 · P95

P45 = 252655059854571780687683274450095709673880513_<45>

P95 = 24742664377819752522172823349240990874103759568271850621675059742047926996980289580771977958019_<95>

Number: n
N=6251359349339630621166108381490606750376571670303750482199645475819777412486638575944263953290323590162412366640843654132109482845536183747
  ( 139 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=252655059854571780687683274450095709673880513 (pp45)
 r2=24742664377819752522172823349240990874103759568271850621675059742047926996980289580771977958019 (pp95)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 32.13 hours.
Scaled time: 46.40 units (timescale=1.444).
Factorization parameters were as follows:
name: KA_3_0_157_7
n: 6251359349339630621166108381490606750376571670303750482199645475819777412486638575944263953290323590162412366640843654132109482845536183747
skew: 0.30
deg: 5
c5: 3000
c0: 7
m: 10000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:183072, AFBsize:183021, largePrimes:7139599 encountered
Relations: rels:6634469, finalFF:457174
Max relations in full relation-set: 28
Initial matrix: 366160 x 457174 with sparse part having weight 40338936.
Pruned matrix : 305523 x 307417 with weight 25494270.
Total sieving time: 28.79 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 2.99 hours.
Total square root time: 0.12 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 32.13 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Sep 25, 2007 (2nd)

By Sinkiti Sibata / GGNFS

5·10¹⁶²-7 = 4(9)₁₆₁3_<163> = 17 · 1163 · 148309339 · 387720132193027_<15> · C136

C136 = P41 · P96

P41 = 32186888333809678325979899492525673198029_<41>

P96 = 136639266967774480350045857113895807555932147258323470751247259644932218298158286602940005007959_<96>

Number: 49993_162
N=4397992827905366561495616972942610757769676397548052455720011518707669668467184795048847173974047956366224189761866099002983083128112811
  ( 136 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=32186888333809678325979899492525673198029 (pp41)
 r2=136639266967774480350045857113895807555932147258323470751247259644932218298158286602940005007959 (pp96)
Version: GGNFS-0.77.1-20060513-k8
Total time: 66.77 hours.
Scaled time: 132.61 units (timescale=1.986).
Factorization parameters were as follows:
name: 49993_162
n: 4397992827905366561495616972942610757769676397548052455720011518707669668467184795048847173974047956366224189761866099002983083128112811
m: 100000000000000000000000000000000
c5: 500
c0: -7
skew: 0.43
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4350001)
Primes: RFBsize:315948, AFBsize:315206, largePrimes:5778555 encountered
Relations: rels:5922064, finalFF:770316
Max relations in full relation-set: 28
Initial matrix: 631220 x 770316 with sparse part having weight 46730298.
Pruned matrix : 518559 x 521779 with weight 31016251.
Total sieving time: 63.45 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.94 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 66.77 hours.
 --------- CPU info (if available) ----------

Sep 25, 2007

By Robert Backstrom / GGNFS, Msieve

(86·10¹⁸²+31)/9 = 9(5)₁₈₁9_<183> = 7 · C183

C183 = P48 · P48 · P87

P48 = 219254706609281472076564248230371923805632108973_<48>

P48 = 667127665052517179233067332728168025449200965073_<48>

P87 = 933254357035504554827120249606468833406095139378559205785196446817284884193061670441653_<87>

Number: n
N=136507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507937
  ( 183 digits)
SNFS difficulty: 183 digits.
Divisors found:

(Completed by MSIEVE 1.26)

Tue Sep 25 08:11:44 2007  prp48 factor: 219254706609281472076564248230371923805632108973
Tue Sep 25 08:11:44 2007  prp48 factor: 667127665052517179233067332728168025449200965073
Tue Sep 25 08:11:44 2007  prp87 factor: 933254357035504554827120249606468833406095139378559205785196446817284884193061670441653

Version: GGNFS-0.77.1-20051202-athlon
Total time: 760.78 hours.
Scaled time: 1004.23 units (timescale=1.320).
Factorization parameters were as follows:
name: KA_9_5_181_9
n: 136507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507937
skew: 0.32
deg: 5
c5: 8600
c0: 31
m: 1000000000000000000000000000000000000
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 10800000)
Primes: RFBsize:283146, AFBsize:283738, largePrimes:9358417 encountered
Relations: rels:9011426, finalFF:643650
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 759.81 hours.
Total relation processing time: 0.97 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,183,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000
total time: 760.78 hours.
 --------- CPU info (if available) ----------

Mem Alloc Error by GGNFS

...
[09/24 14:06:36] GGNFS-0.77.1-20051202-athlon : matbuild
[09/24 14:07:59] largePrimes: 9358417 , relations: 9011426
[09/24 14:18:34] reduceRelSets dropped relation-set weight from 19495262 to 15297055.
[09/24 14:24:25] reduceRelSets dropped relation-set weight from 15297055 to 15246628.
[09/24 14:24:25] After removing heavy rel-sets, weight is 13333792.
[09/24 14:32:44] Heap stats for matbuild run, after cycle-building
[09/24 14:32:44] Max heap usage: 460 MB
[09/24 14:32:44] malloc/realloc errors: 0
[09/24 14:32:44] total malloc's : 515
[09/24 14:32:44] total realloc's: 219
[09/24 14:32:44] rels:9011426, initialFF:0, finalFF:643650
[09/24 14:32:52] Memory allocation error (721935180 bytes requested).
...

Linear Algebra completed by MSIEVE 1.26

...
Tue Sep 25 07:49:04 2007  reading relations for dependency 2
Tue Sep 25 07:49:04 2007  read 390086 cycles
Tue Sep 25 07:49:05 2007  cycles contain 1234166 unique relations
Tue Sep 25 07:50:17 2007  read 1234166 relations
Tue Sep 25 07:50:29 2007  multiplying 1849254 relations
Tue Sep 25 07:56:56 2007  multiply complete, coefficients have about 64.93 million bits
Tue Sep 25 07:56:58 2007  initial square root is modulo 2099293891
Tue Sep 25 08:11:44 2007  prp48 factor: 219254706609281472076564248230371923805632108973
Tue Sep 25 08:11:44 2007  prp48 factor: 667127665052517179233067332728168025449200965073
Tue Sep 25 08:11:44 2007  prp87 factor: 933254357035504554827120249606468833406095139378559205785196446817284884193061670441653
Tue Sep 25 08:11:44 2007  elapsed time 05:11:32

Cygwin on AMD 64 3200+

Sep 24, 2007 (4th)

By JMB / GMP-ECM

(16·10²²⁰-61)/9 = 1(7)₂₁₉1_<221> = 13 · 353 · 1877 · 16492937 · 1805034167_<10> · 937019983238111_<15> · C182

C182 = P35 · C148

P35 = 55949358235598934650206505967480781_<35>

C148 = [1322414960079354351709834861520621170706984511895469829631709464819715591749118547779968053941698236864151284187903149814300379387206849149544675063_<148>]

Sep 24, 2007 (3rd)

By Robert Backstrom / GGNFS

5·10¹⁶³-7 = 4(9)₁₆₂3_<164> = 1244029 · C158

C158 = P40 · P119

P40 = 3045777474311016078416962103126374071511_<40>

P119 = 13195970300684442140409379802151398451013119494061176587343764266942527286513791024515689055116238602995731201645467547_<119>

Number: n
N=40191989093501839587340809579197912588854439888459191867713694777211785255809952983411158421548050728720954254281853558076218480437353148519849617653607753517
  ( 158 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=3045777474311016078416962103126374071511 (pp40)
 r2=13195970300684442140409379802151398451013119494061176587343764266942527286513791024515689055116238602995731201645467547 (pp119)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 63.80 hours.
Scaled time: 92.00 units (timescale=1.442).
Factorization parameters were as follows:
name: KA_4_9_162_3
n: 40191989093501839587340809579197912588854439888459191867713694777211785255809952983411158421548050728720954254281853558076218480437353148519849617653607753517
skew: 0.27
deg: 5
c5: 5000
c0: -7
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3000001)
Primes: RFBsize:216816, AFBsize:217636, largePrimes:7601696 encountered
Relations: rels:7098507, finalFF:494362
Max relations in full relation-set: 28
Initial matrix: 434517 x 494362 with sparse part having weight 44766005.
Pruned matrix : 411191 x 413427 with weight 33800123.
Total sieving time: 57.42 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 6.04 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 63.80 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Sep 24, 2007 (2nd)

By Sinkiti Sibata / GGNFS

5·10¹⁶⁹-7 = 4(9)₁₆₈3_<170> = 43 · 211 · 1472137 · 2321750736611301907097_<22> · 574482675743693221950617_<24> · C115

C115 = P43 · P72

P43 = 5744494079787571396717760190250240838888041_<43>

P72 = 488569723676345326019989715470508850328546498038944485790862224772950377_<72>

Number: 49993_169
N=2806585885222215377350944994569312431165970817862559316770088936318837708911961250594258617432022173022491551741457
  ( 115 digits)
Divisors found:
 r1=5744494079787571396717760190250240838888041 (pp43)
 r2=488569723676345326019989715470508850328546498038944485790862224772950377 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 48.07 hours.
Scaled time: 95.70 units (timescale=1.991).
Factorization parameters were as follows:
name: 49993_169
n: 2806585885222215377350944994569312431165970817862559316770088936318837708911961250594258617432022173022491551741457
skew: 31373.54
# norm 3.83e+15
c5: 60840
c4: -720780132
c3: 72126305586899
c2: 1666649461314850199
c1: -116989157991344921484511
c0: 162800038608129701576075241
# alpha -6.02
Y1: 896315175217
Y0: -8566391803006571745272
# Murphy_E 5.55e-10
# M 2396840833491453209262727670434957761159698617278948458168476366281194806287209404389368742033257071680380836619726
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 3050001)
Primes: RFBsize:250150, AFBsize:250437, largePrimes:7884281 encountered
Relations: rels:8065906, finalFF:781702
Max relations in full relation-set: 28
Initial matrix: 500667 x 781702 with sparse part having weight 75915276.
Pruned matrix : 319011 x 321578 with weight 50104378.
Total sieving time: 45.28 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 2.18 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 48.07 hours.
 --------- CPU info (if available) ----------

5·10¹⁵³-7 = 4(9)₁₅₂3_<154> = 1487 · 12703 · 27064010767_<11> · C136

C136 = P50 · P87

P50 = 23985742229316002405160508997718416270586975005491_<50>

P87 = 407762626593054648807646182158981927854290181355167860837282173381501147582605582632029_<87>

Number: 49993_153
N=9780489252209843258748295325322445828861819876619459830498259544007166236469918061045471477958043159769750664560714769953352476507471239
  ( 136 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=23985742229316002405160508997718416270586975005491 (pp50)
 r2=407762626593054648807646182158981927854290181355167860837282173381501147582605582632029 (pp87)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 41.29 hours.
Scaled time: 27.95 units (timescale=0.677).
Factorization parameters were as follows:
name: 49993_153
n: 9780489252209843258748295325322445828861819876619459830498259544007166236469918061045471477958043159769750664560714769953352476507471239
m: 5000000000000000000000000000000
c5: 8
c0: -35
skew: 1.34
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2300001)
Primes: RFBsize:176302, AFBsize:176798, largePrimes:5470514 encountered
Relations: rels:5308781, finalFF:410488
Max relations in full relation-set: 28
Initial matrix: 353165 x 410488 with sparse part having weight 36573902.
Pruned matrix : 331184 x 333013 with weight 26077344.
Total sieving time: 36.51 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 4.39 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 41.29 hours.
 --------- CPU info (if available) ----------

Sep 24, 2007

By suberi / PRIMO

7·10²⁵⁵⁹+3 is prime!

Sep 23, 2007 (3rd)

By Jo Yeong Uk / GMP-ECM

3·10¹⁶⁹+7 = 3(0)₁₆₈7_<170> = 37 · C168

C168 = P39 · P130

P39 = 321485385345676762706421506544388644469_<39>

P130 = 2522076734340466176982866611144735500345304211081851607078673956180783695480227990278425308960588927381717464690492823021851851119_<130>

Sep 23, 2007 (2nd)

By Sinkiti Sibata / GGNFS

5·10¹⁵⁹-7 = 4(9)₁₅₈3_<160> = 47 · 964644799 · 270706849725621910507211_<24> · C126

C126 = P52 · P75

P52 = 1364391784808783411765902177253121572084574108528241_<52>

P75 = 298583894675727940289845675134760397414301294012470876284306516517828237131_<75>

Number: 49993_159
N=407385412971774246984894055262282656186910895322963362483310889127715264264776948863397719450706989787968437776460909958316571
  ( 126 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=1364391784808783411765902177253121572084574108528241 (pp52)
 r2=298583894675727940289845675134760397414301294012470876284306516517828237131 (pp75)
Version: GGNFS-0.77.1-20060513-k8
Total time: 40.15 hours.
Scaled time: 80.17 units (timescale=1.997).
Factorization parameters were as follows:
name: 49993_159
n: 407385412971774246984894055262282656186910895322963362483310889127715264264776948863397719450706989787968437776460909958316571
m: 100000000000000000000000000000000
c5: 1
c0: -14
skew: 1.7
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3300001)
Primes: RFBsize:283146, AFBsize:283092, largePrimes:5702766 encountered
Relations: rels:5817296, finalFF:727915
Max relations in full relation-set: 28
Initial matrix: 566302 x 727915 with sparse part having weight 43359878.
Pruned matrix : 431450 x 434345 with weight 26402153.
Total sieving time: 37.67 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 2.17 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 40.15 hours.
 --------- CPU info (if available) ----------

Sep 23, 2007

By Robert Backstrom / GGNFS

4·10¹⁶²+7 = 4(0)₁₆₁7_<163> = 11 · 79 · 1139323553_<10> · C151

C151 = P60 · P92

P60 = 234034230184541159881265925110454036781626436280873469868669_<60>

P92 = 17262900077839710421537401417208645828242546967978794855357928428513665188571039974636777079_<92>

Number: n
N=4040109530469872295206417141478966201658930005731568037108063258312773845625926951228352920828858552387046131679020631083739483089980760886171559437851
  ( 151 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=234034230184541159881265925110454036781626436280873469868669 (pp60)
 r2=17262900077839710421537401417208645828242546967978794855357928428513665188571039974636777079 (pp92)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 39.72 hours.
Scaled time: 54.22 units (timescale=1.365).
Factorization parameters were as follows:
name: KA_4_0_161_7
n: 4040109530469872295206417141478966201658930005731568037108063258312773845625926951228352920828858552387046131679020631083739483089980760886171559437851
skew: 0.45
deg: 5
c5: 400
c0: 7
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1800001)
Primes: RFBsize:216816, AFBsize:216976, largePrimes:7127302 encountered
Relations: rels:6610032, finalFF:494318
Max relations in full relation-set: 28
Initial matrix: 433856 x 494318 with sparse part having weight 36516568.
Pruned matrix : 386643 x 388876 with weight 24911065.
Total sieving time: 36.27 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.13 hours.
Total square root time: 0.11 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 39.72 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Sep 22, 2007

By Sinkiti Sibata / GGNFS

5·10¹⁶⁵-7 = 4(9)₁₆₄3_<166> = 914885729 · 4261399463897_<13> · 6040387634947_<13> · 1491052684691540816159207_<25> · C108

C108 = P33 · P75

P33 = 319197319597996510039273971999701_<33>

P75 = 446101691024302128170720348856355665147674572755074743500867309182182952809_<75>

Number: 49993_165
N=142394464043090857513239492807664605923383657649420029924108397359976327605079156360506333452052514645110109
  ( 108 digits)
Divisors found:
 r1=319197319597996510039273971999701 (pp33)
 r2=446101691024302128170720348856355665147674572755074743500867309182182952809 (pp75)
Version: GGNFS-0.77.1-20060513-k8
Total time: 16.02 hours.
Scaled time: 31.80 units (timescale=1.985).
Factorization parameters were as follows:
name: 49993_165
n: 142394464043090857513239492807664605923383657649420029924108397359976327605079156360506333452052514645110109
skew: 13936.08
# norm 1.35e+15
c5: 76800
c4: -4242870768
c3: 25375181134756
c2: 1030238403227851652
c1: 2250557392389371098067
c0: -5950154183708608868842952
# alpha -5.91
Y1: 362384350823
Y0: -284205511495603330335
# Murphy_E 1.34e-09
# M 109003927296022212451091712878426486494476931109986893486521952118176755395827872047646424692080971536718213
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2300001)
Primes: RFBsize:183072, AFBsize:182559, largePrimes:4445338 encountered
Relations: rels:4500132, finalFF:431528
Max relations in full relation-set: 28
Initial matrix: 365712 x 431528 with sparse part having weight 33237805.
Pruned matrix : 316128 x 318020 with weight 20984545.
Total sieving time: 14.64 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.00 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 16.02 hours.
 --------- CPU info (if available) ----------

2·10¹⁸⁹-3 = 1(9)₁₈₈7_<190> = 31618164809434211754592287712179187_<35> · 26515433818872756128486451063540368813_<38> · C118

C118 = P57 · P61

P57 = 484578537409999154675042390540664390207331844965054363441_<57>

P61 = 4923006679232260879844150105623901082760825132994000095977307_<61>

Number: 19997_189
N=2385583376282025837302025573831625807718996619292106854661488654167073439506823897959332181406320971559780911666433387
  ( 118 digits)
Divisors found:
 r1=484578537409999154675042390540664390207331844965054363441 (pp57)
 r2=4923006679232260879844150105623901082760825132994000095977307 (pp61)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 89.74 hours.
Scaled time: 60.75 units (timescale=0.677).
Factorization parameters were as follows:
name: 19997_189
n: 2385583376282025837302025573831625807718996619292106854661488654167073439506823897959332181406320971559780911666433387
skew: 144660.76
# norm 2.74e+16
c5: 9120
c4: -1709436956
c3: -853334330700080
c2: 38221101292867669503
c1: 5419411001140512770228250
c0: -113915253989648848942977150816
# alpha -6.21
Y1: 86650737107
Y0: -48252518012964347678477
# Murphy_E 3.65e-10
# M 654987332633075895838719954518597211946085969700968706963931960289336573203282116904651285610709249461397952456672945
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4110001)
Primes: RFBsize:315948, AFBsize:315530, largePrimes:7677981 encountered
Relations: rels:7786564, finalFF:780897
Max relations in full relation-set: 28
Initial matrix: 631557 x 780897 with sparse part having weight 63899163.
Pruned matrix : 505956 x 509177 with weight 39093412.
Total sieving time: 75.32 hours.
Total relation processing time: 0.76 hours.
Matrix solve time: 13.18 hours.
Time per square root: 0.48 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 89.74 hours.
 --------- CPU info (if available) ----------

Sep 21, 2007 (6th)

By Robert Backstrom / GGNFS

5·10¹⁵⁶-7 = 4(9)₁₅₅3_<157> = 2269 · C154

C154 = P57 · P97

P57 = 702447342551455682763805673011418695171148173600333160411_<57>

P97 = 3137052122420974879105045171402526152498877264559652000048811419905235475853470855786187595915127_<97>

Number: n
N=2203613926840017628911414720141031291317761128250330542089026002644336712208021154693697664169237549581313353900396650506831203173204054649625385632437197
  ( 154 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=702447342551455682763805673011418695171148173600333160411 (pp57)
 r2=3137052122420974879105045171402526152498877264559652000048811419905235475853470855786187595915127 (pp97)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 32.73 hours.
Scaled time: 47.30 units (timescale=1.445).
Factorization parameters were as follows:
name: KA_4_9_155_3
n: 2203613926840017628911414720141031291317761128250330542089026002644336712208021154693697664169237549581313353900396650506831203173204054649625385632437197
skew: 1.00
deg: 5
c5: 50
c0: -7
m: 10000000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1600001)
Primes: RFBsize:148933, AFBsize:149340, largePrimes:7221415 encountered
Relations: rels:6677603, finalFF:340291
Max relations in full relation-set: 28
Initial matrix: 298338 x 340291 with sparse part having weight 35254069.
Pruned matrix : 282176 x 283731 with weight 26733037.
Total sieving time: 29.31 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 2.95 hours.
Total square root time: 0.24 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 32.73 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Sep 21, 2007 (5th)

By Sinkiti Sibata / GGNFS

3·10¹⁵⁹-7 = 2(9)₁₅₈3_<160> = 2659 · 629501473 · 3776223670753814722104781857341_<31> · C117

C117 = P43 · P75

P43 = 2429003868169712771564765938483840128221281_<43>

P75 = 195398061142744316558324686703766895073805079591953321661587802348156465519_<75>

Number: 29993_159
N=474622646348587991570103845490157192795552107865333169185229129045216764037235466499265469910571227154142957278509839
  ( 117 digits)
Divisors found:
 r1=2429003868169712771564765938483840128221281 (pp43)
 r2=195398061142744316558324686703766895073805079591953321661587802348156465519 (pp75)
Version: GGNFS-0.77.1-20060513-k8
Total time: 56.60 hours.
Scaled time: 112.69 units (timescale=1.991).
Factorization parameters were as follows:
name: 29993_159
n: 474622646348587991570103845490157192795552107865333169185229129045216764037235466499265469910571227154142957278509839
skew: 102878.62
# norm 3.14e+16
c5: 34440
c4: -149392696
c3: -462455782301352
c2: -52512162914560500217
c1: 816599221770534738053210
c0: 165609389373825212343298147000
# alpha -6.78
Y1: 2030600269627
Y0: -26782868643055112543701
# Murphy_E 3.95e-10
# M 344120893185492553582171471745909403370088932927055061806908622580423741637740107782212930561733866315489917027001449
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3870001)
Primes: RFBsize:315948, AFBsize:316176, largePrimes:7649847 encountered
Relations: rels:7779364, finalFF:809585
Max relations in full relation-set: 28
Initial matrix: 632210 x 809585 with sparse part having weight 68072410.
Pruned matrix : 480081 x 483306 with weight 39163890.
Total sieving time: 52.80 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 3.04 hours.
Time per square root: 0.42 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 56.60 hours.
 --------- CPU info (if available) ----------

Sep 21, 2007 (4th)

By suberi / PRIMO

5·10²⁴⁷³+9 is prime!

Sep 21, 2007 (3rd)

By Robert Backstrom / GGNFS

5·10¹⁵⁴-7 = 4(9)₁₅₃3_<155> = 19 · 149 · 147343123 · C144

C144 = P58 · P86

P58 = 2329496337443922537883208273725168308815052824721528210923_<58>

P86 = 51456261798342511671036399891501546912876135404430952940563337964752143215157251247207_<86>

Number: n
N=119867173397794507936562028872143053364267557793942124954308317334879039092932793449039649487083341517467372369417965078031872011075677110642061
  ( 144 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=2329496337443922537883208273725168308815052824721528210923 (pp58)
 r2=51456261798342511671036399891501546912876135404430952940563337964752143215157251247207 (pp86)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 19.32 hours.
Scaled time: 26.35 units (timescale=1.364).
Factorization parameters were as follows:
name: KA_4_9_153_3
n: 119867173397794507936562028872143053364267557793942124954308317334879039092932793449039649487083341517467372369417965078031872011075677110642061
skew: 1.00
deg: 5
c5: 1
c0: -14
m: 10000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:183072, AFBsize:182621, largePrimes:6422576 encountered
Relations: rels:5852822, finalFF:412844
Max relations in full relation-set: 28
Initial matrix: 365757 x 412844 with sparse part having weight 26329532.
Pruned matrix : 325573 x 327465 with weight 17263082.
Total sieving time: 17.06 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.76 hours.
Total square root time: 0.33 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 19.32 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Sep 21, 2007 (2nd)

By Jo Yeong Uk / PRIMO

(14·10²⁰⁰³+1)/3 is prime!

Sep 21, 2007

By Jo Yeong Uk / GGNFS

5·10¹⁵⁰-7 = 4(9)₁₄₉3_<151> = 384637449547853_<15> · 100387217672603863429_<21> · C117

C117 = P31 · P86

P31 = 6154380393511946888616304633963_<31>

P86 = 21040482008161263229987519894156551396567478881186385296972651591714274238026715657003_<86>

Number: 49993_150
N=129491129941068553703812537946480368789816344933526174856540977440519983389852818222234719791591816985068314972592889
  ( 117 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=6154380393511946888616304633963 (pp31)
 r2=21040482008161263229987519894156551396567478881186385296972651591714274238026715657003 (pp86)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.34 hours.
Scaled time: 24.17 units (timescale=2.131).
Factorization parameters were as follows:
n: 129491129941068553703812537946480368789816344933526174856540977440519983389852818222234719791591816985068314972592889
m: 1000000000000000000000000000000
c5: 5
c0: -7
skew: 1.07
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:175868, largePrimes:5272948 encountered
Relations: rels:5112371, finalFF:430990
Max relations in full relation-set: 28
Initial matrix: 352235 x 430990 with sparse part having weight 34977477.
Pruned matrix : 305477 x 307302 with weight 22005147.
Total sieving time: 10.84 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.40 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 11.34 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹⁵²-7 = 4(9)₁₅₁3_<153> = 4984608868886021_<16> · 5760022922783149935357790511_<28> · C110

C110 = P30 · P30 · P50

P30 = 188518073602970413450229413063_<30>

P30 = 940840568278596734516455337701_<30>

P50 = 98185120607867205620512879136643224913634476404281_<50>

Number: 49993_152
N=17414648247137902210132824181583304066910194155046022301650741655577181114209034000065980412530628852712325803
  ( 110 digits)
Divisors found:
 r1=188518073602970413450229413063 (pp30)
 r2=940840568278596734516455337701 (pp30)
 r3=98185120607867205620512879136643224913634476404281 (pp50)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 14.68 hours.
Scaled time: 31.13 units (timescale=2.120).
Factorization parameters were as follows:
name: 49993_152
n: 17414648247137902210132824181583304066910194155046022301650741655577181114209034000065980412530628852712325803
skew: 56517.21
# norm 2.42e+15
c5: 2880
c4: 1175164712
c3: -29239402533387
c2: -938352304661497866
c1: 73927841365309126364192
c0: -902182295668313581002209856
# alpha -6.39
Y1: 72628709197
Y0: -1433186298969104262985
# Murphy_E 1.04e-09
# M 12838353175379424893908978938079702592009453283711586973468906081864813655034909619752608931304311664598306820
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1200000, 1920001)
Primes: RFBsize:176302, AFBsize:176892, largePrimes:7434009 encountered
Relations: rels:7156751, finalFF:427712
Max relations in full relation-set: 28
Initial matrix: 353274 x 427712 with sparse part having weight 39905520.
Pruned matrix : 300831 x 302661 with weight 25640907.
Polynomial selection time: 0.78 hours.
Total sieving time: 13.25 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.43 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000
total time: 14.68 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

Sep 20, 2007 (5th)

By Robert Backstrom / GGNFS

3·10¹⁵⁶-7 = 2(9)₁₅₅3_<157> = 20326576471807_<14> · C144

C144 = P57 · P87

P57 = 755863572447083289435283827464011678816063064420816854967_<57>

P87 = 195260141964162497840754186283403004144880025879973776465137141067044484471377181806897_<87>

Number: n
N=147590028461556508171293018028553114061238888148651494440046585451722939356778788070173271532586662801688015902136310673316237331594165849307399
  ( 144 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=755863572447083289435283827464011678816063064420816854967 (pp57)
 r2=195260141964162497840754186283403004144880025879973776465137141067044484471377181806897 (pp87)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 45.23 hours.
Scaled time: 54.00 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_2_9_155_3
n: 147590028461556508171293018028553114061238888148651494440046585451722939356778788070173271532586662801688015902136310673316237331594165849307399
type: snfs
skew: 1.00
deg: 5
c5: 30
c0: -7
m: 10000000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2000001)
Primes: RFBsize:148933, AFBsize:148635, largePrimes:6806936 encountered
Relations: rels:6172026, finalFF:337910
Max relations in full relation-set: 28
Initial matrix: 297635 x 337910 with sparse part having weight 32569506.
Pruned matrix : 284193 x 285745 with weight 24619977.
Total sieving time: 41.64 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 3.19 hours.
Total square root time: 0.10 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 45.23 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Sep 20, 2007 (4th)

By Jo Yeong Uk / GGNFS

5·10¹⁴⁹-7 = 4(9)₁₄₈3_<150> = 13 · 67 · 223 · 61166327 · C137

C137 = P58 · P80

P58 = 1863894902146250689138702961366278706980495490732424870829_<58>

P80 = 22579439841623531991161014465575701572092571425255411323896978985792253366291587_<80>

Number: 49993_149
N=42085702814120047318762251527880567894812152207168529855646296135167386162678994579997839545194550841551120722204859676477586031224415623
  ( 137 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=1863894902146250689138702961366278706980495490732424870829 (pp58)
 r2=22579439841623531991161014465575701572092571425255411323896978985792253366291587 (pp80)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 9.20 hours.
Scaled time: 19.61 units (timescale=2.132).
Factorization parameters were as follows:
n: 42085702814120047318762251527880567894812152207168529855646296135167386162678994579997839545194550841551120722204859676477586031224415623
m: 1000000000000000000000000000000
c5: 1
c0: -14
skew: 1.7
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1500001)
Primes: RFBsize:135072, AFBsize:134923, largePrimes:3682097 encountered
Relations: rels:3704501, finalFF:337628
Max relations in full relation-set: 28
Initial matrix: 270059 x 337628 with sparse part having weight 29012768.
Pruned matrix : 242332 x 243746 with weight 17407984.
Total sieving time: 8.88 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.24 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 9.20 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹⁴⁸-7 = 4(9)₁₄₇3_<149> = 43 · 4871 · C144

C144 = P47 · P97

P47 = 85730161306764919729693936025764142920932871039_<47>

P97 = 2784516388469492464533403078786154427691160272586017433488469433231396033078317295048722652094979_<97>

Number: 49993_148
N=238717039144820078967596549106482122480938444424286116694437415553847402519897065212720753581949172368025284908786219342764247826481358586413181
  ( 144 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=85730161306764919729693936025764142920932871039 (pp47)
 r2=2784516388469492464533403078786154427691160272586017433488469433231396033078317295048722652094979 (pp97)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 12.50 hours.
Scaled time: 26.56 units (timescale=2.124).
Factorization parameters were as follows:
n: 238717039144820078967596549106482122480938444424286116694437415553847402519897065212720753581949172368025284908786219342764247826481358586413181
m: 1000000000000000000000000000000
c5: 1
c0: -140
skew: 2.69
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1725001)
Primes: RFBsize:135072, AFBsize:135583, largePrimes:3874933 encountered
Relations: rels:4005276, finalFF:405690
Max relations in full relation-set: 28
Initial matrix: 270719 x 405690 with sparse part having weight 39826184.
Pruned matrix : 229408 x 230825 with weight 20381958.
Total sieving time: 12.17 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 12.50 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

Sep 20, 2007 (3rd)

By Robert Backstrom / GGNFS

3·10¹⁶²-7 = 2(9)₁₆₁3_<163> = 311 · 839 · C158

C158 = P49 · P50 · P60

P49 = 4051197719261188815701375854427236740369079486103_<49>

P50 = 20165397378055339711076080733916793276540156689149_<50>

P60 = 140737126881900958635390331620494185432391996158454693370011_<60>

Number: n
N=11497380513473013731704793257936066899424747728309233546290370177327932119465448455326928014900605145461025796289412062285142701654473055888766675992319749817
  ( 158 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=4051197719261188815701375854427236740369079486103 (pp49)
 r2=20165397378055339711076080733916793276540156689149 (pp50)
 r3=140737126881900958635390331620494185432391996158454693370011 (pp60)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 45.25 hours.
Scaled time: 65.43 units (timescale=1.446).
Factorization parameters were as follows:
name: KA_2_9_161_3
n: 11497380513473013731704793257936066899424747728309233546290370177327932119465448455326928014900605145461025796289412062285142701654473055888766675992319749817
skew: 0.47
deg: 5
c5: 300
c0: -7
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2100001)
Primes: RFBsize:250150, AFBsize:249771, largePrimes:7357986 encountered
Relations: rels:6887181, finalFF:570721
Max relations in full relation-set: 28
Initial matrix: 499987 x 570721 with sparse part having weight 39576388.
Pruned matrix : 441715 x 444278 with weight 26543781.
Total sieving time: 39.63 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 5.09 hours.
Total square root time: 0.31 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 45.25 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

5·10¹⁴²-7 = 4(9)₁₄₁3_<143> = 29 · 31 · 1979 · 3277843 · C130

C130 = P46 · P85

P46 = 2223141064464610943664418818229457665011638221_<46>

P85 = 3856642203506996485674317701132711550770098652412611342040704528870940226564907142911_<85>

Number: n
N=8573859653563686872153672611065011274732927198251276617077489205709398361640445149078749285697650620290539145986731822988676801331
  ( 130 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=2223141064464610943664418818229457665011638221 (pp46)
 r2=3856642203506996485674317701132711550770098652412611342040704528870940226564907142911 (pp85)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.11 hours.
Scaled time: 22.82 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_4_9_141_3
n: 8573859653563686872153672611065011274732927198251276617077489205709398361640445149078749285697650620290539145986731822988676801331
type: snfs
skew: 1.00
deg: 5
c5: 500
c0: -7
m: 10000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:148933, AFBsize:148765, largePrimes:5656958 encountered
Relations: rels:5036472, finalFF:365043
Max relations in full relation-set: 28
Initial matrix: 297764 x 365043 with sparse part having weight 18678812.
Pruned matrix : 238754 x 240306 with weight 9621800.
Total sieving time: 17.82 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.93 hours.
Total square root time: 0.10 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 19.11 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(52·10¹⁸¹-7)/9 = 5(7)₁₈₁_<182> = 3 · 19 · C181

C181 = P81 · P100

P81 = 401904412375528539331847398345165066791473496316622080484846488508256710720903033_<81>

P100 = 2522105239353325298748130209401148022385513396941975516899451253080021253195404610505390042856114817_<100>

Number: n
N=1013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961
  ( 181 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=401904412375528539331847398345165066791473496316622080484846488508256710720903033 (pp81)
 r2=2522105239353325298748130209401148022385513396941975516899451253080021253195404610505390042856114817 (pp100)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 730.72 hours.
Scaled time: 997.43 units (timescale=1.365).
Factorization parameters were as follows:
name: KA_5_7_181
n: 1013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961013645224171539961
skew: 0.42
deg: 5
c5: 520
c0: -7
m: 1000000000000000000000000000000000000
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 9700001)
Primes: RFBsize:283146, AFBsize:283932, largePrimes:9499562 encountered
Relations: rels:9301430, finalFF:638426
Max relations in full relation-set: 28
Initial matrix: 567145 x 638426 with sparse part having weight 92765702.
Pruned matrix : 539903 x 542802 with weight 78313454.
Total sieving time: 712.95 hours.
Total relation processing time: 0.99 hours.
Matrix solve time: 16.29 hours.
Total square root time: 0.49 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000
total time: 730.72 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Sep 20, 2007 (2nd)

By Jo Yeong Uk / GGNFS

5·10¹⁴³-7 = 4(9)₁₄₂3_<144> = 13 · 665794015879030348762037_<24> · C119

C119 = P43 · P77

P43 = 2457983453888362366242036666452627350164707_<43>

P77 = 23502161675736277599130693612709951586027071255823077510499322192862480222179_<77>

Number: 49993_143
N=57767924529568957888537801310876296895668866171545711112223603502784417848468335253465142833454489613026092525604436553
  ( 119 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=2457983453888362366242036666452627350164707 (pp43)
 r2=23502161675736277599130693612709951586027071255823077510499322192862480222179 (pp77)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.30 hours.
Scaled time: 17.70 units (timescale=2.132).
Factorization parameters were as follows:
n: 57767924529568957888537801310876296895668866171545711112223603502784417848468335253465142833454489613026092525604436553
m: 100000000000000000000000000000
c5: 1
c0: -140
skew: 2.69
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1300001)
Primes: RFBsize:114155, AFBsize:114557, largePrimes:3355292 encountered
Relations: rels:3393674, finalFF:331157
Max relations in full relation-set: 28
Initial matrix: 228776 x 331157 with sparse part having weight 30146465.
Pruned matrix : 195268 x 196475 with weight 14800409.
Total sieving time: 8.09 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 8.30 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹⁴⁶-7 = 4(9)₁₄₅3_<147> = 17 · 14921539 · 248698679 · 471359479252760034787043_<24> · C107

C107 = P47 · P60

P47 = 39419505496131463374918351524556451155850236259_<47>

P60 = 426550611477417551441580681597762746623708391057419314031757_<60>

Number: 49993_146
N=16814414173512297631896560241640536292869348031719843335103615147794108141962215977079516141086042278877063
  ( 107 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=39419505496131463374918351524556451155850236259 (pp47)
 r2=426550611477417551441580681597762746623708391057419314031757 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.51 hours.
Scaled time: 22.53 units (timescale=2.143).
Factorization parameters were as follows:
n: 16814414173512297631896560241640536292869348031719843335103615147794108141962215977079516141086042278877063
m: 100000000000000000000000000000
c5: 50
c0: -7
skew: 0.67
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1575001)
Primes: RFBsize:135072, AFBsize:135423, largePrimes:3793573 encountered
Relations: rels:3866749, finalFF:362728
Max relations in full relation-set: 28
Initial matrix: 270560 x 362728 with sparse part having weight 34071867.
Pruned matrix : 238068 x 239484 with weight 19000621.
Total sieving time: 10.19 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.24 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 10.51 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹⁴⁷-7 = 4(9)₁₄₆3_<148> = 181 · 1935949243_<10> · C137

C137 = P44 · P93

P44 = 39143694405820216125374984826505126817968351_<44>

P93 = 364531993422512812212311418475269937871127766102122723800434357272554629366883846804656575121_<93>

Number: 49993_147
N=14269128951675306587656103056392781244121178891433426670144019869249655079558182381438140303751595107152717138583707250452128119031995471
  ( 137 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=39143694405820216125374984826505126817968351 (pp44)
 r2=364531993422512812212311418475269937871127766102122723800434357272554629366883846804656575121 (pp93)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.32 hours.
Scaled time: 22.14 units (timescale=2.145).
Factorization parameters were as follows:
n: 14269128951675306587656103056392781244121178891433426670144019869249655079558182381438140303751595107152717138583707250452128119031995471
m: 500000000000000000000000000000
c5: 4
c0: -175
skew: 2.13
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1575001)
Primes: RFBsize:135072, AFBsize:134853, largePrimes:3806264 encountered
Relations: rels:3951764, finalFF:434720
Max relations in full relation-set: 28
Initial matrix: 269989 x 434720 with sparse part having weight 39919688.
Pruned matrix : 213923 x 215336 with weight 18154201.
Total sieving time: 10.05 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 10.32 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

Sep 20, 2007

By Sinkiti Sibata / GGNFS

5·10¹⁹⁴-1 = 4(9)₁₉₄_<195> = C195

C195 = P76 · P120

P76 = 2063673432680440504344308255721789938709506185655504408686729651476059482949_<76>

P120 = 242286396714700023343462981244314581366417767442682354276028410445885393174798778445278457127741012032445076995991310451_<120>

Number: 49999_194
N=499999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
  ( 195 digits)
SNFS difficulty: 195 digits.
Divisors found:
 r1=2063673432680440504344308255721789938709506185655504408686729651476059482949 (pp76)
 r2=242286396714700023343462981244314581366417767442682354276028410445885393174798778445278457127741012032445076995991310451 (pp120)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2170.77 hours.
Scaled time: 4335.02 units (timescale=1.997).
Factorization parameters were as follows:
name: 49999_194
n: 499999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
m: 1000000000000000000000000000000000000000
c5: 1
c0: -2
skew: 1.15
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 30600001)
Primes: RFBsize:501962, AFBsize:501936, largePrimes:7672066 encountered
Relations: rels:8446002, finalFF:1128792
Max relations in full relation-set: 28
Initial matrix: 1003962 x 1128792 with sparse part having weight 155448349.
Pruned matrix : 921781 x 926864 with weight 139585169.
Total sieving time: 2144.49 hours.
Total relation processing time: 1.59 hours.
Matrix solve time: 24.21 hours.
Time per square root: 0.47 hours.
Prototype def-par.txt line would be:
snfs,195,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 2170.77 hours.
 --------- CPU info (if available) ----------

5·10¹³⁰-7 = 4(9)₁₂₉3_<131> = 17 · 160668811253268490388087_<24> · C107

C107 = P49 · P58

P49 = 6467580254270363725519254058868497565332259571617_<49>

P58 = 2830399090682433194863117944409611442158552826222489705151_<58>

Number: 49993_130
N=18305833270602497558634047496818074228604958225953465398543733671509497228985003045752560531079663898299167
  ( 107 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=6467580254270363725519254058868497565332259571617 (pp49)
 r2=2830399090682433194863117944409611442158552826222489705151 (pp58)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.74 hours.
Scaled time: 7.52 units (timescale=2.010).
Factorization parameters were as follows:
name: 49993_130
n: 18305833270602497558634047496818074228604958225953465398543733671509497228985003045752560531079663898299167
m: 100000000000000000000000000
c5: 5
c0: -7
skew: 1.07
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:63951, AFBsize:64228, largePrimes:1510813 encountered
Relations: rels:1545060, finalFF:204183
Max relations in full relation-set: 28
Initial matrix: 128244 x 204183 with sparse part having weight 12800443.
Pruned matrix : 105593 x 106298 with weight 5310169.
Total sieving time: 3.62 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 3.74 hours.
 --------- CPU info (if available) ----------

Sep 19, 2007 (4th)

By Jo Yeong Uk / PRIMO

(5·10²¹⁰⁰+13)/9 is prime!

Sep 19, 2007 (3rd)

By Robert Backstrom / GGNFS

5·10¹²⁵-7 = 4(9)₁₂₄3_<126> = 13 · 2857 · 1574782569067_<13> · 5838950571776281_<16> · C94

C94 = P36 · P58

P36 = 292924442772209379166691899342190629_<36>

P58 = 4998105296856734377409878285199029073331658288276776782731_<58>

Number: n
N=1464067208998587059740499172572788768975253189359034678886007716300916068840034369544317227799
  ( 94 digits)
Divisors found:
 r1=292924442772209379166691899342190629 (pp36)
 r2=4998105296856734377409878285199029073331658288276776782731 (pp58)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.66 hours.
Scaled time: 7.97 units (timescale=1.196).
Factorization parameters were as follows:
name: n
n:  1464067208998587059740499172572788768975253189359034678886007716300916068840034369544317227799
m:  2789993933216660492819
deg: 4
c4: 24162840
c3: -41310183912
c2: 305151674828780808
c1: 38958211045003735
c0: -144208424742214707916486
skew: 1635.250
type: gnfs
# adj. I(F,S) = 54.410
# E(F1,F2) = 5.603157e-05
# GGNFS version 0.77.1-20051202-athlon polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1190129837.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [100000, 880001)
Primes: RFBsize:92938, AFBsize:93172, largePrimes:1778839 encountered
Relations: rels:1814450, finalFF:217215
Max relations in full relation-set: 28
Initial matrix: 186189 x 217215 with sparse part having weight 13772099.
Pruned matrix : 164433 x 165427 with weight 8533423.
Total sieving time: 6.03 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.47 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,93,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 6.66 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Sep 19, 2007 (2nd)

By Jo Yeong Uk / GGNFS, GMP-ECM

5·10¹⁴⁵-7 = 4(9)₁₄₄3_<146> = C146

C146 = P69 · P78

P69 = 348607637797598731797334666578807254587298021398884344017102244986489_<69>

P78 = 143427723832688809873861290555759641653195758704762012607777555925493706059137_<78>

Number: 49993_145
N=49999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 146 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=348607637797598731797334666578807254587298021398884344017102244986489 (pp69)
 r2=143427723832688809873861290555759641653195758704762012607777555925493706059137 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.30 hours.
Scaled time: 17.62 units (timescale=2.122).
Factorization parameters were as follows:
n: 49999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
m: 100000000000000000000000000000
c5: 5
c0: -7
skew: 1.07
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1300001)
Primes: RFBsize:114155, AFBsize:114162, largePrimes:3386072 encountered
Relations: rels:3436911, finalFF:340015
Max relations in full relation-set: 28
Initial matrix: 228382 x 340015 with sparse part having weight 31556853.
Pruned matrix : 193007 x 194212 with weight 15015116.
Total sieving time: 8.09 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 8.30 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹³²-7 = 4(9)₁₃₁3_<133> = 1803259 · 21637095769_<11> · 704898240089_<12> · C105

C105 = P41 · P64

P41 = 66744018120546449161802491041419358230857_<41>

P64 = 2723793341179006978601831413759133998675258378764478782653155571_<64>

Number: 49993_132
N=181796912120275398531617563014368827286582977646429455177241425072313600143265207326873879751902953654347
  ( 105 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=66744018120546449161802491041419358230857 (pp41)
 r2=2723793341179006978601831413759133998675258378764478782653155571 (pp64)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.35 hours.
Scaled time: 5.04 units (timescale=2.140).
Factorization parameters were as follows:
n: 181796912120275398531617563014368827286582977646429455177241425072313600143265207326873879751902953654347
m: 500000000000000000000000000
c5: 4
c0: -175
skew: 2.13
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1100001)
Primes: RFBsize:107126, AFBsize:106873, largePrimes:2194322 encountered
Relations: rels:2272551, finalFF:259727
Max relations in full relation-set: 28
Initial matrix: 214063 x 259727 with sparse part having weight 16899820.
Pruned matrix : 189994 x 191128 with weight 9651216.
Total sieving time: 2.21 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 2.35 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

3·10¹⁵⁶+7 = 3(0)₁₅₅7_<157> = 1428660435500894737_<19> · C139

C139 = P59 · P80

P59 = 23751015386450850890960912782656510193131256880878674102473_<59>

P80 = 88411764036120295668516229411892223895453769985635566390071101529293788597427807_<80>

Number: 30007_156
N=2099869167965155124756908942201290754204400058585128654740282907304493380080285074505086695930477835539488663926721378385440839832137666711
  ( 139 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=23751015386450850890960912782656510193131256880878674102473 (pp59)
 r2=88411764036120295668516229411892223895453769985635566390071101529293788597427807 (pp80)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.47 hours.
Scaled time: 52.12 units (timescale=2.130).
Factorization parameters were as follows:
n: 2099869167965155124756908942201290754204400058585128654740282907304493380080285074505086695930477835539488663926721378385440839832137666711
m: 10000000000000000000000000000000
c5: 30
c0: 7
skew: 0.75
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3000001)
Primes: RFBsize:216816, AFBsize:216451, largePrimes:5637735 encountered
Relations: rels:5545407, finalFF:494569
Max relations in full relation-set: 28
Initial matrix: 433334 x 494569 with sparse part having weight 41922437.
Pruned matrix : 408265 x 410495 with weight 30955997.
Total sieving time: 23.46 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.88 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 24.47 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹³³-7 = 4(9)₁₃₂3_<134> = 401238263593464253441_<21> · C114

C114 = P39 · P75

P39 = 162299914415288288281496198151331987381_<39>

P75 = 767802233705694607885077764652977937099475049390304533874402633274801489333_<75>

Number: 49993_133
N=124614236818301411544359062366169325675748332513461267291694167073654610945066429659024926693632485623021562106873
  ( 114 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=162299914415288288281496198151331987381 (pp39)
 r2=767802233705694607885077764652977937099475049390304533874402633274801489333 (pp75)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.90 hours.
Scaled time: 6.13 units (timescale=2.113).
Factorization parameters were as follows:
n: 124614236818301411544359062366169325675748332513461267291694167073654610945066429659024926693632485623021562106873
m: 1000000000000000000000000000
c5: 1
c0: -140
skew: 2.69
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1200001)
Primes: RFBsize:107126, AFBsize:107423, largePrimes:2258417 encountered
Relations: rels:2365136, finalFF:274865
Max relations in full relation-set: 28
Initial matrix: 214613 x 274865 with sparse part having weight 19811144.
Pruned matrix : 188857 x 189994 with weight 10562686.
Total sieving time: 2.75 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 2.90 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹³⁶-7 = 4(9)₁₃₅3_<137> = 19 · 139 · 6967 · 304949 · C124

C124 = P56 · P69

P56 = 43352727754257453263558076969496197958853012323126787749_<56>

P69 = 205547477085329019216150576259951986360308957854427429660726601104519_<69>

Number: 49993_136
N=8911043814654741266385357410993071277936469227783606071546576951629885484600301382670236701307968095738801477446099877737731
  ( 124 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=43352727754257453263558076969496197958853012323126787749 (pp56)
 r2=205547477085329019216150576259951986360308957854427429660726601104519 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.57 hours.
Scaled time: 7.58 units (timescale=2.121).
Factorization parameters were as follows:
n: 8911043814654741266385357410993071277936469227783606071546576951629885484600301382670236701307968095738801477446099877737731
m: 1000000000000000000000000000
c5: 50
c0: -7
skew: 0.67
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1350001)
Primes: RFBsize:107126, AFBsize:107448, largePrimes:2286653 encountered
Relations: rels:2372902, finalFF:249972
Max relations in full relation-set: 28
Initial matrix: 214639 x 249972 with sparse part having weight 19123445.
Pruned matrix : 202249 x 203386 with weight 12879625.
Total sieving time: 3.38 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 3.57 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹³⁷-7 = 4(9)₁₃₆3_<138> = 13 · 673573 · 7297977952249711_<16> · C115

C115 = P34 · P81

P34 = 9394428712264339107505356592635883_<34>

P81 = 832854352226576752484715428137571713119476790537271630219939252608157903031281189_<81>

Number: 49993_137
N=7824190839691669749163653157266934458630643853189079636887156615889238145318912324273611451606146225919988064304887
  ( 115 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=9394428712264339107505356592635883 (pp34)
 r2=832854352226576752484715428137571713119476790537271630219939252608157903031281189 (pp81)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.58 hours.
Scaled time: 7.64 units (timescale=2.136).
Factorization parameters were as follows:
n: 7824190839691669749163653157266934458630643853189079636887156615889238145318912324273611451606146225919988064304887
m: 5000000000000000000000000000
c5: 4
c0: -175
skew: 2.13
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1350001)
Primes: RFBsize:107126, AFBsize:106873, largePrimes:2324504 encountered
Relations: rels:2470570, finalFF:302661
Max relations in full relation-set: 28
Initial matrix: 214063 x 302661 with sparse part having weight 23246989.
Pruned matrix : 183090 x 184224 with weight 11133020.
Total sieving time: 3.42 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 3.58 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

5·10¹⁵¹-7 = 4(9)₁₅₀3_<152> = 1413677 · 7305622079024944242228091_<25> · C121

C121 = P33 · P89

P33 = 293508139448334928739242445881249_<33>

P89 = 16494625527091676916421984392283134811156918776772753098253796574689797190832398167922951_<89>

5·10¹³⁸-7 = 4(9)₁₃₇3_<139> = 23 · 97 · 76129 · 335507 · C125

C125 = P51 · P75

P51 = 589299164638605947647771819491726255852140418406087_<51>

P75 = 148895954377143576247780304403642128934646012521450079487879648263630397923_<75>

Number: 49993_138
N=87744261532518692236722362187251629645597029515691483213116126366750425844988944265188979806400848045894132573044429215357301
  ( 125 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=589299164638605947647771819491726255852140418406087 (pp51)
 r2=148895954377143576247780304403642128934646012521450079487879648263630397923 (pp75)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.39 hours.
Scaled time: 11.50 units (timescale=2.133).
Factorization parameters were as follows:
n: 87744261532518692236722362187251629645597029515691483213116126366750425844988944265188979806400848045894132573044429215357301
m: 10000000000000000000000000000
c5: 1
c0: -140
skew: 2.69
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1050001)
Primes: RFBsize:107126, AFBsize:107423, largePrimes:2239474 encountered
Relations: rels:2359215, finalFF:276225
Max relations in full relation-set: 28
Initial matrix: 214613 x 276225 with sparse part having weight 22517328.
Pruned matrix : 188495 x 189632 with weight 12308616.
Total sieving time: 5.22 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 5.39 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

Sep 19, 2007

By Jo Yeong Uk / GGNFS

2·10¹⁵⁶-7 = 1(9)₁₅₅3_<157> = 61 · 379561891 · 591755936832544670700889_<24> · C123

C123 = P58 · P65

P58 = 2996976568019324627915945752938287251955921580343264766897_<58>

P65 = 48707023203560580789797226764686962335766992120048448009260900471_<65>

Number: 19993_156
N=145973807239044599895795366422383396989943956162809260080362174883363753419104691249139419330074996177706630877434132508487
  ( 123 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=2996976568019324627915945752938287251955921580343264766897 (pp58)
 r2=48707023203560580789797226764686962335766992120048448009260900471 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 16.84 hours.
Scaled time: 35.96 units (timescale=2.135).
Factorization parameters were as follows:
n: 145973807239044599895795366422383396989943956162809260080362174883363753419104691249139419330074996177706630877434132508487
m: 10000000000000000000000000000000
c5: 20
c0: -7
skew: 0.81
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2500001)
Primes: RFBsize:216816, AFBsize:215976, largePrimes:5451035 encountered
Relations: rels:5348208, finalFF:507344
Max relations in full relation-set: 28
Initial matrix: 432858 x 507344 with sparse part having weight 36913541.
Pruned matrix : 378693 x 380921 with weight 24853519.
Total sieving time: 15.92 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.80 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 16.84 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

Sep 18, 2007 (7th)

By JMB / GGNFS

2·10¹⁷³+3 = 2(0)₁₇₂3_<174> = 31 · 3164590541963_<13> · 1377280097548571230432695973091803101076339_<43> · C118

C118 = P53 · P66

P53 = 10704249832674713026912742559336870309487534796404441_<53>

P66 = 138284106376553420246923079942434034576006381033927871198757392949_<66>

Number: N
N=1480227622542794165404399819785920618847153787232185974759390499635827513314206276438905310385107334421379192165686509
  ( 118 digits)
Divisors found:
 r1=10704249832674713026912742559336870309487534796404441 (pp53)
 r2=138284106376553420246923079942434034576006381033927871198757392949 (pp66)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 52.15 hours.
Scaled time: 98.15 units (timescale=1.882).
Factorization parameters were as follows:
name: N
n: 1480227622542794165404399819785920618847153787232185974759390499635827513314206276438905310385107334421379192165686509
skew: 33365.99
# norm 5.52e+15
c5: 8400
c4: 2858359922
c3: 69125290698979
c2: 2226394878652247136
c1: -27649659782574825693836
c0: -71117271795651997618937776
# alpha -4.79
Y1: 2892399891821
Y0: -44586966544883642201365
# Murphy_E 3.86e-10
# M 1116241208575494244563539100262926120008752083455990065001830398269407723172354643387959025093684663593340304927476381
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 10000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 2430001)
Primes: RFBsize:315948, AFBsize:315227, largePrimes:7757737 encountered
Relations: rels:7926431, finalFF:820826
Max relations in full relation-set: 28
Initial matrix: 631253 x 820826 with sparse part having weight 71065693.
Pruned matrix : 476037 x 479257 with weight 42894052.
Total sieving time: 46.30 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 5.31 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 52.15 hours.
 --------- CPU info (if available) ----------

Sep 18, 2007 (6th)

By Sinkiti Sibata / GGNFS, Msieve

5·10¹¹²-7 = 4(9)₁₁₁3_<113> = 31 · 199 · 1726577810038023749_<19> · C91

C91 = P43 · P48

P43 = 6338023959737574815597795059605732175772951_<43>

P48 = 740653709666671254036993453169242903252989973403_<48>

Number: 49993_112
N=4694280957735879835192257868892353847777033806650163825970139352033222478931893194456822253
  ( 91 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=6338023959737574815597795059605732175772951 (pp43)
 r2=740653709666671254036993453169242903252989973403 (pp48)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.95 hours.
Scaled time: 1.32 units (timescale=0.677).
Factorization parameters were as follows:
name: 49993_112
n: 4694280957735879835192257868892353847777033806650163825970139352033222478931893194456822253
m: 10000000000000000000000
c5: 500
c0: -7
skew: 0.43
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:63743, largePrimes:2287037 encountered
Relations: rels:2646059, finalFF:487489
Max relations in full relation-set: 28
Initial matrix: 112907 x 487489 with sparse part having weight 36961708.
Pruned matrix : 59914 x 60542 with weight 4878956.
Total sieving time: 1.79 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,112,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.95 hours.
 --------- CPU info (if available) ----------

5·10¹²⁴-7 = 4(9)₁₂₃3_<125> = 38611 · 450361 · 2871839245138288177663_<22> · C94

C94 = P32 · P62

P32 = 96307871964544146356044436726531_<32>

P62 = 10396239289011278195567666108316680054766182724101112004334711_<62>

Number: 49993_124
N=1001239682358861648336397232573322011186790460010738716001180000426506650931892738839297917541
  ( 94 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=96307871964544146356044436726531 (pp32)
 r2=10396239289011278195567666108316680054766182724101112004334711 (pp62)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.52 hours.
Scaled time: 1.71 units (timescale=0.677).
Factorization parameters were as follows:
name: 49993_124
n: 1001239682358861648336397232573322011186790460010738716001180000426506650931892738839297917541
m: 10000000000000000000000000
c5: 1
c0: -14
skew: 1.7
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:63623, largePrimes:2113124 encountered
Relations: rels:2175709, finalFF:203620
Max relations in full relation-set: 28
Initial matrix: 112785 x 203620 with sparse part having weight 17991882.
Pruned matrix : 92175 x 92802 with weight 5574129.
Total sieving time: 2.28 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.52 hours.
 --------- CPU info (if available) ----------

5·10¹⁰³-7 = 4(9)₁₀₂3_<104> = 1054033 · 11594362361_<11> · C88

C88 = P37 · P51

P37 = 4410131384499304810512717460695947827_<37>

P51 = 927721024511601037911354571948957412235819374408843_<51>

Tue Sep 18 16:15:04 2007  Msieve v. 1.26
Tue Sep 18 16:15:04 2007  random seeds: e103ff01 6e7fc021
Tue Sep 18 16:15:04 2007  factoring 4091371606258460579732267674655946076932554042364590956386352513061582689683113695434161 (88 digits)
Tue Sep 18 16:15:05 2007  commencing quadratic sieve (88-digit input)
Tue Sep 18 16:15:05 2007  using multiplier of 1
Tue Sep 18 16:15:05 2007  using 64kb Pentium 2 sieve core
Tue Sep 18 16:15:05 2007  sieve interval: 14 blocks of size 65536
Tue Sep 18 16:15:05 2007  processing polynomials in batches of 8
Tue Sep 18 16:15:05 2007  using a sieve bound of 1527521 (57818 primes)
Tue Sep 18 16:15:05 2007  using large prime bound of 122201680 (26 bits)
Tue Sep 18 16:15:05 2007  using double large prime bound of 360361878370480 (42-49 bits)
Tue Sep 18 16:15:05 2007  using trial factoring cutoff of 49 bits
Tue Sep 18 16:15:05 2007  polynomial 'A' values have 11 factors
Tue Sep 18 22:29:06 2007  58366 relations (16041 full + 42325 combined from 613107 partial), need 57914
Tue Sep 18 22:29:16 2007  begin with 629148 relations
Tue Sep 18 22:29:19 2007  reduce to 140454 relations in 10 passes
Tue Sep 18 22:29:19 2007  attempting to read 140454 relations
Tue Sep 18 22:29:28 2007  recovered 140454 relations
Tue Sep 18 22:29:28 2007  recovered 115367 polynomials
Tue Sep 18 22:29:33 2007  attempting to build 58366 cycles
Tue Sep 18 22:29:33 2007  found 58366 cycles in 6 passes
Tue Sep 18 22:29:35 2007  distribution of cycle lengths:
Tue Sep 18 22:29:35 2007     length 1 : 16041
Tue Sep 18 22:29:35 2007     length 2 : 11360
Tue Sep 18 22:29:35 2007     length 3 : 10344
Tue Sep 18 22:29:35 2007     length 4 : 7623
Tue Sep 18 22:29:35 2007     length 5 : 5353
Tue Sep 18 22:29:35 2007     length 6 : 3379
Tue Sep 18 22:29:35 2007     length 7 : 2011
Tue Sep 18 22:29:35 2007     length 9+: 2255
Tue Sep 18 22:29:35 2007  largest cycle: 16 relations
Tue Sep 18 22:29:36 2007  matrix is 57818 x 58366 with weight 3358951 (avg 57.55/col)
Tue Sep 18 22:29:39 2007  filtering completed in 3 passes
Tue Sep 18 22:29:39 2007  matrix is 53411 x 53475 with weight 3081715 (avg 57.63/col)
Tue Sep 18 22:29:41 2007  saving the first 48 matrix rows for later
Tue Sep 18 22:29:42 2007  matrix is 53363 x 53475 with weight 2460669 (avg 46.02/col)
Tue Sep 18 22:29:42 2007  matrix includes 64 packed rows
Tue Sep 18 22:29:42 2007  using block size 10922 for processor cache size 256 kB
Tue Sep 18 22:29:42 2007  commencing Lanczos iteration
Tue Sep 18 22:32:34 2007  lanczos halted after 845 iterations
Tue Sep 18 22:32:35 2007  recovered 14 nontrivial dependencies
Tue Sep 18 22:32:48 2007  prp37 factor: 4410131384499304810512717460695947827
Tue Sep 18 22:32:48 2007  prp51 factor: 927721024511601037911354571948957412235819374408843
Tue Sep 18 22:32:48 2007  elapsed time 06:17:44

Sep 18, 2007 (5th)

By Jo Yeong Uk / GMP-ECM

5·10¹⁷⁷-7 = 4(9)₁₇₆3_<178> = C178

C178 = P33 · C146

P33 = 159222322628756092199652384637699_<33>

C146 = [31402631976786545252692940445059838167581831564267435779280007674035294043391904450027457606945967767231885984890715247474553329384690419652493907_<146>]

Sep 18, 2007 (4th)

The factor table of 499...993 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Sep 18, 2007 (3rd)

By Sinkiti Sibata / GGNFS

3·10¹⁵⁴-7 = 2(9)₁₅₃3_<155> = 34019 · 609903171398591373643_<21> · C130

C130 = P43 · P87

P43 = 3638448521596708316295882652136033250258553_<43>

P87 = 397395170759107781009516079528422156485067127226121794287339983126117723660641650772993_<87>

Number: 29993_154
N=1445901871538147156341447649224847712631394873758699363989919101940155761354755440420714445084445119451525115463081130749559659129
  ( 130 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=3638448521596708316295882652136033250258553 (pp43)
 r2=397395170759107781009516079528422156485067127226121794287339983126117723660641650772993 (pp87)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 57.07 hours.
Scaled time: 38.64 units (timescale=0.677).
Factorization parameters were as follows:
name: 29993_154
n: 1445901871538147156341447649224847712631394873758699363989919101940155761354755440420714445084445119451525115463081130749559659129
m: 10000000000000000000000000000000
c5: 3
c0: -70
skew: 1.88
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2900001)
Primes: RFBsize:216816, AFBsize:215951, largePrimes:5611743 encountered
Relations: rels:5508735, finalFF:488116
Max relations in full relation-set: 28
Initial matrix: 432832 x 488116 with sparse part having weight 40130555.
Pruned matrix : 407641 x 409869 with weight 29858979.
Total sieving time: 49.60 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 6.99 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 57.07 hours.
 --------- CPU info (if available) ----------

Sep 18, 2007 (2nd)

By Jo Yeong Uk / PRIMO

(5·10²⁰⁰⁷+1)/3 is prime!

Sep 18, 2007

By Jo Yeong Uk / GGNFS

3·10¹⁷⁹-7 = 2(9)₁₇₈3_<180> = 73 · 3683111 · 16927973 · 584455519 · 482923793970269_<15> · 75814253468842025360202563_<26> · C115

C115 = P42 · P73

P42 = 666955264597468844867283661741291944087841_<42>

P73 = 4618500484221053916134988602864131972644643376658791905760135103112512419_<73>

Number: 29993_179
N=3080333212497190998320588518704248460835256890165010422176507062229667521801892368359086189741076768397158739397379
  ( 115 digits)
Divisors found:
 r1=666955264597468844867283661741291944087841 (pp42)
 r2=4618500484221053916134988602864131972644643376658791905760135103112512419 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 25.35 hours.
Scaled time: 54.10 units (timescale=2.134).
Factorization parameters were as follows:
name: 29993_179
n: 3080333212497190998320588518704248460835256890165010422176507062229667521801892368359086189741076768397158739397379
skew: 64606.11
# norm 5.65e+15
c5: 24480
c4: -1282831244
c3: -285274267141254
c2: 2653256384091794754
c1: 627807025803164651781771
c0: 5959752286338459471323474153
# alpha -5.69
Y1: 974878789993
Y0: -10470265171305626182350
# Murphy_E 5.27e-10
# M 1462313019062199735784145259341739798397661617108705271681928514346601554110168923675620598322111573351965792712109
type: gnfs
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1800000, 3075001)
Primes: RFBsize:256726, AFBsize:257074, largePrimes:7591771 encountered
Relations: rels:7548192, finalFF:646497
Max relations in full relation-set: 28
Initial matrix: 513883 x 646497 with sparse part having weight 56504637.
Pruned matrix : 406596 x 409229 with weight 33984511.
Polynomial selection time: 1.33 hours.
Total sieving time: 22.77 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.96 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000
total time: 25.35 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

3·10¹⁵⁵+7 = 3(0)₁₅₄7_<156> = 307 · 947 · 17011 · 85013863614622230403517_<23> · C123

C123 = P50 · P73

P50 = 81026516161317424585126385687853691355677579362917_<50>

P73 = 8806151149339157734770802696564069152769229056077368044884311562147487877_<73>

Number: 30007_155
N=713531748420933277541673822962652894654142637485514664700401998801446798784016564278662446558305517823810235223089640857209
  ( 123 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=81026516161317424585126385687853691355677579362917 (pp50)
 r2=8806151149339157734770802696564069152769229056077368044884311562147487877 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 16.65 hours.
Scaled time: 35.65 units (timescale=2.141).
Factorization parameters were as follows:
n: 713531748420933277541673822962652894654142637485514664700401998801446798784016564278662446558305517823810235223089640857209
m: 10000000000000000000000000000000
c5: 3
c0: 7
skew: 1.18
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2500001)
Primes: RFBsize:216816, AFBsize:216206, largePrimes:5559375 encountered
Relations: rels:5517505, finalFF:555907
Max relations in full relation-set: 28
Initial matrix: 433087 x 555907 with sparse part having weight 41903022.
Pruned matrix : 345203 x 347432 with weight 26197869.
Total sieving time: 15.98 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.56 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 16.65 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

Sep 17, 2007 (2nd)

By Jo Yeong Uk / GGNFS

4·10¹⁷⁷+7 = 4(0)₁₇₆7_<178> = 419 · 173767929557963321729_<21> · 272757861127713014089301_<24> · 55596506082506498754154195877_<29> · C103

C103 = P37 · P67

P37 = 2168624917890105707938720036681408679_<37>

P67 = 1670579402649688089552461215114367735067686171584466742428310437779_<67>

Number: 40007_177
N=3622860119900081675144939418188208681175682968519562762569963159265022505636801426201586907652900083941
  ( 103 digits)
Divisors found:
 r1=2168624917890105707938720036681408679 (pp37)
 r2=1670579402649688089552461215114367735067686171584466742428310437779 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.70 hours.
Scaled time: 12.10 units (timescale=2.122).
Factorization parameters were as follows:
name: 40007_177
n: 3622860119900081675144939418188208681175682968519562762569963159265022505636801426201586907652900083941
skew: 5201.92
# norm 2.88e+14
c5: 538560
c4: 53023360
c3: -50292647881684
c2: -6925540917256562
c1: 749244940025056718037
c0: -1154576317830065586983730
# alpha -6.47
Y1: 58997159591
Y0: -23204032905420498401
# Murphy_E 2.42e-09
# M 1370455034032052557571471097180820566906316879206462490274763309076187559978205487356334531363056920027
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1620001)
Primes: RFBsize:135072, AFBsize:135194, largePrimes:4450489 encountered
Relations: rels:4488383, finalFF:403745
Max relations in full relation-set: 28
Initial matrix: 270349 x 403745 with sparse part having weight 33923516.
Pruned matrix : 193755 x 195170 with weight 15534745.
Polynomial selection time: 0.35 hours.
Total sieving time: 5.06 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 5.70 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

2·10¹⁵⁵-7 = 1(9)₁₅₄3_<156> = 4339 · 5303 · 1439617218001_<13> · 961207979097509279_<18> · C118

C118 = P35 · P83

P35 = 80965371749079875135193964006734647_<35>

P83 = 77580934154601854923447083339687231799885525920119624203485250965115554274629179933_<83>

Number: 19993_155
N=6281369174468227010565931881995665318163438158792180025253984512757518274749245757587968753964874412460492994748238651
  ( 118 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=80965371749079875135193964006734647 (pp35)
 r2=77580934154601854923447083339687231799885525920119624203485250965115554274629179933 (pp83)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 16.76 hours.
Scaled time: 35.87 units (timescale=2.141).
Factorization parameters were as follows:
n: 6281369174468227010565931881995665318163438158792180025253984512757518274749245757587968753964874412460492994748238651
m: 10000000000000000000000000000000
c5: 2
c0: -7
skew: 1.28
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2500001)
Primes: RFBsize:216816, AFBsize:216386, largePrimes:5531502 encountered
Relations: rels:5461621, finalFF:532447
Max relations in full relation-set: 28
Initial matrix: 433267 x 532447 with sparse part having weight 40040051.
Pruned matrix : 362515 x 364745 with weight 25713600.
Total sieving time: 15.99 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.65 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 16.76 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

Sep 17, 2007

By Jo Yeong Uk / PRIMO

(5·10²⁰⁰²+7)/3 is prime!

Sep 16, 2007 (2nd)

By Jo Yeong Uk / GGNFS

7·10¹⁵³+3 = 7(0)₁₅₂3_<154> = 73 · 131 · 23323831 · 1846251383033_<13> · C131

C131 = P58 · P73

P58 = 2379079812909254428043276041211980572721289410506055623377_<58>

P73 = 7145031581347695270977233930386125972534532154126683920313280001705450711_<73>

Number: 70003_153
N=16998600397783389175759249569289061087069302188459355668140254648218552381501175502221072936905279990154489333515869992693852871047
  ( 131 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=2379079812909254428043276041211980572721289410506055623377 (pp58)
 r2=7145031581347695270977233930386125972534532154126683920313280001705450711 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 20.08 hours.
Scaled time: 42.73 units (timescale=2.128).
Factorization parameters were as follows:
n: 16998600397783389175759249569289061087069302188459355668140254648218552381501175502221072936905279990154489333515869992693852871047
m: 10000000000000000000000000000000
c5: 7
c0: 300
skew: 2.12
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2700001)
Primes: RFBsize:216816, AFBsize:216676, largePrimes:5675578 encountered
Relations: rels:5689109, finalFF:598690
Max relations in full relation-set: 28
Initial matrix: 433559 x 598690 with sparse part having weight 47345346.
Pruned matrix : 332263 x 334494 with weight 29525513.
Total sieving time: 19.32 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.62 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 20.08 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

2·10¹⁶³-7 = 1(9)₁₆₂3_<164> = 13 · 201757487 · 164834767007237_<15> · 129162229318541414865248023_<27> · C114

C114 = P49 · P66

P49 = 2870602702071050972528733922531425863733789921251_<49>

P66 = 124766945602396491462945015979925208408928505160969226719559459403_<66>

Number: 19993_163
N=358156331175391198893339808547858557746935279886252689505085670398402621508842992831589269212432640565739501473153
  ( 114 digits)
Divisors found:
 r1=2870602702071050972528733922531425863733789921251 (pp49)
 r2=124766945602396491462945015979925208408928505160969226719559459403 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 21.80 hours.
Scaled time: 46.41 units (timescale=2.129).
Factorization parameters were as follows:
name: 19993_163
n: 358156331175391198893339808547858557746935279886252689505085670398402621508842992831589269212432640565739501473153
skew: 45628.38
# norm 6.02e+15
c5: 51840
c4: -3683687742
c3: -219889653043975
c2: 9456954518204852587
c1: 291767181530166543087243
c0: -21035126965595459418314492
# alpha -5.76
Y1: 58235380021
Y0: -5859783753033214798315
# Murphy_E 5.80e-10
# M 44894003223997302383774582468193933612947797133112838301158642168226836618277433846086123864581870351008011079287
type: gnfs
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1800000, 2925001)
Primes: RFBsize:256726, AFBsize:257368, largePrimes:7412290 encountered
Relations: rels:7272447, finalFF:595178
Max relations in full relation-set: 28
Initial matrix: 514169 x 595178 with sparse part having weight 46315095.
Pruned matrix : 446792 x 449426 with weight 29929625.
Total sieving time: 20.50 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 1.01 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000
total time: 21.80 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407686)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.11 BogoMIPS).

Sep 16, 2007

By Jo Yeong Uk / GMP-ECM

(73·10¹⁹²-1)/9 = 8(1)₁₉₂_<193> = C193

C193 = P41 · C153

P41 = 73256271947274662782040893968743123700881_<41>

C153 = [110722411822280385931003784443497819857603220976577157566466357414344260125670777720438670653233237078832661859484778212857408425370362300763453787759831_<153>]

Sep 15, 2007 (3rd)

By Jo Yeong Uk / GGNFS

2·10¹⁸⁰-3 = 1(9)₁₇₉7_<181> = 2593 · 51067720369_<11> · 2039081640448510323571_<22> · 112032125257256292325042410655727_<33> · C113

C113 = P39 · P74

P39 = 905172686450661562749851540460137766673_<39>

P74 = 73041953120006531682243304867114152425466458123310047541535943923877620801_<74>

Number: 19997_180
N=66115580929239593359723808855458909629091457719484972084609617544199525101235044807799431332453896293536909365073
  ( 113 digits)
Divisors found:
 r1=905172686450661562749851540460137766673 (pp39)
 r2=73041953120006531682243304867114152425466458123310047541535943923877620801 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 19.07 hours.
Scaled time: 40.84 units (timescale=2.142).
Factorization parameters were as follows:
name: 19997_180
n: 66115580929239593359723808855458909629091457719484972084609617544199525101235044807799431332453896293536909365073
skew: 50900.26
# norm 4.78e+15
c5: 35640
c4: 2092026780
c3: -257421258914871
c2: -3597313150952401664
c1: 336073469633725578681108
c0: 880253753751683250101584592
# alpha -6.29
Y1: 891128745329
Y0: -4504765787799004324305
# Murphy_E 6.77e-10
# M 31447131488392542736505992818019557460517464114991795498415980855609373894140662627343843911601067913431897504545
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1400000, 2310001)
Primes: RFBsize:203362, AFBsize:203921, largePrimes:7460034 encountered
Relations: rels:7203107, finalFF:459537
Max relations in full relation-set: 28
Initial matrix: 407366 x 459537 with sparse part having weight 41639635.
Pruned matrix : 368891 x 370991 with weight 29954447.
Polynomial selection time: 1.04 hours.
Total sieving time: 17.05 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.71 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000
total time: 19.07 hours.
 --------- CPU info (if available) ----------

3·10¹⁵³+7 = 3(0)₁₅₂7_<154> = 31 · 1960320883_<10> · 234995429723777_<15> · C129

C129 = P59 · P71

P59 = 12766708087797880775647643713694004841381361147278295433889_<59>

P71 = 16454854639373394037106403236176282020045812281709905847229481803749603_<71>

Number: 30007_153
N=210074325808026790448996368590420356086009745382036315917389148054666342924659655032019177558676920733305767288001767113996496067
  ( 129 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=12766708087797880775647643713694004841381361147278295433889 (pp59)
 r2=16454854639373394037106403236176282020045812281709905847229481803749603 (pp71)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 16.75 hours.
Scaled time: 35.43 units (timescale=2.116).
Factorization parameters were as follows:
n: 210074325808026790448996368590420356086009745382036315917389148054666342924659655032019177558676920733305767288001767113996496067
m: 10000000000000000000000000000000
c5: 3
c0: 700
skew: 2.98
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2500001)
Primes: RFBsize:216816, AFBsize:216741, largePrimes:5443893 encountered
Relations: rels:5315927, finalFF:487026
Max relations in full relation-set: 28
Initial matrix: 433623 x 487026 with sparse part having weight 35101675.
Pruned matrix : 395950 x 398182 with weight 25217603.
Total sieving time: 15.90 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.73 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 16.75 hours.
 --------- CPU info (if available) ----------

Sep 15, 2007 (2nd)

By Sinkiti Sibata / GGNFS

4·10¹⁵³+7 = 4(0)₁₅₂7_<154> = 15122759 · 24745976488388042357_<20> · C128

C128 = P63 · P65

P63 = 309312185819485412279995450362993507710825827912972995314067713_<63>

P65 = 34556307836253073852792654157706035652442377990012162822070317853_<65>

Number: 40007_153
N=10688687110682450660439951947485525140658610226471628564203051191314620050655242128626856748244492908709436441566630388274780189
  ( 128 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=309312185819485412279995450362993507710825827912972995314067713 (pp63)
 r2=34556307836253073852792654157706035652442377990012162822070317853 (pp65)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 34.45 hours.
Scaled time: 22.81 units (timescale=0.662).
Factorization parameters were as follows:
name: 40007_153
n: 10688687110682450660439951947485525140658610226471628564203051191314620050655242128626856748244492908709436441566630388274780189
m: 2000000000000000000000000000000
c5: 125
c0: 7
skew: 0.56
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176043, largePrimes:5482109 encountered
Relations: rels:5371718, finalFF:399515
Max relations in full relation-set: 0
Initial matrix: 352410 x 399515 with sparse part having weight 26957995.
Pruned matrix : 325683 x 327509 with weight 20456304.
Total sieving time: 30.73 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.36 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 34.45 hours.
 --------- CPU info (if available) ----------

Sep 15, 2007

By Jo Yeong Uk / PRIMO

(25·10²⁰¹⁸-7)/9 is prime!

Sep 14, 2007 (4th)

By Jo Yeong Uk / GGNFS

4·10¹⁵⁴+7 = 4(0)₁₅₃7_<155> = 11 · 342802429 · 25012593481129_<14> · 9378914296479408781_<19> · C113

C113 = P37 · P76

P37 = 4999642122681669494026196348160121217_<37>

P76 = 9044263464946840747038283509739191493041103507550062570873462979319591737141_<76>

Number: 40007_154
N=45218080587979093989708475325381839456130749535604419753028667196019088987174074624391266950271169021962161020597
  ( 113 digits)
Divisors found:
 r1=4999642122681669494026196348160121217 (pp37)
 r2=9044263464946840747038283509739191493041103507550062570873462979319591737141 (pp76)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 19.99 hours.
Scaled time: 42.53 units (timescale=2.127).
Factorization parameters were as follows:
name: 40007_154
n: 45218080587979093989708475325381839456130749535604419753028667196019088987174074624391266950271169021962161020597
skew: 31283.77
# norm 1.65e+16
c5: 68040
c4: 13966398846
c3: -414229534697503
c2: 932493901125242698
c1: 180032739590643387395624
c0: 35538889773243182429407920
# alpha -6.92
Y1: 836403879509
Y0: -3668643396033347782541
# Murphy_E 6.56e-10
# M 28071116392022513803667070326716114062434066061004312341816282378150721023164556206800033729572617394388783406386
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1400000, 2380001)
Primes: RFBsize:203362, AFBsize:203919, largePrimes:7534644 encountered
Relations: rels:7339518, finalFF:490981
Max relations in full relation-set: 28
Initial matrix: 407361 x 490981 with sparse part having weight 46092839.
Pruned matrix : 345308 x 347408 with weight 30104251.
Polynomial selection time: 1.07 hours.
Total sieving time: 18.05 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.61 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000
total time: 19.99 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Total of 4 processors activated (19246.10 BogoMIPS).

Sep 14, 2007 (3rd)

By Alban Nonymous

10¹²³¹+1 is divisible by 8500614695927155829161050714503_<31>

10¹³¹³+1 is divisible by 34620946390749763175836315244453_<32>

10¹³⁴⁵+1 is divisible by 21044037584000626448961059324881_<32>

10¹³⁵⁴+1 is divisible by 36764627737869172094680667009_<29>

10¹³⁹¹+1 is divisible by 155490403648623445664788291934117_<33>

10¹⁴⁰⁵+1 is divisible by 83260647980205591593475319975561_<32>

10¹⁴³⁹+1 is divisible by 75673683062427966236317236967_<29>

10¹⁴⁵⁹+1 is divisible by 794157316664184535777113799277_<30>

10¹⁵⁷⁴+1 is divisible by 31760068204068839447245615309_<29>

10¹⁵⁹⁴+1 is divisible by 4281518523436324087802519357629_<31>

10¹⁶¹²+1 is divisible by 144685957475846477676841682164313_<33>

10¹⁶⁶¹+1 is divisible by 260721284044113991032016909263383_<33>

10¹⁶⁸⁷+1 is divisible by 135355988585304270436638671970733_<33>

10¹⁷²⁷+1 is divisible by 197450481378401142788807346609757_<33>

10¹⁷⁶¹+1 is divisible by 221356639156600314082995856870369_<33>

10¹⁸⁴⁴+1 is divisible by 9125072483779648050066911421569_<31>

10¹⁸⁵⁴+1 is divisible by 122708016673764191207130969289_<30>

Reference: Factorizations of numbers of the form 10^n+1 (Alfred Reich)

Sep 14, 2007 (2nd)

By Jo Yeong Uk / GGNFS

3·10¹⁶²+7 = 3(0)₁₆₁7_<163> = C163

C163 = P49 · P55 · P60

P49 = 3733216672222512252402080024047876262175838601063_<49>

P55 = 1801107624738145935914817354265795383914325232132040341_<55>

P60 = 446167973934504101158694839309139582095409259666991720176029_<60>

Number: 30007_162
N=3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
  ( 163 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=3733216672222512252402080024047876262175838601063 (pp49)
 r2=1801107624738145935914817354265795383914325232132040341 (pp55)
 r3=446167973934504101158694839309139582095409259666991720176029 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 43.21 hours.
Scaled time: 91.29 units (timescale=2.113).
Factorization parameters were as follows:
n: 3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
m: 100000000000000000000000000000000
c5: 300
c0: 7
skew: 0.47
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 4800001)
Primes: RFBsize:348513, AFBsize:348181, largePrimes:5776537 encountered
Relations: rels:5923973, finalFF:791467
Max relations in full relation-set: 28
Initial matrix: 696760 x 791467 with sparse part having weight 43570598.
Pruned matrix : 617703 x 621250 with weight 30629496.
Total sieving time: 41.23 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 1.80 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 43.21 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Total of 4 processors activated (19246.10 BogoMIPS).

Sep 14, 2007

By Sinkiti Sibata / GGNFS

4·10¹⁴⁹+7 = 4(0)₁₄₈7_<150> = 19 · 37² · 79 · 156593 · 156967 · 6118218475309117_<16> · C118

C118 = P45 · P73

P45 = 458151166462975414839515281092455846471073253_<45>

P73 = 2825279191259063103973675923003172457201413683427285242607338783549973213_<73>

Number: 40007_149
N=1294404957058911574763733833658886023194297370404618272196308663603704846302793844151119322689824792125201967510771889
  ( 118 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=458151166462975414839515281092455846471073253 (pp45)
 r2=2825279191259063103973675923003172457201413683427285242607338783549973213 (pp73)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 26.65 hours.
Scaled time: 18.20 units (timescale=0.683).
Factorization parameters were as follows:
name: 40007_149
n: 1294404957058911574763733833658886023194297370404618272196308663603704846302793844151119322689824792125201967510771889
m: 1000000000000000000000000000000
c5: 2
c0: 35
skew: 1.77
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 1550001)
Primes: RFBsize:114155, AFBsize:113967, largePrimes:2700927 encountered
Relations: rels:2700881, finalFF:256445
Max relations in full relation-set: 0
Initial matrix: 228187 x 256445 with sparse part having weight 13732659.
Pruned matrix : 217172 x 218376 with weight 10745713.
Total sieving time: 25.50 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.94 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 26.65 hours.
 --------- CPU info (if available) ----------

Sep 13, 2007 (2nd)

By Robert Backstrom / GGNFS

4·10¹⁶¹+7 = 4(0)₁₆₀7_<162> = 37 · C161

C161 = P60 · P101

P60 = 135634950176910695018973466825893607656590609530685636796371_<60>

P101 = 79705199852324998153571878460082630852438535935125517735082254432468091835256979745543882602791947641_<101>

Number: n
N=10810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810811
  ( 161 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=135634950176910695018973466825893607656590609530685636796371 (pp60)
 r2=79705199852324998153571878460082630852438535935125517735082254432468091835256979745543882602791947641 (pp101)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.22 hours.
Scaled time: 51.03 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_4_0_160_7
n: 10810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810811
skew: 0.71
deg: 5
c5: 40
c0: 7
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:250150, AFBsize:249831, largePrimes:7163858 encountered
Relations: rels:6733578, finalFF:603451
Max relations in full relation-set: 28
Initial matrix: 500047 x 603451 with sparse part having weight 36708271.
Pruned matrix : 409178 x 411742 with weight 20824560.
Total sieving time: 31.18 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.64 hours.
Total square root time: 0.20 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 35.22 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Sep 13, 2007

By Jo Yeong Uk / GMP-ECM, GGNFS

4·10¹⁵⁹+7 = 4(0)₁₅₈7_<160> = 1759 · 665251 · 380206966797325875839_<21> · C130

C130 = P35 · P96

P35 = 38552289465776278156018648781010077_<35>

P96 = 233205275767539960164870481835449750381744466297103083038069953484504186782020869825210096921041_<96>

2·10¹⁵²-7 = 1(9)₁₅₁3_<153> = 43 · 204334865038223_<15> · 16693847621802210188347_<23> · C115

C115 = P54 · P61

P54 = 327984025003795812551523975755537204514529776773084171_<54>

P61 = 4157286246714744149068820102379243249246807718475885348533501_<61>

Number: 19993_152
N=1363523476290425092172349444739152306924486329874070738366011303585880390988622988895824915088159406187843686312671
  ( 115 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=327984025003795812551523975755537204514529776773084171 (pp54)
 r2=4157286246714744149068820102379243249246807718475885348533501 (pp61)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 15.90 hours.
Scaled time: 33.88 units (timescale=2.131).
Factorization parameters were as follows:
n: 1363523476290425092172349444739152306924486329874070738366011303585880390988622988895824915088159406187843686312671
m: 2000000000000000000000000000000
c5: 25
c0: -28
skew: 1.02
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2200001)
Primes: RFBsize:176302, AFBsize:176668, largePrimes:5516420 encountered
Relations: rels:5423681, finalFF:472836
Max relations in full relation-set: 28
Initial matrix: 353034 x 472836 with sparse part having weight 41918739.
Pruned matrix : 303636 x 305465 with weight 23920078.
Total sieving time: 15.34 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.44 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 15.90 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Total of 4 processors activated (19246.10 BogoMIPS).

4·10¹⁶⁰+7 = 4(0)₁₅₉7_<161> = 11 · 1136957848708636651_<19> · C142

C142 = P35 · P108

P35 = 25817512708582211180172834678179339_<35>

P108 = 123882095407939278236523043249249576804371883991910405477004505369234945547803086828965151030213745119507133_<108>

Sep 12, 2007 (8th)

By Yousuke Koide

10¹³⁸³+1 is divisible by 19106661240397987951762164436636893943_<38>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 12, 2007 (7th)

By suberi / GMP-ECM

2·10¹⁸⁹-3 = 1(9)₁₈₈7_<190> = 26515433818872756128486451063540368813_<38> · C152

C152 = P35 · C118

P35 = 31618164809434211754592287712179187_<35>

C118 = [2385583376282025837302025573831625807718996619292106854661488654167073439506823897959332181406320971559780911666433387_<118>]

Sep 12, 2007 (6th)

By Sinkiti Sibata / GGNFS

4·10¹⁴⁴+7 = 4(0)₁₄₃7_<145> = 11 · 179 · 18849577301_<11> · 752837899459199_<15> · C117

C117 = P35 · P82

P35 = 48338648874827112317609973195674549_<35>

P82 = 2961533694098241796253566194687162650499134657877589080508209090117714412844440753_<82>

Number: 40007_144
N=143156537369984557247257807124511565476769024965337464560184628079260630402615596072010099193813141404565420500495397
  ( 117 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=48338648874827112317609973195674549 (pp35)
 r2=2961533694098241796253566194687162650499134657877589080508209090117714412844440753 (pp82)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 13.12 hours.
Scaled time: 8.96 units (timescale=0.683).
Factorization parameters were as follows:
name: 40007_144
n: 143156537369984557247257807124511565476769024965337464560184628079260630402615596072010099193813141404565420500495397
m: 100000000000000000000000000000
c5: 2
c0: 35
skew: 1.77
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1850001)
Primes: RFBsize:100021, AFBsize:99918, largePrimes:2650465 encountered
Relations: rels:2603751, finalFF:227166
Max relations in full relation-set: 0
Initial matrix: 200004 x 227166 with sparse part having weight 17999391.
Pruned matrix : 191344 x 192408 with weight 13832480.
Total sieving time: 12.00 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.91 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 13.12 hours.
 --------- CPU info (if available) ----------

Sep 12, 2007 (5th)

By Jo Yeong Uk / PRIMO

(8·10²⁰⁹⁰-53)/9 is prime!

Sep 12, 2007 (4th)

By Robert Backstrom / GGNFS

4·10¹⁴⁸+7 = 4(0)₁₄₇7_<149> = 11 · 23 · 2447 · C143

C143 = P66 · P78

P66 = 245114463615524143538086032433891970756683404064249115073005692163_<66>

P78 = 263594632206945158216136499659187321494630614449650644664224883579346714068479_<78>

Number: n
N=64610856885336727557015043022754328523593462027391772776538505647796527489496697577577448226512742068613499469383337829172124938013959175630077
  ( 143 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=245114463615524143538086032433891970756683404064249115073005692163 (pp66)
 r2=263594632206945158216136499659187321494630614449650644664224883579346714068479 (pp78)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 11.66 hours.
Scaled time: 8.43 units (timescale=0.723).
Factorization parameters were as follows:
name: KA_4_0_147_7
n: 64610856885336727557015043022754328523593462027391772776538505647796527489496697577577448226512742068613499469383337829172124938013959175630077
skew: 0.56
deg: 5
c5: 125
c0: 7
m: 200000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:148933, AFBsize:148595, largePrimes:6600171 encountered
Relations: rels:5970160, finalFF:355083
Max relations in full relation-set: 28
Initial matrix: 297593 x 355083 with sparse part having weight 26405611.
Pruned matrix : 257089 x 258640 with weight 16503342.
Total sieving time: 7.87 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 3.09 hours.
Total square root time: 0.47 hours, sqrts: 5.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 11.66 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Sep 12, 2007 (3rd)

By Jo Yeong Uk / GGNFS

4·10¹⁵⁷+7 = 4(0)₁₅₆7_<158> = 17 · 19875157 · 1469183047_<10> · 42169567669_<11> · 46007753657_<11> · 292957231827292399177_<21> · C99

C99 = P40 · P59

P40 = 8814970410242325051502600691310445528441_<40>

P59 = 16083084130339877401016180137996623124776743395012266452129_<59>

Number: 40007_157
N=141771910714383936723190602488517820827004390019966573920874057536635436839306793283547283634500889
  ( 99 digits)
Divisors found:
 r1=8814970410242325051502600691310445528441 (pp40)
 r2=16083084130339877401016180137996623124776743395012266452129 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.05 hours.
Scaled time: 6.54 units (timescale=2.142).
Factorization parameters were as follows:
name: 40007_157
n: 141771910714383936723190602488517820827004390019966573920874057536635436839306793283547283634500889
skew: 4008.53
# norm 3.45e+13
c5: 21960
c4: -71874162
c3: -4406460702773
c2: 2450429555282521
c1: 12809475412520706169
c0: 5116825832921210112837
# alpha -5.07
Y1: 14932061617
Y0: -5780858056141522292
# Murphy_E 4.14e-09
# M 88781377175097529873633494690642072436766223929986758768355796430593531738087159338827855254497350
type: gnfs
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [650000, 1050001)
Primes: RFBsize:100021, AFBsize:99853, largePrimes:3742855 encountered
Relations: rels:3574058, finalFF:242656
Max relations in full relation-set: 28
Initial matrix: 199952 x 242656 with sparse part having weight 17822918.
Pruned matrix : 173035 x 174098 with weight 10123182.
Polynomial selection time: 0.23 hours.
Total sieving time: 2.58 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,98,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1300000,1300000,26,26,48,48,2.5,2.5,50000
total time: 3.05 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Total of 4 processors activated (19246.10 BogoMIPS).

3·10¹⁸⁴-1 = 2(9)₁₈₄_<185> = C185

C185 = P62 · P124

P62 = 10073641022189321360228001328707180659381468877455557544719139_<62>

P124 = 2978069194040036330503581914737461793403041082476154833888528931755723356899703483852214198475678536123147506448805613562741_<124>

Number: 29999_184
N=29999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
  ( 185 digits)
SNFS difficulty: 185 digits.
Divisors found:
 r1=10073641022189321360228001328707180659381468877455557544719139 (pp62)
 r2=2978069194040036330503581914737461793403041082476154833888528931755723356899703483852214198475678536123147506448805613562741 (pp124)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 343.63 hours.
Scaled time: 729.87 units (timescale=2.124).
Factorization parameters were as follows:
n: 29999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
m: 10000000000000000000000000000000000000
c5: 3
c0: -10
skew: 1.27
type: snfs
Factor base limits: 11000000/11000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [5500000, 11100001)
Primes: RFBsize:726517, AFBsize:727028, largePrimes:11282043 encountered
Relations: rels:11683743, finalFF:1645813
Max relations in full relation-set: 28
Initial matrix: 1453610 x 1645813 with sparse part having weight 94399149.
Pruned matrix : 1285739 x 1293071 with weight 69947957.
Total sieving time: 331.30 hours.
Total relation processing time: 0.39 hours.
Matrix solve time: 11.81 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,11000000,11000000,28,28,50,50,2.6,2.6,100000
total time: 343.63 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Total of 4 processors activated (19246.10 BogoMIPS).

Sep 12, 2007 (2nd)

By Sinkiti Sibata / GGNFS

4·10¹⁴³+7 = 4(0)₁₄₂7_<144> = 37 · 43 · 2953 · 85208610560597464386908162003_<29> · C108

C108 = P31 · P78

P31 = 1000749795659211467211625369787_<31>

P78 = 998429423289612292605918747746093298336322693193270765403387192272005415284169_<78>

Number: 40007_143
N=999178041337223852488855483773425882364042283838812522867286562602400394959670087123679083063501766312002003
  ( 108 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=1000749795659211467211625369787 (pp31)
 r2=998429423289612292605918747746093298336322693193270765403387192272005415284169 (pp78)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 12.96 hours.
Scaled time: 8.85 units (timescale=0.683).
Factorization parameters were as follows:
name: 40007_143
n: 999178041337223852488855483773425882364042283838812522867286562602400394959670087123679083063501766312002003
m: 20000000000000000000000000000
c5: 125
c0: 7
skew: 0.56
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1850001)
Primes: RFBsize:100021, AFBsize:99858, largePrimes:2670610 encountered
Relations: rels:2631232, finalFF:227950
Max relations in full relation-set: 0
Initial matrix: 199944 x 227950 with sparse part having weight 17712373.
Pruned matrix : 190831 x 191894 with weight 13565004.
Total sieving time: 11.85 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.90 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 12.96 hours.
 --------- CPU info (if available) ----------

Sep 12, 2007

By Robert Backstrom / GGNFS

5·10¹⁸²-3 = 4(9)₁₈₁7_<183> = 7² · C182

C182 = P47 · P135

P47 = 29770834642130994832881614532449420836505709773_<47>

P135 = 342754301493868147025468004954466202887529212100972680571593317530253611454746160580734860582053102922819500742588146493363342762650561_<135>

Number: n
N=10204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653
  ( 182 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=29770834642130994832881614532449420836505709773 (pp47)
 r2=342754301493868147025468004954466202887529212100972680571593317530253611454746160580734860582053102922819500742588146493363342762650561 (pp135)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 526.30 hours.
Scaled time: 759.46 units (timescale=1.443).
Factorization parameters were as follows:
name: KA_4_9_181_7
n: 10204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653
skew: 1.36
deg: 5
c5: 500
c0: -3
m: 1000000000000000000000000000000000000
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 7900001)
Primes: RFBsize:283146, AFBsize:282917, largePrimes:9091651 encountered
Relations: rels:8782511, finalFF:640766
Max relations in full relation-set: 28
Initial matrix: 566129 x 640766 with sparse part having weight 83377454.
Pruned matrix : 535642 x 538536 with weight 69043920.
Total sieving time: 508.12 hours.
Total relation processing time: 0.68 hours.
Matrix solve time: 17.38 hours.
Total square root time: 0.12 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000
total time: 526.30 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Sep 11, 2007 (4th)

By Sinkiti Sibata / GGNFS

4·10¹³⁹+7 = 4(0)₁₃₈7_<140> = 47 · 59 · 61 · 7229 · 8623 · 10837 · C123

C123 = P50 · P74

P50 = 31986300717986806917050274578788541806841309083879_<50>

P74 = 10943861459545403346659982155635581621711169730625226161155822473142568559_<74>

Number: 40007_139
N=350053643661005279748843704503251430769753790262193682777340431379729126555588061839938125103056209629639011990529239160361
  ( 123 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=31986300717986806917050274578788541806841309083879 (pp50)
 r2=10943861459545403346659982155635581621711169730625226161155822473142568559 (pp74)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 8.92 hours.
Scaled time: 6.09 units (timescale=0.683).
Factorization parameters were as follows:
name: 40007_139
n: 350053643661005279748843704503251430769753790262193682777340431379729126555588061839938125103056209629639011990529239160361
m: 10000000000000000000000000000
c5: 2
c0: 35
skew: 1.77
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1300001)
Primes: RFBsize:78498, AFBsize:63938, largePrimes:1494045 encountered
Relations: rels:1474401, finalFF:159762
Max relations in full relation-set: 0
Initial matrix: 142501 x 159762 with sparse part having weight 13322206.
Pruned matrix : 137478 x 138254 with weight 9904526.
Total sieving time: 8.38 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.40 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.92 hours.
 --------- CPU info (if available) ----------

Sep 11, 2007 (3rd)

By Robert Backstrom / GGNFS

3·10¹⁵¹+7 = 3(0)₁₅₀7_<152> = 37 · 73 · 1244863 · 20628811590269_<14> · C129

C129 = P64 · P66

P64 = 1197832543309205649377891301884244716228803440401897936550987217_<64>

P66 = 361081131072503212385537651948543045335365693158346674560705560593_<66>

Number: n
N=432514729573541165878814502602851075559541863386033196591231623575925857266862190179793058170814822307811485963457490435561939681
  ( 129 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=1197832543309205649377891301884244716228803440401897936550987217 (pp64)
 r2=361081131072503212385537651948543045335365693158346674560705560593 (pp66)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 27.46 hours.
Scaled time: 32.81 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_3_0_150_7
n: 432514729573541165878814502602851075559541863386033196591231623575925857266862190179793058170814822307811485963457490435561939681
type: snfs
skew: 1.00
deg: 5
c5: 30
c0: 7
m: 1000000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1150001)
Primes: RFBsize:148933, AFBsize:148635, largePrimes:6069369 encountered
Relations: rels:5430747, finalFF:346854
Max relations in full relation-set: 28
Initial matrix: 297635 x 346854 with sparse part having weight 25044237.
Pruned matrix : 262468 x 264020 with weight 16394510.
Total sieving time: 25.39 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 1.78 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 27.46 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Sep 11, 2007 (2nd)

By Sinkiti Sibata / GGNFS

4·10¹⁴⁰+7 = 4(0)₁₃₉7_<141> = 11 · 37 · 84263 · 21289799939_<11> · 339012053851_<12> · 5722935804716380853_<19> · C93

C93 = P39 · P55

P39 = 246523695335114998234346215684034044871_<39>

P55 = 1145419047714673326600757462103639786711752383269528461_<55>

Number: 40007_140
N=282372936349849676344049794975421655211442692035412953083742345621409096950554935978685573531
  ( 93 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=246523695335114998234346215684034044871 (pp39)
 r2=1145419047714673326600757462103639786711752383269528461 (pp55)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 8.01 hours.
Scaled time: 5.47 units (timescale=0.683).
Factorization parameters were as follows:
n: 282372936349849676344049794975421655211442692035412953083742345621409096950554935978685573531
m: 10000000000000000000000000000
c5: 4
c0: 7
skew: 1.12
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1350001)
Primes: RFBsize:100021, AFBsize:100128, largePrimes:2522999 encountered
Relations: rels:2447285, finalFF:225591
Max relations in full relation-set: 0
Initial matrix: 200213 x 225591 with sparse part having weight 13214244.
Pruned matrix : 190912 x 191977 with weight 9721443.
Total sieving time: 7.15 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.69 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 8.01 hours.
 --------- CPU info (if available) ----------

Sep 11, 2007

By Jo Yeong Uk / GGNFS

4·10¹³²+7 = 4(0)₁₃₁7_<133> = 11 · 1383665436911_<13> · 15993881312447791_<17> · C104

C104 = P42 · P63

P42 = 105178237608324529255932346205701327687403_<42>

P63 = 156227130243012416024084470042988923198135605773570637061345279_<63>

Number: 40007_132
N=16431694225566222948609513601281972899576566543250776087667169652945304700613585557818414923365161820437
  ( 104 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=105178237608324529255932346205701327687403 (pp42)
 r2=156227130243012416024084470042988923198135605773570637061345279 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.47 hours.
Scaled time: 5.23 units (timescale=2.118).
Factorization parameters were as follows:
n: 16431694225566222948609513601281972899576566543250776087667169652945304700613585557818414923365161820437
m: 200000000000000000000000000
c5: 25
c0: 14
skew: 0.89
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 1000001)
Primes: RFBsize:78498, AFBsize:78371, largePrimes:1569406 encountered
Relations: rels:1611834, finalFF:216226
Max relations in full relation-set: 28
Initial matrix: 156933 x 216226 with sparse part having weight 10703211.
Pruned matrix : 133627 x 134475 with weight 5265424.
Total sieving time: 2.38 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 2.47 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Total of 4 processors activated (19246.10 BogoMIPS).

4·10¹³³+7 = 4(0)₁₃₂7_<134> = 103 · 139 · 581182594323229533763_<21> · C109

C109 = P35 · P75

P35 = 26266897688914103600761963556264623_<35>

P75 = 183014957204357914443774593629154442488846573682381077826399652046581216079_<75>

Number: 40007_133
N=4807235156427862477801484912313373050636771228697485220905861647175509857379509740170422840569881678066473217
  ( 109 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=26266897688914103600761963556264623 (pp35)
 r2=183014957204357914443774593629154442488846573682381077826399652046581216079 (pp75)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.48 hours.
Scaled time: 5.32 units (timescale=2.144).
Factorization parameters were as follows:
n: 4807235156427862477801484912313373050636771228697485220905861647175509857379509740170422840569881678066473217
m: 1000000000000000000000000000
c5: 1
c0: 175
skew: 2.81
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1100001)
Primes: RFBsize:107126, AFBsize:107108, largePrimes:2183290 encountered
Relations: rels:2279537, finalFF:274333
Max relations in full relation-set: 28
Initial matrix: 214298 x 274333 with sparse part having weight 17720307.
Pruned matrix : 182909 x 184044 with weight 9107441.
Total sieving time: 2.27 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 2.48 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Total of 4 processors activated (19246.10 BogoMIPS).

Sep 10, 2007 (4th)

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve

4·10¹⁴²+7 = 4(0)₁₄₁7_<143> = 11 · 128425333 · 330484919 · 1110686627_<10> · C116

C116 = P31 · P86

P31 = 2229599509718725418315923215401_<31>

P86 = 34597646459065868838026205405922156262284783213861761567480768713986485734911023224453_<86>

4·10¹⁰⁵+7 = 4(0)₁₀₄7_<106> = C106

C106 = P37 · P70

P37 = 1043329248228030997017608973380352553_<37>

P70 = 3833880826012994445256424591562881885990352920890139603449554354425519_<70>

Number: 40007_105
N=4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
  ( 106 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=1043329248228030997017608973380352553 (pp37)
 r2=3833880826012994445256424591562881885990352920890139603449554354425519 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.37 hours.
Scaled time: 0.79 units (timescale=2.144).
Factorization parameters were as follows:
n: 4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
m: 1000000000000000000000
c5: 4
c0: 7
skew: 1.12
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 240001)
Primes: RFBsize:30757, AFBsize:30779, largePrimes:1084096 encountered
Relations: rels:1048724, finalFF:128939
Max relations in full relation-set: 28
Initial matrix: 61600 x 128939 with sparse part having weight 5037821.
Pruned matrix : 40561 x 40933 with weight 1175515.
Total sieving time: 0.35 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,105,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.37 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Total of 4 processors activated (19246.10 BogoMIPS).

4·10¹¹⁷+7 = 4(0)₁₁₆7_<118> = 3372533359686783953_<19> · C100

C100 = P46 · P54

P46 = 7571231308415109663829195119389645559083504639_<46>

P54 = 156652461213639440290493125833595279391925366872158121_<54>

Number: 40007_117
N=1186052018880990557463388064411320977047917277971455374837039249136844921468320398869036762045023319
  ( 100 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=7571231308415109663829195119389645559083504639 (pp46)
 r2=156652461213639440290493125833595279391925366872158121 (pp54)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.85 hours.
Scaled time: 1.81 units (timescale=2.142).
Factorization parameters were as follows:
n: 1186052018880990557463388064411320977047917277971455374837039249136844921468320398869036762045023319
m: 200000000000000000000000
c5: 25
c0: 14
skew: 0.89
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 420001)
Primes: RFBsize:49098, AFBsize:49126, largePrimes:2081921 encountered
Relations: rels:2247563, finalFF:299949
Max relations in full relation-set: 28
Initial matrix: 98288 x 299949 with sparse part having weight 25856697.
Pruned matrix : 64697 x 65252 with weight 4307300.
Total sieving time: 0.80 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 0.85 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Total of 4 processors activated (19246.10 BogoMIPS).

4·10¹³⁰+7 = 4(0)₁₂₉7_<131> = 11 · 1444520412397380043861_<22> · C109

C109 = P36 · P73

P36 = 408504680191109431162215803581538597_<36>

P73 = 6162353197057531640657105318413959662898339394094871838459411864184198861_<73>

Number: 40007_130
N=2517350121988647718566832619749419527856760925822505300539585253388798073057602635805421866091633938194938017
  ( 109 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=408504680191109431162215803581538597 (pp36)
 r2=6162353197057531640657105318413959662898339394094871838459411864184198861 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.80 hours.
Scaled time: 3.85 units (timescale=2.143).
Factorization parameters were as follows:
n: 2517350121988647718566832619749419527856760925822505300539585253388798073057602635805421866091633938194938017
m: 100000000000000000000000000
c5: 4
c0: 7
skew: 1.12
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 850001)
Primes: RFBsize:78498, AFBsize:78491, largePrimes:1505533 encountered
Relations: rels:1534239, finalFF:204166
Max relations in full relation-set: 28
Initial matrix: 157053 x 204166 with sparse part having weight 9603809.
Pruned matrix : 132553 x 133402 with weight 4860764.
Total sieving time: 1.72 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.80 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Total of 4 processors activated (19246.10 BogoMIPS).

4·10¹²⁷+7 = 4(0)₁₂₆7_<128> = 606497 · 2268865117_<10> · 211856473010664580779859_<24> · C90

C90 = P39 · P51

P39 = 377275926509092007527238672431385514979_<39>

P51 = 363682014571282571218438761205122109617347029045963_<51>

Mon Sep 10 22:32:35 2007  
Mon Sep 10 22:32:35 2007  
Mon Sep 10 22:32:35 2007  Msieve v. 1.25
Mon Sep 10 22:32:35 2007  random seeds: 1cdda497 27465ce9
Mon Sep 10 22:32:35 2007  factoring 137208469002073731963742143203405569527855447772540937594569482584938095837884419815979777 (90 digits)
Mon Sep 10 22:32:35 2007  commencing quadratic sieve (89-digit input)
Mon Sep 10 22:32:35 2007  using multiplier of 1
Mon Sep 10 22:32:35 2007  using 32kb Intel Core sieve core
Mon Sep 10 22:32:35 2007  sieve interval: 35 blocks of size 32768
Mon Sep 10 22:32:35 2007  processing polynomials in batches of 6
Mon Sep 10 22:32:35 2007  using a sieve bound of 1565341 (59667 primes)
Mon Sep 10 22:32:35 2007  using large prime bound of 125227280 (26 bits)
Mon Sep 10 22:32:35 2007  using double large prime bound of 376580721415840 (42-49 bits)
Mon Sep 10 22:32:35 2007  using trial factoring cutoff of 49 bits
Mon Sep 10 22:32:35 2007  polynomial 'A' values have 11 factors
Mon Sep 10 23:20:35 2007  59861 relations (16019 full + 43842 combined from 631769 partial), need 59763
Mon Sep 10 23:20:36 2007  begin with 647788 relations
Mon Sep 10 23:20:36 2007  reduce to 145237 relations in 10 passes
Mon Sep 10 23:20:36 2007  attempting to read 145237 relations
Mon Sep 10 23:20:37 2007  recovered 145237 relations
Mon Sep 10 23:20:37 2007  recovered 120863 polynomials
Mon Sep 10 23:20:37 2007  attempting to build 59861 cycles
Mon Sep 10 23:20:37 2007  found 59861 cycles in 6 passes
Mon Sep 10 23:20:38 2007  distribution of cycle lengths:
Mon Sep 10 23:20:38 2007     length 1 : 16019
Mon Sep 10 23:20:38 2007     length 2 : 11430
Mon Sep 10 23:20:38 2007     length 3 : 10659
Mon Sep 10 23:20:38 2007     length 4 : 7965
Mon Sep 10 23:20:38 2007     length 5 : 5631
Mon Sep 10 23:20:38 2007     length 6 : 3573
Mon Sep 10 23:20:38 2007     length 7 : 2094
Mon Sep 10 23:20:38 2007     length 9+: 2490
Mon Sep 10 23:20:38 2007  largest cycle: 18 relations
Mon Sep 10 23:20:38 2007  matrix is 59667 x 59861 with weight 3591214 (avg 59.99/col)
Mon Sep 10 23:20:38 2007  filtering completed in 3 passes
Mon Sep 10 23:20:38 2007  matrix is 55719 x 55783 with weight 3372987 (avg 60.47/col)
Mon Sep 10 23:20:39 2007  saving the first 48 matrix rows for later
Mon Sep 10 23:20:39 2007  matrix is 55671 x 55783 with weight 2801744 (avg 50.23/col)
Mon Sep 10 23:20:39 2007  matrix includes 64 packed rows
Mon Sep 10 23:20:39 2007  using block size 22313 for processor cache size 4096 kB
Mon Sep 10 23:20:39 2007  commencing Lanczos iteration
Mon Sep 10 23:20:58 2007  lanczos halted after 882 iterations
Mon Sep 10 23:20:58 2007  recovered 14 nontrivial dependencies
Mon Sep 10 23:20:58 2007  prp39 factor: 377275926509092007527238672431385514979
Mon Sep 10 23:20:58 2007  prp51 factor: 363682014571282571218438761205122109617347029045963
Mon Sep 10 23:20:58 2007  elapsed time 00:48:23

Sep 10, 2007 (3rd)

By suberi / GMP-ECM

2·10¹⁸⁰-3 = 1(9)₁₇₉7_<181> = 2593 · 51067720369_<11> · 2039081640448510323571_<22> · C145

C145 = P33 · C113

P33 = 112032125257256292325042410655727_<33>

C113 = [66115580929239593359723808855458909629091457719484972084609617544199525101235044807799431332453896293536909365073_<113>]

Sep 10, 2007 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

3·10¹⁶⁰+7 = 3(0)₁₅₉7_<161> = 19 · 37 · 5987 · 190783 · 2301583954628587_<16> · 30214589326193078803_<20> · C114

C114 = P39 · P76

P39 = 168821492926505124753835321037510889107_<39>

P76 = 3182333894509189879957908738033612846872644789961813377047250471481774358607_<76>

Number: 30007_160
N=537246359061660705186390632240506481498326672090893936382168433356729665263223577193112313073083261784303227993949
  ( 114 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=168821492926505124753835321037510889107 (pp39)
 r2=3182333894509189879957908738033612846872644789961813377047250471481774358607 (pp76)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 62.61 hours.
Scaled time: 42.82 units (timescale=0.684).
Factorization parameters were as follows:
name: 30007_160
n: 537246359061660705186390632240506481498326672090893936382168433356729665263223577193112313073083261784303227993949
m: 100000000000000000000000000000000
c5: 3
c0: 7
skew: 1.18
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3500001)
Primes: RFBsize:283146, AFBsize:282807, largePrimes:5650728 encountered
Relations: rels:5709851, finalFF:639843
Max relations in full relation-set: 0
Initial matrix: 566018 x 639843 with sparse part having weight 34788105.
Pruned matrix : 505676 x 508570 with weight 25305535.
Total sieving time: 53.13 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 9.00 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 62.61 hours.
 --------- CPU info (if available) ----------

4·10¹⁰²+7 = 4(0)₁₀₁7_<103> = 11² · C101

C101 = P46 · P56

P46 = 2585280752085942635036731470745668477195362783_<46>

P56 = 12786948269736886765489577885313149519498166924858577249_<56>

Number: 40007_102
N=33057851239669421487603305785123966942148760330578512396694214876033057851239669421487603305785123967
  ( 101 digits)
SNFS difficulty: 102 digits.
Divisors found:
 r1=2585280752085942635036731470745668477195362783 (pp46)
 r2=12786948269736886765489577885313149519498166924858577249 (pp56)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 0.61 hours.
Scaled time: 0.42 units (timescale=0.683).
Factorization parameters were as follows:
name: 40007_102
n: 33057851239669421487603305785123966942148760330578512396694214876033057851239669421487603305785123967
m: 200000000000000000000
c5: 25
c0: 14
skew: 0.89
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [250000, 290001)
Primes: RFBsize:37706, AFBsize:41617, largePrimes:1013476 encountered
Relations: rels:951414, finalFF:91482
Max relations in full relation-set: 0
Initial matrix: 79387 x 91482 with sparse part having weight 2362982.
Pruned matrix : 65477 x 65937 with weight 1513258.
Total sieving time: 0.53 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,102,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 0.61 hours.
 --------- CPU info (if available) ----------

4·10¹³⁶+7 = 4(0)₁₃₅7_<137> = 11 · 79 · 113 · 151 · 967 · 8035637264791904171821_<22> · 151132305869278356285433_<24> · C82

C82 = P41 · P42

P41 = 13843131922546324190310604226546490969103_<41>

P42 = 165938194222088675576956806070665609433217_<42>

Mon Sep 10 12:56:10 2007  
Mon Sep 10 12:56:10 2007  
Mon Sep 10 12:56:10 2007  Msieve v. 1.26
Mon Sep 10 12:56:10 2007  random seeds: ae13a040 ea7e6816
Mon Sep 10 12:56:10 2007  factoring 2297104313605487751994058909995621445226670899397396722147182347374454856888894351 (82 digits)
Mon Sep 10 12:56:11 2007  commencing quadratic sieve (82-digit input)
Mon Sep 10 12:56:11 2007  using multiplier of 1
Mon Sep 10 12:56:11 2007  using 64kb Pentium 2 sieve core
Mon Sep 10 12:56:11 2007  sieve interval: 6 blocks of size 65536
Mon Sep 10 12:56:11 2007  processing polynomials in batches of 17
Mon Sep 10 12:56:11 2007  using a sieve bound of 1338397 (51471 primes)
Mon Sep 10 12:56:11 2007  using large prime bound of 125809318 (26 bits)
Mon Sep 10 12:56:11 2007  using trial factoring cutoff of 27 bits
Mon Sep 10 12:56:11 2007  polynomial 'A' values have 10 factors
Mon Sep 10 14:47:10 2007  51608 relations (26063 full + 25545 combined from 276098 partial), need 51567
Mon Sep 10 14:47:12 2007  begin with 302161 relations
Mon Sep 10 14:47:12 2007  reduce to 73959 relations in 2 passes
Mon Sep 10 14:47:12 2007  attempting to read 73959 relations
Mon Sep 10 14:47:15 2007  recovered 73959 relations
Mon Sep 10 14:47:15 2007  recovered 65324 polynomials
Mon Sep 10 14:47:15 2007  attempting to build 51608 cycles
Mon Sep 10 14:47:15 2007  found 51608 cycles in 1 passes
Mon Sep 10 14:47:15 2007  distribution of cycle lengths:
Mon Sep 10 14:47:15 2007     length 1 : 26063
Mon Sep 10 14:47:15 2007     length 2 : 25545
Mon Sep 10 14:47:15 2007  largest cycle: 2 relations
Mon Sep 10 14:47:16 2007  matrix is 51471 x 51608 with weight 1602662 (avg 31.05/col)
Mon Sep 10 14:47:19 2007  filtering completed in 4 passes
Mon Sep 10 14:47:19 2007  matrix is 44265 x 44329 with weight 1349414 (avg 30.44/col)
Mon Sep 10 14:47:21 2007  saving the first 48 matrix rows for later
Mon Sep 10 14:47:21 2007  matrix is 44217 x 44329 with weight 1066574 (avg 24.06/col)
Mon Sep 10 14:47:21 2007  matrix includes 64 packed rows
Mon Sep 10 14:47:21 2007  commencing Lanczos iteration
Mon Sep 10 14:50:30 2007  lanczos halted after 700 iterations
Mon Sep 10 14:50:31 2007  recovered 5 nontrivial dependencies
Mon Sep 10 14:50:32 2007  prp41 factor: 13843131922546324190310604226546490969103
Mon Sep 10 14:50:32 2007  prp42 factor: 165938194222088675576956806070665609433217
Mon Sep 10 14:50:32 2007  elapsed time 01:54:22

4·10¹²⁰+7 = 4(0)₁₁₉7_<121> = 11 · 1250831 · 51158077863472778717_<20> · C94

C94 = P41 · P54

P41 = 16163441146585422712119803589901420539893_<41>

P54 = 351577137058775393064141868807182275859318715677825467_<54>

Number: 40007_120
N=5682696363334512849721537896612724909471809965504303562702985349408048099863665858911364855031
  ( 94 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=16163441146585422712119803589901420539893 (pp41)
 r2=351577137058775393064141868807182275859318715677825467 (pp54)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 2.14 hours.
Scaled time: 1.46 units (timescale=0.683).
Factorization parameters were as follows:
name: 40007_120
n: 5682696363334512849721537896612724909471809965504303562702985349408048099863665858911364855031
m: 1000000000000000000000000
c5: 4
c0: 7
skew: 1.12
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63998, largePrimes:2233386 encountered
Relations: rels:2497504, finalFF:145478
Max relations in full relation-set: 0
Initial matrix: 113160 x 145478 with sparse part having weight 5118153.
Pruned matrix : 93207 x 93836 with weight 3055007.
Total sieving time: 1.96 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.14 hours.
 --------- CPU info (if available) ----------

4·10¹⁰⁶+7 = 4(0)₁₀₅7_<107> = 11 · 11887 · 96607700155906921_<17> · C85

C85 = P35 · P50

P35 = 64819024777953578883539736640240237_<35>

P50 = 48851826656369687093848975611401730998510732736463_<50>

Mon Sep 10 12:52:04 2007  Msieve v. 1.26
Mon Sep 10 12:52:04 2007  random seeds: d51dc9a3 8d7922ad
Mon Sep 10 12:52:04 2007  factoring 3166527762487519882929791626294636973417702535337351459863375266451834768004729661731 (85 digits)
Mon Sep 10 12:52:05 2007  commencing quadratic sieve (85-digit input)
Mon Sep 10 12:52:06 2007  using multiplier of 1
Mon Sep 10 12:52:06 2007  using 64kb Pentium 2 sieve core
Mon Sep 10 12:52:06 2007  sieve interval: 6 blocks of size 65536
Mon Sep 10 12:52:06 2007  processing polynomials in batches of 17
Mon Sep 10 12:52:06 2007  using a sieve bound of 1426129 (54070 primes)
Mon Sep 10 12:52:06 2007  using large prime bound of 116942578 (26 bits)
Mon Sep 10 12:52:06 2007  using trial factoring cutoff of 27 bits
Mon Sep 10 12:52:06 2007  polynomial 'A' values have 11 factors
Mon Sep 10 16:46:56 2007  
Mon Sep 10 16:46:56 2007  
Mon Sep 10 16:46:56 2007  Msieve v. 1.26
Mon Sep 10 16:46:57 2007  random seeds: 2317f812 12a05399
Mon Sep 10 16:46:57 2007  factoring 3166527762487519882929791626294636973417702535337351459863375266451834768004729661731 (85 digits)
Mon Sep 10 16:46:57 2007  commencing quadratic sieve (85-digit input)
Mon Sep 10 16:46:58 2007  using multiplier of 1
Mon Sep 10 16:46:58 2007  using 64kb Pentium 2 sieve core
Mon Sep 10 16:46:58 2007  sieve interval: 6 blocks of size 65536
Mon Sep 10 16:46:58 2007  processing polynomials in batches of 17
Mon Sep 10 16:46:58 2007  using a sieve bound of 1426129 (54070 primes)
Mon Sep 10 16:46:58 2007  using large prime bound of 116942578 (26 bits)
Mon Sep 10 16:46:58 2007  using trial factoring cutoff of 27 bits
Mon Sep 10 16:46:58 2007  polynomial 'A' values have 11 factors
Mon Sep 10 16:47:01 2007  restarting with 21856 full and 243609 partial relations
Mon Sep 10 17:26:58 2007  54200 relations (26099 full + 28101 combined from 290676 partial), need 54166
Mon Sep 10 17:27:01 2007  begin with 316775 relations
Mon Sep 10 17:27:01 2007  reduce to 78679 relations in 2 passes
Mon Sep 10 17:27:01 2007  attempting to read 78679 relations
Mon Sep 10 17:27:05 2007  recovered 78679 relations
Mon Sep 10 17:27:05 2007  recovered 75104 polynomials
Mon Sep 10 17:27:06 2007  attempting to build 54200 cycles
Mon Sep 10 17:27:06 2007  found 54200 cycles in 1 passes
Mon Sep 10 17:27:06 2007  distribution of cycle lengths:
Mon Sep 10 17:27:06 2007     length 1 : 26099
Mon Sep 10 17:27:06 2007     length 2 : 28101
Mon Sep 10 17:27:06 2007  largest cycle: 2 relations
Mon Sep 10 17:27:06 2007  matrix is 54070 x 54200 with weight 1761587 (avg 32.50/col)
Mon Sep 10 17:27:08 2007  filtering completed in 3 passes
Mon Sep 10 17:27:08 2007  matrix is 42387 x 42451 with weight 1482165 (avg 34.91/col)
Mon Sep 10 17:27:10 2007  saving the first 48 matrix rows for later
Mon Sep 10 17:27:10 2007  matrix is 42339 x 42451 with weight 1055687 (avg 24.87/col)
Mon Sep 10 17:27:10 2007  matrix includes 64 packed rows
Mon Sep 10 17:27:10 2007  commencing Lanczos iteration
Mon Sep 10 17:29:38 2007  lanczos halted after 670 iterations
Mon Sep 10 17:29:39 2007  recovered 17 nontrivial dependencies
Mon Sep 10 17:29:40 2007  prp35 factor: 64819024777953578883539736640240237
Mon Sep 10 17:29:40 2007  prp50 factor: 48851826656369687093848975611401730998510732736463
Mon Sep 10 17:29:40 2007  elapsed time 00:42:43

4·10¹²³+7 = 4(0)₁₂₂7_<124> = 67 · 79 · 1459 · 2333 · 19949 · 33829 · 46451 · C100

C100 = P45 · P55

P45 = 893003465557677469001745507020861686789619767_<45>

P55 = 7931029477391238937468273562091619341494204808802031281_<55>

Number: 40007_123
N=7082436808750471977331869139572712189502812999808595720773130522724928764839469912722939255229931527
  ( 100 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=893003465557677469001745507020861686789619767 (pp45)
 r2=7931029477391238937468273562091619341494204808802031281 (pp55)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 2.59 hours.
Scaled time: 1.77 units (timescale=0.683).
Factorization parameters were as follows:
name: 40007_123
n: 7082436808750471977331869139572712189502812999808595720773130522724928764839469912722939255229931527
m: 2000000000000000000000000
c5: 125
c0: 7
skew: 0.56
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:63758, largePrimes:2177651 encountered
Relations: rels:2321280, finalFF:137515
Max relations in full relation-set: 0
Initial matrix: 112921 x 137515 with sparse part having weight 6377289.
Pruned matrix : 100907 x 101535 with weight 4197773.
Total sieving time: 2.36 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.59 hours.
 --------- CPU info (if available) ----------

4·10¹²⁴+7 = 4(0)₁₂₃7_<125> = 11³ · 29 · 709 · 1801 · 2531 · 260722306516963_<15> · C97

C97 = P47 · P50

P47 = 67816150798627989304720548529530399180885482189_<47>

P50 = 18135123580998002481347196781299085919725495181681_<50>

Number: 40007_124
N=1229854275520714967260471838947950713893193162791736456300050444358471249630604163174163844579709
  ( 97 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=67816150798627989304720548529530399180885482189 (pp47)
 r2=18135123580998002481347196781299085919725495181681 (pp50)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 2.58 hours.
Scaled time: 1.76 units (timescale=0.683).
Factorization parameters were as follows:
name: 40007_124
n: 1229854275520714967260471838947950713893193162791736456300050444358471249630604163174163844579709
m: 10000000000000000000000000
c5: 2
c0: 35
skew: 1.77
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:63938, largePrimes:2187471 encountered
Relations: rels:2353021, finalFF:136777
Max relations in full relation-set: 0
Initial matrix: 113101 x 136777 with sparse part having weight 5875625.
Pruned matrix : 100625 x 101254 with weight 3925534.
Total sieving time: 2.35 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.58 hours.
 --------- CPU info (if available) ----------

Sep 10, 2007

The factor table of 400...007 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Sep 9, 2007 (3rd)

By Robert Backstrom / GGNFS

3·10¹⁴⁴+7 = 3(0)₁₄₃7_<145> = 23 · 459383 · 128248879471_<12> · 1352119565902402853_<19> · C109

C109 = P42 · P67

P42 = 412360496428279684134266762455314955302583_<42>

P67 = 3970752049300281989132003305040428926587105565745390502436467127587_<67>

Number: n
N=1637381286243073167428156705928812402202347963241767077546317363263128053960163775922772278248987696451657221
  ( 109 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=412360496428279684134266762455314955302583 (pp42)
 r2=3970752049300281989132003305040428926587105565745390502436467127587 (pp67)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 13.30 hours.
Scaled time: 15.91 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_3_0_143_7
n: 1637381286243073167428156705928812402202347963241767077546317363263128053960163775922772278248987696451657221
type: snfs
skew: 1.00
deg: 5
c5: 3
c0: 70
m: 100000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1600001)
Primes: RFBsize:148933, AFBsize:148155, largePrimes:6391676 encountered
Relations: rels:5742559, finalFF:361324
Max relations in full relation-set: 28
Initial matrix: 297153 x 361324 with sparse part having weight 25349389.
Pruned matrix : 259545 x 261094 with weight 15462821.
Total sieving time: 11.30 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 1.71 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 13.30 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Sep 9, 2007 (2nd)

By Yousuke Koide

10⁹¹¹+1 is divisible by 12555609937128249776670687863910703_<35>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 9, 2007

By Robert Backstrom / GGNFS

(16·10¹⁸¹-61)/9 = 1(7)₁₈₀1_<182> = 11 · C181

C181 = P84 · P97

P84 = 875423954337579283724570530051042761164622675183831303860786988601476587061520145977_<84>

P97 = 1846147353123941432037361969644146179225690892776532016346590270070332318078159872250761970493993_<97>

Number: n
N=1616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161
  ( 181 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=875423954337579283724570530051042761164622675183831303860786988601476587061520145977 (pp84)
 r2=1846147353123941432037361969644146179225690892776532016346590270070332318078159872250761970493993 (pp97)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 455.66 hours.
Scaled time: 540.87 units (timescale=1.187).
Factorization parameters were as follows:
name: KA_1_7_180_1
n: 1616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161
type: snfs
skew: 1.65
deg: 5
c5: 5
c0: -61
m: 2000000000000000000000000000000000000
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 5400001)
Primes: RFBsize:283146, AFBsize:283778, largePrimes:8451586 encountered
Relations: rels:8040019, finalFF:636287
Max relations in full relation-set: 28
Initial matrix: 566989 x 636287 with sparse part having weight 69987297.
Pruned matrix : 537909 x 540807 with weight 56556721.
Total sieving time: 440.13 hours.
Total relation processing time: 0.50 hours.
Matrix solve time: 14.43 hours.
Total square root time: 0.60 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.6,2.6,100000
total time: 455.66 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Sep 7, 2007 (5th)

GMP-ECM 6.1.3 has been released.

Sep 7, 2007 (4th)

By Sinkiti Sibata / GGNFS

3·10¹⁴⁰+7 = 3(0)₁₃₉7_<141> = 886591 · 21345509 · C128

C128 = P57 · P71

P57 = 870020740547606992047908247418054629224598409723907992361_<57>

P71 = 18220563960260903608607526139448840316782587407515464316476336274810173_<71>

Number: 30007_140
N=15852268549901230174324386508028804607528286278559127718419294725472196231167351989448701028316117068813288359277306912809088453
  ( 128 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=870020740547606992047908247418054629224598409723907992361 (pp57)
 r2=18220563960260903608607526139448840316782587407515464316476336274810173 (pp71)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 12.05 hours.
Scaled time: 8.18 units (timescale=0.679).
Factorization parameters were as follows:
name: 30007_140
n: 15852268549901230174324386508028804607528286278559127718419294725472196231167351989448701028316117068813288359277306912809088453
m: 10000000000000000000000000000
c5: 3
c0: 7
skew: 1.18
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1675001)
Primes: RFBsize:78498, AFBsize:63643, largePrimes:1566102 encountered
Relations: rels:1559976, finalFF:160050
Max relations in full relation-set: 0
Initial matrix: 142206 x 160050 with sparse part having weight 15608362.
Pruned matrix : 137606 x 138381 with weight 12130130.
Total sieving time: 11.40 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.49 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 12.05 hours.
 --------- CPU info (if available) ----------

Sep 7, 2007 (3rd)

By Shaopu Lin

10⁶¹⁰+1 is divisible by 27186363592392725942593454290345801336551729326489701011779461_<62>, cofactor is prime.

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 7, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM

3·10¹⁷¹+7 = 3(0)₁₇₀7_<172> = C172

C172 = P44 · C128

P44 = 31620332097111024989233352721851562907652707_<44>

C128 = [94875663885708949340722098875716958576811202800602452263648706419261724778781975587671373398601569684090092604704674588003973901_<128>]

Sep 7, 2007

By Sinkiti Sibata / GGNFS

3·10¹³⁸+7 = 3(0)₁₃₇7_<139> = 31 · 30347 · C133

C133 = P35 · P40 · P59

P35 = 27582727203473715137972750799973321_<35>

P40 = 9338357328303256578758498008894337760073_<40>

P59 = 12380440690635148293553334360514326357608119969517531812347_<59>

Number: 30007_138
N=3188921262345111436853512649919160845999551425075763454324549272553911371374329396432872675940758346735660749800426677664901775910251
  ( 133 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=27582727203473715137972750799973321 (pp35)
 r2=9338357328303256578758498008894337760073 (pp40)
 r3=12380440690635148293553334360514326357608119969517531812347 (pp59)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 11.09 hours.
Scaled time: 7.53 units (timescale=0.679).
Factorization parameters were as follows:
name: 30007_138
n: 3188921262345111436853512649919160845999551425075763454324549272553911371374329396432872675940758346735660749800426677664901775910251
m: 1000000000000000000000000000
c5: 3000
c0: 7
skew: 0.3
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1525001)
Primes: RFBsize:78498, AFBsize:63898, largePrimes:1530665 encountered
Relations: rels:1508359, finalFF:159826
Max relations in full relation-set: 0
Initial matrix: 142463 x 159826 with sparse part having weight 16585980.
Pruned matrix : 138060 x 138836 with weight 12364485.
Total sieving time: 10.41 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.52 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 11.09 hours.
 --------- CPU info (if available) ----------

Sep 6, 2007

By JMB / GGNFS

3·10¹⁷⁴+7 = 3(0)₁₇₃7_<175> = 2131 · 2539 · 388785044783_<12> · 372247744413533552867_<21> · 3918018457203894704610101_<25> · C111

C111 = P41 · P71

P41 = 83101205384307732797112639371594904845329_<41>

P71 = 11766835380003014836384610732539311187782328395943642994305646727529367_<71>

Number: N
N=977838203636969263622248987068537357449295333609103753437784788553386921946103919242214810477100330081440276743
  ( 111 digits)
Divisors found:
 r1=83101205384307732797112639371594904845329 (pp41)
 r2=11766835380003014836384610732539311187782328395943642994305646727529367 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 48.39 hours.
Scaled time: 43.21 units (timescale=0.893).
Factorization parameters were as follows:
name: N
n: 977838203636969263622248987068537357449295333609103753437784788553386921946103919242214810477100330081440276743
skew: 37355.45
# norm 3.46e+15
c5: 34020
c4: -62247927
c3: 40964358765630
c2: -919130756124140464
c1: -117696980178055287871024
c0: -943686829374413022658503360
# alpha -6.74
Y1: 512727852197
Y0: -1957521676766462803349
# Murphy_E 8.69e-10
# M 429058690311523254003492787243369289356028090221678835208754814859752251708490910300982484190538642312749052680
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 10000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1600000, 1900001)
Relations: rels:7170449, finalFF:547721
Initial matrix: 460925 x 547721 with sparse part having weight 44666784.
Pruned matrix : 422725 x 425093 with weight 25906024.
Total sieving time: 40.38 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 7.33 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,10000
total time: 48.39 hours.
 --------- CPU info (if available) ----------

Sep 5, 2007 (3rd)

By Sinkiti Sibata / GGNFS

3·10¹⁵²+7 = 3(0)₁₅₁7_<153> = 8347351 · 7811046197_<10> · 858719673857_<12> · 250559653015574120385408539_<27> · C98

C98 = P39 · P59

P39 = 577938539278524803843369748270872920429_<39>

P59 = 37001485905141343750684997572615954124281964070904019247443_<59>

Number: 30007_152
N=21384584715152312399410371055118338529381577034286595544703207108885189504169973874072912200713047
  ( 98 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=577938539278524803843369748270872920429 (pp39)
 r2=37001485905141343750684997572615954124281964070904019247443 (pp59)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 36.57 hours.
Scaled time: 24.97 units (timescale=0.683).
Factorization parameters were as follows:
name: 30007_152
n: 21384584715152312399410371055118338529381577034286595544703207108885189504169973874072912200713047
m: 1000000000000000000000000000000
c5: 300
c0: 7
skew: 0.47
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 4000000
)
Primes: RFBsize:176302, AFBsize:176433, largePrimes:5580476 encountered
Relations: rels:5520272, finalFF:399263
Max relations in full relation-set: 0
Initial matrix: 352801 x 399263 with sparse part having weight 25768097.
Pruned matrix : 328424 x 330252 with weight 19913239.
Total sieving time: 33.78 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 2.40 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 36.57 hours.
 --------- CPU info (if available) ----------

Sep 5, 2007 (2nd)

By Jo Yeong Uk / GGNFS

3·10¹³³+7 = 3(0)₁₃₂7_<134> = 37 · 29581 · C128

C128 = P38 · P90

P38 = 71206879090633339569010774993897538969_<38>

P90 = 384932630573456592303493441248187029453637827755687637553671267379325800269120529793395199_<90>

Number: 30007_133
N=27409851283283553997863858923322768358433143261242378919266110368507177269558527798614340651459072066894655718562956316920009831
  ( 128 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=71206879090633339569010774993897538969 (pp38)
 r2=384932630573456592303493441248187029453637827755687637553671267379325800269120529793395199 (pp90)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.83 hours.
Scaled time: 6.02 units (timescale=2.128).
Factorization parameters were as follows:
n: 27409851283283553997863858923322768358433143261242378919266110368507177269558527798614340651459072066894655718562956316920009831
m: 200000000000000000000000000
c5: 375
c0: 28
skew: 0.6
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [700000, 1200001)
Primes: RFBsize:107126, AFBsize:107333, largePrimes:1824277 encountered
Relations: rels:1912873, finalFF:260803
Max relations in full relation-set: 28
Initial matrix: 214526 x 260803 with sparse part having weight 13896029.
Pruned matrix : 187120 x 188256 with weight 7957202.
Total sieving time: 2.68 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,45,45,2.3,2.3,50000
total time: 2.83 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407685)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405130)
Total of 4 processors activated (19246.11 BogoMIPS).

3·10¹³⁶+7 = 3(0)₁₃₅7_<137> = 37 · C135

C135 = P46 · P90

P46 = 6556535936327394866605979149660371778651962509_<46>

P90 = 123664511059628497811157288760274150729201758246527989892496823924203364385516946923141479_<90>

Number: 30007_136
N=810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810811
  ( 135 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=6556535936327394866605979149660371778651962509 (pp46)
 r2=123664511059628497811157288760274150729201758246527989892496823924203364385516946923141479 (pp90)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.25 hours.
Scaled time: 9.13 units (timescale=2.146).
Factorization parameters were as follows:
n: 810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810811
m: 1000000000000000000000000000
c5: 30
c0: 7
skew: 0.75
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [700000, 1500001)
Primes: RFBsize:107126, AFBsize:106593, largePrimes:1867694 encountered
Relations: rels:1959724, finalFF:256837
Max relations in full relation-set: 28
Initial matrix: 213786 x 256837 with sparse part having weight 17263562.
Pruned matrix : 196794 x 197926 with weight 10886320.
Total sieving time: 4.07 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,45,45,2.3,2.3,50000
total time: 4.25 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407685)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405130)
Total of 4 processors activated (19246.11 BogoMIPS).

Sep 5, 2007

By JMB

3·10¹⁶⁴+7 = 3(0)₁₆₃7_<165> = 93463 · 102367 · 5561993 · 2697746404826036755483_<22> · 4075016412566873951820653_<25> · C102

C102 = P38 · P64

P38 = 85121969595848139659769186241637634013_<38>

P64 = 6024471790877011640388025283913980838326383051453673075231227837_<64>

Sep 4, 2007 (4th)

By Yousuke Koide

(10¹²⁰⁵-1)/9 is divisible by 1231304918915627269216328559032281_<34>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 4, 2007 (3rd)

By Jo Yeong Uk / GGNFS

3·10¹³²+7 = 3(0)₁₃₁7_<133> = C133

C133 = P44 · P90

P44 = 20590611374091488546520676374415000816224551_<44>

P90 = 145697470827641601340741249542086188044830839410971692164392935223681417160709307626970657_<90>

Number: 30007_132
N=3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
  ( 133 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=20590611374091488546520676374415000816224551 (pp44)
 r2=145697470827641601340741249542086188044830839410971692164392935223681417160709307626970657 (pp90)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.88 hours.
Scaled time: 6.17 units (timescale=2.143).
Factorization parameters were as follows:
n: 3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
m: 100000000000000000000000000
c5: 300
c0: 7
skew: 0.47
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 1100001)
Primes: RFBsize:78498, AFBsize:78821, largePrimes:1567294 encountered
Relations: rels:1589863, finalFF:196603
Max relations in full relation-set: 28
Initial matrix: 157385 x 196603 with sparse part having weight 11951565.
Pruned matrix : 143201 x 144051 with weight 6940341.
Total sieving time: 2.78 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 2.88 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167564k/8912896k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.37 BogoMIPS (lpj=2407685)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405130)
Total of 4 processors activated (19246.11 BogoMIPS).

Sep 4, 2007 (2nd)

By JMB

3·10¹⁹⁴+7 = 3(0)₁₉₃7_<195> = 1734986326637479007_<19> · 431168604266382453431_<21> · 248787236500857218390561_<24> · 439982137238951968875436976379228563_<36> · C97

C97 = P40 · P58

P40 = 2181760916727482904956744337987008327579_<40>

P58 = 1679220662527382761557265816940310453170712534544646764943_<58>

Sep 4, 2007

By Sinkiti Sibata / Msieve, GGNFS

3·10¹²⁸+7 = 3(0)₁₂₇7_<129> = 2685101 · 33851255863_<11> · 12978558218195034379386149_<26> · C87

C87 = P36 · P51

P36 = 275313088291577407642928246977003907_<36>

P51 = 923703385381580265251720036954725538332661715176123_<51>

Mon Sep 03 18:48:38 2007  
Mon Sep 03 18:48:38 2007  Msieve v. 1.26
Mon Sep 03 18:48:38 2007  random seeds: 07d98b2f 62ae921d
Mon Sep 03 18:48:38 2007  factoring 254307631694787959686868018280051591889464233755615179663625686766286102906651364112561 (87 digits)
Mon Sep 03 18:48:39 2007  commencing quadratic sieve (87-digit input)
Mon Sep 03 18:48:39 2007  using multiplier of 1
Mon Sep 03 18:48:39 2007  using 64kb Pentium 2 sieve core
Mon Sep 03 18:48:39 2007  sieve interval: 10 blocks of size 65536
Mon Sep 03 18:48:39 2007  processing polynomials in batches of 11
Mon Sep 03 18:48:39 2007  using a sieve bound of 1489667 (56613 primes)
Mon Sep 03 18:48:39 2007  using large prime bound of 119173360 (26 bits)
Mon Sep 03 18:48:40 2007  using double large prime bound of 344447000754720 (42-49 bits)
Mon Sep 03 18:48:40 2007  using trial factoring cutoff of 49 bits
Mon Sep 03 18:48:40 2007  polynomial 'A' values have 11 factors
Tue Sep 04 00:36:23 2007  56728 relations (16053 full + 40675 combined from 592602 partial), need 56709
Tue Sep 04 00:36:31 2007  begin with 608655 relations
Tue Sep 04 00:36:33 2007  reduce to 134614 relations in 8 passes
Tue Sep 04 00:36:33 2007  attempting to read 134614 relations
Tue Sep 04 00:36:45 2007  recovered 134614 relations
Tue Sep 04 00:36:45 2007  recovered 109845 polynomials
Tue Sep 04 00:36:57 2007  attempting to build 56728 cycles
Tue Sep 04 00:36:57 2007  found 56728 cycles in 5 passes
Tue Sep 04 00:37:01 2007  distribution of cycle lengths:
Tue Sep 04 00:37:01 2007     length 1 : 16053
Tue Sep 04 00:37:01 2007     length 2 : 11398
Tue Sep 04 00:37:01 2007     length 3 : 9968
Tue Sep 04 00:37:01 2007     length 4 : 7465
Tue Sep 04 00:37:01 2007     length 5 : 4987
Tue Sep 04 00:37:01 2007     length 6 : 3064
Tue Sep 04 00:37:01 2007     length 7 : 1814
Tue Sep 04 00:37:01 2007     length 9+: 1979
Tue Sep 04 00:37:01 2007  largest cycle: 20 relations
Tue Sep 04 00:37:03 2007  matrix is 56613 x 56728 with weight 3003083 (avg 52.94/col)
Tue Sep 04 00:37:07 2007  filtering completed in 3 passes
Tue Sep 04 00:37:07 2007  matrix is 52023 x 52087 with weight 2793711 (avg 53.64/col)
Tue Sep 04 00:37:10 2007  saving the first 48 matrix rows for later
Tue Sep 04 00:37:10 2007  matrix is 51975 x 52087 with weight 2063890 (avg 39.62/col)
Tue Sep 04 00:37:10 2007  matrix includes 64 packed rows
Tue Sep 04 00:37:10 2007  using block size 10922 for processor cache size 256 kB
Tue Sep 04 00:37:11 2007  commencing Lanczos iteration
Tue Sep 04 00:40:42 2007  lanczos halted after 824 iterations
Tue Sep 04 00:40:43 2007  recovered 15 nontrivial dependencies
Tue Sep 04 00:40:47 2007  prp36 factor: 275313088291577407642928246977003907
Tue Sep 04 00:40:47 2007  prp51 factor: 923703385381580265251720036954725538332661715176123
Tue Sep 04 00:40:47 2007  elapsed time 05:52:09

3·10¹³¹+7 = 3(0)₁₃₀7_<132> = 61 · 3889 · 16673127629_<11> · 654750113451724387_<18> · C99

C99 = P45 · P54

P45 = 367843730195277468720927798645873350770134361_<45>

P54 = 314917983297778113935616240983926140815612293301748461_<54>

Number: 30007_131
N=115840605681828788775531586500134003303645081903753785388762305681265629442829309689100981194968421
  ( 99 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=367843730195277468720927798645873350770134361 (pp45)
 r2=314917983297778113935616240983926140815612293301748461 (pp54)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 6.51 hours.
Scaled time: 4.44 units (timescale=0.682).
Factorization parameters were as follows:
name: 30007_131
n: 115840605681828788775531586500134003303645081903753785388762305681265629442829309689100981194968421
m: 100000000000000000000000000
c5: 30
c0: 7
skew: 0.75
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1100001)
Primes: RFBsize:63951, AFBsize:63528, largePrimes:1493297 encountered
Relations: rels:1473265, finalFF:143512
Max relations in full relation-set: 0
Initial matrix: 127546 x 143512 with sparse part having weight 10871550.
Pruned matrix : 123368 x 124069 with weight 8318483.
Total sieving time: 6.09 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 6.51 hours.
 --------- CPU info (if available) ----------

Sep 3, 2007 (4th)

By Sinkiti Sibata / GGNFS

3·10¹¹⁶+7 = 3(0)₁₁₅7_<117> = 941 · 7229 · 1005413 · 1768241 · C98

C98 = P45 · P53

P45 = 793456171721645674090119834605962552118405123_<45>

P53 = 31263997790510739426533319802087948467956549868101057_<53>

Number: 30007_116
N=24806611999572640200041003401784198951563928958349169644810919349055407530420374739405603430515011
  ( 98 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=793456171721645674090119834605962552118405123 (pp45)
 r2=31263997790510739426533319802087948467956549868101057 (pp53)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 2.15 hours.
Scaled time: 1.47 units (timescale=0.683).
Factorization parameters were as follows:
name: 30007_116
n: 24806611999572640200041003401784198951563928958349169644810919349055407530420374739405603430515011
m: 100000000000000000000000
c5: 30
c0: 7
skew: 0.75
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63528, largePrimes:2164983 encountered
Relations: rels:2305072, finalFF:137525
Max relations in full relation-set: 0
Initial matrix: 112693 x 137525 with sparse part having weight 6350152.
Pruned matrix : 99939 x 100566 with weight 4135837.
Total sieving time: 1.92 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.15 hours.
 --------- CPU info (if available) ----------

Sep 3, 2007 (3rd)

By Yousuke Koide

(10¹¹⁶⁵-1)/9 is divisible by 8789828644372924439634809703641_<31>

(10¹⁵⁰³-1)/9 is divisible by 3641337799926827172864056731857529_<34>

10⁶³⁶+1 is divisible by 706882718657645277228087439919935993_<36>, cofactor is prime.

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 3, 2007 (2nd)

By Kurt Beschorner

10⁶³⁵+1 is divisible by 202367638102311029520083171135894724910091_<42>, cofactor is prime.

Reference: Factorizations of numbers of the form 10^n+1 (Alfred Reich)

Sep 3, 2007

The factor table of 300...007 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Sep 2, 2007 (3rd)

By R.D. Silverman

(10³⁴⁵-1)/9 is divisible by 35645906496364306434849378023333297827811383782580351_<53>, cofactor is prime.

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 2, 2007 (2nd)

By Yousuke Koide

(10¹⁴⁰¹-1)/9 is divisible by 619629939179595688144939635183289_<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 2, 2007

By Sinkiti Sibata / GGNFS

3·10¹⁵¹-7 = 2(9)₁₅₀3_<152> = 19 · 156901 · C146

C146 = P64 · P82

P64 = 2776542823659779412773229802771285257042021400690501832194379669_<64>

P82 = 3624412053738393293775064001860434687254067055643958807515278373333482272091019563_<82>

Number: 29993_151
N=10063335277793338675846217477396910354803011889159741694310089600582868379289790176105012916290829047750190448620132238934440389665759736528464647
  ( 146 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=2776542823659779412773229802771285257042021400690501832194379669 (pp64)
 r2=3624412053738393293775064001860434687254067055643958807515278373333482272091019563 (pp82)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 37.52 hours.
Scaled time: 25.63 units (timescale=0.683).
Factorization parameters were as follows:
name: 29993_151
n: 10063335277793338675846217477396910354803011889159741694310089600582868379289790176105012916290829047750190448620132238934440389665759736528464647
m: 1000000000000000000000000000000
c5: 30
c0: -7
skew: 0.75
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2200001)
Primes: RFBsize:176302, AFBsize:175908, largePrimes:5608103 encountered
Relations: rels:5543957, finalFF:398769
Max relations in full relation-set: 0
Initial matrix: 352277 x 398769 with sparse part having weight 27944746.
Pruned matrix : 328978 x 330803 with weight 21639137.
Total sieving time: 33.50 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 3.62 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 37.52 hours.
 --------- CPU info (if available) ----------

August 2007

Aug 31, 2007

By Sinkiti Sibata / GGNFS

3·10¹⁴⁸-7 = 2(9)₁₄₇3_<149> = 41 · 293 · 23176583 · C138

C138 = P45 · P93

P45 = 420246714641792212696158791990420325985853003_<45>

P93 = 256398832799819491996337343700283603386076585422635350041027234530711778924253071751054434289_<93>

Number: 29993_148
N=107750767122114335539918675404254523033081059324968763324951362955270960653144758698026016767014068999370645903693836817954006385276819867
  ( 138 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=420246714641792212696158791990420325985853003 (pp45)
 r2=256398832799819491996337343700283603386076585422635350041027234530711778924253071751054434289 (pp93)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 25.94 hours.
Scaled time: 17.71 units (timescale=0.683).
Factorization parameters were as follows:
name: 29993_148
n: 107750767122114335539918675404254523033081059324968763324951362955270960653144758698026016767014068999370645903693836817954006385276819867
m: 100000000000000000000000000000
c5: 3000
c0: -7
skew: 0.3
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 3150001)
Primes: RFBsize:114155, AFBsize:114337, largePrimes:2805135 encountered
Relations: rels:2752699, finalFF:257378
Max relations in full relation-set: 0
Initial matrix: 228559 x 257378 with sparse part having weight 32600512.
Pruned matrix : 220942 x 222148 with weight 25462064.
Total sieving time: 23.64 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.99 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 25.94 hours.
 --------- CPU info (if available) ----------

Aug 30, 2007

By Sinkiti Sibata / GGNFS

3·10¹⁵⁰-7 = 2(9)₁₄₉3_<151> = 83 · 189651047 · C141

C141 = P53 · P89

P53 = 16655019752526043619345197086882937152885261185068417_<53>

P89 = 11443075559040216743203773330203910152796400883206795006697965100458043235549364132362629_<89>

Number: 29993_150
N=190584649465462808903938036705578268690445781961768618815589675746482134493536309892422886710060193892941055624300006842351026644099218988293
  ( 141 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=16655019752526043619345197086882937152885261185068417 (pp53)
 r2=11443075559040216743203773330203910152796400883206795006697965100458043235549364132362629 (pp89)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 32.25 hours.
Scaled time: 22.03 units (timescale=0.683).
Factorization parameters were as follows:
name: 29993_150
n: 190584649465462808903938036705578268690445781961768618815589675746482134493536309892422886710060193892941055624300006842351026644099218988293
m: 1000000000000000000000000000000
c5: 3
c0: -7
skew: 1.18
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 1750001)
Primes: RFBsize:114155, AFBsize:113722, largePrimes:2720694 encountered
Relations: rels:2701121, finalFF:257590
Max relations in full relation-set: 0
Initial matrix: 227942 x 257590 with sparse part having weight 18606649.
Pruned matrix : 217974 x 219177 with weight 14397030.
Total sieving time: 30.84 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 1.19 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 32.25 hours.
 --------- CPU info (if available) ----------

Aug 28, 2007 (2nd)

By Jo Yeong Uk / GGNFS snfs, GMP-ECM

2·10¹⁷⁰-7 = 1(9)₁₆₉3_<171> = C171

C171 = P50 · P56 · P66

P50 = 12830114637211177323355529618441346334457779697621_<50>

P56 = 21211698624128416961087313467823336589027450130654173021_<56>

P66 = 734892831044394689750114258247584690226884187718469681813063218073_<66>

Number: 19993_170
N=199999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 171 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=12830114637211177323355529618441346334457779697621 (pp50)
 r2=21211698624128416961087313467823336589027450130654173021 (pp56)
 r3=734892831044394689750114258247584690226884187718469681813063218073 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 75.19 hours.
Scaled time: 161.22 units (timescale=2.144).
Factorization parameters were as follows:
n: 199999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
m: 10000000000000000000000000000000000
c5: 2
c0: -7
skew: 1.28
type: snfs
Factor base limits: 7200000/7200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [3600000, 7100001)
Primes: RFBsize:489319, AFBsize:488568, largePrimes:6562233 encountered
Relations: rels:7021806, finalFF:1101502
Max relations in full relation-set: 28
Initial matrix: 977952 x 1101502 with sparse part having weight 56019192.
Pruned matrix : 870570 x 875523 with weight 39881257.
Total sieving time: 70.10 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 4.88 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,7200000,7200000,27,27,49,49,2.6,2.6,100000
total time: 75.19 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.10 BogoMIPS).

3·10¹³⁷-7 = 2(9)₁₃₆3_<138> = 233 · 701 · 5477 · 21661 · 488603 · C119

C119 = P52 · P67

P52 = 6476427849686591970532300943502577690100886356016287_<52>

P67 = 4892540299472487410211328047955667103685004673915706548024083374513_<67>

Number: 29993_137
N=31686184251217596357918040854365672841886369996089982649246803699536335662325290122709751508408702299412468090548693231
  ( 119 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=6476427849686591970532300943502577690100886356016287 (pp52)
 r2=4892540299472487410211328047955667103685004673915706548024083374513 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.06 hours.
Scaled time: 8.71 units (timescale=2.144).
Factorization parameters were as follows:
n: 31686184251217596357918040854365672841886369996089982649246803699536335662325290122709751508408702299412468090548693231
m: 1000000000000000000000000000
c5: 300
c0: -7
skew: 0.47
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [700000, 1450001)
Primes: RFBsize:107126, AFBsize:107463, largePrimes:1828766 encountered
Relations: rels:1902577, finalFF:244082
Max relations in full relation-set: 28
Initial matrix: 214655 x 244082 with sparse part having weight 14922660.
Pruned matrix : 203114 x 204251 with weight 10251762.
Total sieving time: 3.87 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,45,45,2.3,2.3,50000
total time: 4.06 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.10 BogoMIPS).

3·10¹⁶⁰-7 = 2(9)₁₅₉3_<161> = 127 · 40829 · 1767818010311_<13> · 16453710424472833724720213_<26> · C117

C117 = P42 · P76

P42 = 156576499347676290337540161614647420749481_<42>

P76 = 1270342440851204099715174694929205958381506676212657967303937958146615630937_<76>

3·10¹⁴⁶-7 = 2(9)₁₄₅3_<147> = C147

C147 = P46 · P102

P46 = 1854775915575395694657042218355139211068315081_<46>

P102 = 161744606170893075229127752358828695970725053902533763048339214947771986894331414501673269180172824753_<102>

Number: 29993_146
N=299999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 147 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=1854775915575395694657042218355139211068315081 (pp46)
 r2=161744606170893075229127752358828695970725053902533763048339214947771986894331414501673269180172824753 (pp102)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.47 hours.
Scaled time: 24.54 units (timescale=2.139).
Factorization parameters were as follows:
n: 299999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
m: 100000000000000000000000000000
c5: 30
c0: -7
skew: 0.75
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1650001)
Primes: RFBsize:135072, AFBsize:134628, largePrimes:3935573 encountered
Relations: rels:4115354, finalFF:442086
Max relations in full relation-set: 28
Initial matrix: 269767 x 442086 with sparse part having weight 44669293.
Pruned matrix : 216898 x 218310 with weight 21091258.
Total sieving time: 11.13 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 11.47 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.10 BogoMIPS).

Aug 28, 2007

By Sinkiti Sibata / GGNFS snfs

3·10¹³³-7 = 2(9)₁₃₂3_<134> = 19 · 23 · 29 · 41 · 4133 · 845895553 · 15285736889_<11> · C106

C106 = P50 · P56

P50 = 63642234051349873089290850183434749198604956677859_<50>

P56 = 16976338245683764819391125937000990768709124738416339799_<56>

Number: 29993_133
N=1080412091966688465073393571002351107257249643609478820582139591078383292048067595486362712519605523810341
  ( 106 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=63642234051349873089290850183434749198604956677859 (pp50)
 r2=16976338245683764819391125937000990768709124738416339799 (pp56)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 6.23 hours.
Scaled time: 4.26 units (timescale=0.683).
Factorization parameters were as follows:
name: 29993_133
n: 1080412091966688465073393571002351107257249643609478820582139591078383292048067595486362712519605523810341
m: 100000000000000000000000000
c5: 3000
c0: -7
skew: 0.3
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1050001)
Primes: RFBsize:63951, AFBsize:63898, largePrimes:1485231 encountered
Relations: rels:1478487, finalFF:143556
Max relations in full relation-set: 0
Initial matrix: 127916 x 143556 with sparse part having weight 8668341.
Pruned matrix : 123225 x 123928 with weight 6769206.
Total sieving time: 5.87 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 6.23 hours.
 --------- CPU info (if available) ----------

3·10¹⁴⁰-7 = 2(9)₁₃₉3_<141> = 163 · 257 · 22303 · 277717378709055933498757_<24> · C109

C109 = P38 · P71

P38 = 37093886403445655363232597242736014387_<38>

P71 = 31169644391610806846824618395203670558943768245441618617177544108945299_<71>

Number: 29993_140
N=1156203248298208234556461217638104374790212162863416385692985595553452438217200154827872278873776193460016713
  ( 109 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=37093886403445655363232597242736014387 (pp38)
 r2=31169644391610806846824618395203670558943768245441618617177544108945299 (pp71)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 11.33 hours.
Scaled time: 7.74 units (timescale=0.683).
Factorization parameters were as follows:
name: 29993_140
n: 1156203248298208234556461217638104374790212162863416385692985595553452438217200154827872278873776193460016713
m: 10000000000000000000000000000
c5: 3
c0: -7
skew: 1.18
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1600001)
Primes: RFBsize:78498, AFBsize:63643, largePrimes:1541967 encountered
Relations: rels:1525645, finalFF:159967
Max relations in full relation-set: 0
Initial matrix: 142206 x 159967 with sparse part having weight 16090240.
Pruned matrix : 137684 x 138459 with weight 12233010.
Total sieving time: 10.69 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.48 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 11.33 hours.
 --------- CPU info (if available) ----------

Aug 27, 2007 (4th)

By Jo Yeong Uk / GGNFS snfs

3·10¹²⁸-7 = 2(9)₁₂₇3_<129> = 41 · 59 · 54773 · C121

C121 = P46 · P75

P46 = 7537788328018616405984189140699812345322214029_<46>

P75 = 300382702420089950889070923665817867552296755414839069498484220494663049491_<75>

Number: 29993_128
N=2264221228240843430860612299610477719961224154829802377186244279416764084156061387777267380382909546467657520568921509239
  ( 121 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=7537788328018616405984189140699812345322214029 (pp46)
 r2=300382702420089950889070923665817867552296755414839069498484220494663049491 (pp75)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.00 hours.
Scaled time: 4.28 units (timescale=2.143).
Factorization parameters were as follows:
n: 2264221228240843430860612299610477719961224154829802377186244279416764084156061387777267380382909546467657520568921509239
m: 20000000000000000000000000
c5: 375
c0: -28
skew: 0.6
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 900001)
Primes: RFBsize:78498, AFBsize:78556, largePrimes:1541786 encountered
Relations: rels:1589228, finalFF:219946
Max relations in full relation-set: 28
Initial matrix: 157121 x 219946 with sparse part having weight 11082418.
Pruned matrix : 127164 x 128013 with weight 5146045.
Total sieving time: 1.92 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 2.00 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.10 BogoMIPS).

Aug 27, 2007 (3rd)

By Sinkiti Sibata / GGNFS snfs

3·10¹²⁴-7 = 2(9)₁₂₃3_<125> = 499 · 50123 · 4979165454103_<13> · C105

C105 = P29 · P76

P29 = 32069277584934255341895947641_<29>

P76 = 7511694512964920660213222237541918019312926923461518825741959466812334839383_<76>

Number: 29993_124
N=240894616469499568232342324414062368452631433109656235581566054386083610865203017018054074083650312745503
  ( 105 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=32069277584934255341895947641 (pp29)
 r2=7511694512964920660213222237541918019312926923461518825741959466812334839383 (pp76)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 3.48 hours.
Scaled time: 2.38 units (timescale=0.683).
Factorization parameters were as follows:
name: 29993_124
n: 240894616469499568232342324414062368452631433109656235581566054386083610865203017018054074083650312745503
m: 10000000000000000000000000
c5: 3
c0: -70
skew: 1.88
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 700001)
Primes: RFBsize:49098, AFBsize:63523, largePrimes:2122134 encountered
Relations: rels:2121787, finalFF:127648
Max relations in full relation-set: 0
Initial matrix: 112686 x 127648 with sparse part having weight 11268270.
Pruned matrix : 108940 x 109567 with weight 8489035.
Total sieving time: 3.12 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.48 hours.
 --------- CPU info (if available) ----------

Aug 27, 2007 (2nd)

By Jo Yeong Uk / GGNFS snfs, GMP-ECM

3·10¹⁰²-7 = 2(9)₁₀₁3_<103> = 5503 · C99

C99 = P43 · P57

P43 = 3539577321355187357058316586614016942558507_<43>

P57 = 154017595180034784335600556931964288371618563510589261333_<57>

Number: 29993_102
N=545157186988915137197892058876976194802834817372342358713429038706160276212974741050336180265309831
  ( 99 digits)
SNFS difficulty: 102 digits.
Divisors found:
 r1=3539577321355187357058316586614016942558507 (pp43)
 r2=154017595180034784335600556931964288371618563510589261333 (pp57)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.35 hours.
Scaled time: 0.76 units (timescale=2.144).
Factorization parameters were as follows:
n: 545157186988915137197892058876976194802834817372342358713429038706160276212974741050336180265309831
m: 100000000000000000000
c5: 300
c0: -7
skew: 0.47
type: snfs
Factor base limits: 240000/240000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [120000, 195001)
Primes: RFBsize:21221, AFBsize:21254, largePrimes:888627 encountered
Relations: rels:745957, finalFF:50115
Max relations in full relation-set: 28
Initial matrix: 42541 x 50115 with sparse part having weight 1437684.
Pruned matrix : 37570 x 37846 with weight 922534.
Total sieving time: 0.34 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,102,5,0,0,0,0,0,0,0,0,240000,240000,25,25,43,43,2.1,2.1,15000
total time: 0.35 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.10 BogoMIPS).

3·10¹⁰⁷-7 = 2(9)₁₀₆3_<108> = 73² · 31957 · C100

C100 = P30 · P34 · P37

P30 = 277589851523296053332037672941_<30>

P34 = 1002459894818158467774433246518331_<34>

P37 = 6330513515041898460559917424038309211_<37>

Number: 29993_107
N=1761609046186588232628906784240055920987324559373280100718000725465837400560765961236391885739829381
  ( 100 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=277589851523296053332037672941 (pp30)
 r2=1002459894818158467774433246518331 (pp34)
 r3=6330513515041898460559917424038309211 (pp37)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.45 hours.
Scaled time: 0.95 units (timescale=2.129).
Factorization parameters were as follows:
n: 1761609046186588232628906784240055920987324559373280100718000725465837400560765961236391885739829381
m: 1000000000000000000000
c5: 300
c0: -7
skew: 0.47
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 260001)
Primes: RFBsize:30757, AFBsize:30684, largePrimes:962858 encountered
Relations: rels:879575, finalFF:80338
Max relations in full relation-set: 28
Initial matrix: 61507 x 80338 with sparse part having weight 3456094.
Pruned matrix : 53164 x 53535 with weight 1683537.
Total sieving time: 0.42 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,107,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.45 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.10 BogoMIPS).

3·10¹¹¹-7 = 2(9)₁₁₀3_<112> = 23 · 373003 · C105

C105 = P44 · P62

P44 = 27835335642957025433655367694790412609627019_<44>

P62 = 12562747515193989773402390442014510943362606451247158043351463_<62>

Number: 29993_111
N=349688293683149068972402483299761314427008338550488403811649026252149271675050054965171628762981157978797
  ( 105 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=27835335642957025433655367694790412609627019 (pp44)
 r2=12562747515193989773402390442014510943362606451247158043351463 (pp62)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.69 hours.
Scaled time: 1.46 units (timescale=2.124).
Factorization parameters were as follows:
n: 349688293683149068972402483299761314427008338550488403811649026252149271675050054965171628762981157978797
m: 10000000000000000000000
c5: 30
c0: -7
skew: 0.75
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 320001)
Primes: RFBsize:30757, AFBsize:30494, largePrimes:1020947 encountered
Relations: rels:931251, finalFF:80704
Max relations in full relation-set: 28
Initial matrix: 61318 x 80704 with sparse part having weight 3972837.
Pruned matrix : 55579 x 55949 with weight 2017566.
Total sieving time: 0.66 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.69 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.10 BogoMIPS).

3·10¹²⁹-7 = 2(9)₁₂₈3_<130> = C130

C130 = P29 · P48 · P55

P29 = 13634014563100632163485094139_<29>

P48 = 139215960043020963366563162682325387847822463557_<48>

P55 = 1580550856695477889083277991070258583743421455170186591_<55>

Number: 29993_129
N=2999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 130 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=13634014563100632163485094139 (pp29)
 r2=139215960043020963366563162682325387847822463557 (pp48)
 r3=1580550856695477889083277991070258583743421455170186591 (pp55)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.83 hours.
Scaled time: 6.07 units (timescale=2.146).
Factorization parameters were as follows:
n: 2999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
m: 100000000000000000000000000
c5: 3
c0: -70
skew: 1.88
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 1100001)
Primes: RFBsize:78498, AFBsize:78021, largePrimes:1578298 encountered
Relations: rels:1600735, finalFF:197381
Max relations in full relation-set: 28
Initial matrix: 156584 x 197381 with sparse part having weight 12021455.
Pruned matrix : 141849 x 142695 with weight 6882715.
Total sieving time: 2.73 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 2.83 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.10 BogoMIPS).

3·10¹¹⁶-7 = 2(9)₁₁₅3_<117> = 5711 · C113

C113 = P43 · P71

P43 = 3219174617934997967729103654362313099113789_<43>

P71 = 16317910987225509303709497983754427492567247926719168101616013003489667_<71>

Number: 29993_116
N=52530204867798984416039222552967956575030642619506216074242689546489231308002101208194711959376641568902118718263
  ( 113 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=3219174617934997967729103654362313099113789 (pp43)
 r2=16317910987225509303709497983754427492567247926719168101616013003489667 (pp71)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.83 hours.
Scaled time: 1.78 units (timescale=2.145).
Factorization parameters were as follows:
n: 52530204867798984416039222552967956575030642619506216074242689546489231308002101208194711959376641568902118718263
m: 100000000000000000000000
c5: 30
c0: -7
skew: 0.75
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 420001)
Primes: RFBsize:49098, AFBsize:48776, largePrimes:1881701 encountered
Relations: rels:1830654, finalFF:116660
Max relations in full relation-set: 28
Initial matrix: 97941 x 116660 with sparse part having weight 9492117.
Pruned matrix : 92238 x 92791 with weight 6099665.
Total sieving time: 0.77 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 0.83 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.10 BogoMIPS).

3·10¹⁴⁹-7 = 2(9)₁₄₈3_<150> = 179 · 521 · 3463 · 5282612227_<10> · 35419352915554933199557_<23> · C109

C109 = P35 · P75

P35 = 21272798033221076607577777047006013_<35>

P75 = 233380215802854007300467394780726271343697166092228509059711875575719508047_<75>

3·10¹²⁶-7 = 2(9)₁₂₅3_<127> = 17 · C126

C126 = P37 · P89

P37 = 1947761627248864935777984869025486217_<37>

P89 = 90601737793013067707297429917950567899839201443202358104654069381901149336940160966925537_<89>

Number: 29993_126
N=176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529
  ( 126 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=1947761627248864935777984869025486217 (pp37)
 r2=90601737793013067707297429917950567899839201443202358104654069381901149336940160966925537 (pp89)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.98 hours.
Scaled time: 4.25 units (timescale=2.144).
Factorization parameters were as follows:
n: 176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529
m: 10000000000000000000000000
c5: 30
c0: -7
skew: 0.75
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 900001)
Primes: RFBsize:78498, AFBsize:77956, largePrimes:1553141 encountered
Relations: rels:1599584, finalFF:219775
Max relations in full relation-set: 28
Initial matrix: 156521 x 219775 with sparse part having weight 11340321.
Pruned matrix : 126978 x 127824 with weight 5262878.
Total sieving time: 1.91 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 1.98 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.10 BogoMIPS).

3·10¹⁶⁷-7 = 2(9)₁₆₆3_<168> = C168

C168 = P42 · P126

P42 = 655467036657994741996643867126553366964783_<42>

P126 = 457688919841947776110399176672643492197644369408954631966772160173721908536961345672536829147905758344010973197701056308278871_<126>

Aug 27, 2007

By Sinkiti Sibata / GGNFS gnfs, snfs

3·10¹³¹-7 = 2(9)₁₃₀3_<132> = 67 · 73 · 1019 · 116345861 · 977792987 · 556928995904051921_<18> · C90

C90 = P35 · P56

P35 = 59726562069597109314324525106720499_<35>

P56 = 15906850721045874492067807848099118867247459356850020189_<56>

Number: 29993_131
N=950061506922361956173978053504580512762590466557036500602670856517685312193088447730154311
  ( 90 digits)
Divisors found:
 r1=59726562069597109314324525106720499 (pp35)
 r2=15906850721045874492067807848099118867247459356850020189 (pp56)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 4.36 hours.
Scaled time: 2.98 units (timescale=0.683).
Factorization parameters were as follows:
name: 29993_131
n:  950061506922361956173978053504580512762590466557036500602670856517685312193088447730154311
m:  576763940886060425848
deg: 4
c4: 8585376
c3: 46043290
c2: -8500336392011611
c1: -3690164694860894122
c0: -277517425059888154185
skew: 1635.250
type: gnfs
# adj. I(F,S) = 51.668
# E(F1,F2) = 1.698649e-04
# GGNFS version 0.77.1-20060722-pentium4 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=58.00000000, seed=1188125202.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 700000
alim: 700000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.4
alambda: 2.4
qintsize: 40000

type: gnfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [350000, 710001)
Primes: RFBsize:56543, AFBsize:56519, largePrimes:1558747 encountered
Relations: rels:1522078, finalFF:127569
Max relations in full relation-set: 0
Initial matrix: 113135 x 127569 with sparse part having weight 11105184.
Pruned matrix : 108854 x 109483 with weight 7940686.
Polynomial selection time: 0.17 hours.
Total sieving time: 3.84 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,89,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,25,25,44,44,2.4,2.4,40000
total time: 4.36 hours.
 --------- CPU info (if available) ----------

3·10¹¹⁷-7 = 2(9)₁₁₆3_<118> = 65663146013_<11> · 1115445346207_<13> · C95

C95 = P33 · P63

P33 = 218367804382939724096025924452209_<33>

P63 = 187569691815535808504272490616328250324358050799297959129311747_<63>

Number: 29993_117
N=40959181770543213619060402870043933276823141622498530960829661372304663576743954789636163799123
  ( 95 digits)
Divisors found:
 r1=218367804382939724096025924452209 (pp33)
 r2=187569691815535808504272490616328250324358050799297959129311747 (pp63)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 10.53 hours.
Scaled time: 7.19 units (timescale=0.683).
Factorization parameters were as follows:
name: 29993_117
n:  40959181770543213619060402870043933276823141622498530960829661372304663576743954789636163799123
m:  5448565826898695520624
deg: 4
c4: 46475328
c3: 101344500712
c2: -472255512414059034
c1: -394563556785377973
c0: 235363264286578010957443
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.318
# E(F1,F2) = 3.772756e-05
# GGNFS version 0.77.1-20060722-pentium4 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1188142345.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1440001)
Primes: RFBsize:92938, AFBsize:92847, largePrimes:1898276 encountered
Relations: rels:1986717, finalFF:212386
Max relations in full relation-set: 0
Initial matrix: 185859 x 212386 with sparse part having weight 15227931.
Pruned matrix : 173280 x 174273 with weight 11148304.
Polynomial selection time: 0.17 hours.
Total sieving time: 9.50 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.66 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 10.53 hours.
 --------- CPU info (if available) ----------

3·10¹²²-7 = 2(9)₁₂₁3_<123> = 227 · 541 · 5821 · 2440113394861_<13> · C102

C102 = P47 · P55

P47 = 83874866130091704225931620360708407017715883677_<47>

P55 = 2050494856118000514981197734640153342657783824277403827_<55>

Number: 29993_122
N=171984981557338943720876089963265461754031849148782559859775844954175603505748020782384283778686631879
  ( 102 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=83874866130091704225931620360708407017715883677 (pp47)
 r2=2050494856118000514981197734640153342657783824277403827 (pp55)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 2.62 hours.
Scaled time: 1.79 units (timescale=0.683).
Factorization parameters were as follows:
name: 29993_122
n: 171984981557338943720876089963265461754031849148782559859775844954175603505748020782384283778686631879
m: 1000000000000000000000000
c5: 300
c0: -7
skew: 0.47
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:64153, largePrimes:2107885 encountered
Relations: rels:2154235, finalFF:132169
Max relations in full relation-set: 0
Initial matrix: 113317 x 132169 with sparse part having weight 7558650.
Pruned matrix : 105278 x 105908 with weight 5324836.
Total sieving time: 2.35 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.62 hours.
 --------- CPU info (if available) ----------

3·10¹²³-7 = 2(9)₁₂₂3_<124> = 41 · 73 · 25229 · 80436896303091941_<17> · C99

C99 = P47 · P53

P47 = 25717660438571745381489038333885826323571075209_<47>

P53 = 19205593766110280619993552722286434599284651570080801_<53>

Number: 29993_123
N=493922938997974498580414521518774754063241395387693330419187722978244874523656899408600794577962409
  ( 99 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=25717660438571745381489038333885826323571075209 (pp47)
 r2=19205593766110280619993552722286434599284651570080801 (pp53)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 2.60 hours.
Scaled time: 1.78 units (timescale=0.683).
Factorization parameters were as follows:
name: 29993_123
n: 493922938997974498580414521518774754063241395387693330419187722978244874523656899408600794577962409
m: 1000000000000000000000000
c5: 3000
c0: -7
skew: 0.3
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:63898, largePrimes:2059050 encountered
Relations: rels:2063041, finalFF:130571
Max relations in full relation-set: 0
Initial matrix: 113063 x 130571 with sparse part having weight 8675304.
Pruned matrix : 106089 x 106718 with weight 6142343.
Total sieving time: 2.31 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.60 hours.
 --------- CPU info (if available) ----------

Aug 26, 2007 (2nd)

By Sinkiti Sibata / Msieve v. 1.26, GGNFS

3·10¹⁰⁹-7 = 2(9)₁₀₈3_<110> = 83 · 56809 · 16216515547_<11> · 1243071210473_<13> · C81

C81 = P37 · P45

P37 = 2248059687775148500471809593908702163_<37>

P45 = 140399198593424783364159287344550310097264723_<45>

Sun Aug 26 13:50:58 2007  Msieve v. 1.26
Sun Aug 26 13:50:58 2007  random seeds: 1451f000 cc105488
Sun Aug 26 13:50:58 2007  factoring 315625778553815587004811754086956831579675851159971598797911152419592933173695849 (81 digits)
Sun Aug 26 13:50:59 2007  commencing quadratic sieve (81-digit input)
Sun Aug 26 13:50:59 2007  using multiplier of 41
Sun Aug 26 13:50:59 2007  using 64kb Pentium 2 sieve core
Sun Aug 26 13:50:59 2007  sieve interval: 6 blocks of size 65536
Sun Aug 26 13:50:59 2007  processing polynomials in batches of 17
Sun Aug 26 13:50:59 2007  using a sieve bound of 1317713 (50343 primes)
Sun Aug 26 13:50:59 2007  using large prime bound of 129135874 (26 bits)
Sun Aug 26 13:50:59 2007  using trial factoring cutoff of 27 bits
Sun Aug 26 13:50:59 2007  polynomial 'A' values have 10 factors
Sun Aug 26 15:12:14 2007  50617 relations (26609 full + 24008 combined from 267360 partial), need 50439
Sun Aug 26 15:12:16 2007  begin with 293969 relations
Sun Aug 26 15:12:16 2007  reduce to 71642 relations in 2 passes
Sun Aug 26 15:12:16 2007  attempting to read 71642 relations
Sun Aug 26 15:12:19 2007  recovered 71642 relations
Sun Aug 26 15:12:19 2007  recovered 60192 polynomials
Sun Aug 26 15:12:19 2007  attempting to build 50617 cycles
Sun Aug 26 15:12:19 2007  found 50617 cycles in 1 passes
Sun Aug 26 15:12:19 2007  distribution of cycle lengths:
Sun Aug 26 15:12:19 2007     length 1 : 26609
Sun Aug 26 15:12:19 2007     length 2 : 24008
Sun Aug 26 15:12:19 2007  largest cycle: 2 relations
Sun Aug 26 15:12:19 2007  matrix is 50343 x 50617 with weight 1561449 (avg 30.85/col)
Sun Aug 26 15:12:22 2007  filtering completed in 4 passes
Sun Aug 26 15:12:22 2007  matrix is 42140 x 42204 with weight 1269497 (avg 30.08/col)
Sun Aug 26 15:12:24 2007  saving the first 48 matrix rows for later
Sun Aug 26 15:12:24 2007  matrix is 42092 x 42204 with weight 1011189 (avg 23.96/col)
Sun Aug 26 15:12:24 2007  matrix includes 64 packed rows
Sun Aug 26 15:12:24 2007  commencing Lanczos iteration
Sun Aug 26 15:15:12 2007  lanczos halted after 667 iterations
Sun Aug 26 15:15:13 2007  recovered 13 nontrivial dependencies
Sun Aug 26 15:15:13 2007  prp37 factor: 2248059687775148500471809593908702163
Sun Aug 26 15:15:13 2007  prp45 factor: 140399198593424783364159287344550310097264723
Sun Aug 26 15:15:13 2007  elapsed time 01:24:15

3·10¹⁰¹-7 = 2(9)₁₀₀3_<102> = 61 · 270538861909140599_<18> · C83

C83 = P34 · P50

P34 = 1503944237661379360868402573256481_<34>

P50 = 12087320199218433786007971497669328028718661880027_<50>

Number: 29993_101
N=18178655562382559504603600172348702425295980655038020769681684834586255227122204987
  ( 83 digits)
Divisors found:
 r1=1503944237661379360868402573256481 (pp34)
 r2=12087320199218433786007971497669328028718661880027 (pp50)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 2.70 hours.
Scaled time: 1.84 units (timescale=0.683).
Factorization parameters were as follows:
name: 29993_101
n:  18178655562382559504603600172348702425295980655038020769681684834586255227122204987
m:  13520163201302496320
deg: 4
c4: 544044
c3: 1525702999
c2: -2090212604885881
c1: -5785762335682389
c0: 1219195069438556895867
skew: 1379.250
type: gnfs
# adj. I(F,S) = 47.935
# E(F1,F2) = 1.453982e-03
# GGNFS version 0.77.1-20060722-pentium4 polyselect.
# Options were: 
# lcd=1, enumLCD=12, maxS1=56.00000000, seed=1188103115.
# maxskew=1500.0
# These parameters should be manually set:
rlim: 550000
alim: 550000
lpbr: 24
lpba: 24
mfbr: 40
mfba: 40
rlambda: 1.9
alambda: 1.9
qintsize: 10000

type: gnfs
Factor base limits: 550000/550000
Large primes per side: 3
Large prime bits: 24/24
Max factor residue bits: 40/40
Sieved algebraic special-q in [275000, 555001)
Primes: RFBsize:45322, AFBsize:45360, largePrimes:833800 encountered
Relations: rels:815718, finalFF:104325
Max relations in full relation-set: 0
Initial matrix: 90757 x 104325 with sparse part having weight 2839349.
Pruned matrix : 78966 x 79483 with weight 2017468.
Polynomial selection time: 0.10 hours.
Total sieving time: 2.49 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
gnfs,82,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,550000,550000,24,24,40,40,1.9,1.9,10000
total time: 2.70 hours.
 --------- CPU info (if available) ----------

3·10¹¹⁹-7 = 2(9)₁₁₈3_<120> = 78368605499_<11> · 53095903456340370936693577_<26> · C83

C83 = P39 · P45

P39 = 188290868464416554619696945024940247957_<39>

P45 = 382903082208360177830892669855412560821185463_<45>

Number: 29993_119
N=72097153886714024932882352086117787528471155467902080177717553304923243985903849091
  ( 83 digits)
Divisors found:
 r1=188290868464416554619696945024940247957 (pp39)
 r2=382903082208360177830892669855412560821185463 (pp45)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 2.71 hours.
Scaled time: 1.85 units (timescale=0.683).
Factorization parameters were as follows:
name: 29993_119
n:  72097153886714024932882352086117787528471155467902080177717553304923243985903849091
m:  15077363100825086328
deg: 4
c4: 1395136
c3: 4169473474
c2: -4457287606760667
c1: -10940135386059515
c0: 222330235747687799275
skew: 1379.250
type: gnfs
# adj. I(F,S) = 48.893
# E(F1,F2) = 1.238494e-03
# GGNFS version 0.77.1-20060722-pentium4 polyselect.
# Options were: 
# lcd=1, enumLCD=2, maxS1=56.00000000, seed=1188114582.
# maxskew=1500.0
# These parameters should be manually set:
rlim: 550000
alim: 550000
lpbr: 24
lpba: 24
mfbr: 40
mfba: 40
rlambda: 1.9
alambda: 1.9
qintsize: 10000

type: gnfs
Factor base limits: 550000/550000
Large primes per side: 3
Large prime bits: 24/24
Max factor residue bits: 40/40
Sieved algebraic special-q in [275000, 555001)
Primes: RFBsize:45322, AFBsize:45273, largePrimes:832054 encountered
Relations: rels:813824, finalFF:104604
Max relations in full relation-set: 0
Initial matrix: 90669 x 104604 with sparse part having weight 2856065.
Pruned matrix : 78768 x 79285 with weight 2014929.
Polynomial selection time: 0.14 hours.
Total sieving time: 2.45 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
gnfs,82,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,550000,550000,24,24,40,40,1.9,1.9,10000
total time: 2.71 hours.
 --------- CPU info (if available) ----------

Aug 26, 2007

The factor table of 299...993 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Aug 25, 2007 (3rd)

By Yousuke Koide

(10¹¹²⁷-1)/9 is divisible by 241553587165443690259691154554887409_<36>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Aug 25, 2007 (2nd)

By Sinkiti Sibata / GGNFS gnfs

2·10¹⁶¹-7 = 1(9)₁₆₀3_<162> = 31 · 313 · 142448923 · 17325841849_<11> · 15585783388091791295501248633_<29> · C111

C111 = P36 · P76

P36 = 266553003634306871217586370997016387_<36>

P76 = 2010287774860919418202526881731198334032989116402867831616415928274528790943_<76>

Number: 19993_161
N=535848244558505326981889880448516590560696883242115262678313109743369334051689534371625931132298086183468182941
  ( 111 digits)
Divisors found:
 r1=266553003634306871217586370997016387 (pp36)
 r2=2010287774860919418202526881731198334032989116402867831616415928274528790943 (pp76)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 40.17 hours.
Scaled time: 27.43 units (timescale=0.683).
Factorization parameters were as follows:
name: 19993_161
n: 535848244558505326981889880448516590560696883242115262678313109743369334051689534371625931132298086183468182941
skew: 38462.86
# norm 1.20e+15
c5: 14400
c4: 1189258772
c3: -61157220101536
c2: -1665797028207107129
c1: 35529798518665248099674
c0: 456489891463513885112956704
# alpha -6.23
Y1: 579357828269
Y0: -2061265089212221663831
# Murphy_E 1.01e-09
# M 180678419163438711842001077111863466249073647594527557717463130782957750173637314545849972614753799691397384718
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2300001)
Primes: RFBsize:230209, AFBsize:229517, largePrimes:7279052 encountered
Relations: rels:6986811, finalFF:516183
Max relations in full relation-set: 0
Initial matrix: 459803 x 516183 with sparse part having weight 43767277.
Pruned matrix : 413366 x 415729 with weight 29134753.
Polynomial selection time: 2.18 hours.
Total sieving time: 30.39 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 6.89 hours.
Time per square root: 0.39 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 40.17 hours.
 --------- CPU info (if available) ----------

Aug 25, 2007

By Jo Yeong Uk / GGNFS

10¹⁸²-3 = (9)₁₈₁7_<182> = C182

C182 = P62 · P121

P62 = 65534081280247754710444002932518609571718586565539736236949437_<62>

P121 = 1525923581233455345160090558666254929382951100902891094757531494547444044927553100912619162340394581853825038559214658881_<121>

Number: 99997_182
N=99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997
  ( 182 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=65534081280247754710444002932518609571718586565539736236949437 (pp62)
 r2=1525923581233455345160090558666254929382951100902891094757531494547444044927553100912619162340394581853825038559214658881 (pp121)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 266.82 hours.
Scaled time: 572.61 units (timescale=2.146).
Factorization parameters were as follows:
n: 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997
m: 1000000000000000000000000000000000000
c5: 100
c0: -3
skew: 0.5
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [5000000, 9300001)
Primes: RFBsize:664579, AFBsize:665255, largePrimes:11054485 encountered
Relations: rels:11325581, finalFF:1493802
Max relations in full relation-set: 28
Initial matrix: 1329898 x 1493802 with sparse part having weight 90406090.
Pruned matrix : 1184081 x 1190794 with weight 65471125.
Total sieving time: 254.23 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 12.13 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000
total time: 266.82 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.10 BogoMIPS).

Aug 24, 2007

By Jo Yeong Uk / GGNFS gnfs

2·10¹⁶⁵-7 = 1(9)₁₆₄3_<166> = 59797 · 246613 · 23678089 · 41577973901_<11> · 34612991488332463201_<20> · 336810499334585532769_<21> · C98

C98 = P46 · P52

P46 = 8373248538781344557355140845393442753439917323_<46>

P52 = 1411256395841790563687916889769452582264264863948791_<52>

Number: 19993_165
N=11816800554328099620625661265085248289285152349800401170173394776530045681226710459572934345806493
  ( 98 digits)
Divisors found:
 r1=8373248538781344557355140845393442753439917323 (pp46)
 r2=1411256395841790563687916889769452582264264863948791 (pp52)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.74 hours.
Scaled time: 5.88 units (timescale=2.144).
Factorization parameters were as follows:
name: 19993_165
n: 11816800554328099620625661265085248289285152349800401170173394776530045681226710459572934345806493
skew: 1237.28
# norm 1.21e+13
c5: 113220
c4: 480980685
c3: 2430122298256
c2: -1110451066817246
c1: -1086725127653307920
c0: 201867094610748041685
# alpha -5.21
Y1: 14369106697
Y0: -2533455370402983104
# Murphy_E 4.96e-09
# M 9593727833258514037579465404153082108432528258843425541809868831355743798983219962802223254495886
type: gnfs
rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [650000, 1000001)
Primes: RFBsize:100021, AFBsize:100606, largePrimes:3733014 encountered
Relations: rels:3561953, finalFF:244813
Max relations in full relation-set: 28
Initial matrix: 200709 x 244813 with sparse part having weight 18256185.
Pruned matrix : 171699 x 172766 with weight 10219484.
Polynomial selection time: 0.20 hours.
Total sieving time: 2.33 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1300000,1300000,26,26,48,48,2.5,2.5,50000
total time: 2.74 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.10 BogoMIPS).

Aug 23, 2007 (2nd)

By Yousuke Koide

(10¹⁰⁰⁷-1)/9 is divisible by 172358178102983968116191222304067_<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Aug 23, 2007

By Sinkiti Sibata / GGNFS

2·10¹⁶⁰-7 = 1(9)₁₅₉3_<161> = 9778720056013703211871_<22> · 3697455345403613029511363255055491_<34> · C105

C105 = P35 · P70

P35 = 88983955588580213717636993253398599_<35>

P70 = 6216319634016996326346051640131835569522780364047133332828651637579787_<70>

Number: 19993_160
N=553152710237787609065609048212168477170736374711112981864333893174433466742570138896896172282264776518413
  ( 105 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=88983955588580213717636993253398599 (pp35)
 r2=6216319634016996326346051640131835569522780364047133332828651637579787 (pp70)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 66.09 hours.
Scaled time: 45.14 units (timescale=0.683).
Factorization parameters were as follows:
name: 19993_160
n: 553152710237787609065609048212168477170736374711112981864333893174433466742570138896896172282264776518413
m: 100000000000000000000000000000000
c5: 2
c0: -7
skew: 1.28
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:282562, largePrimes:5694547 encountered
Relations: rels:5775416, finalFF:641262
Max relations in full relation-set: 0
Initial matrix: 565773 x 641262 with sparse part having weight 34681631.
Pruned matrix : 504212 x 507104 with weight 25688162.
Total sieving time: 56.46 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 9.15 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 66.09 hours.
 --------- CPU info (if available) ----------

Aug 20, 2007 (2nd)

By Robert Backstrom / GGNFS

2·10¹⁴⁸-7 = 1(9)₁₄₇3_<149> = 727 · 55259 · 689461 · 71275313 · C128

C128 = P48 · P80

P48 = 116574430973904193855146706732208499099941411897_<48>

P80 = 86904130976575581951526367276706846060506184025707483584177277127705512595780481_<80>

Number: n
N=10130799617875939439341399345302520071267999743485898743887114293281557156798471710018762477085932643315539431360437715813782457
  ( 128 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=116574430973904193855146706732208499099941411897 (pp48)
 r2=86904130976575581951526367276706846060506184025707483584177277127705512595780481 (pp80)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 17.29 hours.
Scaled time: 20.70 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_1_9_147_3
n: 10130799617875939439341399345302520071267999743485898743887114293281557156798471710018762477085932643315539431360437715813782457
type: snfs
skew: 1.00
deg: 5
c5: 125
c0: -14
m: 200000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2000001)
Primes: RFBsize:148933, AFBsize:149045, largePrimes:6657395 encountered
Relations: rels:5980839, finalFF:339775
Max relations in full relation-set: 28
Initial matrix: 298043 x 339775 with sparse part having weight 27123958.
Pruned matrix : 283441 x 284995 with weight 19686152.
Total sieving time: 14.52 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 2.42 hours.
Total square root time: 0.09 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 17.29 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

2·10¹⁵³-7 = 1(9)₁₅₂3_<154> = 449 · 677 · C148

C148 = P46 · P103

P46 = 3762028438491263860353713420746250519837842493_<46>

P103 = 1748931950489219682449972965472311190393808085080580038420592920946818270596715052250792592387757778537_<103>

Number: n
N=6579531734726439519299411460886328719984998667644823717895997341869179170518434203037769801923197126060538271491217970017073884851615110552581972741
  ( 148 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=3762028438491263860353713420746250519837842493 (pp46)
 r2=1748931950489219682449972965472311190393808085080580038420592920946818270596715052250792592387757778537 (pp103)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 26.79 hours.
Scaled time: 36.59 units (timescale=1.366).
Factorization parameters were as follows:
name: KA_1_9_152_3
n: 6579531734726439519299411460886328719984998667644823717895997341869179170518434203037769801923197126060538271491217970017073884851615110552581972741
skew: 1.00
deg: 5
c5: 125
c0: -14
m: 2000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:203362, AFBsize:204052, largePrimes:6864428 encountered
Relations: rels:6333807, finalFF:471535
Max relations in full relation-set: 28
Initial matrix: 407479 x 471535 with sparse part having weight 32214453.
Pruned matrix : 354626 x 356727 with weight 20521709.
Total sieving time: 23.94 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.55 hours.
Total square root time: 0.10 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 26.79 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(17·10¹⁶⁴-71)/9 = 1(8)₁₆₃1_<165> = 216583463554531_<15> · C150

C150 = P43 · P47 · P61

P43 = 5393696868579157005523711065632147602089029_<43>

P47 = 38447484784957009504048982784105217220178467777_<47>

P61 = 4205587262171089272039659014159109528298565349557528731191647_<61>

Number: n
N=872129782158233792110440795362543649954023480251741539294763244976946979043259196816200705125877018942721308771218136883684994106138959566906294693851
  ( 150 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=5393696868579157005523711065632147602089029 (pp43)
 r2=38447484784957009504048982784105217220178467777 (pp47)
 r3=4205587262171089272039659014159109528298565349557528731191647 (pp61)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 96.76 hours.
Scaled time: 140.39 units (timescale=1.451).
Factorization parameters were as follows:
name: KA_1_8_163_1
n: 872129782158233792110440795362543649954023480251741539294763244976946979043259196816200705125877018942721308771218136883684994106138959566906294693851
skew: 1.00
deg: 5
c5: 17
c0: -710
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 4400001)
Primes: RFBsize:250150, AFBsize:249432, largePrimes:8074559 encountered
Relations: rels:7600831, finalFF:561306
Max relations in full relation-set: 28
Initial matrix: 499647 x 561306 with sparse part having weight 54689824.
Pruned matrix : 472890 x 475452 with weight 43077382.
Total sieving time: 87.19 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 9.05 hours.
Total square root time: 0.20 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 96.76 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

3·10¹⁶⁰+1 = 3(0)₁₅₉1_<161> = 12697 · 44454007667553277_<17> · C140

C140 = P59 · P82

P59 = 29275289584766911761299359521184239465004060018132044373477_<59>

P82 = 1815549170260446417865866950799703327121370197342878399772057644753731002595701977_<82>

Number: n
N=53150727714757855596028755975143659660511735972840980625776628679939604228946393189742287388651544032546054205292253547945196114285975264029
  ( 140 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=29275289584766911761299359521184239465004060018132044373477 (pp59)
 r2=1815549170260446417865866950799703327121370197342878399772057644753731002595701977 (pp82)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 31.82 hours.
Scaled time: 41.46 units (timescale=1.303).
Factorization parameters were as follows:
name: KA_3_0_159_1
n: 53150727714757855596028755975143659660511735972840980625776628679939604228946393189742287388651544032546054205292253547945196114285975264029
skew: 1.00
deg: 5
c5: 3
c0: 1
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:250150, AFBsize:249986, largePrimes:7004434 encountered
Relations: rels:6536240, finalFF:574940
Max relations in full relation-set: 48
Initial matrix: 500201 x 574940 with sparse part having weight 35481689.
Pruned matrix : 432298 x 434863 with weight 21149842.
Total sieving time: 27.52 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.95 hours.
Total square root time: 0.14 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 31.82 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Aug 20, 2007

By Sinkiti Sibata / GGNFS

2·10¹⁵⁰-7 = 1(9)₁₄₉3_<151> = 11952940053651615413333135761471_<32> · C120

C120 = P55 · P65

P55 = 5135103254216728139255928526842762174060283210192549973_<55>

P65 = 32584125786762908430335253253731098461829476256546485262340435371_<65>

Number: 19993_150
N=167322850363413418158164834583548112090064493980285945977571771138046552314385841614896291617004196921469969657494294983
  ( 120 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=5135103254216728139255928526842762174060283210192549973 (pp55)
 r2=32584125786762908430335253253731098461829476256546485262340435371 (pp65)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 32.39 hours.
Scaled time: 22.12 units (timescale=0.683).
Factorization parameters were as follows:
name: 19993_150
n: 167322850363413418158164834583548112090064493980285945977571771138046552314385841614896291617004196921469969657494294983
m: 1000000000000000000000000000000
c5: 2
c0: -7
skew: 1.28
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 1750001)
Primes: RFBsize:114155, AFBsize:113917, largePrimes:2699817 encountered
Relations: rels:2662344, finalFF:256787
Max relations in full relation-set: 0
Initial matrix: 228137 x 256787 with sparse part having weight 20597364.
Pruned matrix : 219117 x 220321 with weight 15817334.
Total sieving time: 30.89 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 1.28 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 32.39 hours.
 --------- CPU info (if available) ----------

2·10¹⁵⁴-7 = 1(9)₁₅₃3_<155> = 67² · 229 · 55049 · 50009407956250793_<17> · 61602475925415368717517641_<26> · C102

C102 = P39 · P63

P39 = 351490277394110695323131847836679690401_<39>

P63 = 326386567160734215007637212280611893892518870849999885489152869_<63>

Number: 19993_154
N=114721705029038009684258993602678013088151782796643426876986034777151039743560427927268917878680910469
  ( 102 digits)
Divisors found:
 r1=351490277394110695323131847836679690401 (pp39)
 r2=326386567160734215007637212280611893892518870849999885489152869 (pp63)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 12.31 hours.
Scaled time: 8.41 units (timescale=0.683).
Factorization parameters were as follows:
name: 19993_154
n: 114721705029038009684258993602678013088151782796643426876986034777151039743560427927268917878680910469
skew: 6838.50
# norm 1.98e+14
c5: 57420
c4: 806981968
c3: -8759452266381
c2: 58156300282939815
c1: 72656612070836578217
c0: -291819258638452880648082
# alpha -6.34
Y1: 18567356473
Y0: -18201837623511379385
# Murphy_E 2.96e-09
# M 87987576487836068557265036980859895901729801322279531052036278029304020648302296853134444042946255226
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1750001)
Primes: RFBsize:169511, AFBsize:170137, largePrimes:4352283 encountered
Relations: rels:4419667, finalFF:389432
Max relations in full relation-set: 0
Initial matrix: 339732 x 389432 with sparse part having weight 18830906.
Pruned matrix : 292135 x 293897 with weight 12311149.
Polynomial selection time: 0.73 hours.
Total sieving time: 9.40 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.79 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 12.31 hours.
 --------- CPU info (if available) ----------

Aug 19, 2007 (3rd)

By Bruce Dodson

10⁶¹⁰+1 is divisible by 30177150878514090521547663054628235944221777770161_<50>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Aug 19, 2007 (2nd)

By Robert Backstrom / GGNFS

7·10¹⁵⁶+3 = 7(0)₁₅₅3_<157> = 131869366750590330739_<21> · C137

C137 = P34 · P104

P34 = 1122763019112328991917896688146547_<34>

P104 = 47278753694379635584088304024046021007264290269515393607169408994420953596008025338686045504887530367691_<104>

Number: n
N=53082836237769857722135010860503485221907656970354532121622796129493381197886353182035304221918803574861216603875564877388744020202012977
  ( 137 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=1122763019112328991917896688146547 (pp34)
 r2=47278753694379635584088304024046021007264290269515393607169408994420953596008025338686045504887530367691 (pp104)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 48.61 hours.
Scaled time: 58.14 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_7_0_155_3
n: 53082836237769857722135010860503485221907656970354532121622796129493381197886353182035304221918803574861216603875564877388744020202012977
type: snfs
skew: 1.00
deg: 5
c5: 70
c0: 3
m: 10000000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2100001)
Primes: RFBsize:148933, AFBsize:148155, largePrimes:7023899 encountered
Relations: rels:6408331, finalFF:334175
Max relations in full relation-set: 28
Initial matrix: 297155 x 334175 with sparse part having weight 35120249.
Pruned matrix : 287404 x 288953 with weight 27659186.
Total sieving time: 44.44 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 3.56 hours.
Total square root time: 0.31 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 48.61 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(2·10¹⁶⁵-11)/9 = (2)₁₆₄1_<165> = 13 · 724499 · C158

C158 = P39 · P119

P39 = 454131008520969815015609614546162302581_<39>

P119 = 51954741289049915090131599165962689609766478375843775620784761410878644041216476959039033357173188712948113263437198543_<119>

Number: n
N=23594259059042309260736063257529815799737497351986812979857828781015700528356860525711000314829995754331053620631660076849097123797295916236038996732938339483
  ( 158 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=454131008520969815015609614546162302581 (pp39)
 r2=51954741289049915090131599165962689609766478375843775620784761410878644041216476959039033357173188712948113263437198543 (pp119)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 49.52 hours.
Scaled time: 65.56 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_2_164_1
n: 23594259059042309260736063257529815799737497351986812979857828781015700528356860525711000314829995754331053620631660076849097123797295916236038996732938339483
skew: 1.00
deg: 5
c5: 2
c0: -11
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2100001)
Primes: RFBsize:250150, AFBsize:250187, largePrimes:7289192 encountered
Relations: rels:6812467, finalFF:578182
Max relations in full relation-set: 48
Initial matrix: 500404 x 578182 with sparse part having weight 42208298.
Pruned matrix : 436256 x 438822 with weight 26433646.
Total sieving time: 44.02 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 5.18 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 49.52 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

2·10¹³⁴-7 = 1(9)₁₃₃3_<135> = 2857 · 27927023 · C124

C124 = P50 · P74

P50 = 53144573565322907925832295743438999653609663807679_<50>

P74 = 47166775363319527326178169171770117349576735102560712103900237618601981697_<74>

Number: n
N=2506658163134994748187870797893663432529551237390369677630812454096726037917263172448982542288494354114405110663168086051263
  ( 124 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=53144573565322907925832295743438999653609663807679 (pp50)
 r2=47166775363319527326178169171770117349576735102560712103900237618601981697 (pp74)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.42 hours.
Scaled time: 5.81 units (timescale=1.315).
Factorization parameters were as follows:
name: KA_1_9_133_3
n: 2506658163134994748187870797893663432529551237390369677630812454096726037917263172448982542288494354114405110663168086051263
skew: 1.00
deg: 5
c5: 1
c0: -35
m: 1000000000000000000000000000
type: snfs
rlim: 1200000
alim: 1200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 550001)
Primes: RFBsize:92938, AFBsize:93179, largePrimes:5793654 encountered
Relations: rels:5159522, finalFF:291661
Max relations in full relation-set: 48
Initial matrix: 186181 x 291661 with sparse part having weight 28321965.
Pruned matrix : 147755 x 148749 with weight 9548185.
Total sieving time: 3.69 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.57 hours.
Total square root time: 0.03 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,48,48,2.5,2.5,75000
total time: 4.42 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

2·10¹⁴⁶-7 = 1(9)₁₄₅3_<147> = 31² · 47 · C142

C142 = P42 · P43 · P58

P42 = 435789728193384491010265428807562407041323_<42>

P43 = 7824864009218661541825600129317326360954459_<43>

P58 = 1298538893538002080810765152446905474596595362243224337247_<58>

Number: n
N=4428011601390395642836584231850687448801115858923550379701994819226426373237097881196448734695684902694445059446055748666061505081143312595479
  ( 142 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=435789728193384491010265428807562407041323 (pp42)
 r2=7824864009218661541825600129317326360954459 (pp43)
 r3=1298538893538002080810765152446905474596595362243224337247 (pp58)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.67 hours.
Scaled time: 10.36 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_1_9_145_3
n: 4428011601390395642836584231850687448801115858923550379701994819226426373237097881196448734695684902694445059446055748666061505081143312595479
type: snfs
skew: 1.00
deg: 5
c5: 20
c0: -7
m: 100000000000000000000000000000
rlim: 1800000
alim: 1800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1050001)
Primes: RFBsize:135072, AFBsize:134113, largePrimes:5640095 encountered
Relations: rels:4976824, finalFF:312780
Max relations in full relation-set: 28
Initial matrix: 269251 x 312780 with sparse part having weight 17817889.
Pruned matrix : 235514 x 236924 with weight 10920385.
Total sieving time: 7.28 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.10 hours.
Total square root time: 0.11 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.3,2.3,100000
total time: 8.67 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

2·10¹⁵⁷-7 = 1(9)₁₅₆3_<158> = 13 · 19 · C155

C155 = P50 · P106

P50 = 34394983393086726911525485365768764383612514728573_<50>

P106 = 2354170635689371043056236203816500880637102917069176450408667904943221662630923232028232978839918295665403_<106>

Number: n
N=80971659919028340080971659919028340080971659919028340080971659919028340080971659919028340080971659919028340080971659919028340080971659919028340080971659919
  ( 155 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=34394983393086726911525485365768764383612514728573 (pp50)
 r2=2354170635689371043056236203816500880637102917069176450408667904943221662630923232028232978839918295665403 (pp106)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 31.86 hours.
Scaled time: 43.52 units (timescale=1.366).
Factorization parameters were as follows:
name: KA_1_9_156_3
n: 80971659919028340080971659919028340080971659919028340080971659919028340080971659919028340080971659919028340080971659919028340080971659919028340080971659919
skew: 1.00
deg: 5
c5: 200
c0: -7
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:216816, AFBsize:216921, largePrimes:6966596 encountered
Relations: rels:6455257, finalFF:502554
Max relations in full relation-set: 28
Initial matrix: 433802 x 502554 with sparse part having weight 33690650.
Pruned matrix : 377727 x 379960 with weight 21241570.
Total sieving time: 28.24 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.20 hours.
Total square root time: 0.21 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 31.86 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

2·10¹³⁸-7 = 1(9)₁₃₇3_<139> = 658279 · C133

C133 = P44 · P90

P44 = 20210881938782879485293912186383278080876647_<44>

P90 = 150326217455104768578918165545438708371606106048971235069662906160218582347415312161469961_<90>

Number: n
N=3038225433288924604916760218691466688136793061908400541411772212086364596166670970819363825976523632076976479577808193790171036900767
  ( 133 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=20210881938782879485293912186383278080876647 (pp44)
 r2=150326217455104768578918165545438708371606106048971235069662906160218582347415312161469961 (pp90)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.57 hours.
Scaled time: 8.62 units (timescale=1.311).
Factorization parameters were as follows:
name: KA_1_9_137_3
n: 3038225433288924604916760218691466688136793061908400541411772212086364596166670970819363825976523632076976479577808193790171036900767
skew: 1.00
deg: 5
c5: 125
c0: -14
m: 2000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 750001)
Primes: RFBsize:114155, AFBsize:114067, largePrimes:6195557 encountered
Relations: rels:5510791, finalFF:295473
Max relations in full relation-set: 48
Initial matrix: 228287 x 295473 with sparse part having weight 28469908.
Pruned matrix : 197360 x 198565 with weight 13852233.
Total sieving time: 5.39 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.94 hours.
Total square root time: 0.08 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,75000
total time: 6.57 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Aug 19, 2007

By JMB / GMP-ECM

2·10¹⁶⁰-7 = 1(9)₁₅₉3_<161> = 9778720056013703211871_<22> · C139

C139 = P34 · C105

P34 = 3697455345403613029511363255055491_<34>

C105 = [553152710237787609065609048212168477170736374711112981864333893174433466742570138896896172282264776518413_<105>]

Aug 18, 2007 (3rd)

By JMB / GMP-ECM

2·10¹⁵⁸-7 = 1(9)₁₅₇3_<159> = 953 · 25057 · C151

C151 = P31 · C121

P31 = 2414090848213589432916932990633_<31>

C121 = [3469400305515585275088518477571852718127951025814114467282749380810057951257353312433363378995962611612031180850967588601_<121>]

2·10¹³⁷-7 = 1(9)₁₃₆3_<138> = 748003 · 33310522579_<11> · C121

C121 = P28 · P94

P28 = 2390131300820543368485406409_<28>

P94 = 3358330630726815585866665148198037542537791667019952702420547131059345414855706436951109119321_<94>

Aug 18, 2007 (2nd)

By Sinkiti Sibata / GGNFS

2·10¹¹³-7 = 1(9)₁₁₂3_<114> = 433 · 193594939 · 6438265937_<10> · C93

C93 = P42 · P52

P42 = 103768776474506761548880707440030104142231_<42>

P52 = 3571186177883878701163022523856197962069162111081437_<52>

Number: 19993_113
N=370577620241680351107960936083701744464801655582601702548670887408021026411042271800671865947
  ( 93 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=103768776474506761548880707440030104142231 (pp42)
 r2=3571186177883878701163022523856197962069162111081437 (pp52)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 1.84 hours.
Scaled time: 1.26 units (timescale=0.683).
Factorization parameters were as follows:
name: 19993_113
n: 370577620241680351107960936083701744464801655582601702548670887408021026411042271800671865947
m: 20000000000000000000000
c5: 125
c0: -14
skew: 0.65
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:63823, largePrimes:1971406 encountered
Relations: rels:1935298, finalFF:127077
Max relations in full relation-set: 0
Initial matrix: 112986 x 127077 with sparse part having weight 7926145.
Pruned matrix : 106103 x 106731 with weight 5732448.
Total sieving time: 1.58 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.84 hours.
 --------- CPU info (if available) ----------

2·10¹²¹-7 = 1(9)₁₂₀3_<122> = 13 · 19² · 29 · 67 · 449 · 105683783 · 560286053 · C95

C95 = P32 · P63

P32 = 84709044758553106779503153611219_<32>

P63 = 973895486213706256874024049169829152280917871863189669742989003_<63>

Number: 19993_121
N=82497756331829683462558669352925498586702592066075493931163282676698334873528872233466454424657
  ( 95 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=84709044758553106779503153611219 (pp32)
 r2=973895486213706256874024049169829152280917871863189669742989003 (pp63)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 2.15 hours.
Scaled time: 1.46 units (timescale=0.677).
Factorization parameters were as follows:
name: 19993_121
n: 82497756331829683462558669352925498586702592066075493931163282676698334873528872233466454424657
m: 1000000000000000000000000
c5: 20
c0: -7
skew: 0.81
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63823, largePrimes:2192336 encountered
Relations: rels:2389469, finalFF:130435
Max relations in full relation-set: 0
Initial matrix: 112987 x 130435 with sparse part having weight 4525679.
Pruned matrix : 99255 x 99883 with weight 3222049.
Total sieving time: 1.95 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.15 hours.
 --------- CPU info (if available) ----------

2·10¹³¹-7 = 1(9)₁₃₀3_<132> = 31 · 43 · 547 · 17191 · C122

C122 = P39 · P83

P39 = 336512056301210231838855734796868432039_<39>

P83 = 47414453712323773154974881733917128690695953514154501437581484178811965886517575607_<83>

Number: 19993_131
N=15955535317132624037259941748282345796884680309287211931921457057513056386029490246875124343730473568510897621965723672673
  ( 122 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=336512056301210231838855734796868432039 (pp39)
 r2=47414453712323773154974881733917128690695953514154501437581484178811965886517575607 (pp83)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 4.50 hours.
Scaled time: 3.07 units (timescale=0.683).
Factorization parameters were as follows:
name: 19993_131
n: 15955535317132624037259941748282345796884680309287211931921457057513056386029490246875124343730473568510897621965723672673
m: 100000000000000000000000000
c5: 20
c0: -7
skew: 0.81
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:63951, AFBsize:63823, largePrimes:1471860 encountered
Relations: rels:1489112, finalFF:145656
Max relations in full relation-set: 0
Initial matrix: 127840 x 145656 with sparse part having weight 5859360.
Pruned matrix : 120924 x 121627 with weight 4468738.
Total sieving time: 4.22 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.50 hours.
 --------- CPU info (if available) ----------

Aug 18, 2007

By Robert Backstrom / GGNFS, Msieve

2·10¹⁰³-7 = 1(9)₁₀₂3_<104> = 13 · 19 · 109 · 27271 · 45843061261_<11> · C84

C84 = P37 · P48

P37 = 1499785301098546070559433483576047617_<37>

P48 = 396189332056518295199839376172030596884900883633_<48>

Sat Aug 18 00:41:33 2007  Msieve v. 1.25
Sat Aug 18 00:41:33 2007  random seeds: 45574060 fe00702c
Sat Aug 18 00:41:33 2007  factoring 594198936670417142250034428006910675032083389876682398379113331137221661036983952561 (84 digits)
Sat Aug 18 00:41:34 2007  commencing quadratic sieve (84-digit input)
Sat Aug 18 00:41:34 2007  using multiplier of 1
Sat Aug 18 00:41:34 2007  using 64kb Opteron sieve core
Sat Aug 18 00:41:34 2007  sieve interval: 6 blocks of size 65536
Sat Aug 18 00:41:34 2007  processing polynomials in batches of 17
Sat Aug 18 00:41:34 2007  using a sieve bound of 1409171 (53774 primes)
Sat Aug 18 00:41:34 2007  using large prime bound of 119779535 (26 bits)
Sat Aug 18 00:41:34 2007  using trial factoring cutoff of 27 bits
Sat Aug 18 00:41:34 2007  polynomial 'A' values have 11 factors
Sat Aug 18 01:03:48 2007  54036 relations (27875 full + 26161 combined from 277827 partial), need 53870
Sat Aug 18 01:03:49 2007  begin with 305702 relations
Sat Aug 18 01:03:49 2007  reduce to 76900 relations in 2 passes
Sat Aug 18 01:03:49 2007  attempting to read 76900 relations
Sat Aug 18 01:03:49 2007  recovered 76900 relations
Sat Aug 18 01:03:49 2007  recovered 69605 polynomials
Sat Aug 18 01:03:50 2007  attempting to build 54036 cycles
Sat Aug 18 01:03:50 2007  found 54036 cycles in 1 passes
Sat Aug 18 01:03:50 2007  distribution of cycle lengths:
Sat Aug 18 01:03:50 2007     length 1 : 27875
Sat Aug 18 01:03:50 2007     length 2 : 26161
Sat Aug 18 01:03:50 2007  largest cycle: 2 relations
Sat Aug 18 01:03:50 2007  matrix is 53774 x 54036 with weight 1726315 (avg 31.95/col)
Sat Aug 18 01:03:50 2007  filtering completed in 4 passes
Sat Aug 18 01:03:50 2007  matrix is 46254 x 46318 with weight 1449783 (avg 31.30/col)
Sat Aug 18 01:03:51 2007  saving the first 48 matrix rows for later
Sat Aug 18 01:03:51 2007  matrix is 46206 x 46318 with weight 1037966 (avg 22.41/col)
Sat Aug 18 01:03:51 2007  matrix includes 64 packed rows
Sat Aug 18 01:03:51 2007  commencing Lanczos iteration
Sat Aug 18 01:04:42 2007  lanczos halted after 732 iterations
Sat Aug 18 01:04:42 2007  recovered 9 nontrivial dependencies
Sat Aug 18 01:04:42 2007  prp37 factor: 1499785301098546070559433483576047617
Sat Aug 18 01:04:42 2007  prp48 factor: 396189332056518295199839376172030596884900883633
Sat Aug 18 01:04:42 2007  elapsed time 00:23:09

2·10¹⁰¹-7 = 1(9)₁₀₀3_<102> = 23 · 31 · C99

C99 = P32 · P67

P32 = 40817008110892419885360745295659_<32>

P67 = 6872255508630705731993785461808742826606432539570772235049035346579_<67>

Number: n
N=280504908835904628330995792426367461430575035063113604488078541374474053295932678821879382889200561
  ( 99 digits)
SNFS difficulty: 101 digits.
Divisors found:
 r1=40817008110892419885360745295659 (pp32)
 r2=6872255508630705731993785461808742826606432539570772235049035346579 (pp67)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.58 hours.
Scaled time: 0.69 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_1_9_100_3
n: 280504908835904628330995792426367461430575035063113604488078541374474053295932678821879382889200561
type: snfs
skew: 1.00
deg: 5
c5: 20
c0: -7
m: 100000000000000000000
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 150001)
Primes: RFBsize:41538, AFBsize:41592, largePrimes:3289182 encountered
Relations: rels:2767321, finalFF:227176
Max relations in full relation-set: 28
Initial matrix: 83196 x 227176 with sparse part having weight 6114936.
Pruned matrix : 41906 x 42385 with weight 1147122.
Total sieving time: 0.50 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.01 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,101,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.2,2.2,20000
total time: 0.58 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

2·10¹⁰⁷-7 = 1(9)₁₀₆3_<108> = C108

C108 = P53 · P55

P53 = 82054863816299707259814398629080646350578566200027409_<53>

P55 = 2437393601039298755451892933667568529233231518271465577_<55>

Number: n
N=199999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 108 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=82054863816299707259814398629080646350578566200027409 (pp53)
 r2=2437393601039298755451892933667568529233231518271465577 (pp55)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.81 hours.
Scaled time: 1.07 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_1_9_106_3
n: 199999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
skew: 1.00
deg: 5
c5: 200
c0: -7
m: 1000000000000000000000
type: snfs
rlim: 600000
alim: 600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 150001)
Primes: RFBsize:49098, AFBsize:49236, largePrimes:3580731 encountered
Relations: rels:2988128, finalFF:136292
Max relations in full relation-set: 48
Initial matrix: 98399 x 136292 with sparse part having weight 7847627.
Pruned matrix : 78677 x 79232 with weight 2761136.
Total sieving time: 0.70 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.04 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,107,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000
total time: 0.81 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

2·10¹¹⁶-7 = 1(9)₁₁₅3_<117> = 31 · 15287 · 57388723099_<11> · 7056481988900947_<16> · C85

C85 = P38 · P47

P38 = 53770152002195367607766769002285035703_<38>

P47 = 19381615468650712446069311543584612837099830391_<47>

Sat Aug 18 01:11:25 2007  Msieve v. 1.25
Sat Aug 18 01:11:25 2007  random seeds: 8c7476f8 0ac7e520
Sat Aug 18 01:11:25 2007  factoring 1042152409797449813919505804291041079610830022103112436355806625120281914418679449873 (85 digits)
Sat Aug 18 01:11:25 2007  commencing quadratic sieve (84-digit input)
Sat Aug 18 01:11:25 2007  using multiplier of 23
Sat Aug 18 01:11:25 2007  using 64kb Opteron sieve core
Sat Aug 18 01:11:25 2007  sieve interval: 6 blocks of size 65536
Sat Aug 18 01:11:25 2007  processing polynomials in batches of 17
Sat Aug 18 01:11:25 2007  using a sieve bound of 1412767 (54118 primes)
Sat Aug 18 01:11:25 2007  using large prime bound of 118672428 (26 bits)
Sat Aug 18 01:11:25 2007  using double large prime bound of 341845303975812 (41-49 bits)
Sat Aug 18 01:11:25 2007  using trial factoring cutoff of 49 bits
Sat Aug 18 01:11:25 2007  polynomial 'A' values have 11 factors
Sat Aug 18 01:41:18 2007  54532 relations (16323 full + 38209 combined from 574167 partial), need 54214
Sat Aug 18 01:41:18 2007  begin with 590490 relations
Sat Aug 18 01:41:19 2007  reduce to 127649 relations in 9 passes
Sat Aug 18 01:41:19 2007  attempting to read 127649 relations
Sat Aug 18 01:41:20 2007  recovered 127649 relations
Sat Aug 18 01:41:20 2007  recovered 105145 polynomials
Sat Aug 18 01:41:20 2007  attempting to build 54532 cycles
Sat Aug 18 01:41:20 2007  found 54532 cycles in 6 passes
Sat Aug 18 01:41:21 2007  distribution of cycle lengths:
Sat Aug 18 01:41:21 2007     length 1 : 16323
Sat Aug 18 01:41:21 2007     length 2 : 10945
Sat Aug 18 01:41:21 2007     length 3 : 9517
Sat Aug 18 01:41:21 2007     length 4 : 6903
Sat Aug 18 01:41:21 2007     length 5 : 4676
Sat Aug 18 01:41:21 2007     length 6 : 2756
Sat Aug 18 01:41:21 2007     length 7 : 1628
Sat Aug 18 01:41:21 2007     length 9+: 1784
Sat Aug 18 01:41:21 2007  largest cycle: 20 relations
Sat Aug 18 01:41:21 2007  matrix is 54118 x 54532 with weight 2861941 (avg 52.48/col)
Sat Aug 18 01:41:21 2007  filtering completed in 3 passes
Sat Aug 18 01:41:21 2007  matrix is 49283 x 49347 with weight 2589053 (avg 52.47/col)
Sat Aug 18 01:41:22 2007  saving the first 48 matrix rows for later
Sat Aug 18 01:41:22 2007  matrix is 49235 x 49347 with weight 1923717 (avg 38.98/col)
Sat Aug 18 01:41:22 2007  matrix includes 64 packed rows
Sat Aug 18 01:41:22 2007  commencing Lanczos iteration
Sat Aug 18 01:42:37 2007  lanczos halted after 780 iterations
Sat Aug 18 01:42:37 2007  recovered 16 nontrivial dependencies
Sat Aug 18 01:42:37 2007  prp38 factor: 53770152002195367607766769002285035703
Sat Aug 18 01:42:37 2007  prp47 factor: 19381615468650712446069311543584612837099830391
Sat Aug 18 01:42:37 2007  elapsed time 00:31:12

7·10¹⁵⁷+3 = 7(0)₁₅₆3_<158> = 229 · 20670690483852242291_<20> · C137

C137 = P54 · P83

P54 = 289487332555897025292304347439098723403965940378647989_<54>

P83 = 51083189905954193522289990799875185494212136099456609629347350039925026063426710793_<83>

Number: n
N=14787936384321003708141216422843185879204009734434037034013241495186860920918712525674496781342997140195863042629969015291500910654045277
  ( 137 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=289487332555897025292304347439098723403965940378647989 (pp54)
 r2=51083189905954193522289990799875185494212136099456609629347350039925026063426710793 (pp83)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 31.10 hours.
Scaled time: 42.45 units (timescale=1.365).
Factorization parameters were as follows:
name: KA_7_0_156_3
n: 14787936384321003708141216422843185879204009734434037034013241495186860920918712525674496781342997140195863042629969015291500910654045277
skew: 1.00
deg: 5
c5: 700
c0: 3
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:216816, AFBsize:216741, largePrimes:6935490 encountered
Relations: rels:6416479, finalFF:495576
Max relations in full relation-set: 28
Initial matrix: 433624 x 495576 with sparse part having weight 32902854.
Pruned matrix : 382603 x 384835 with weight 21351181.
Total sieving time: 28.05 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 2.62 hours.
Total square root time: 0.22 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 31.10 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

2·10¹²⁹-7 = 1(9)₁₂₈3_<130> = 83639 · 3574169 · 129553992197347_<15> · 261030882891310001_<18> · C87

C87 = P31 · P57

P31 = 1486751042568008988903546205849_<31>

P57 = 133065397594874242418254943012440252718810034095919697541_<57>

Sat Aug 18 01:57:43 2007  Msieve v. 1.25
Sat Aug 18 01:57:43 2007  random seeds: cba2d240 7c081f2e
Sat Aug 18 01:57:43 2007  factoring 197835118603905915720214023895293099346240518843919779049358943033088066153354205117309 (87 digits)
Sat Aug 18 01:57:43 2007  commencing quadratic sieve (86-digit input)
Sat Aug 18 01:57:43 2007  using multiplier of 11
Sat Aug 18 01:57:43 2007  using 64kb Opteron sieve core
Sat Aug 18 01:57:43 2007  sieve interval: 10 blocks of size 65536
Sat Aug 18 01:57:43 2007  processing polynomials in batches of 11
Sat Aug 18 01:57:43 2007  using a sieve bound of 1477219 (56333 primes)
Sat Aug 18 01:57:43 2007  using large prime bound of 118177520 (26 bits)
Sat Aug 18 01:57:43 2007  using double large prime bound of 339283405529280 (41-49 bits)
Sat Aug 18 01:57:43 2007  using trial factoring cutoff of 49 bits
Sat Aug 18 01:57:43 2007  polynomial 'A' values have 11 factors
Sat Aug 18 02:41:39 2007  56816 relations (15831 full + 40985 combined from 595388 partial), need 56429
Sat Aug 18 02:41:40 2007  begin with 611219 relations
Sat Aug 18 02:41:41 2007  reduce to 136446 relations in 10 passes
Sat Aug 18 02:41:41 2007  attempting to read 136446 relations
Sat Aug 18 02:41:42 2007  recovered 136446 relations
Sat Aug 18 02:41:42 2007  recovered 114684 polynomials
Sat Aug 18 02:41:42 2007  attempting to build 56816 cycles
Sat Aug 18 02:41:42 2007  found 56816 cycles in 5 passes
Sat Aug 18 02:41:43 2007  distribution of cycle lengths:
Sat Aug 18 02:41:43 2007     length 1 : 15831
Sat Aug 18 02:41:43 2007     length 2 : 11249
Sat Aug 18 02:41:43 2007     length 3 : 9985
Sat Aug 18 02:41:43 2007     length 4 : 7344
Sat Aug 18 02:41:43 2007     length 5 : 5110
Sat Aug 18 02:41:43 2007     length 6 : 3192
Sat Aug 18 02:41:43 2007     length 7 : 1864
Sat Aug 18 02:41:43 2007     length 9+: 2241
Sat Aug 18 02:41:43 2007  largest cycle: 22 relations
Sat Aug 18 02:41:43 2007  matrix is 56333 x 56816 with weight 3281518 (avg 57.76/col)
Sat Aug 18 02:41:44 2007  filtering completed in 3 passes
Sat Aug 18 02:41:44 2007  matrix is 51901 x 51965 with weight 3009122 (avg 57.91/col)
Sat Aug 18 02:41:44 2007  saving the first 48 matrix rows for later
Sat Aug 18 02:41:44 2007  matrix is 51853 x 51965 with weight 2376073 (avg 45.72/col)
Sat Aug 18 02:41:44 2007  matrix includes 64 packed rows
Sat Aug 18 02:41:44 2007  using block size 20786 for processor cache size 512 kB
Sat Aug 18 02:41:45 2007  commencing Lanczos iteration
Sat Aug 18 02:42:09 2007  lanczos halted after 821 iterations
Sat Aug 18 02:42:09 2007  recovered 18 nontrivial dependencies
Sat Aug 18 02:42:10 2007  prp31 factor: 1486751042568008988903546205849
Sat Aug 18 02:42:10 2007  prp57 factor: 133065397594874242418254943012440252718810034095919697541
Sat Aug 18 02:42:10 2007  elapsed time 00:44:27

2·10¹⁰⁵-7 = 1(9)₁₀₄3_<106> = 249871 · 19798132157_<11> · C90

C90 = P40 · P51

P40 = 3163117297741861192762916686673115456869_<40>

P51 = 127812881122780074917861322196995275825625504898951_<51>

Sat Aug 18 02:48:52 2007  Msieve v. 1.25
Sat Aug 18 02:48:52 2007  random seeds: 17aa9510 0f4a9a94
Sat Aug 18 02:48:52 2007  factoring 404287135153689852139853507001355860700950742482453612994941638390577044704142200043844419 (90 digits)
Sat Aug 18 02:48:52 2007  commencing quadratic sieve (90-digit input)
Sat Aug 18 02:48:52 2007  using multiplier of 35
Sat Aug 18 02:48:52 2007  using 64kb Opteron sieve core
Sat Aug 18 02:48:52 2007  sieve interval: 18 blocks of size 65536
Sat Aug 18 02:48:52 2007  processing polynomials in batches of 6
Sat Aug 18 02:48:52 2007  using a sieve bound of 1584941 (59865 primes)
Sat Aug 18 02:48:52 2007  using large prime bound of 126795280 (26 bits)
Sat Aug 18 02:48:52 2007  using double large prime bound of 385110612518640 (42-49 bits)
Sat Aug 18 02:48:52 2007  using trial factoring cutoff of 49 bits
Sat Aug 18 02:48:52 2007  polynomial 'A' values have 12 factors
Sat Aug 18 04:06:48 2007  60026 relations (16158 full + 43868 combined from 635630 partial), need 59961
Sat Aug 18 04:06:48 2007  begin with 651788 relations
Sat Aug 18 04:06:49 2007  reduce to 145703 relations in 10 passes
Sat Aug 18 04:06:49 2007  attempting to read 145703 relations
Sat Aug 18 04:06:51 2007  recovered 145703 relations
Sat Aug 18 04:06:51 2007  recovered 125654 polynomials
Sat Aug 18 04:06:51 2007  attempting to build 60026 cycles
Sat Aug 18 04:06:51 2007  found 60026 cycles in 5 passes
Sat Aug 18 04:06:51 2007  distribution of cycle lengths:
Sat Aug 18 04:06:51 2007     length 1 : 16158
Sat Aug 18 04:06:51 2007     length 2 : 11640
Sat Aug 18 04:06:51 2007     length 3 : 10601
Sat Aug 18 04:06:51 2007     length 4 : 8002
Sat Aug 18 04:06:51 2007     length 5 : 5438
Sat Aug 18 04:06:51 2007     length 6 : 3507
Sat Aug 18 04:06:51 2007     length 7 : 2180
Sat Aug 18 04:06:51 2007     length 9+: 2500
Sat Aug 18 04:06:51 2007  largest cycle: 19 relations
Sat Aug 18 04:06:51 2007  matrix is 59865 x 60026 with weight 3621110 (avg 60.33/col)
Sat Aug 18 04:06:52 2007  filtering completed in 3 passes
Sat Aug 18 04:06:52 2007  matrix is 55875 x 55939 with weight 3404274 (avg 60.86/col)
Sat Aug 18 04:06:53 2007  saving the first 48 matrix rows for later
Sat Aug 18 04:06:53 2007  matrix is 55827 x 55939 with weight 2670443 (avg 47.74/col)
Sat Aug 18 04:06:53 2007  matrix includes 64 packed rows
Sat Aug 18 04:06:53 2007  using block size 21845 for processor cache size 512 kB
Sat Aug 18 04:06:53 2007  commencing Lanczos iteration
Sat Aug 18 04:07:22 2007  lanczos halted after 884 iterations
Sat Aug 18 04:07:22 2007  recovered 17 nontrivial dependencies
Sat Aug 18 04:07:23 2007  prp40 factor: 3163117297741861192762916686673115456869
Sat Aug 18 04:07:23 2007  prp51 factor: 127812881122780074917861322196995275825625504898951
Sat Aug 18 04:07:23 2007  elapsed time 01:18:31

2·10¹¹⁸-7 = 1(9)₁₁₇3_<119> = 7603 · 15467 · 36691 · 560783 · 44963591969_<11> · C90

C90 = P39 · P51

P39 = 228255834357666971162546058313791223921_<39>

P51 = 805381494221740368380247875416367103097200384770669_<51>

Sat Aug 18 06:06:11 2007  Msieve v. 1.25
Sat Aug 18 06:06:11 2007  random seeds: 5f6a4b80 2ab61692
Sat Aug 18 06:06:11 2007  factoring 183833024939807888384756175161493723771813679252307301971496985010466178538582354411973149 (90 digits)
Sat Aug 18 06:06:11 2007  commencing quadratic sieve (89-digit input)
Sat Aug 18 06:06:11 2007  using multiplier of 5
Sat Aug 18 06:06:11 2007  using 64kb Opteron sieve core
Sat Aug 18 06:06:11 2007  sieve interval: 18 blocks of size 65536
Sat Aug 18 06:06:11 2007  processing polynomials in batches of 6
Sat Aug 18 06:06:11 2007  using a sieve bound of 1575227 (59526 primes)
Sat Aug 18 06:06:11 2007  using large prime bound of 126018160 (26 bits)
Sat Aug 18 06:06:11 2007  using double large prime bound of 380872498093920 (42-49 bits)
Sat Aug 18 06:06:11 2007  using trial factoring cutoff of 49 bits
Sat Aug 18 06:06:11 2007  polynomial 'A' values have 11 factors
Sat Aug 18 07:19:05 2007  59934 relations (15603 full + 44331 combined from 637765 partial), need 59622
Sat Aug 18 07:19:06 2007  begin with 653368 relations
Sat Aug 18 07:19:07 2007  reduce to 146935 relations in 11 passes
Sat Aug 18 07:19:07 2007  attempting to read 146935 relations
Sat Aug 18 07:19:08 2007  recovered 146935 relations
Sat Aug 18 07:19:08 2007  recovered 124808 polynomials
Sat Aug 18 07:19:09 2007  attempting to build 59934 cycles
Sat Aug 18 07:19:09 2007  found 59934 cycles in 6 passes
Sat Aug 18 07:19:09 2007  distribution of cycle lengths:
Sat Aug 18 07:19:09 2007     length 1 : 15603
Sat Aug 18 07:19:09 2007     length 2 : 11295
Sat Aug 18 07:19:09 2007     length 3 : 10597
Sat Aug 18 07:19:09 2007     length 4 : 8235
Sat Aug 18 07:19:09 2007     length 5 : 5780
Sat Aug 18 07:19:09 2007     length 6 : 3694
Sat Aug 18 07:19:09 2007     length 7 : 2249
Sat Aug 18 07:19:09 2007     length 9+: 2481
Sat Aug 18 07:19:09 2007  largest cycle: 18 relations
Sat Aug 18 07:19:09 2007  matrix is 59526 x 59934 with weight 3646667 (avg 60.84/col)
Sat Aug 18 07:19:10 2007  filtering completed in 3 passes
Sat Aug 18 07:19:10 2007  matrix is 55752 x 55815 with weight 3412104 (avg 61.13/col)
Sat Aug 18 07:19:11 2007  saving the first 48 matrix rows for later
Sat Aug 18 07:19:11 2007  matrix is 55704 x 55815 with weight 2806624 (avg 50.28/col)
Sat Aug 18 07:19:11 2007  matrix includes 64 packed rows
Sat Aug 18 07:19:11 2007  using block size 21845 for processor cache size 512 kB
Sat Aug 18 07:19:11 2007  commencing Lanczos iteration
Sat Aug 18 07:19:45 2007  lanczos halted after 883 iterations
Sat Aug 18 07:19:45 2007  recovered 18 nontrivial dependencies
Sat Aug 18 07:19:46 2007  prp39 factor: 228255834357666971162546058313791223921
Sat Aug 18 07:19:46 2007  prp51 factor: 805381494221740368380247875416367103097200384770669
Sat Aug 18 07:19:46 2007  elapsed time 01:13:35

Aug 17, 2007 (2nd)

The factor table of 199...993 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Aug 17, 2007

By Sinkiti Sibata / GGNFS

8·10¹⁴⁷+3 = 8(0)₁₄₆3_<148> = 31466053047841_<14> · 446393418652404001_<18> · C117

C117 = P55 · P63

P55 = 2323850000470988610164769082031528440943605820371041061_<55>

P63 = 245087883633789932212635585467307279310123198991773916587660103_<63>

Number: 80003_147
N=569547478497816335653236580096415110037272527469806007281214758971851303247684071335941951908761857655410364124489283
  ( 117 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=2323850000470988610164769082031528440943605820371041061 (pp55)
 r2=245087883633789932212635585467307279310123198991773916587660103 (pp63)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 18.83 hours.
Scaled time: 12.86 units (timescale=0.683).
Factorization parameters were as follows:
name: 80003_147
n: 569547478497816335653236580096415110037272527469806007281214758971851303247684071335941951908761857655410364124489283
m: 200000000000000000000000000000
c5: 25
c0: 3
skew: 0.65
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2450001)
Primes: RFBsize:114155, AFBsize:114287, largePrimes:2708471 encountered
Relations: rels:2648929, finalFF:256730
Max relations in full relation-set: 0
Initial matrix: 228506 x 256730 with sparse part having weight 24970341.
Pruned matrix : 219964 x 221170 with weight 19140475.
Total sieving time: 17.03 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.55 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 18.83 hours.
 --------- CPU info (if available) ----------

Aug 16, 2007 (2nd)

By Sinkiti Sibata / GGNFS

8·10¹⁶¹+3 = 8(0)₁₆₀3_<162> = 19 · 23 · 31 · 129126249073062336423461145334519_<33> · C126

C126 = P52 · P75

P52 = 2631015527810085421291051911982281677569752486170207_<52>

P75 = 173823667706511661436246647779256732900511330139840852735400152888111969953_<75>

Number: 80003_161
N=457332768836732679329717365438668873227519038326297743384522304228837178049370592246469798154252278726522579730705927227790271
  ( 126 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=2631015527810085421291051911982281677569752486170207 (pp52)
 r2=173823667706511661436246647779256732900511330139840852735400152888111969953 (pp75)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 65.82 hours.
Scaled time: 44.96 units (timescale=0.683).
Factorization parameters were as follows:
name: 80003_161
n: 457332768836732679329717365438668873227519038326297743384522304228837178049370592246469798154252278726522579730705927227790271
m: 200000000000000000000000000000000
c5: 5
c0: 6
skew: 1.04
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 3750001)
Primes: RFBsize:315948, AFBsize:315696, largePrimes:5655636 encountered
Relations: rels:5780972, finalFF:715488
Max relations in full relation-set: 0
Initial matrix: 631709 x 715488 with sparse part having weight 33633166.
Pruned matrix : 558137 x 561359 with weight 23584636.
Total sieving time: 54.70 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 10.64 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 65.82 hours.
 --------- CPU info (if available) ----------

Aug 16, 2007

By Robert Backstrom / GGNFS

(7·10¹⁶⁴-43)/9 = (7)₁₆₃3_<164> = 23 · 711289786791481_<15> · C148

C148 = P52 · P96

P52 = 6711531394644396265684065465544051167200478004582667_<52>

P96 = 708368916114260301416021742929112249942005710589804708659563255988563220760762909875017169699513_<96>

Number: n
N=4754240219491080788312230946104229406177747980744173052452025549226149029482922498597241709937906716835807695523262461778588861036905275229358141171
  ( 148 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=6711531394644396265684065465544051167200478004582667 (pp52)
 r2=708368916114260301416021742929112249942005710589804708659563255988563220760762909875017169699513 (pp96)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 68.29 hours.
Scaled time: 98.61 units (timescale=1.444).
Factorization parameters were as follows:
name: KA_7_163_3
n: 4754240219491080788312230946104229406177747980744173052452025549226149029482922498597241709937906716835807695523262461778588861036905275229358141171
skew: 1.00
deg: 5
c5: 7
c0: -430
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3100001)
Primes: RFBsize:250150, AFBsize:249976, largePrimes:7609891 encountered
Relations: rels:7117769, finalFF:563963
Max relations in full relation-set: 28
Initial matrix: 500191 x 563963 with sparse part having weight 43297342.
Pruned matrix : 456543 x 459107 with weight 32040185.
Total sieving time: 61.30 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 6.64 hours.
Total square root time: 0.09 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 68.29 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

8·10¹⁴⁸+3 = 8(0)₁₄₇3_<149> = 7 · 11 · 29 · 317 · 509 · 13229 · C137

C137 = P43 · P95

P43 = 1633127480251888041774589540737718105895353_<43>

P95 = 10277254618113551226936717541671467485926625997768564715394439356053800695383219974495822267431_<95>

Number: n
N=16784066938386863809673549107097123019053594081024750091689098181846065843165170875752881062581853809077533297118793759110758492866148143
  ( 137 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=1633127480251888041774589540737718105895353 (pp43)
 r2=10277254618113551226936717541671467485926625997768564715394439356053800695383219974495822267431 (pp95)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 17.86 hours.
Scaled time: 21.39 units (timescale=1.198).
Factorization parameters were as follows:
name: KA_8_0_147_3
n: 16784066938386863809673549107097123019053594081024750091689098181846065843165170875752881062581853809077533297118793759110758492866148143
type: snfs
skew: 1.00
deg: 5
c5: 2
c0: 75
m: 1000000000000000000000000000000
rlim: 1800000
alim: 1800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 800001)
Primes: RFBsize:135072, AFBsize:134848, largePrimes:5661412 encountered
Relations: rels:5066697, finalFF:360387
Max relations in full relation-set: 28
Initial matrix: 269985 x 360387 with sparse part having weight 21720490.
Pruned matrix : 199413 x 200826 with weight 10892762.
Total sieving time: 16.73 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.86 hours.
Total square root time: 0.10 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.3,2.3,100000
total time: 17.86 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

7·10¹⁶³-3 = 6(9)₁₆₂7_<164> = 521 · 8929 · 20049478817_<11> · C147

C147 = P32 · P116

P32 = 18834724717582733339854276484953_<32>

P116 = 39846954049113870438326350054437585548327057756753553930562437288636637623138186710621577302650844411531338277069533_<116>

Number: n
N=750506410349228396108340941035609903362273370421470668905748757604180204449969666910202490334397310209946975430176004793022692543599630852809236949
  ( 147 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=18834724717582733339854276484953 (pp32)
 r2=39846954049113870438326350054437585548327057756753553930562437288636637623138186710621577302650844411531338277069533 (pp116)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 69.78 hours.
Scaled time: 94.62 units (timescale=1.356).
Factorization parameters were as follows:
name: KA_6_9_162_7
n: 750506410349228396108340941035609903362273370421470668905748757604180204449969666910202490334397310209946975430176004793022692543599630852809236949
skew: 1.00
deg: 5
c5: 7000
c0: -3
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2900001)
Primes: RFBsize:250150, AFBsize:249771, largePrimes:7592845 encountered
Relations: rels:7109288, finalFF:566068
Max relations in full relation-set: 28
Initial matrix: 499988 x 566068 with sparse part having weight 44087913.
Pruned matrix : 452753 x 455316 with weight 32088899.
Total sieving time: 64.59 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 4.73 hours.
Total square root time: 0.15 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 69.78 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(83·10¹⁶³+61)/9 = 9(2)₁₆₂9_<164> = 3² · 11 · 405948153112321_<15> · C148

C148 = P45 · P103

P45 = 266614931935353132585870319448121552669271271_<45>

P103 = 8606872108912684768820232718493204401373246518359328695784136236316614714942900588215155616801419951681_<103>

Number: n
N=2294720621494044723501193022587510995379466046473791605416061226154482486212075390007842580455013701527981276373027895660286461909530014578301456551
  ( 148 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=266614931935353132585870319448121552669271271 (pp45)
 r2=8606872108912684768820232718493204401373246518359328695784136236316614714942900588215155616801419951681 (pp103)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 89.26 hours.
Scaled time: 117.91 units (timescale=1.321).
Factorization parameters were as follows:
name: KA_9_2_162_9
n: 2294720621494044723501193022587510995379466046473791605416061226154482486212075390007842580455013701527981276373027895660286461909530014578301456551
skew: 1.00
deg: 5
c5: 83000
c0: 61
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3500001)
Primes: RFBsize:250150, AFBsize:249877, largePrimes:7740802 encountered
Relations: rels:7222735, finalFF:569028
Max relations in full relation-set: 48
Initial matrix: 500094 x 569028 with sparse part having weight 54550980.
Pruned matrix : 469886 x 472450 with weight 38556850.
Total sieving time: 80.47 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 8.13 hours.
Total square root time: 0.34 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 89.26 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Aug 15, 2007 (2nd)

By Robert Backstrom / GGNFS

(2·10¹⁶⁴+1)/3 = (6)₁₆₃7_<164> = 593 · 90617845494707_<14> · C148

C148 = P69 · P79

P69 = 905685704538199081405478788593241373745603366270356038442638975449577_<69>

P79 = 1369817790937139389142693698471450846149527260439060627521041224566510416295921_<79>

Number: n
N=1240624391073862584177081105224640061651512320190878112287750695849877675218001116528687519332352510520546136007485011619473977733985821548046275417
  ( 148 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=905685704538199081405478788593241373745603366270356038442638975449577 (pp69)
 r2=1369817790937139389142693698471450846149527260439060627521041224566510416295921 (pp79)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 51.41 hours.
Scaled time: 61.53 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_6_163_7
n: 1240624391073862584177081105224640061651512320190878112287750695849877675218001116528687519332352510520546136007485011619473977733985821548046275417
type: snfs
skew: 1.00
deg: 5
c5: 1
c0: 5
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2000001)
Primes: RFBsize:250150, AFBsize:249616, largePrimes:7240131 encountered
Relations: rels:6756925, finalFF:561200
Max relations in full relation-set: 28
Initial matrix: 499830 x 561200 with sparse part having weight 36079230.
Pruned matrix : 447952 x 450515 with weight 24495508.
Total sieving time: 45.60 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 5.25 hours.
Total square root time: 0.23 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 51.41 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Aug 15, 2007

By JMB / MSieve, GMP-ECM

8·10¹⁶⁵+3 = 8(0)₁₆₄3_<166> = 17 · 83 · 2221 · 12653 · 1033040033209816345546009288939_<31> · 19558081525904346337653953996359_<32> · C94

C94 = P44 · P51

P44 = 31235192130845769254279459512560137999028121_<44>

P51 = 319693142674609372256180538787347658839023974155301_<51>

8·10¹⁷²+3 = 8(0)₁₇₁3_<173> = 7 · 11² · 53 · 261587 · 13420331 · C156

C156 = P35 · C122

P35 = 14742878852145643127878371424312249_<35>

C122 = [34432537221857307847885115428554920425568029885965301615634596789076443254421769772956443274804876835533993545735639636561_<122>]

Aug 14, 2007 (2nd)

By JMB / GMP-ECM

8·10¹⁷⁰+3 = 8(0)₁₆₉3_<171> = 11 · 73 · 25087 · 32666806785659_<14> · C151

C151 = P33 · P118

P33 = 518810619846876503372769619770433_<33>

P118 = 2343204381484500438488187466170885890773141731069741607646382933532921328434754372068190854059489563670232771599467309_<118>

8·10¹⁶⁵+3 = 8(0)₁₆₄3_<166> = 17 · 83 · 2221 · 12653 · 19558081525904346337653953996359_<32> · C125

C125 = P31 · C94

P31 = 1033040033209816345546009288939_<31>

C94 = [9985676734355312445998651932324904435324205513572694026740373190359859585183702210559920219421_<94>]

Aug 14, 2007

By Sinkiti Sibata / GGNFS

8·10¹⁸⁹+3 = 8(0)₁₈₈3_<190> = 619 · 1847 · 2087 · 17854618292333_<14> · 66686803592942902296799_<23> · 921080685636059212526826174467963_<33> · C112

C112 = P47 · P66

P47 = 17588503812768618802899470677477549249528890421_<47>

P66 = 173817279856071866628575928062476489118502849448260284689789701413_<66>

Number: 80003_189
N=3057185889473590067108879535881711047802061887351934101508239518685119755420999299188104236165875118418785864873
  ( 112 digits)
Divisors found:
 r1=17588503812768618802899470677477549249528890421 (pp47)
 r2=173817279856071866628575928062476489118502849448260284689789701413 (pp66)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 44.29 hours.
Scaled time: 30.21 units (timescale=0.682).
Factorization parameters were as follows:
name: 80003_189
n: 3057185889473590067108879535881711047802061887351934101508239518685119755420999299188104236165875118418785864873
skew: 42151.48
# norm 8.84e+15
c5: 37440
c4: -298371218
c3: -300194331630874
c2: -2696942357896617447
c1: -27789569306702796022486
c0: 469893487864104658111591365
# alpha -6.89
Y1: 204062775301
Y0: -2412110836924559280358
# Murphy_E 8.26e-10
# M 1005760143397642380352074720913871517578447049436816287197307383505060650599072483745071851791769646797691653031
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2550001)
Primes: RFBsize:250150, AFBsize:250023, largePrimes:7400988 encountered
Relations: rels:7270904, finalFF:564212
Max relations in full relation-set: 0
Initial matrix: 500263 x 564212 with sparse part having weight 39359534.
Pruned matrix : 442161 x 444726 with weight 27121752.
Polynomial selection time: 1.87 hours.
Total sieving time: 34.72 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 7.00 hours.
Time per square root: 0.34 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 44.29 hours.
 --------- CPU info (if available) ----------

Aug 13, 2007 (2nd)

By Jo Yeong Uk / GGNFS

7·10¹⁷⁹-3 = 6(9)₁₇₈7_<180> = C180

C180 = P74 · P106

P74 = 83251080449638728944649575376467201073537285846278352308844383882413696253_<74>

P106 = 8408299282355291944507594847871979982320198163187651997979672667927349257101780731688554079997824589461249_<106>

Number: 69997_179
N=699999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997
  ( 180 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=83251080449638728944649575376467201073537285846278352308844383882413696253 (pp74)
 r2=8408299282355291944507594847871979982320198163187651997979672667927349257101780731688554079997824589461249 (pp106)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 259.62 hours.
Scaled time: 556.63 units (timescale=2.144).
Factorization parameters were as follows:
n: 699999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997
m: 1000000000000000000000000000000000000
c5: 7
c0: -30
skew: 1.34
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [5000000, 9200001)
Primes: RFBsize:664579, AFBsize:664690, largePrimes:11188054 encountered
Relations: rels:11548928, finalFF:1569648
Max relations in full relation-set: 28
Initial matrix: 1329334 x 1569648 with sparse part having weight 96955888.
Pruned matrix : 1111881 x 1118591 with weight 66486936.
Total sieving time: 248.05 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 11.11 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000
total time: 259.62 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.10 BogoMIPS).

Aug 13, 2007

By Robert Backstrom / GGNFS

(5·10¹⁶³-41)/9 = (5)₁₆₂1_<163> = 6197 · 16253 · 7766599 · C148

C148 = P41 · P108

P41 = 44413093788181068954686083501992838352239_<41>

P108 = 159908133455531109958414064342395777100821881761406305592132607285851371898166471209881193256579918516686151_<108>

Number: n
N=7102014928653478112505380375170028150587599569829032560645158534704706517857033098640933711918896001508344830631819199337896740041018214185551142089
  ( 148 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=44413093788181068954686083501992838352239 (pp41)
 r2=159908133455531109958414064342395777100821881761406305592132607285851371898166471209881193256579918516686151 (pp108)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 69.01 hours.
Scaled time: 91.16 units (timescale=1.321).
Factorization parameters were as follows:
name: KA_5_162_1
n: 7102014928653478112505380375170028150587599569829032560645158534704706517857033098640933711918896001508344830631819199337896740041018214185551142089
skew: 1.91
deg: 5
c5: 8
c0: -205
m: 500000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2900001)
Primes: RFBsize:250150, AFBsize:250182, largePrimes:7611933 encountered
Relations: rels:7124868, finalFF:583205
Max relations in full relation-set: 48
Initial matrix: 500397 x 583205 with sparse part having weight 50754245.
Pruned matrix : 443931 x 446496 with weight 33952521.
Total sieving time: 61.81 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 6.84 hours.
Total square root time: 0.09 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 69.01 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10¹⁵⁰+3 = 8(0)₁₄₉3_<151> = 11² · 333847094812043_<15> · C135

C135 = P63 · P73

P63 = 123915190735934296426572399348483454050629019309155367871597523_<63>

P73 = 1598204928807240823149342852972588765245266509250337333568977262671359787_<73>

Number: n
N=198041868588259539803544224019989437375283062870153485808447332705304657558186289935035160659072536263589755720823920126704382391007601
  ( 135 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=123915190735934296426572399348483454050629019309155367871597523 (pp63)
 r2=1598204928807240823149342852972588765245266509250337333568977262671359787 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 16.97 hours.
Scaled time: 20.32 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_8_0_149_3
n: 198041868588259539803544224019989437375283062870153485808447332705304657558186289935035160659072536263589755720823920126704382391007601
type: snfs
skew: 1.00
deg: 5
c5: 8
c0: 3
m: 1000000000000000000000000000000
rlim: 1800000
alim: 1800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 800001)
Primes: RFBsize:135072, AFBsize:135053, largePrimes:5515066 encountered
Relations: rels:4864048, finalFF:313876
Max relations in full relation-set: 28
Initial matrix: 270190 x 313876 with sparse part having weight 18476130.
Pruned matrix : 235766 x 237180 with weight 11424414.
Total sieving time: 15.58 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.12 hours.
Total square root time: 0.10 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.3,2.3,100000
total time: 16.97 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

8·10¹⁵⁹+3 = 8(0)₁₅₈3_<160> = 53 · 1249 · 15803 · C151

C151 = P63 · P89

P63 = 153231313845746405825884701365885833226325571486615400562069271_<63>

P89 = 49907361884479263130985185256128895476821348429200465525031812515377456758530477125109523_<89>

Number: n
N=7647370632133883748883439676346985948647594574867711170484935573163178215153995040284393630963460365084651885728655779192405179039901887446685387767733
  ( 151 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=153231313845746405825884701365885833226325571486615400562069271 (pp63)
 r2=49907361884479263130985185256128895476821348429200465525031812515377456758530477125109523 (pp89)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 29.43 hours.
Scaled time: 42.61 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_8_0_158_3
n: 7647370632133883748883439676346985948647594574867711170484935573163178215153995040284393630963460365084651885728655779192405179039901887446685387767733
skew: 1.00
deg: 5
c5: 4
c0: 15
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:216816, AFBsize:216826, largePrimes:7196792 encountered
Relations: rels:6799215, finalFF:597924
Max relations in full relation-set: 28
Initial matrix: 433706 x 597924 with sparse part having weight 41582443.
Pruned matrix : 302044 x 304276 with weight 22428346.
Total sieving time: 26.46 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.67 hours.
Total square root time: 0.11 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 29.43 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

8·10¹⁶³+3 = 8(0)₁₆₂3_<164> = C164

C164 = P45 · P52 · P69

P45 = 263814841588028840292075635769021187187588777_<45>

P52 = 2946574066938041203271903376456481181720414869700453_<52>

P69 = 102913749296606783576701454837580698830029182185894558528664578737263_<69>

Number: n
N=80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
  ( 164 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=263814841588028840292075635769021187187588777 (pp45)
 r2=2946574066938041203271903376456481181720414869700453 (pp52)
 r3=102913749296606783576701454837580698830029182185894558528664578737263 (pp69)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 62.05 hours.
Scaled time: 84.20 units (timescale=1.357).
Factorization parameters were as follows:
name: KA_8_0_162_3
n: 80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
skew: 1.00
deg: 5
c5: 2
c0: 75
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2500001)
Primes: RFBsize:250150, AFBsize:249511, largePrimes:7415037 encountered
Relations: rels:6927576, finalFF:563657
Max relations in full relation-set: 28
Initial matrix: 499726 x 563657 with sparse part having weight 39806187.
Pruned matrix : 449061 x 451623 with weight 27825880.
Total sieving time: 57.09 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 4.42 hours.
Total square root time: 0.28 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 62.05 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Aug 12, 2007 (4th)

By Jo Yeong Uk / GGNFS gnfs

8·10¹⁷⁶+3 = 8(0)₁₇₅3_<177> = 11 · 29 · 31 · 97 · 62483 · 122288966750943559327954013_<27> · 13203393905721557635469906716094551_<35> · C106

C106 = P43 · P64

P43 = 4919037198222532817308550055704182012037503_<43>

P64 = 1680548460217191645379213872474567141004274448100352481467434493_<64>

Number: 80003_176
N=8266680389223966046190855264388717362005347788894913038658978035326508882118999267460085367871413111790979
  ( 106 digits)
Divisors found:
 r1=4919037198222532817308550055704182012037503 (pp43)
 r2=1680548460217191645379213872474567141004274448100352481467434493 (pp64)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.56 hours.
Scaled time: 22.54 units (timescale=2.135).
Factorization parameters were as follows:
name: 80003_176
n: 8266680389223966046190855264388717362005347788894913038658978035326508882118999267460085367871413111790979
skew: 8767.65
# norm 5.59e+14
c5: 116160
c4: 400128896
c3: 21447396988402
c2: 200361732810880499
c1: -1755467344504781210762
c0: 512626880120314573894360
# alpha -5.94
Y1: 2910066641
Y0: -148065849568313383617
# Murphy_E 1.51e-09
# M 3579913611478992133536848804092742505729175910292785985960854211602842315010438921637008484004440532117018
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1440001)
Primes: RFBsize:135072, AFBsize:135363, largePrimes:4572261 encountered
Relations: rels:4637401, finalFF:384253
Max relations in full relation-set: 28
Initial matrix: 270519 x 384253 with sparse part having weight 37006164.
Pruned matrix : 210066 x 211482 with weight 18180369.
Polynomial selection time: 0.48 hours.
Total sieving time: 9.69 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 10.56 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405131)
Total of 4 processors activated (19246.10 BogoMIPS).

Aug 12, 2007 (3rd)

By Robert Backstrom / GGNFS

7·10¹⁶¹+3 = 7(0)₁₆₀3_<162> = 29 · 37 · 73 · 1403225401_<10> · C148

C148 = P40 · P109

P40 = 3753845625711756879793515975255349607797_<40>

P109 = 1696569329960212414283207012646965391569808922194244639849139334297461697448507406571284397297756255793527431_<109>

Number: n
N=6368659357987869688073561004013094128236058980958992215610258085707689898194797495537752585473375498765201263898209639690325753644190663517010979507
  ( 148 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=3753845625711756879793515975255349607797 (pp40)
 r2=1696569329960212414283207012646965391569808922194244639849139334297461697448507406571284397297756255793527431 (pp109)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 52.92 hours.
Scaled time: 76.63 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_7_0_160_3
n: 6368659357987869688073561004013094128236058980958992215610258085707689898194797495537752585473375498765201263898209639690325753644190663517010979507
skew: 0.53
deg: 5
c5: 70
c0: 3
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2400001)
Primes: RFBsize:250150, AFBsize:249361, largePrimes:7501056 encountered
Relations: rels:7035914, finalFF:574163
Max relations in full relation-set: 28
Initial matrix: 499578 x 574163 with sparse part having weight 42428847.
Pruned matrix : 441215 x 443776 with weight 29106337.
Total sieving time: 46.77 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 5.57 hours.
Total square root time: 0.34 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 52.92 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(8·10¹⁶⁴-71)/9 = (8)₁₆₃1_<164> = 3⁴ · 499 · C160

C160 = P79 · P81

P79 = 6702863948665376016824925578772117152858124361875429504392949157960651371083473_<79>

P81 = 328096432855899090449878151867788591711321056497892958204836930069357451062128363_<81>

Number: n
N=2199185751475516190130604143815752217741381253590857984831116279197627078574157918030849078128822803357057049627375464234367225534745760382218483606444713844699
  ( 160 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=6702863948665376016824925578772117152858124361875429504392949157960651371083473 (pp79)
 r2=328096432855899090449878151867788591711321056497892958204836930069357451062128363 (pp81)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 92.52 hours.
Scaled time: 110.83 units (timescale=1.198).
Factorization parameters were as follows:
name: KA_8_163_1
n: 2199185751475516190130604143815752217741381253590857984831116279197627078574157918030849078128822803357057049627375464234367225534745760382218483606444713844699
type: snfs
skew: 2.45
deg: 5
c5: 4
c0: -355
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3600001)
Primes: RFBsize:250150, AFBsize:250837, largePrimes:7783343 encountered
Relations: rels:7291842, finalFF:562621
Max relations in full relation-set: 28
Initial matrix: 501051 x 562621 with sparse part having weight 46426453.
Pruned matrix : 472306 x 474875 with weight 35341023.
Total sieving time: 83.37 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 8.48 hours.
Total square root time: 0.30 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 92.52 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Aug 12, 2007 (2nd)

By Sinkiti Sibata / GGNFS

8·10¹⁴²+3 = 8(0)₁₄₁3_<143> = 7 · 11 · 2052821 · 555623953052671_<15> · 66874197333983887_<17> · C104

C104 = P43 · P61

P43 = 7352063485952674581275466674908134761977993_<43>

P61 = 1852675630827404483230700868124109595424698262269677635106219_<61>

Number: 80003_142
N=13620988856720497819323489328579752204608642469675042020812530924002228230975710728961746240569095438467
  ( 104 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=7352063485952674581275466674908134761977993 (pp43)
 r2=1852675630827404483230700868124109595424698262269677635106219 (pp61)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 10.17 hours.
Scaled time: 6.93 units (timescale=0.682).
Factorization parameters were as follows:
name: 80003_142
n: 13620988856720497819323489328579752204608642469675042020812530924002228230975710728961746240569095438467
m: 20000000000000000000000000000
c5: 25
c0: 3
skew: 0.65
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1550001)
Primes: RFBsize:100021, AFBsize:100163, largePrimes:2522518 encountered
Relations: rels:2425661, finalFF:224441
Max relations in full relation-set: 0
Initial matrix: 200248 x 224441 with sparse part having weight 19391779.
Pruned matrix : 193093 x 194158 with weight 13708815.
Total sieving time: 9.05 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.93 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 10.17 hours.
 --------- CPU info (if available) ----------

Aug 12, 2007

By Jo Yeong Uk / GMP-ECM

8·10¹⁶⁹+3 = 8(0)₁₆₈3_<170> = C170

C170 = P37 · P134

P37 = 1224246060187948513536044665977519421_<37>

P134 = 65346340577741579518249257770472291479731205704109850662463019782005485937532123816920926149530479698626097812995924318713137169466943_<134>

Aug 11, 2007 (3rd)

By Sinkiti Sibata / GGNFS gnfs

10¹⁷⁷+9 = 1(0)₁₇₆9_<178> = 33223 · 58440312251_<11> · 744650270536087_<15> · 1299108566054859101828202487_<28> · C120

C120 = P29 · P43 · P49

P29 = 47281281988259427195595389853_<29>

P43 = 6045096991231523085796053943692409216016933_<43>

P49 = 1862766037506329182860674793008889448818081551293_<49>

Number: 10009_177
N=532415668670779658238030449477892100777113679642064502418427003147194580334216529773302144542970825544807513606040387757
  ( 120 digits)
Divisors found:
 r1=47281281988259427195595389853 (pp29)
 r2=6045096991231523085796053943692409216016933 (pp43)
 r3=1862766037506329182860674793008889448818081551293 (pp49)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 103.73 hours.
Scaled time: 70.75 units (timescale=0.682).
Factorization parameters were as follows:
name: 10009_177
n: 532415668670779658238030449477892100777113679642064502418427003147194580334216529773302144542970825544807513606040387757
skew: 48264.27
# norm 2.43e+16
c5: 75600
c4: 16297075446
c3: -73949054544926
c2: -41520893798791949092
c1: 676986651332945360199391
c0: -51146483475813285206452764
# alpha -5.94
Y1: 12936640435517
Y0: -93227321831539954601855
# Murphy_E 3.10e-10
# M 480158086077406144788789117762923709702782058085914313143143829119151924171861230494781642332247911106356265369031255073
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4170001)
Primes: RFBsize:315948, AFBsize:316216, largePrimes:7549833 encountered
Relations: rels:7503324, finalFF:708238
Max relations in full relation-set: 0
Initial matrix: 632249 x 708238 with sparse part having weight 69993656.
Pruned matrix : 571237 x 574462 with weight 47768804.
Polynomial selection time: 5.21 hours.
Total sieving time: 78.11 hours.
Total relation processing time: 0.69 hours.
Matrix solve time: 19.22 hours.
Time per square root: 0.50 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 103.73 hours.
 --------- CPU info (if available) ----------

(2·10¹⁹³-11)/9 = (2)₁₉₂1_<193> = 23 · 181 · 277 · 3511 · 281650732446817_<15> · 54780711280843190885242223364871889_<35> · 35938228281219889499007772234416370507_<38> · C96

C96 = P42 · P55

P42 = 679822382825034769795684390738450884934873_<42>

P55 = 1456061780748313525137900176910207059850883947091570327_<55>

Number: 22221_193
N=989863389328781839230043303989307230434755222530043430476647889044550036356250295190656694313471
  ( 96 digits)
Divisors found:
 r1=679822382825034769795684390738450884934873 (pp42)
 r2=1456061780748313525137900176910207059850883947091570327 (pp55)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 12.06 hours.
Scaled time: 8.22 units (timescale=0.682).
Factorization parameters were as follows:
name: 22221_193
n:  989863389328781839230043303989307230434755222530043430476647889044550036356250295190656694313471
m:  9969085082195574864923
deg: 4
c4: 100219920
c3: 489291912
c2: -3426064493939695
c1: 7273856613595100453
c0: -1638550796927040570617
skew: 1635.250
type: gnfs
# adj. I(F,S) = 51.150
# E(F1,F2) = 2.262164e-05
# GGNFS version 0.77.1-20060722-pentium4 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1186765353.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1620001)
Primes: RFBsize:92938, AFBsize:92821, largePrimes:1911630 encountered
Relations: rels:1990482, finalFF:208813
Max relations in full relation-set: 0
Initial matrix: 185833 x 208813 with sparse part having weight 19174383.
Pruned matrix : 176230 x 177223 with weight 14578587.
Polynomial selection time: 0.17 hours.
Total sieving time: 10.85 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.84 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,95,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 12.06 hours.
 --------- CPU info (if available) ----------

Aug 11, 2007 (2nd)

By JMB / GMP-ECM

8·10¹⁷⁶+3 = 8(0)₁₇₅3_<177> = 11 · 29 · 31 · 97 · 62483 · 122288966750943559327954013_<27> · C141

C141 = P35 · C106

P35 = 13203393905721557635469906716094551_<35>

C106 = [8266680389223966046190855264388717362005347788894913038658978035326508882118999267460085367871413111790979_<106>]

8·10¹⁷⁵+3 = 8(0)₁₇₄3_<176> = 2311 · 8719 · 10144789 · 189170845637_<12> · C151

C151 = P35 · P116

P35 = 64291971599470835512165635997396471_<35>

P116 = 32178766751417498825847425179242872864738948414927779187900762406084025362150026649375978793241187540045915304472389_<116>

8·10¹⁸⁹+3 = 8(0)₁₈₈3_<190> = 619 · 1847 · 2087 · 17854618292333_<14> · 66686803592942902296799_<23> · C145

C145 = P33 · C112

P33 = 921080685636059212526826174467963_<33>

C112 = [3057185889473590067108879535881711047802061887351934101508239518685119755420999299188104236165875118418785864873_<112>]

Aug 11, 2007

By Robert Backstrom / GGNFS

8·10¹⁴⁵+3 = 8(0)₁₄₄3_<146> = 11766775508491_<14> · 605396612359960159_<18> · C116

C116 = P50 · P66

P50 = 51046027337556414770008979411652470215926317473591_<50>

P66 = 220004003518038430086171786263037474229055943495226606880307715457_<66>

Number: n
N=11230330377953647351813832317701470309443467192544987569991922681053152302088521038361975470850797594365793139996087
  ( 116 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=51046027337556414770008979411652470215926317473591 (pp50)
 r2=220004003518038430086171786263037474229055943495226606880307715457 (pp66)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 7.75 hours.
Scaled time: 9.76 units (timescale=1.260).
Factorization parameters were as follows:
name: KA_8_0_144_3
n: 11230330377953647351813832317701470309443467192544987569991922681053152302088521038361975470850797594365793139996087
skew: 1.00
deg: 5
c5: 8
c0: 3
m: 100000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:148933, AFBsize:149135, largePrimes:6365962 encountered
Relations: rels:5765123, finalFF:372600
Max relations in full relation-set: 28
Initial matrix: 298133 x 372600 with sparse part having weight 24992928.
Pruned matrix : 240431 x 241985 with weight 13737511.
Total sieving time: 6.21 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.30 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 7.75 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10¹⁵³+3 = 8(0)₁₅₂3_<154> = 151 · 347 · 2843 · C146

C146 = P73 · P74

P73 = 1902048496423825078608398414836733249964757502655492013897910231644363411_<73>

P74 = 28234826233775491249880369404044758618051858710202572340818371819411450863_<74>

Number: n
N=53704008784740644981520484142176234524761914856979746560176003073910054820985037452269471329883311728322482583806733611354063944463717843541573693
  ( 146 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=1902048496423825078608398414836733249964757502655492013897910231644363411 (pp73)
 r2=28234826233775491249880369404044758618051858710202572340818371819411450863 (pp74)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.88 hours.
Scaled time: 32.17 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_8_0_152_3
n: 53704008784740644981520484142176234524761914856979746560176003073910054820985037452269471329883311728322482583806733611354063944463717843541573693
type: snfs
skew: 1.00
deg: 5
c5: 250
c0: 3
m: 2000000000000000000000000000000
rlim: 1800000
alim: 1800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1200000)
Primes: RFBsize:135072, AFBsize:134848, largePrimes:5889592 encountered
Relations: rels:5236925, finalFF:309112
Max relations in full relation-set: 28
Initial matrix: 269986 x 309112 with sparse part having weight 23758236.
Pruned matrix : 245541 x 246954 with weight 16261877.
Total sieving time: 24.71 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.63 hours.
Total square root time: 0.34 hours, sqrts: 5.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.3,2.3,100000
total time: 26.88 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Aug 10, 2007 (2nd)

By Robert Backstrom / GGNFS

8·10¹³⁸+3 = 8(0)₁₃₇3_<139> = 11 · 73 · 114702851 · C128

C128 = P37 · P45 · P48

P37 = 1670593388520748238821421178145481837_<37>

P45 = 104636458414847985111598726280566932595983083_<45>

P48 = 496874190989597803112505558533083407730421846981_<48>

Number: n
N=86856080845160518253064258730936858983574839513012302022899381995276333715215501484147076660404979494712817786900486579971431051
  ( 128 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=1670593388520748238821421178145481837 (pp37)
 r2=104636458414847985111598726280566932595983083 (pp45)
 r3=496874190989597803112505558533083407730421846981 (pp48)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 5.54 hours.
Scaled time: 7.56 units (timescale=1.364).
Factorization parameters were as follows:
name: KA_8_0_137_3
n: 86856080845160518253064258730936858983574839513012302022899381995276333715215501484147076660404979494712817786900486579971431051
skew: 1.00
deg: 5
c5: 250
c0: 3
m: 2000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 550001)
Primes: RFBsize:114155, AFBsize:113962, largePrimes:5547105 encountered
Relations: rels:4879377, finalFF:259041
Max relations in full relation-set: 28
Initial matrix: 228183 x 259041 with sparse part having weight 16762861.
Pruned matrix : 205241 x 206445 with weight 11006091.
Total sieving time: 4.58 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.70 hours.
Total square root time: 0.11 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,75000
total time: 5.54 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10¹⁴⁴+3 = 8(0)₁₄₃3_<145> = 11 · 683 · C142

C142 = P51 · P91

P51 = 393806677683834962330167370796793978219439105832001_<51>

P91 = 2703918032157216794192284740946405968077357310935054868472060871084932805552853385839924731_<91>

Number: n
N=1064820976973246372953547184879542126979901504059629974710501796885398642353254359110874484227339278583788100625582323971782244110208971116731
  ( 142 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=393806677683834962330167370796793978219439105832001 (pp51)
 r2=2703918032157216794192284740946405968077357310935054868472060871084932805552853385839924731 (pp91)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.79 hours.
Scaled time: 8.99 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_8_0_143_3
n: 1064820976973246372953547184879542126979901504059629974710501796885398642353254359110874484227339278583788100625582323971782244110208971116731
skew: 1.00
deg: 5
c5: 4
c0: 15
m: 100000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 850001)
Primes: RFBsize:114155, AFBsize:113727, largePrimes:6267824 encountered
Relations: rels:5579150, finalFF:297337
Max relations in full relation-set: 48
Initial matrix: 227946 x 297337 with sparse part having weight 29469240.
Pruned matrix : 198102 x 199305 with weight 14244835.
Total sieving time: 5.61 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.99 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000
total time: 6.79 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10¹⁵⁴+3 = 8(0)₁₅₃3_<155> = 7² · 11 · 73 · C151

C151 = P70 · P81

P70 = 6763250917489964555182738767583283902011275699423252245547421266789261_<70>

P81 = 300623454884502196692218573721100636698457518684754797248879483662802680386190709_<81>

Number: n
N=2033191857066612448217144890334714209469591074287747477571352326733931430604620428495183876788573461763285638041019645716318906142780898162502859176049
  ( 151 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=6763250917489964555182738767583283902011275699423252245547421266789261 (pp70)
 r2=300623454884502196692218573721100636698457518684754797248879483662802680386190709 (pp81)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 17.23 hours.
Scaled time: 24.95 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_8_0_153_3
n: 2033191857066612448217144890334714209469591074287747477571352326733931430604620428495183876788573461763285638041019645716318906142780898162502859176049
skew: 1.00
deg: 5
c5: 4
c0: 15
m: 10000000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 850001)
Primes: RFBsize:148933, AFBsize:148725, largePrimes:6495234 encountered
Relations: rels:5901096, finalFF:356866
Max relations in full relation-set: 28
Initial matrix: 297722 x 356866 with sparse part having weight 28838481.
Pruned matrix : 256532 x 258084 with weight 18263570.
Total sieving time: 15.26 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.67 hours.
Total square root time: 0.14 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 17.23 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(10¹⁶⁵+11)/3 = (3)₁₆₄7_<165> = 17 · 5623 · 36251 · 40841 · C151

C151 = P39 · P112

P39 = 251375332502629231539468126698454636637_<39>

P112 = 9369636094184618241793486374540111317162701410154625358284353734039880944057232414047815901279320321000606011721_<112>

Number: n
N=2355295388604294669648572183314730221423189911340492129466961410071358157729919347954433141504960864116536706486551542372736924805270377019388818022277
  ( 151 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=251375332502629231539468126698454636637 (pp39)
 r2=9369636094184618241793486374540111317162701410154625358284353734039880944057232414047815901279320321000606011721 (pp112)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 48.70 hours.
Scaled time: 66.62 units (timescale=1.368).
Factorization parameters were as follows:
name: KA_3_164_7
n: 2355295388604294669648572183314730221423189911340492129466961410071358157729919347954433141504960864116536706486551542372736924805270377019388818022277
skew: 1.62
deg: 5
c5: 1
c0: 11
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2000001)
Primes: RFBsize:250150, AFBsize:249887, largePrimes:7439713 encountered
Relations: rels:7043065, finalFF:634459
Max relations in full relation-set: 28
Initial matrix: 500101 x 634459 with sparse part having weight 42656542.
Pruned matrix : 388359 x 390923 with weight 24700758.
Total sieving time: 45.21 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 3.12 hours.
Total square root time: 0.11 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 48.70 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Aug 10, 2007

By JMB / GMP-ECM

8·10¹⁶⁵+3 = 8(0)₁₆₄3_<166> = 17 · 83 · 2221 · 12653 · C156

C156 = P32 · C125

P32 = 19558081525904346337653953996359_<32>

C125 = [10315603825280902403145997952176939809173663207855210896021945321896591973517956833167339304970176688502856732303629068284319_<125>]

8·10¹⁹⁷+3 = 8(0)₁₉₆3_<198> = 17 · 19 · 49701979 · 780808607 · C179

C179 = P29 · C151

P29 = 26076920319273076996675767301_<29>

C151 = [2447444719548378339619829614249789627085695960053062447396841606685367979050190055438702256834046939845645421862753151405036735916578790278144353058537_<151>]

8·10¹⁷⁷+3 = 8(0)₁₇₆3_<178> = 385193 · C173

C173 = P34 · P139

P34 = 2734184657326888957539301452070127_<34>

P139 = 7595979059565388610562921211099574234745355573365762780772087213624892584821367744840306376847974198287155385422756473803526652906088908773_<139>

Aug 9, 2007 (4th)

By JMB / GMP-ECM B1=3000000

(2·10¹⁹³-11)/9 = (2)₁₉₂1_<193> = 23 · 181 · 277 · 3511 · 281650732446817_<15> · 54780711280843190885242223364871889_<35> · C134

C134 = P38 · C96

P38 = 35938228281219889499007772234416370507_<38>

C96 = [989863389328781839230043303989307230434755222530043430476647889044550036356250295190656694313471_<96>]

Aug 9, 2007 (3rd)

By Robert Backstrom / Msieve, GGNFS

8·10¹¹⁶+3 = 8(0)₁₁₅3_<117> = 11 · 31 · 501077 · 30244611063283188190841459_<26> · C84

C84 = P35 · P49

P35 = 47772235073471907793622686848045341_<35>

P49 = 3240466788618869376438883648133185467425146712141_<49>

Thu Aug 09 14:29:32 2007  Msieve v. 1.25
Thu Aug 09 14:29:32 2007  random seeds: 96c33e48 849923a9
Thu Aug 09 14:29:32 2007  factoring 154804341173679230387244001472705605593917034967797099265321043659212166198643185081 (84 digits)
Thu Aug 09 14:29:32 2007  commencing quadratic sieve (83-digit input)
Thu Aug 09 14:29:32 2007  using multiplier of 1
Thu Aug 09 14:29:32 2007  using 64kb Opteron sieve core
Thu Aug 09 14:29:32 2007  sieve interval: 6 blocks of size 65536
Thu Aug 09 14:29:32 2007  processing polynomials in batches of 17
Thu Aug 09 14:29:32 2007  using a sieve bound of 1392701 (52970 primes)
Thu Aug 09 14:29:32 2007  using large prime bound of 121164987 (26 bits)
Thu Aug 09 14:29:32 2007  using trial factoring cutoff of 27 bits
Thu Aug 09 14:29:32 2007  polynomial 'A' values have 11 factors
Thu Aug 09 14:55:43 2007  53067 relations (26868 full + 26199 combined from 280831 partial), need 53066
Thu Aug 09 14:55:44 2007  begin with 307699 relations
Thu Aug 09 14:55:44 2007  reduce to 75934 relations in 2 passes
Thu Aug 09 14:55:44 2007  attempting to read 75934 relations
Thu Aug 09 14:55:45 2007  recovered 75934 relations
Thu Aug 09 14:55:45 2007  recovered 69763 polynomials
Thu Aug 09 14:55:45 2007  attempting to build 53067 cycles
Thu Aug 09 14:55:45 2007  found 53067 cycles in 1 passes
Thu Aug 09 14:55:45 2007  distribution of cycle lengths:
Thu Aug 09 14:55:45 2007     length 1 : 26868
Thu Aug 09 14:55:45 2007     length 2 : 26199
Thu Aug 09 14:55:45 2007  largest cycle: 2 relations
Thu Aug 09 14:55:45 2007  matrix is 52970 x 53067 with weight 1684778 (avg 31.75/col)
Thu Aug 09 14:55:45 2007  filtering completed in 4 passes
Thu Aug 09 14:55:45 2007  matrix is 46050 x 46114 with weight 1439023 (avg 31.21/col)
Thu Aug 09 14:55:46 2007  saving the first 48 matrix rows for later
Thu Aug 09 14:55:46 2007  matrix is 46002 x 46114 with weight 1048370 (avg 22.73/col)
Thu Aug 09 14:55:46 2007  matrix includes 64 packed rows
Thu Aug 09 14:55:46 2007  commencing Lanczos iteration
Thu Aug 09 14:56:38 2007  lanczos halted after 729 iterations
Thu Aug 09 14:56:38 2007  recovered 9 nontrivial dependencies
Thu Aug 09 14:56:38 2007  prp35 factor: 47772235073471907793622686848045341
Thu Aug 09 14:56:38 2007  prp49 factor: 3240466788618869376438883648133185467425146712141
Thu Aug 09 14:56:38 2007  elapsed time 00:27:06

8·10¹⁰²+3 = 8(0)₁₀₁3_<103> = 11 · 59 · 2909 · 250321394839_<12> · C86

C86 = P32 · P54

P32 = 73893077891192132187902179374341_<32>

P54 = 229086681980295270219691452305688749689507823847518717_<54>

Thu Aug 09 14:31:54 2007  Msieve v. 1.25
Thu Aug 09 14:31:54 2007  random seeds: e58a55a8 3980cc5c
Thu Aug 09 14:31:54 2007  factoring 16927920035404719454950678067803074038183144629096960489580783099151622954488347040497 (86 digits)
Thu Aug 09 14:31:55 2007  commencing quadratic sieve (85-digit input)
Thu Aug 09 14:31:55 2007  using multiplier of 1
Thu Aug 09 14:31:55 2007  using 64kb Opteron sieve core
Thu Aug 09 14:31:55 2007  sieve interval: 7 blocks of size 65536
Thu Aug 09 14:31:55 2007  processing polynomials in batches of 15
Thu Aug 09 14:31:55 2007  using a sieve bound of 1449953 (55333 primes)
Thu Aug 09 14:31:55 2007  using large prime bound of 115996240 (26 bits)
Thu Aug 09 14:31:55 2007  using double large prime bound of 328094552866320 (41-49 bits)
Thu Aug 09 14:31:55 2007  using trial factoring cutoff of 49 bits
Thu Aug 09 14:31:55 2007  polynomial 'A' values have 11 factors
Thu Aug 09 15:12:48 2007  55692 relations (15689 full + 40003 combined from 580417 partial), need 55429
Thu Aug 09 15:12:49 2007  begin with 596106 relations
Thu Aug 09 15:12:50 2007  reduce to 132442 relations in 9 passes
Thu Aug 09 15:12:50 2007  attempting to read 132442 relations
Thu Aug 09 15:12:51 2007  recovered 132442 relations
Thu Aug 09 15:12:51 2007  recovered 111632 polynomials
Thu Aug 09 15:12:51 2007  attempting to build 55692 cycles
Thu Aug 09 15:12:52 2007  found 55691 cycles in 4 passes
Thu Aug 09 15:12:52 2007  distribution of cycle lengths:
Thu Aug 09 15:12:52 2007     length 1 : 15689
Thu Aug 09 15:12:52 2007     length 2 : 11064
Thu Aug 09 15:12:52 2007     length 3 : 9749
Thu Aug 09 15:12:52 2007     length 4 : 7447
Thu Aug 09 15:12:52 2007     length 5 : 4954
Thu Aug 09 15:12:52 2007     length 6 : 3059
Thu Aug 09 15:12:52 2007     length 7 : 1772
Thu Aug 09 15:12:52 2007     length 9+: 1957
Thu Aug 09 15:12:52 2007  largest cycle: 16 relations
Thu Aug 09 15:12:52 2007  matrix is 55333 x 55691 with weight 2873455 (avg 51.60/col)
Thu Aug 09 15:12:52 2007  filtering completed in 3 passes
Thu Aug 09 15:12:52 2007  matrix is 50648 x 50712 with weight 2633663 (avg 51.93/col)
Thu Aug 09 15:12:53 2007  saving the first 48 matrix rows for later
Thu Aug 09 15:12:53 2007  matrix is 50600 x 50712 with weight 1927165 (avg 38.00/col)
Thu Aug 09 15:12:53 2007  matrix includes 64 packed rows
Thu Aug 09 15:12:53 2007  using block size 20284 for processor cache size 512 kB
Thu Aug 09 15:12:53 2007  commencing Lanczos iteration
Thu Aug 09 15:13:14 2007  lanczos halted after 801 iterations
Thu Aug 09 15:13:14 2007  recovered 16 nontrivial dependencies
Thu Aug 09 15:13:14 2007  prp32 factor: 73893077891192132187902179374341
Thu Aug 09 15:13:14 2007  prp54 factor: 229086681980295270219691452305688749689507823847518717
Thu Aug 09 15:13:14 2007  elapsed time 00:41:20

8·10¹⁰⁷+3 = 8(0)₁₀₆3_<108> = 19² · 53 · C104

C104 = P52(4311...) · P52(9698...)

P52(4311...) = 4311041529493168981918983158515670589329095421550917_<52>

P52(9698...) = 9698949742404051679952742591797529833940595342191923_<52>

Number: n
N=41812575131970940260283280196519103120263419223331416923639784665238070349657659541106987926618930643391
  ( 104 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=4311041529493168981918983158515670589329095421550917 (pp52)
 r2=9698949742404051679952742591797529833940595342191923 (pp52)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.82 hours.
Scaled time: 0.98 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_8_0_106_3
n: 41812575131970940260283280196519103120263419223331416923639784665238070349657659541106987926618930643391
type: snfs
skew: 2.45
deg: 5
c5: 25
c0: 3
m: 2000000000000000000000
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 150001)
Primes: RFBsize:41538, AFBsize:41527, largePrimes:3147623 encountered
Relations: rels:2766724, finalFF:215667
Max relations in full relation-set: 28
Initial matrix: 83129 x 215667 with sparse part having weight 9858859.
Pruned matrix : 43285 x 43764 with weight 1396638.
Total sieving time: 0.71 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.01 hours.
Total square root time: 0.03 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,107,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.4,2.4,50000
total time: 0.82 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

8·10¹⁰⁸+3 = 8(0)₁₀₇3_<109> = 11 · 5527 · C105

C105 = P31 · P74

P31 = 9958256083822556593072164658877_<31>

P74 = 13213703178894954610665804924839486965167161792188153823634168464500913387_<74>

Number: n
N=131585440071056137638370314324719969735348783657088343174827705314406960869779758869681069789627777686399
  ( 105 digits)
SNFS difficulty: 108 digits.
Divisors found:
 r1=9958256083822556593072164658877 (pp31)
 r2=13213703178894954610665804924839486965167161792188153823634168464500913387 (pp74)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.96 hours.
Scaled time: 1.27 units (timescale=1.318).
Factorization parameters were as follows:
name: KA_8_0_107_3
n: 131585440071056137638370314324719969735348783657088343174827705314406960869779758869681069789627777686399
skew: 1.91
deg: 5
c5: 250
c0: 3
m: 2000000000000000000000
type: snfs
rlim: 600000
alim: 600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 150001)
Primes: RFBsize:49098, AFBsize:48961, largePrimes:3846138 encountered
Relations: rels:3291694, finalFF:187322
Max relations in full relation-set: 48
Initial matrix: 98125 x 187322 with sparse part having weight 11179634.
Pruned matrix : 63307 x 63861 with weight 2245348.
Total sieving time: 0.84 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.02 hours.
Total square root time: 0.03 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,108,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000
total time: 0.96 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10¹¹⁷+3 = 8(0)₁₁₆3_<118> = 17 · 23 · 95569 · 3626149 · C104

C104 = P42 · P62

P42 = 743563094142647141671434594596447952314537_<42>

P62 = 79402233062151798302517520827673963545042250342272076178284489_<62>

Number: n
N=59040570097529187032128911277836039384013278371200389290158971364162462588485899647445468362305596316593
  ( 104 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=743563094142647141671434594596447952314537 (pp42)
 r2=79402233062151798302517520827673963545042250342272076178284489 (pp62)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.14 hours.
Scaled time: 1.64 units (timescale=1.443).
Factorization parameters were as follows:
name: KA_8_0_116_3
n: 59040570097529187032128911277836039384013278371200389290158971364162462588485899647445468362305596316593
skew: 1.00
deg: 5
c5: 25
c0: 3
m: 200000000000000000000000
type: snfs
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:63951, AFBsize:63918, largePrimes:4177926 encountered
Relations: rels:3612878, finalFF:208283
Max relations in full relation-set: 28
Initial matrix: 127933 x 208283 with sparse part having weight 10962041.
Pruned matrix : 86287 x 86990 with weight 3088440.
Total sieving time: 1.00 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.05 hours.
Total square root time: 0.02 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000
total time: 1.14 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

8·10¹²⁶+3 = 8(0)₁₂₅3_<127> = 11 · 103 · 227 · 60103 · C117

C117 = P43 · P75

P43 = 2949429481414692226044768697960391260971797_<43>

P75 = 175468859339115509595120669476348065354330998690902949927637469395852909063_<75>

Number: n
N=517533026804995032345061488216330006916176164718700807307201581209237696213471414277684828267532924867161658848696211
  ( 117 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=2949429481414692226044768697960391260971797 (pp43)
 r2=175468859339115509595120669476348065354330998690902949927637469395852909063 (pp75)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 2.10 hours.
Scaled time: 2.86 units (timescale=1.363).
Factorization parameters were as follows:
name: KA_8_0_125_3
n: 517533026804995032345061488216330006916176164718700807307201581209237696213471414277684828267532924867161658848696211
skew: 1.00
deg: 5
c5: 80
c0: 3
m: 10000000000000000000000000
type: snfs
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 250001)
Primes: RFBsize:63951, AFBsize:63988, largePrimes:4577180 encountered
Relations: rels:3968605, finalFF:202139
Max relations in full relation-set: 28
Initial matrix: 128005 x 202139 with sparse part having weight 13983078.
Pruned matrix : 98139 x 98843 with weight 4654958.
Total sieving time: 1.87 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.11 hours.
Total square root time: 0.03 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000
total time: 2.10 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10¹³⁰+3 = 8(0)₁₂₉3_<131> = 7 · 11 · 73 · 1301 · 1879 · 3920377 · 125920165279_<12> · C104

C104 = P47 · P57

P47 = 15660751854468820254646065544043536489389591847_<47>

P57 = 753072171293408570603918263199513415256851689104201069517_<57>

Number: n
N=11793676403132109337177444136713268893806641945749404632686412140850069050669393720927990575945503427899
  ( 104 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=15660751854468820254646065544043536489389591847 (pp47)
 r2=753072171293408570603918263199513415256851689104201069517 (pp57)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.27 hours.
Scaled time: 2.96 units (timescale=1.305).
Factorization parameters were as follows:
name: KA_8_0_129_3
n: 11793676403132109337177444136713268893806641945749404632686412140850069050669393720927990575945503427899
skew: 1.00
deg: 5
c5: 8
c0: 3
m: 100000000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 300001)
Primes: RFBsize:78498, AFBsize:78246, largePrimes:4755487 encountered
Relations: rels:4123226, finalFF:215781
Max relations in full relation-set: 48
Initial matrix: 156809 x 215781 with sparse part having weight 16140594.
Pruned matrix : 127889 x 128737 with weight 6317106.
Total sieving time: 1.93 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.20 hours.
Total square root time: 0.04 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000
total time: 2.27 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10¹²⁹+3 = 8(0)₁₂₈3_<130> = 4373 · 82883 · C122

C122 = P46 · P76

P46 = 9383621683393851037733688168129743757022677767_<46>

P76 = 2352201687843988988161223366148433683159763965903221828415227547320810905051_<76>

Number: n
N=22072170761768469666239173783026516686523849108802583384253601362287757765121417259381934136261701937246009840562805701117
  ( 122 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=9383621683393851037733688168129743757022677767 (pp46)
 r2=2352201687843988988161223366148433683159763965903221828415227547320810905051 (pp76)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.89 hours.
Scaled time: 3.46 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_8_0_128_3
n: 22072170761768469666239173783026516686523849108802583384253601362287757765121417259381934136261701937246009840562805701117
type: snfs
skew: 1.00
deg: 5
c5: 4
c0: 15
m: 100000000000000000000000000
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 450001)
Primes: RFBsize:78498, AFBsize:78411, largePrimes:3620998 encountered
Relations: rels:2967951, finalFF:178355
Max relations in full relation-set: 28
Initial matrix: 156973 x 178355 with sparse part having weight 5919463.
Pruned matrix : 130863 x 131711 with weight 3517685.
Total sieving time: 2.62 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.16 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.2,2.2,50000
total time: 2.89 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

8·10¹³¹+3 = 8(0)₁₃₀3_<132> = 31 · 18556133 · C124

C124 = P30 · P94

P30 = 140515311157889484872449865329_<30>

P94 = 9897309858587474462533808559524778559507284816320764852168510088136599686173598612238548962409_<94>

Number: n
N=1390723574405466150002891922752752766517296638572619177330924811028871850790561074961733849709228297345315740432104733417561
  ( 124 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=140515311157889484872449865329 (pp30)
 r2=9897309858587474462533808559524778559507284816320764852168510088136599686173598612238548962409 (pp94)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.46 hours.
Scaled time: 3.56 units (timescale=1.446).
Factorization parameters were as follows:
name: KA_8_0_130_3
n: 1390723574405466150002891922752752766517296638572619177330924811028871850790561074961733849709228297345315740432104733417561
skew: 1.00
deg: 5
c5: 80
c0: 3
m: 100000000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 350001)
Primes: RFBsize:78498, AFBsize:78611, largePrimes:4642958 encountered
Relations: rels:3975934, finalFF:178377
Max relations in full relation-set: 28
Initial matrix: 157175 x 178377 with sparse part having weight 11167450.
Pruned matrix : 144022 x 144871 with weight 7345153.
Total sieving time: 2.06 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.26 hours.
Total square root time: 0.05 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000
total time: 2.46 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

8·10¹³²+3 = 8(0)₁₃₁3_<133> = 11 · 10091 · 41507 · 72923 · C119

C119 = P59 · P60

P59 = 59137933926855043059088194258782854822196623669244767645811_<59>

P60 = 402634584408763303069783264206996096355933083613814946383593_<60>

Number: n
N=23810977449432183899061928385609941180131057745684131742392932620719752663657136531720801972378829641765634246765578923
  ( 119 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=59137933926855043059088194258782854822196623669244767645811 (pp59)
 r2=402634584408763303069783264206996096355933083613814946383593 (pp60)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 2.77 hours.
Scaled time: 3.78 units (timescale=1.364).
Factorization parameters were as follows:
name: KA_8_0_131_3
n: 23810977449432183899061928385609941180131057745684131742392932620719752663657136531720801972378829641765634246765578923
skew: 1.00
deg: 5
c5: 25
c0: 3
m: 200000000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 350001)
Primes: RFBsize:78498, AFBsize:78411, largePrimes:4990879 encountered
Relations: rels:4353452, finalFF:209067
Max relations in full relation-set: 28
Initial matrix: 156973 x 209067 with sparse part having weight 14999686.
Pruned matrix : 132523 x 133371 with weight 7082557.
Total sieving time: 2.37 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.26 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000
total time: 2.77 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10¹³⁴+3 = 8(0)₁₃₃3_<135> = 11 · 149 · 43405903 · 643534253 · C116

C116 = P53 · P63

P53 = 99025999314875960050767509377639719951680928982163689_<53>

P63 = 176457993407320655445898143590093815879839497274040644855506527_<63>

Number: n
N=17473929134257721901626949367676531901183471917932969856802783667946806325413661744285936035329994212640218521898103
  ( 116 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=99025999314875960050767509377639719951680928982163689 (pp53)
 r2=176457993407320655445898143590093815879839497274040644855506527 (pp63)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.16 hours.
Scaled time: 4.11 units (timescale=1.301).
Factorization parameters were as follows:
name: KA_8_0_133_3
n: 17473929134257721901626949367676531901183471917932969856802783667946806325413661744285936035329994212640218521898103
skew: 1.00
deg: 5
c5: 4
c0: 15
m: 1000000000000000000000000000
type: snfs
rlim: 1200000
alim: 1200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 400001)
Primes: RFBsize:92938, AFBsize:92529, largePrimes:4943597 encountered
Relations: rels:4272145, finalFF:210944
Max relations in full relation-set: 48
Initial matrix: 185531 x 210944 with sparse part having weight 15009718.
Pruned matrix : 169069 x 170060 with weight 9148254.
Total sieving time: 2.53 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.44 hours.
Total square root time: 0.09 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,48,48,2.5,2.5,75000
total time: 3.16 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10¹³⁶+3 = 8(0)₁₃₅3_<137> = 7 · 11 · 525529 · 3285647117_<10> · C120

C120 = P54 · P67

P54 = 143530513309195232999340064204983398299225538897530547_<54>

P67 = 4192155846886791687644896239201840126733252957278980362790474381809_<67>

Number: n
N=601702280575805267699515045826589007810490254765282153660216860433071030113676661720770461574543961771608356536518619523
  ( 120 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=143530513309195232999340064204983398299225538897530547 (pp54)
 r2=4192155846886791687644896239201840126733252957278980362790474381809 (pp67)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.95 hours.
Scaled time: 4.27 units (timescale=1.446).
Factorization parameters were as follows:
name: KA_8_0_135_3
n: 601702280575805267699515045826589007810490254765282153660216860433071030113676661720770461574543961771608356536518619523
skew: 1.00
deg: 5
c5: 5
c0: 6
m: 2000000000000000000000000000
type: snfs
rlim: 1200000
alim: 1200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 450001)
Primes: RFBsize:92938, AFBsize:93119, largePrimes:5260301 encountered
Relations: rels:4633571, finalFF:246993
Max relations in full relation-set: 28
Initial matrix: 186122 x 246993 with sparse part having weight 17116585.
Pruned matrix : 152676 x 153670 with weight 8112545.
Total sieving time: 2.48 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.34 hours.
Total square root time: 0.03 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,48,48,2.5,2.5,75000
total time: 2.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

8·10¹³⁵+3 = 8(0)₁₃₄3_<136> = 47 · 107 · 167 · 445141 · 64394703446581_<14> · C111

C111 = P42 · P69

P42 = 671518907669361327306106053768429944141723_<42>

P69 = 494864033010832382214144161118931762517426636975925163439107088158187_<69>

Number: n
N=332310554892288926436831772045323636037576637237580462259403763467341105224779770796417611307390273406570736201
  ( 111 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=671518907669361327306106053768429944141723 (pp42)
 r2=494864033010832382214144161118931762517426636975925163439107088158187 (pp69)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.65 hours.
Scaled time: 2.39 units (timescale=0.654).
Factorization parameters were as follows:
name: KA_8_0_134_3
n: 332310554892288926436831772045323636037576637237580462259403763467341105224779770796417611307390273406570736201
type: snfs
skew: 1.00
deg: 5
c5: 8
c0: 3
m: 1000000000000000000000000000
rlim: 1200000
alim: 1200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 550001)
Primes: RFBsize:92938, AFBsize:92739, largePrimes:4242280 encountered
Relations: rels:3637701, finalFF:220619
Max relations in full relation-set: 28
Initial matrix: 185742 x 220619 with sparse part having weight 11033317.
Pruned matrix : 156303 x 157295 with weight 6162049.
Total sieving time: 3.16 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.34 hours.
Total square root time: 0.03 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,48,48,2.3,2.3,75000
total time: 3.65 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Aug 9, 2007 (2nd)

The factor table of 800...003 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Aug 9, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(8·10¹⁶⁴-17)/9 = (8)₁₆₃7_<164> = 3 · 151 · 48781123 · C154

C154 = P69 · P86

P69 = 122357220642452584209664973630349681033155453532931520441153082441941_<69>

P86 = 32875160220972597758764681161227086029639996457194993224995199129738972707239023844853_<86>

Number: n
N=4022513232813524398211303045208836597289264340939797746512434565865799965289774544812734306459747688749162392566060216989979878271103883598312223964179673
  ( 154 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=122357220642452584209664973630349681033155453532931520441153082441941 (pp69)
 r2=32875160220972597758764681161227086029639996457194993224995199129738972707239023844853 (pp86)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 65.65 hours.
Scaled time: 86.53 units (timescale=1.318).
Factorization parameters were as follows:
name: KA_8_163_7
n: 4022513232813524398211303045208836597289264340939797746512434565865799965289774544812734306459747688749162392566060216989979878271103883598312223964179673
skew: 1.84
deg: 5
c5: 4
c0: -85
m: 1000000000000000000000000000000000
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2700000)
Primes: RFBsize:283146, AFBsize:283447, largePrimes:7572788 encountered
Relations: rels:7122775, finalFF:638638
Max relations in full relation-set: 28
Initial matrix: 566657 x 638638 with sparse part having weight 44039280.
Pruned matrix : 507869 x 510766 with weight 29149793.
Total sieving time: 58.05 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 7.07 hours.
Total square root time: 0.27 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000
total time: 65.65 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Aug 8, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon

(7·10¹⁶⁴+11)/9 = (7)₁₆₃9_<164> = 511123815986207_<15> · C150

C150 = P42 · P108

P42 = 395215337436906000005934571501636192952207_<42>

P108 = 385030933976339826493877379968305215655393397579526887571960054940570793779333975437642428406825564469725571_<108>

Number: n
N=152170130495106219796450999003009138605715611628956873355664530278848244167737884492518709827802444530255770541483818513470450546436825988489608785197
  ( 150 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=395215337436906000005934571501636192952207 (pp42)
 r2=385030933976339826493877379968305215655393397579526887571960054940570793779333975437642428406825564469725571 (pp108)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 86.65 hours.
Scaled time: 117.85 units (timescale=1.360).
Factorization parameters were as follows:
name: KA_7_163_9
n: 152170130495106219796450999003009138605715611628956873355664530278848244167737884492518709827802444530255770541483818513470450546436825988489608785197
skew: 1.73
deg: 5
c5: 7
c0: 110
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3800001)
Primes: RFBsize:250150, AFBsize:250327, largePrimes:7881745 encountered
Relations: rels:7397798, finalFF:565193
Max relations in full relation-set: 28
Initial matrix: 500542 x 565193 with sparse part having weight 50214723.
Pruned matrix : 471840 x 474406 with weight 38505738.
Total sieving time: 79.17 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 6.00 hours.
Total square root time: 1.18 hours, sqrts: 7.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 86.65 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁶⁴-3 = 6(9)₁₆₃7_<165> = 47 · 193 · 1621 · 2267 · C155

C155 = P42 · P113

P42 = 610889581248729734327409484516692590832461_<42>

P113 = 34375230566759292489277721179939552331809978623383280776559465068189748526644096155791768378027428880241905345241_<113>

Number: n
N=20999470206256118682944798667139458618641061580335085268363922120761568297261969524524443030033995145039545360363662467592334735070279038086473229794668101
  ( 155 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=610889581248729734327409484516692590832461 (pp42)
 r2=34375230566759292489277721179939552331809978623383280776559465068189748526644096155791768378027428880241905345241 (pp113)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 71.77 hours.
Scaled time: 103.50 units (timescale=1.442).
Factorization parameters were as follows:
name: KA_6_9_163_7
n: 20999470206256118682944798667139458618641061580335085268363922120761568297261969524524443030033995145039545360363662467592334735070279038086473229794668101
skew: 1.34
deg: 5
c5: 7
c0: -30
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3400001)
Primes: RFBsize:250150, AFBsize:249671, largePrimes:7747415 encountered
Relations: rels:7257732, finalFF:563161
Max relations in full relation-set: 28
Initial matrix: 499886 x 563161 with sparse part having weight 46183744.
Pruned matrix : 466798 x 469361 with weight 34859573.
Total sieving time: 64.19 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 7.23 hours.
Total square root time: 0.09 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 71.77 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Aug 7, 2007

By JMB / GMP-ECM B1=3000000

(2·10¹⁹³-11)/9 = (2)₁₉₂1_<193> = 23 · 181 · 277 · 3511 · 281650732446817_<15> · C169

C169 = P35 · C134

P35 = 54780711280843190885242223364871889_<35>

C134 = [35573936452919801666661978767493840314935627092380374712790703051952660053016745490719105773995659310348247513610333155438457937199797_<134>]

Aug 6, 2007 (2nd)

By JMB / GMP-ECM B1=1000000

(2·10²⁰⁰-11)/9 = (2)₁₉₉1_<200> = 3 · 7 · 14001880603763633983098127_<26> · C173

C173 = P36 · C138

P36 = 249790641645802510176227421442280099_<36>

C138 = [302555921974370475370998169294219199252084902441380482697802372630541007145563557322381282854361483076742218761588448860732153113329663037_<138>]

Aug 6, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(8·10¹⁶³-53)/9 = (8)₁₆₂3_<163> = 3 · 2087570567_<10> · C154

C154 = P40 · P114

P40 = 1901722501401858363651894167934894678547_<40>

P114 = 746342052674360387307334925536045196341796871193013347158150552642871903024652042586940759722677149467693386559389_<114>

Number: n
N=1419335475313282170337747898973401727867416787047928791267999786357863016835187523010791214591292406817576559060081327043811957980610368972960789479727783
  ( 154 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=1901722501401858363651894167934894678547 (pp40)
 r2=746342052674360387307334925536045196341796871193013347158150552642871903024652042586940759722677149467693386559389 (pp114)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 67.10 hours.
Scaled time: 88.83 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_8_162_3
n: 1419335475313282170337747898973401727867416787047928791267999786357863016835187523010791214591292406817576559060081327043811957980610368972960789479727783
skew: 0.73
deg: 5
c5: 250
c0: -53
m: 200000000000000000000000000000000
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2700001)
Primes: RFBsize:283146, AFBsize:283257, largePrimes:7662329 encountered
Relations: rels:7226501, finalFF:653830
Max relations in full relation-set: 48
Initial matrix: 566469 x 653828 with sparse part having weight 45553298.
Pruned matrix : 494193 x 497089 with weight 29199532.
Total sieving time: 59.93 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 6.79 hours.
Total square root time: 0.10 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000
total time: 67.10 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁴³+3 = 7(0)₁₄₂3_<144> = 37 · 107 · 181 · 42929 · 55778925763273769417_<20> · C114

C114 = P50 · P64

P50 = 99615388886871440186141889727022388487187792018971_<50>

P64 = 4095308385474807274359199791739966295408609792078800566560390219_<64>

Number: n
N=407955737430738536692939991644316206131841159102557048096582503950767590461218943000918208625655443001223610844649
  ( 114 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=99615388886871440186141889727022388487187792018971 (pp50)
 r2=4095308385474807274359199791739966295408609792078800566560390219 (pp64)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.69 hours.
Scaled time: 11.45 units (timescale=1.318).
Factorization parameters were as follows:
name: KA_7_0_142_3
n: 407955737430738536692939991644316206131841159102557048096582503950767590461218943000918208625655443001223610844649
skew: 0.21
deg: 5
c5: 7000
c0: 3
m: 10000000000000000000000000000
type: snfs
rlim: 1300000
alim: 1300000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:100021, AFBsize:100188, largePrimes:6536058 encountered
Relations: rels:5813023, finalFF:258829
Max relations in full relation-set: 48
Initial matrix: 200276 x 258829 with sparse part having weight 33020205.
Pruned matrix : 185384 x 186449 with weight 17965451.
Total sieving time: 7.28 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.13 hours.
Total square root time: 0.09 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,28,28,48,48,2.5,2.5,100000
total time: 8.69 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(5·10¹⁶⁴+31)/9 = (5)₁₆₃9_<164> = 17 · 51907 · 20894983 · C151

C151 = P38 · P113

P38 = 32744384953346829276967265860867079327_<38>

P113 = 92018210830867189627110800207659209711575697364865394156667931972180333326904385340235396502563540887671080754821_<113>

Number: n
N=3013079718164143841497655666928758205678816669159984408897339155449092269654212483918172491212764027974836353746129082075124381070656207009312844685467
  ( 151 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=32744384953346829276967265860867079327 (pp38)
 r2=92018210830867189627110800207659209711575697364865394156667931972180333326904385340235396502563540887671080754821 (pp113)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 54.24 hours.
Scaled time: 64.65 units (timescale=1.192).
Factorization parameters were as follows:
name: KA_5_163_9
n: 3013079718164143841497655666928758205678816669159984408897339155449092269654212483918172491212764027974836353746129082075124381070656207009312844685467
type: snfs
skew: 2.28
deg: 5
c5: 1
c0: 62
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2100001)
Primes: RFBsize:250150, AFBsize:250072, largePrimes:7300517 encountered
Relations: rels:6821415, finalFF:564991
Max relations in full relation-set: 28
Initial matrix: 500286 x 564991 with sparse part having weight 37801274.
Pruned matrix : 447562 x 450127 with weight 25647572.
Total sieving time: 48.36 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 5.42 hours.
Total square root time: 0.12 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 54.24 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Aug 5, 2007 (6th)

By Yousuke Koide

(10¹²⁶⁵-1)/9 is divisible by 937659362930322328142805649502351_<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Aug 5, 2007 (5th)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 gnfs

7·10¹⁶⁴+3 = 7(0)₁₆₃3_<165> = 19 · 23 · 37 · 337 · 929 · 269413 · 347533 · 3469921837_<10> · 10858699084919331104580583379_<29> · 329805675824054241199035943707983_<33> · 118849963103897079083614037915925391439183742364207872856583449031842800979_<75>

C107 = P33 · P75

P33 = 329805675824054241199035943707983_<33>

P75 = 118849963103897079083614037915925391439183742364207872856583449031842800979_<75>

Number: 70003_164
N=39197392403144687459815035426745024063531397479986412229829216553848174308140333001931690855527749962515357
  ( 107 digits)
Divisors found:
 r1=329805675824054241199035943707983 (pp33)
 r2=118849963103897079083614037915925391439183742364207872856583449031842800979 (pp75)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 19.99 hours.
Scaled time: 13.63 units (timescale=0.682).
Factorization parameters were as follows:
name: 70003_164
n: 39197392403144687459815035426745024063531397479986412229829216553848174308140333001931690855527749962515357
skew: 20910.15
# norm 1.06e+15
c5: 9720
c4: 2125480070
c3: -30292207723211
c2: -241365060444554346
c1: 6224386460235202586792
c0: 9860520441272134662836800
# alpha -6.80
Y1: 174301888739
Y0: -331977164050768224741
# Murphy_E 1.59e-09
# M 19494045783360941309357024716550423366184593205803102929257298699651293357014392618726071159638485253850725
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2300001)
Primes: RFBsize:183072, AFBsize:182671, largePrimes:4488141 encountered
Relations: rels:4624312, finalFF:419683
Max relations in full relation-set: 0
Initial matrix: 365820 x 419683 with sparse part having weight 23910189.
Pruned matrix : 319973 x 321866 with weight 16314933.
Polynomial selection time: 1.16 hours.
Total sieving time: 15.72 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 2.66 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 19.99 hours.
 --------- CPU info (if available) ----------

Aug 5, 2007 (4th)

By JMB / GMP-ECM B1=3000000

(2·10¹⁷⁴-11)/9 = (2)₁₇₃1_<174> = 14519 · 48049681 · C162

C162 = P39 · C123

P39 = 498348657919234104075045395918906731471_<39>

C123 = [639185595393241060368558509801103716904374062098782041091490513631206214345337531118525083250572654266352921615626524660709_<123>]

Aug 5, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(5·10¹⁶⁴-17)/3 = 1(6)₁₆₃1_<165> = 7 · 89 · 397 · 5894957 · C153

C153 = P45 · P108

P45 = 161298457539788941817796286115085431869711519_<45>

P108 = 708694953619147226673103188232021943957327776601583178016851560378815912464731109927271144169197806764708557_<108>

Number: n
N=114311402885000712403892487530808345971552888111341690651388701164490192899870173759027180390972569507303387784542444950170703623051519404536221700768083
  ( 153 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=161298457539788941817796286115085431869711519 (pp45)
 r2=708694953619147226673103188232021943957327776601583178016851560378815912464731109927271144169197806764708557 (pp108)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 40.28 hours.
Scaled time: 57.93 units (timescale=1.438).
Factorization parameters were as follows:
name: KA_1_6_163_1
n: 114311402885000712403892487530808345971552888111341690651388701164490192899870173759027180390972569507303387784542444950170703623051519404536221700768083
skew: 2.02
deg: 5
c5: 1
c0: -34
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1900001)
Primes: RFBsize:250150, AFBsize:249831, largePrimes:7181141 encountered
Relations: rels:6707182, finalFF:566395
Max relations in full relation-set: 28
Initial matrix: 500045 x 566395 with sparse part having weight 35400182.
Pruned matrix : 443290 x 445854 with weight 23187095.
Total sieving time: 35.22 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 4.79 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 40.28 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Aug 5, 2007 (2nd)

By JMB / GMP-ECM B1=1000000

(2·10¹⁷³-11)/9 = (2)₁₇₂1_<173> = 3 · 4780584353_<10> · C163

C163 = P32 · P131

P32 = 37913745669376504562053041209773_<32>

P131 = 40868486384377850363075248339637631162815021698805356262193295482622750962455291582666552767183399762886016728604351667010921652203_<131>

(2·10¹⁹⁶-11)/9 = (2)₁₉₅1_<196> = 165443 · 247462843 · C182

C182 = P33 · C150

P33 = 258199423348160658302432304492257_<33>

C150 = [210219899230871720367863640427655425071639482317984140098945614468521925473775770678828557000890931928428063480054499871330273471885150271347346444797_<150>]

Aug 5, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060513-k8

(14·10¹⁹⁰-41)/9 = 1(5)₁₈₉1_<191> = C191

C191 = P41 · P150

P41 = 35979232514979028691658608275491778123813_<41>

P150 = 432348176106296870587027279656162097057836779149603113487443591832639183538536761174932277931864748203116574693057107906194995991781437958621511650227_<150>

Number: 15551_190
N=15555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555551
  ( 191 digits)
SNFS difficulty: 191 digits.
Divisors found:
 r1=35979232514979028691658608275491778123813 (pp41)
 r2=432348176106296870587027279656162097057836779149603113487443591832639183538536761174932277931864748203116574693057107906194995991781437958621511650227 (pp150)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1349.01 hours.
Scaled time: 2702.07 units (timescale=2.003).
Factorization parameters were as follows:
name: 15551_190
n: 15555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555551
m: 100000000000000000000000000000000000000
c5: 14
c0: -41
skew: 1.24
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 19800001)
Primes: RFBsize:501962, AFBsize:502607, largePrimes:7128971 encountered
Relations: rels:7710294, finalFF:1147825
Max relations in full relation-set: 28
Initial matrix: 1004635 x 1147825 with sparse part having weight 130586785.
Pruned matrix : 900542 x 905629 with weight 111974876.
Total sieving time: 1328.99 hours.
Total relation processing time: 0.88 hours.
Matrix solve time: 18.70 hours.
Time per square root: 0.44 hours.
Prototype def-par.txt line would be:
snfs,191,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 1349.01 hours.
 --------- CPU info (if available) ----------

Aug 4, 2007 (4th)

By JMB / GMP-ECM B1=1000000

(2·10¹⁸⁴-11)/9 = (2)₁₈₃1_<184> = 1326093162203393_<16> · 5817057857572301_<16> · C136

C136 = P34 · P102

P34 = 1754676921979215318291368793294107_<34>

P102 = 698512124268376321562816716178278625864224388509844952931589370471677010602977158625180855254980820277_<102>

Aug 4, 2007 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

7·10¹⁴⁷+3 = 7(0)₁₄₆3_<148> = 31 · 151451 · 7030015143559119037524563_<25> · C117

C117 = P32 · P85

P32 = 49184959607580348859573544470471_<32>

P85 = 4311968914702968224249026994416631354378899830941813009414303440243079537179314918331_<85>

Number: 70003_147
N=212084016898807566754857352490161533118634629504259292309654861162435026120974930470578532991845919966137704006103901
  ( 117 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=49184959607580348859573544470471 (pp32)
 r2=4311968914702968224249026994416631354378899830941813009414303440243079537179314918331 (pp85)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 22.87 hours.
Scaled time: 15.60 units (timescale=0.682).
Factorization parameters were as follows:
name: 70003_147
n: 212084016898807566754857352490161533118634629504259292309654861162435026120974930470578532991845919966137704006103901
m: 100000000000000000000000000000
c5: 700
c0: 3
skew: 0.34
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2850001)
Primes: RFBsize:114155, AFBsize:114337, largePrimes:2762094 encountered
Relations: rels:2702598, finalFF:256255
Max relations in full relation-set: 0
Initial matrix: 228559 x 256255 with sparse part having weight 29944652.
Pruned matrix : 220754 x 221960 with weight 23313853.
Total sieving time: 20.76 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.83 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 22.87 hours.
 --------- CPU info (if available) ----------

Aug 4, 2007 (2nd)

By JMB / GMP-ECM B1=1000000

(2·10¹⁸²-11)/9 = (2)₁₈₁1_<182> = 3 · 7³ · 15590527644441643987_<20> · C160

C160 = P28 · P132

P28 = 3859810844261017292702989709_<28>

P132 = 358876710814360315317023330251097074583196051792006020792471873976522644363636948726993210189326153704314907059958585059249644910303_<132>

(2·10¹⁸⁰-11)/9 = (2)₁₇₉1_<180> = 29 · 2699 · 27799 · C171

C171 = P32 · P139

P32 = 64863739486980795803630431431379_<32>

P139 = 1574546342648474722022271751727776130594766428709953635443779531729815050710283278155800017708651481579996117040508836655706483328393873031_<139>

Aug 4, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp

7·10¹⁵²+3 = 7(0)₁₅₁3_<153> = 37 · 505533211217_<12> · C140

C140 = P39 · P101

P39 = 710664466259752258736962985632455239789_<39>

P101 = 52660141650353797139373582732951853429418586057828085008415146466989469864283870303119649117935460563_<101>

Number: n
N=37423691459111630694213075267719021502276516612327799793244021635177923501617996604911113655109015687913454442940049105499674605998317941207
  ( 140 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=710664466259752258736962985632455239789 (pp39)
 r2=52660141650353797139373582732951853429418586057828085008415146466989469864283870303119649117935460563 (pp101)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.23 hours.
Scaled time: 31.40 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_7_0_151_3
n: 37423691459111630694213075267719021502276516612327799793244021635177923501617996604911113655109015687913454442940049105499674605998317941207
type: snfs
skew: 0.34
deg: 5
c5: 700
c0: 3
m: 1000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1000001)
Primes: RFBsize:216816, AFBsize:216741, largePrimes:6016357 encountered
Relations: rels:5499110, finalFF:498155
Max relations in full relation-set: 28
Initial matrix: 433624 x 498155 with sparse part having weight 22030485.
Pruned matrix : 366825 x 369057 with weight 12772769.
Total sieving time: 23.88 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.02 hours.
Total square root time: 0.14 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 26.23 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

7·10¹⁵⁰+3 = 7(0)₁₄₉3_<151> = 71 · 89 · 191 · 5813 · 69387272384806722377_<20> · C122

C122 = P52 · P70

P52 = 2860432727051506986615284475786112947115219635815431_<52>

P70 = 5026948551624322877511681422548970043126094617265313823362275760438297_<70>

Number: n
N=14379248154270385139813463545958394801202417801191544982206419087617630689229379296085630002943418668516430905971555961007
  ( 122 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=2860432727051506986615284475786112947115219635815431 (pp52)
 r2=5026948551624322877511681422548970043126094617265313823362275760438297 (pp70)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 14.95 hours.
Scaled time: 20.40 units (timescale=1.365).
Factorization parameters were as follows:
name: KA_7_0_149_3
n: 14379248154270385139813463545958394801202417801191544982206419087617630689229379296085630002943418668516430905971555961007
skew: 0.84
deg: 5
c5: 7
c0: 3
m: 1000000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 700001)
Primes: RFBsize:148933, AFBsize:148270, largePrimes:5983637 encountered
Relations: rels:5373975, finalFF:333157
Max relations in full relation-set: 28
Initial matrix: 297268 x 333157 with sparse part having weight 22706688.
Pruned matrix : 269197 x 270747 with weight 15488628.
Total sieving time: 13.19 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.53 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 14.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Aug 3, 2007 (4th)

By Yousuke Koide

(10¹¹³⁵-1)/9 is divisible by 19556724483255900086046136607479201_<35>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Aug 3, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp

7·10¹⁵⁸+3 = 7(0)₁₅₇3_<159> = 37 · C158

C158 = P52 · P106

P52 = 4683555637807654711165402911872475397796795663167619_<52>

P106 = 4039435074966837668459019948543510692643700803297645131234240674842966427190365006893589626840507633222701_<106>

Number: n
N=18918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918919
  ( 158 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=4683555637807654711165402911872475397796795663167619 (pp52)
 r2=4039435074966837668459019948543510692643700803297645131234240674842966427190365006893589626840507633222701 (pp106)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 38.49 hours.
Scaled time: 51.00 units (timescale=1.325).
Factorization parameters were as follows:
name: KA_7_0_157_3
n: 18918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918919
skew: 0.21
deg: 5
c5: 7000
c0: 3
m: 10000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1600001)
Primes: RFBsize:250150, AFBsize:249771, largePrimes:7165440 encountered
Relations: rels:6701601, finalFF:585929
Max relations in full relation-set: 48
Initial matrix: 499988 x 585929 with sparse part having weight 38496719.
Pruned matrix : 424349 x 426912 with weight 22476047.
Total sieving time: 34.02 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 4.17 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 38.49 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁴⁸+3 = 7(0)₁₄₇3_<149> = 541 · 94793 · C142

C142 = P37 · P48 · P58

P37 = 1248139200509574640907510234705365019_<37>

P48 = 668778149760661722591247508440960905084930985277_<48>

P58 = 1635232116045943944454517876533152037422559560020696414537_<58>

Number: n
N=1364974401952552982797637104512560523696218862959553488013662535779635256610215160329990751518441398909225555838538581966703087433649813048231
  ( 142 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=1248139200509574640907510234705365019 (pp37)
 r2=668778149760661722591247508440960905084930985277 (pp48)
 r3=1635232116045943944454517876533152037422559560020696414537 (pp58)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 16.09 hours.
Scaled time: 21.91 units (timescale=1.362).
Factorization parameters were as follows:
name: KA_7_0_147_3
n: 1364974401952552982797637104512560523696218862959553488013662535779635256610215160329990751518441398909225555838538581966703087433649813048231
skew: 0.21
deg: 5
c5: 7000
c0: 3
m: 100000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2000001)
Primes: RFBsize:114155, AFBsize:114347, largePrimes:7377130 encountered
Relations: rels:6857385, finalFF:270003
Max relations in full relation-set: 28
Initial matrix: 228569 x 270003 with sparse part having weight 30080076.
Pruned matrix : 218314 x 219520 with weight 22382143.
Total sieving time: 14.03 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 1.64 hours.
Total square root time: 0.17 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000
total time: 16.09 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁶⁵+3 = 7(0)₁₆₄3_<166> = C166

C166 = P36 · P49 · P83

P36 = 152833588533830632515504625196129899_<36>

P49 = 2783607568442084600657258901797095301845534239737_<49>

P83 = 16453989692271955709439095429034688807841041398306296314589415102129894839413356881_<83>

Number: n
N=7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
  ( 166 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=152833588533830632515504625196129899 (pp36)
 r2=2783607568442084600657258901797095301845534239737 (pp49)
 r3=16453989692271955709439095429034688807841041398306296314589415102129894839413356881 (pp83)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 52.97 hours.
Scaled time: 76.80 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_7_0_164_3
n: 7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
skew: 0.84
deg: 5
c5: 7
c0: 3
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2400001)
Primes: RFBsize:250150, AFBsize:249766, largePrimes:7413466 encountered
Relations: rels:6928393, finalFF:560270
Max relations in full relation-set: 28
Initial matrix: 499981 x 560270 with sparse part having weight 40280814.
Pruned matrix : 452422 x 454985 with weight 28649122.
Total sieving time: 46.55 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 5.70 hours.
Total square root time: 0.49 hours, sqrts: 6.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 52.97 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Aug 3, 2007 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

7·10¹³⁸+3 = 7(0)₁₃₇3_<139> = 17 · 8243 · 68483 · 259690877 · 416873729 · 472302839 · C104

C104 = P32 · P72

P32 = 39500434691109480414761661938549_<32>

P72 = 361158125739483496643032610400546386075176007047634753673066706124874797_<72>

Number: 70003_138
N=14265902958935973680620930474842135188483839358780870437646100498699296745754482441030588187552932849553
  ( 104 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=39500434691109480414761661938549 (pp32)
 r2=361158125739483496643032610400546386075176007047634753673066706124874797 (pp72)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 12.90 hours.
Scaled time: 8.80 units (timescale=0.682).
Factorization parameters were as follows:
name: 70003_138
n: 14265902958935973680620930474842135188483839358780870437646100498699296745754482441030588187552932849553
m: 1000000000000000000000000000
c5: 7000
c0: 3
skew: 0.21
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1750001)
Primes: RFBsize:78498, AFBsize:64153, largePrimes:1565292 encountered
Relations: rels:1549696, finalFF:159894
Max relations in full relation-set: 0
Initial matrix: 142718 x 159894 with sparse part having weight 17823941.
Pruned matrix : 138506 x 139283 with weight 13759036.
Total sieving time: 12.18 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.54 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 12.90 hours.
 --------- CPU info (if available) ----------

7·10¹⁰⁸+3 = 7(0)₁₀₇3_<109> = 15932731 · C102

C102 = P35 · P68

P35 = 21135103243411643094225839323775893_<35>

P68 = 20787556496228678876263628963578198111397575572164064323810422220341_<68>

Number: 70003_108
N=439347152726045522264827040637289363637658854593101458877326178418502138773321409870034208196950039513
  ( 102 digits)
SNFS difficulty: 108 digits.
Divisors found:
 r1=21135103243411643094225839323775893 (pp35)
 r2=20787556496228678876263628963578198111397575572164064323810422220341 (pp68)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 1.97 hours.
Scaled time: 1.30 units (timescale=0.661).
Factorization parameters were as follows:
name: 70003_108
n: 439347152726045522264827040637289363637658854593101458877326178418502138773321409870034208196950039513
m: 1000000000000000000000
c5: 7000
c0: 3
skew: 0.21
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:64153, largePrimes:2383720 encountered
Relations: rels:2939110, finalFF:154239
Max relations in full relation-set: 0
Initial matrix: 113318 x 154239 with sparse part having weight 3864688.
Pruned matrix : 79599 x 80229 with weight 1974973.
Total sieving time: 1.80 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,108,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.97 hours.
 --------- CPU info (if available) ----------

Aug 3, 2007

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000

7·10¹⁸⁰+3 = 7(0)₁₇₉3_<181> = C181

C181 = P37 · C145

P37 = 1661635052382325894228860798388965059_<37>

C145 = [4212718063430313817949556918391010227926614475612398920219025346271127082558521092818662843579474726787185571200372160360259201106912513664366017_<145>]

Aug 2, 2007 (4th)

By Robert Backstrom / GMP-ECM 5.0 B1=536000, GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp

(10¹⁶⁴+11)/3 = (3)₁₆₃7_<164> = 37 · 8419 · 279007 · C153

C153 = P31 · P48 · P75

P31 = 4161801207038325803680462744351_<31>

P48 = 154736176694355509814594114434265558831989783897_<48>

P75 = 595563698951275492246179266439849085291671641089578658213681985453227855151_<75>

Number: n
N=92155249753668515805069774853618530650531992960849125594638260650099015648789979128441694079227557758205130066181308303447
  ( 122 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=154736176694355509814594114434265558831989783897 (pp48)
 r2=595563698951275492246179266439849085291671641089578658213681985453227855151 (pp75)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 96.22 hours.
Scaled time: 115.08 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_3_163_7

n: 92155249753668515805069774853618530650531992960849125594638260650099015648789979128441694079227557758205130066181308303447

# n: 383531829659736005765621077922788434765907478295374100321404205450489861931970595643574521924764095540194512505080222201006312737689809245844169493077897

type: snfs
skew: 0.43
deg: 5
c5: 1
c0: 110
m: 1000000000000000000000000000000000
rlim: 3600000
alim: 3600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3600001)
Primes: RFBsize:256726, AFBsize:257022, largePrimes:7802543 encountered
Relations: rels:7325962, finalFF:593422
Max relations in full relation-set: 28
Initial matrix: 513812 x 593422 with sparse part having weight 45665185.
Pruned matrix : 470389 x 473022 with weight 33187299.
Total sieving time: 88.29 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 7.43 hours.
Total square root time: 0.14 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3600000,3600000,28,28,48,48,2.5,2.5,100000
total time: 96.22 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

7·10¹³⁵+3 = 7(0)₁₃₄3_<136> = 75019561 · 127203697 · C120

C120 = P48 · P73

P48 = 498282829674007715259141593888416290550964085919_<48>

P73 = 1472135771787141323267702134218700861789671776680188265909145553844113061_<73>

Number: n
N=733539978030426032474138343766645879888898534474528389024587518339851243854978692112465545639290426570208439273154088059
  ( 120 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=498282829674007715259141593888416290550964085919 (pp48)
 r2=1472135771787141323267702134218700861789671776680188265909145553844113061 (pp73)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 3.62 hours.
Scaled time: 4.92 units (timescale=1.358).
Factorization parameters were as follows:
name: KA_7_0_134_3
n: 733539978030426032474138343766645879888898534474528389024587518339851243854978692112465545639290426570208439273154088059
skew: 0.84
deg: 5
c5: 7
c0: 3
m: 1000000000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 550001)
Primes: RFBsize:78498, AFBsize:78031, largePrimes:5443174 encountered
Relations: rels:4746285, finalFF:189754
Max relations in full relation-set: 28
Initial matrix: 156594 x 189754 with sparse part having weight 15131695.
Pruned matrix : 142669 x 143515 with weight 9259290.
Total sieving time: 3.03 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.43 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,75000
total time: 3.62 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹³²+3 = 7(0)₁₃₁3_<133> = 31 · 1897144835436283709_<19> · C114

C114 = P49 · P65

P49 = 1514672391291856973675707124754820474913203927051_<49>

P65 = 78580927206153670651740539814203277361304443804223185859614493507_<65>

Number: n
N=119024360921276121842517421424303849703442150179435383100670930768158762553946642889669912459689870973548741157857
  ( 114 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=1514672391291856973675707124754820474913203927051 (pp49)
 r2=78580927206153670651740539814203277361304443804223185859614493507 (pp65)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.29 hours.
Scaled time: 5.12 units (timescale=1.193).
Factorization parameters were as follows:
name: KA_7_0_131_3
n: 119024360921276121842517421424303849703442150179435383100670930768158762553946642889669912459689870973548741157857
type: snfs
skew: 0.34
deg: 5
c5: 700
c0: 3
m: 100000000000000000000000000
rlim: 900000
alim: 900000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 900000/900000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 700001)
Primes: RFBsize:71274, AFBsize:71340, largePrimes:3740700 encountered
Relations: rels:3055228, finalFF:161685
Max relations in full relation-set: 28
Initial matrix: 142681 x 161685 with sparse part having weight 7259713.
Pruned matrix : 128325 x 129102 with weight 4802914.
Total sieving time: 3.74 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.40 hours.
Total square root time: 0.05 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,900000,900000,28,28,48,48,2.2,2.2,50000
total time: 4.29 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Aug 2, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp

9·10¹⁶³+1 = 9(0)₁₆₂1_<164> = 7² · 13 · 179 · 470008183 · C151

C151 = P36 · P45 · P71

P36 = 259481291797001816650176355670832013_<36>

P45 = 580459551785892461725007555092462668798367841_<45>

P71 = 11149788091046450752175493549254706615173820321550790352125382027235333_<71>

Number: n
N=1679363179430100904238066369647856492488978635545047894559404239979036929530217645752206682742665314434231355893232990238004850731203395449127465734689
  ( 151 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=259481291797001816650176355670832013 (pp36)
 r2=580459551785892461725007555092462668798367841 (pp45)
 r3=11149788091046450752175493549254706615173820321550790352125382027235333 (pp71)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 66.05 hours.
Scaled time: 47.23 units (timescale=0.715).
Factorization parameters were as follows:
name: KA_9_0_162_1
n: 1679363179430100904238066369647856492488978635545047894559404239979036929530217645752206682742665314434231355893232990238004850731203395449127465734689
skew: 0.16
deg: 5
c5: 9000
c0: 1
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2700001)
Primes: RFBsize:250150, AFBsize:250001, largePrimes:7541796 encountered
Relations: rels:7066191, finalFF:569227
Max relations in full relation-set: 28
Initial matrix: 500218 x 569227 with sparse part having weight 42649432.
Pruned matrix : 448769 x 451334 with weight 30222203.
Total sieving time: 59.53 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 4.98 hours.
Total square root time: 1.25 hours, sqrts: 6.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 66.05 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹²⁷+3 = 7(0)₁₂₆3_<128> = 277 · 683 · C123

C123 = P60 · P64

P60 = 101758248455110600982078958785140824830321627783059244018899_<60>

P64 = 3636034073135055601486854090198041730366400527898690994554262567_<64>

Number: n
N=369996458605324777605700059727999746288142670634438213234244757943031116702168707813796639375023124778662832798600356253733
  ( 123 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=101758248455110600982078958785140824830321627783059244018899 (pp60)
 r2=3636034073135055601486854090198041730366400527898690994554262567 (pp64)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 2.70 hours.
Scaled time: 3.67 units (timescale=1.358).
Factorization parameters were as follows:
name: KA_7_0_126_3
n: 369996458605324777605700059727999746288142670634438213234244757943031116702168707813796639375023124778662832798600356253733
skew: 0.34
deg: 5
c5: 700
c0: 3
m: 10000000000000000000000000
type: snfs
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 400001)
Primes: RFBsize:63951, AFBsize:63898, largePrimes:4621659 encountered
Relations: rels:3934593, finalFF:151818
Max relations in full relation-set: 28
Initial matrix: 127916 x 151818 with sparse part having weight 11015888.
Pruned matrix : 117329 x 118032 with weight 6729113.
Total sieving time: 2.34 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.20 hours.
Total square root time: 0.07 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000
total time: 2.70 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹²⁵+3 = 7(0)₁₂₄3_<126> = 37 · 499 · C122

C122 = P53 · P70

P53 = 13699452564493006814819701274146501315424887911148777_<53>

P70 = 2767531402418291140749455418859878737861230939330176281407585478703253_<70>

Number: n
N=37913665168174186210258354546931701240318474787412663164166170178194226290418675188214266370578995829496831500839516871581
  ( 122 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=13699452564493006814819701274146501315424887911148777 (pp53)
 r2=2767531402418291140749455418859878737861230939330176281407585478703253 (pp70)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 2.02 hours.
Scaled time: 2.73 units (timescale=1.352).
Factorization parameters were as follows:
name: KA_7_0_124_3
n: 37913665168174186210258354546931701240318474787412663164166170178194226290418675188214266370578995829496831500839516871581
skew: 0.84
deg: 5
c5: 7
c0: 3
m: 10000000000000000000000000
type: snfs
rlim: 700000
alim: 700000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 300001)
Primes: RFBsize:56543, AFBsize:56283, largePrimes:5007709 encountered
Relations: rels:4440675, finalFF:243454
Max relations in full relation-set: 28
Initial matrix: 112891 x 243454 with sparse part having weight 20075677.
Pruned matrix : 80668 x 81296 with weight 4508727.
Total sieving time: 1.76 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.08 hours.
Total square root time: 0.08 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,700000,700000,28,28,48,48,2.5,2.5,50000
total time: 2.02 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Aug 2, 2007 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

7·10¹³⁷+3 = 7(0)₁₃₆3_<138> = 37² · 73 · 373 · 521 · 18719 · 249341 · 960331 · 1467499879_<10> · C103

C103 = P30 · P74

P30 = 139631923964055191736784404269_<30>

P74 = 39243261185324721562992298947369650901900632234898044840233858916987494957_<74>

Number: 70003_137
N=5479612061930819937675113993646705222614196918682242006504828855291692670246697931177796783015886771433
  ( 103 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=139631923964055191736784404269 (pp30)
 r2=39243261185324721562992298947369650901900632234898044840233858916987494957 (pp74)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 9.59 hours.
Scaled time: 6.54 units (timescale=0.682).
Factorization parameters were as follows:
name: 70003_137
n: 5479612061930819937675113993646705222614196918682242006504828855291692670246697931177796783015886771433
m: 1000000000000000000000000000
c5: 700
c0: 3
skew: 0.34
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1375001)
Primes: RFBsize:78498, AFBsize:63898, largePrimes:1539023 encountered
Relations: rels:1533849, finalFF:161515
Max relations in full relation-set: 0
Initial matrix: 142463 x 161515 with sparse part having weight 13047221.
Pruned matrix : 136623 x 137399 with weight 9876416.
Total sieving time: 9.04 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.40 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 9.59 hours.
 --------- CPU info (if available) ----------

7·10¹⁴⁰+3 = 7(0)₁₃₉3_<141> = 37 · 8930917 · 113901888018295570523922817_<27> · C107

C107 = P33 · P74

P33 = 278323359075849334609317178348129_<33>

P74 = 66822032691525636457754568132542380413223137289570793768530446299737118299_<74>

Number: 70003_140
N=18598132598981632690429372380577188394736092833600211994959614409569142544257818749339461669680023478312571
  ( 107 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=278323359075849334609317178348129 (pp33)
 r2=66822032691525636457754568132542380413223137289570793768530446299737118299 (pp74)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 9.94 hours.
Scaled time: 6.78 units (timescale=0.682).
Factorization parameters were as follows:
name: 70003_140
n: 18598132598981632690429372380577188394736092833600211994959614409569142544257818749339461669680023478312571
m: 10000000000000000000000000000
c5: 7
c0: 3
skew: 0.84
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1550001)
Primes: RFBsize:100021, AFBsize:99538, largePrimes:2645025 encountered
Relations: rels:2617239, finalFF:224213
Max relations in full relation-set: 0
Initial matrix: 199624 x 224213 with sparse part having weight 12939835.
Pruned matrix : 190257 x 191319 with weight 10105839.
Total sieving time: 9.03 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.72 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 9.94 hours.
 --------- CPU info (if available) ----------

Aug 2, 2007

By Yousuke Koide

10⁹²⁶+1 is divisible by 222918345451775051784679332634923849829_<39>

10¹⁶⁵⁹+1 is divisible by154527628727094706891588937475019_<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Aug 1, 2007 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

(43·10¹⁶⁰-7)/9 = 4(7)₁₆₀_<161> = 5007179 · 7008751163_<10> · 4421264001211142317908244507_<28> · C117

C117 = P59 · P59

P59 = 10962690224883063587814306144466516475374288984362790602653_<59>

P59 = 28088503235042124615343896925550058586948441134278026650631_<59>

Number: 47777_160
N=307925559846392608191890342655880287652240774038193999902100985083530393790025178760683643373658220133542015572724043
  ( 117 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=10962690224883063587814306144466516475374288984362790602653 (pp59)
 r2=28088503235042124615343896925550058586948441134278026650631 (pp59)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 92.60 hours.
Scaled time: 63.15 units (timescale=0.682).
Factorization parameters were as follows:
name: 47777_160
n: 307925559846392608191890342655880287652240774038193999902100985083530393790025178760683643373658220133542015572724043
m: 100000000000000000000000000000000
c5: 43
c0: -7
skew: 0.7
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4450001)
Primes: RFBsize:315948, AFBsize:316331, largePrimes:5787779 encountered
Relations: rels:5898099, finalFF:709902
Max relations in full relation-set: 0
Initial matrix: 632346 x 709902 with sparse part having weight 39393248.
Pruned matrix : 573683 x 576908 with weight 30096165.
Total sieving time: 78.88 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 13.14 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 92.60 hours.
 --------- CPU info (if available) ----------

Aug 1, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

7·10¹²⁰+3 = 7(0)₁₁₉3_<121> = 23 · 366479 · 490913 · C109

C109 = P30 · P79

P30 = 787073943986243214424803305243_<30>

P79 = 2149319812250807291486495152588101029793779750183550066121886943689304730180801_<79>

Number: n
N=1691673621516014680304576988516586290004567558148171765518815439071657240016879833070443049183852561781239643
  ( 109 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=787073943986243214424803305243 (pp30)
 r2=2149319812250807291486495152588101029793779750183550066121886943689304730180801 (pp79)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.62 hours.
Scaled time: 2.35 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_7_0_119_3
n: 1691673621516014680304576988516586290004567558148171765518815439071657240016879833070443049183852561781239643
skew: 0.34
deg: 5
c5: 7
c0: 3
m: 1000000000000000000000000
type: snfs
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 250001)
Primes: RFBsize:63951, AFBsize:63643, largePrimes:4609625 encountered
Relations: rels:4046821, finalFF:240563
Max relations in full relation-set: 28
Initial matrix: 127659 x 240563 with sparse part having weight 15790458.
Pruned matrix : 84816 x 85518 with weight 3791952.
Total sieving time: 1.46 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.06 hours.
Total square root time: 0.03 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000
total time: 1.62 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

7·10¹⁴⁵+3 = 7(0)₁₄₄3_<146> = 73 · 28793 · 63545947 · 288853667 · 53326121669_<11> · 1531658044549_<13> · C101

C101 = P44 · P57

P44 = 54389898345654421049856493544427544048520119_<44>

P57 = 408415728230237921555405467245794348472339374239159426157_<57>

Number: n
N=22213689941209063158208924297571722939004404285708946735588677498261543842008297054574418225109352683
  ( 101 digits)
Divisors found:
 r1=54389898345654421049856493544427544048520119 (pp44)
 r2=408415728230237921555405467245794348472339374239159426157 (pp57)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 5.98 hours.
Scaled time: 8.61 units (timescale=1.440).
Factorization parameters were as follows:
name: n
n: 22213689941209063158208924297571722939004404285708946735588677498261543842008297054574418225109352683
skew: 9797.27
# norm 1.17e+14
c5: 52860
c4: 698483228
c3: -14911543473265
c2: -55584912348479370
c1: 671780603124125519596
c0: 65049529035605759990224
# alpha -6.39
Y1: 18029502491
Y0: -13325918615022094611
# Murphy_E 3.27e-09
# M 11752346036422637204237551646785296678119824290663937408764580117521053325165969638739266765025892067
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 800001)
Primes: RFBsize:135072, AFBsize:135185, largePrimes:3524807 encountered
Relations: rels:3561278, finalFF:435975
Max relations in full relation-set: 28
Initial matrix: 270338 x 435975 with sparse part having weight 24359364.
Pruned matrix : 135847 x 137262 with weight 7808751.
Total sieving time: 5.46 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.28 hours.
Total square root time: 0.10 hours, sqrts: 2.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 5.98 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

7·10¹⁶⁶-3 = 6(9)₁₆₅7_<167> = 67 · 173 · C163

C163 = P42 · P49 · P74

P42 = 153583387324042801184481984693585153371533_<42>

P49 = 2067097285247959280399851585395695989586036741113_<49>

P74 = 19022691978446235710973810593733140748567297663247313327626391472876229823_<74>

Number: n
N=6039168320248468639461651281166422224139418514364593218876714692433784833060132861703045466310068156328185661288931067207316021050815287723233543266327322922957467
  ( 163 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=153583387324042801184481984693585153371533 (pp42)
 r2=2067097285247959280399851585395695989586036741113 (pp49)
 r3=19022691978446235710973810593733140748567297663247313327626391472876229823 (pp74)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 97.45 hours.
Scaled time: 128.92 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_6_9_165_7
n: 6039168320248468639461651281166422224139418514364593218876714692433784833060132861703045466310068156328185661288931067207316021050815287723233543266327322922957467
skew: 0.53
deg: 5
c5: 70
c0: -3
m: 1000000000000000000000000000000000
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 4000001)
Primes: RFBsize:283146, AFBsize:281947, largePrimes:7979224 encountered
Relations: rels:7489789, finalFF:636155
Max relations in full relation-set: 48
Initial matrix: 565160 x 636155 with sparse part having weight 53405311.
Pruned matrix : 527962 x 530851 with weight 38879892.
Total sieving time: 87.02 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 9.88 hours.
Total square root time: 0.23 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000
total time: 97.45 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

July 2007

Jul 31, 2007 (3rd)

By Robert Backstrom / Msieve v. 1.25

7·10¹²²+3 = 7(0)₁₂₁3_<123> = 17³ · 37 · 34057 · 121139 · 447641 · 1966357949_<10> · C94

C94 = P41 · P53

P41 = 36803587049889567164794261972333592412847_<41>

P53 = 28812211472214508546521155757658327809127986705923647_<53>

Tue Jul 31 22:22:05 2007  
Tue Jul 31 22:22:05 2007  
Tue Jul 31 22:22:05 2007  Msieve v. 1.25
Tue Jul 31 22:22:05 2007  random seeds: 2df35130 45e71b74
Tue Jul 31 22:22:05 2007  factoring 1060392733017473507363436391125662056426006504379915175604094685956234092303916292830483893009 (94 digits)
Tue Jul 31 22:22:05 2007  commencing quadratic sieve (93-digit input)
Tue Jul 31 22:22:05 2007  using multiplier of 1
Tue Jul 31 22:22:05 2007  using 64kb Opteron sieve core
Tue Jul 31 22:22:05 2007  sieve interval: 18 blocks of size 65536
Tue Jul 31 22:22:05 2007  processing polynomials in batches of 6
Tue Jul 31 22:22:05 2007  using a sieve bound of 1986401 (74118 primes)
Tue Jul 31 22:22:05 2007  using large prime bound of 256245729 (27 bits)
Tue Jul 31 22:22:05 2007  using double large prime bound of 1366412668937199 (42-51 bits)
Tue Jul 31 22:22:05 2007  using trial factoring cutoff of 51 bits
Tue Jul 31 22:22:05 2007  polynomial 'A' values have 12 factors
Wed Aug 01 00:39:21 2007  74518 relations (18810 full + 55708 combined from 1024843 partial), need 74214
Wed Aug 01 00:39:22 2007  begin with 1043653 relations
Wed Aug 01 00:39:23 2007  reduce to 190550 relations in 13 passes
Wed Aug 01 00:39:23 2007  attempting to read 190550 relations
Wed Aug 01 00:39:26 2007  recovered 190550 relations
Wed Aug 01 00:39:26 2007  recovered 169642 polynomials
Wed Aug 01 00:39:26 2007  attempting to build 74518 cycles
Wed Aug 01 00:39:26 2007  found 74518 cycles in 5 passes
Wed Aug 01 00:39:27 2007  distribution of cycle lengths:
Wed Aug 01 00:39:27 2007     length 1 : 18810
Wed Aug 01 00:39:27 2007     length 2 : 13413
Wed Aug 01 00:39:27 2007     length 3 : 12787
Wed Aug 01 00:39:27 2007     length 4 : 10167
Wed Aug 01 00:39:27 2007     length 5 : 7362
Wed Aug 01 00:39:27 2007     length 6 : 4755
Wed Aug 01 00:39:27 2007     length 7 : 3092
Wed Aug 01 00:39:27 2007     length 9+: 4132
Wed Aug 01 00:39:27 2007  largest cycle: 20 relations
Wed Aug 01 00:39:27 2007  matrix is 74118 x 74518 with weight 4440747 (avg 59.59/col)
Wed Aug 01 00:39:28 2007  filtering completed in 3 passes
Wed Aug 01 00:39:28 2007  matrix is 70053 x 70117 with weight 4190795 (avg 59.77/col)
Wed Aug 01 00:39:29 2007  saving the first 48 matrix rows for later
Wed Aug 01 00:39:29 2007  matrix is 70005 x 70117 with weight 3152619 (avg 44.96/col)
Wed Aug 01 00:39:29 2007  matrix includes 64 packed rows
Wed Aug 01 00:39:29 2007  using block size 21845 for processor cache size 512 kB
Wed Aug 01 00:39:29 2007  commencing Lanczos iteration
Wed Aug 01 00:40:15 2007  lanczos halted after 1108 iterations
Wed Aug 01 00:40:15 2007  recovered 16 nontrivial dependencies
Wed Aug 01 00:40:16 2007  prp41 factor: 36803587049889567164794261972333592412847
Wed Aug 01 00:40:16 2007  prp53 factor: 28812211472214508546521155757658327809127986705923647
Wed Aug 01 00:40:16 2007  elapsed time 02:18:11

AMD 64 3400+

Jul 31, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, Msieve v. 1.25

(2·10¹⁶⁴-17)/3 = (6)₁₆₃1_<164> = 29 · 107 · 210109 · C156

C156 = P45 · P54 · P58

P45 = 146792919660212633045160717534069008610074051_<45>

P54 = 135010317731924137634438672025990319457714916359755721_<54>

P58 = 5159531184859186656457275600237553641883637652588888601333_<58>

Number: n
N=102254471776071177570846050856197117511781240018413760317596990300367300976872093287863039783787909447720167299911482751852977440673142905577002399944662743
  ( 156 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=146792919660212633045160717534069008610074051 (pp45)
 r2=135010317731924137634438672025990319457714916359755721 (pp54)
 r3=5159531184859186656457275600237553641883637652588888601333 (pp58)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 50.11 hours.
Scaled time: 72.91 units (timescale=1.455).
Factorization parameters were as follows:
name: KA_6_163_1
n: 102254471776071177570846050856197117511781240018413760317596990300367300976872093287863039783787909447720167299911482751852977440673142905577002399944662743
skew: 2.43
deg: 5
c5: 1
c0: -85
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2300001)
Primes: RFBsize:250150, AFBsize:250371, largePrimes:7491975 encountered
Relations: rels:7069787, finalFF:615528
Max relations in full relation-set: 28
Initial matrix: 500585 x 615528 with sparse part having weight 43347706.
Pruned matrix : 408266 x 410832 with weight 26760517.
Total sieving time: 44.47 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 4.99 hours.
Total square root time: 0.43 hours, sqrts: 6.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 50.11 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

7·10¹³⁶+3 = 7(0)₁₃₅3_<137> = C137

C137 = P33 · P43 · P63

P33 = 189532579450789969799143826592293_<33>

P43 = 2381835865531583487969941738318774107993447_<43>

P63 = 155060912820934332646084226028944988675098343203271382941181793_<63>

Number: n
N=70000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
  ( 137 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=189532579450789969799143826592293 (pp33)
 r2=2381835865531583487969941738318774107993447 (pp43)
 r3=155060912820934332646084226028944988675098343203271382941181793 (pp63)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 5.52 hours.
Scaled time: 8.03 units (timescale=1.455).
Factorization parameters were as follows:
name: KA_7_0_135_3
n: 70000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
skew: 0.53
deg: 5
c5: 70
c0: 3
m: 1000000000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:78498, AFBsize:78021, largePrimes:6514103 encountered
Relations: rels:5824178, finalFF:190944
Max relations in full relation-set: 28
Initial matrix: 156586 x 190944 with sparse part having weight 19426214.
Pruned matrix : 147516 x 148362 with weight 12985709.
Total sieving time: 4.77 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.53 hours.
Total square root time: 0.07 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,75000
total time: 5.52 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

7·10¹¹⁷+3 = 7(0)₁₁₆3_<118> = 31 · C117

C117 = P54 · P63

P54 = 796610382478821640289686993942482559318724926882166707_<54>

P63 = 283459086875391589955150402968360965955345854041338678737403759_<63>

Number: n
N=225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451613
  ( 117 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=796610382478821640289686993942482559318724926882166707 (pp54)
 r2=283459086875391589955150402968360965955345854041338678737403759 (pp63)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.23 hours.
Scaled time: 1.78 units (timescale=1.451).
Factorization parameters were as follows:
name: KA_7_0_116_3
n: 225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451613
skew: 0.34
deg: 5
c5: 700
c0: 3
m: 100000000000000000000000
type: snfs
rlim: 600000
alim: 600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:49098, AFBsize:48976, largePrimes:3849937 encountered
Relations: rels:3225255, finalFF:131768
Max relations in full relation-set: 28
Initial matrix: 98141 x 131768 with sparse part having weight 8495908.
Pruned matrix : 84202 x 84756 with weight 3752118.
Total sieving time: 1.07 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.05 hours.
Total square root time: 0.04 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000
total time: 1.23 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

7·10¹³¹+3 = 7(0)₁₃₀3_<132> = 37 · 167 · 821 · 86381 · 8277265193_<10> · 1909043502241_<13> · 11221997190059_<14> · C85

C85 = P42 · P44

P42 = 245476063044641766698278446037400797293497_<42>

P44 = 36697498431299323192437388994595232599875443_<44>

Tue Jul 31 18:27:11 2007  
Tue Jul 31 18:27:11 2007  
Tue Jul 31 18:27:11 2007  Msieve v. 1.25
Tue Jul 31 18:27:11 2007  random seeds: 51a0e488 172d0ce2
Tue Jul 31 18:27:11 2007  factoring 9008357438502274995224625264375573726008762745952381754409588880984018651293713894171 (85 digits)
Tue Jul 31 18:27:11 2007  commencing quadratic sieve (85-digit input)
Tue Jul 31 18:27:11 2007  using multiplier of 59
Tue Jul 31 18:27:11 2007  using 64kb Opteron sieve core
Tue Jul 31 18:27:11 2007  sieve interval: 6 blocks of size 65536
Tue Jul 31 18:27:11 2007  processing polynomials in batches of 17
Tue Jul 31 18:27:11 2007  using a sieve bound of 1442509 (54972 primes)
Tue Jul 31 18:27:11 2007  using large prime bound of 115400720 (26 bits)
Tue Jul 31 18:27:11 2007  using double large prime bound of 325068826146400 (41-49 bits)
Tue Jul 31 18:27:11 2007  using trial factoring cutoff of 49 bits
Tue Jul 31 18:27:11 2007  polynomial 'A' values have 11 factors
Tue Jul 31 18:57:24 2007  55354 relations (16849 full + 38505 combined from 558450 partial), need 55068
Tue Jul 31 18:57:25 2007  begin with 575299 relations
Tue Jul 31 18:57:25 2007  reduce to 126894 relations in 9 passes
Tue Jul 31 18:57:25 2007  attempting to read 126894 relations
Tue Jul 31 18:57:27 2007  recovered 126894 relations
Tue Jul 31 18:57:27 2007  recovered 104607 polynomials
Tue Jul 31 18:57:27 2007  attempting to build 55354 cycles
Tue Jul 31 18:57:27 2007  found 55354 cycles in 5 passes
Tue Jul 31 18:57:27 2007  distribution of cycle lengths:
Tue Jul 31 18:57:27 2007     length 1 : 16849
Tue Jul 31 18:57:27 2007     length 2 : 11673
Tue Jul 31 18:57:27 2007     length 3 : 9808
Tue Jul 31 18:57:27 2007     length 4 : 6856
Tue Jul 31 18:57:27 2007     length 5 : 4419
Tue Jul 31 18:57:27 2007     length 6 : 2741
Tue Jul 31 18:57:27 2007     length 7 : 1489
Tue Jul 31 18:57:27 2007     length 9+: 1519
Tue Jul 31 18:57:27 2007  largest cycle: 18 relations
Tue Jul 31 18:57:28 2007  matrix is 54972 x 55354 with weight 2949435 (avg 53.28/col)
Tue Jul 31 18:57:28 2007  filtering completed in 3 passes
Tue Jul 31 18:57:28 2007  matrix is 49563 x 49627 with weight 2651538 (avg 53.43/col)
Tue Jul 31 18:57:29 2007  saving the first 48 matrix rows for later
Tue Jul 31 18:57:29 2007  matrix is 49515 x 49627 with weight 2025706 (avg 40.82/col)
Tue Jul 31 18:57:29 2007  matrix includes 64 packed rows
Tue Jul 31 18:57:29 2007  commencing Lanczos iteration
Tue Jul 31 18:58:45 2007  lanczos halted after 785 iterations
Tue Jul 31 18:58:46 2007  recovered 12 nontrivial dependencies
Tue Jul 31 18:58:46 2007  prp42 factor: 245476063044641766698278446037400797293497
Tue Jul 31 18:58:46 2007  prp44 factor: 36697498431299323192437388994595232599875443
Tue Jul 31 18:58:46 2007  elapsed time 00:31:35

AMD 64 3400+

7·10¹³³+3 = 7(0)₁₃₂3_<134> = 29 · 59 · 1741 · 19286399236854181_<17> · 46083256114156603252213_<23> · C89

C89 = P40 · P49

P40 = 8783383808652802647890907770843019907393_<40>

P49 = 3010184316154118713322706068056130317359871964857_<49>

Tue Jul 31 19:07:15 2007  
Tue Jul 31 19:07:15 2007  
Tue Jul 31 19:07:15 2007  Msieve v. 1.25
Tue Jul 31 19:07:15 2007  random seeds: d5724f40 7200004e
Tue Jul 31 19:07:15 2007  factoring 26439604183568695431333540511848343933708312285905784586381054531841927202958085090487801 (89 digits)
Tue Jul 31 19:07:15 2007  commencing quadratic sieve (89-digit input)
Tue Jul 31 19:07:15 2007  using multiplier of 1
Tue Jul 31 19:07:15 2007  using 64kb Opteron sieve core
Tue Jul 31 19:07:15 2007  sieve interval: 15 blocks of size 65536
Tue Jul 31 19:07:15 2007  processing polynomials in batches of 7
Tue Jul 31 19:07:15 2007  using a sieve bound of 1544831 (58667 primes)
Tue Jul 31 19:07:15 2007  using large prime bound of 123586480 (26 bits)
Tue Jul 31 19:07:15 2007  using double large prime bound of 367745783685200 (42-49 bits)
Tue Jul 31 19:07:15 2007  using trial factoring cutoff of 49 bits
Tue Jul 31 19:07:15 2007  polynomial 'A' values have 11 factors
Tue Jul 31 19:50:38 2007  58799 relations (16800 full + 41999 combined from 610095 partial), need 58763
Tue Jul 31 19:50:38 2007  begin with 626895 relations
Tue Jul 31 19:50:39 2007  reduce to 139283 relations in 10 passes
Tue Jul 31 19:50:39 2007  attempting to read 139283 relations
Tue Jul 31 19:50:40 2007  recovered 139283 relations
Tue Jul 31 19:50:40 2007  recovered 109037 polynomials
Tue Jul 31 19:50:40 2007  attempting to build 58799 cycles
Tue Jul 31 19:50:41 2007  found 58799 cycles in 5 passes
Tue Jul 31 19:50:41 2007  distribution of cycle lengths:
Tue Jul 31 19:50:41 2007     length 1 : 16800
Tue Jul 31 19:50:41 2007     length 2 : 11719
Tue Jul 31 19:50:41 2007     length 3 : 10451
Tue Jul 31 19:50:41 2007     length 4 : 7497
Tue Jul 31 19:50:41 2007     length 5 : 5180
Tue Jul 31 19:50:41 2007     length 6 : 3241
Tue Jul 31 19:50:41 2007     length 7 : 1863
Tue Jul 31 19:50:41 2007     length 9+: 2048
Tue Jul 31 19:50:41 2007  largest cycle: 18 relations
Tue Jul 31 19:50:41 2007  matrix is 58667 x 58799 with weight 3374117 (avg 57.38/col)
Tue Jul 31 19:50:42 2007  filtering completed in 3 passes
Tue Jul 31 19:50:42 2007  matrix is 53856 x 53920 with weight 3132205 (avg 58.09/col)
Tue Jul 31 19:50:43 2007  saving the first 48 matrix rows for later
Tue Jul 31 19:50:43 2007  matrix is 53808 x 53920 with weight 2508505 (avg 46.52/col)
Tue Jul 31 19:50:43 2007  matrix includes 64 packed rows
Tue Jul 31 19:50:43 2007  using block size 21568 for processor cache size 512 kB
Tue Jul 31 19:50:43 2007  commencing Lanczos iteration
Tue Jul 31 19:51:11 2007  lanczos halted after 852 iterations
Tue Jul 31 19:51:11 2007  recovered 17 nontrivial dependencies
Tue Jul 31 19:51:11 2007  prp40 factor: 8783383808652802647890907770843019907393
Tue Jul 31 19:51:11 2007  prp49 factor: 3010184316154118713322706068056130317359871964857
Tue Jul 31 19:51:11 2007  elapsed time 00:43:56

AMD 64 3400+

7·10¹⁰⁹+3 = 7(0)₁₀₈3_<110> = 61 · 283 · 6833 · 3752738047_<10> · C93

C93 = P35 · P58

P35 = 94998794192060872628935849323365693_<35>

P58 = 1664577444559100089652031980780871295487207378438987754367_<58>

Tue Jul 31 20:06:20 2007  
Tue Jul 31 20:06:20 2007  
Tue Jul 31 20:06:20 2007  Msieve v. 1.25
Tue Jul 31 20:06:20 2007  random seeds: 58a7aa10 e5a73f18
Tue Jul 31 20:06:20 2007  factoring 158132850072416566802699765435756674614463053664908574703804989105665472581049135992398731331 (93 digits)
Tue Jul 31 20:06:20 2007  commencing quadratic sieve (92-digit input)
Tue Jul 31 20:06:20 2007  using multiplier of 5
Tue Jul 31 20:06:20 2007  using 64kb Opteron sieve core
Tue Jul 31 20:06:20 2007  sieve interval: 18 blocks of size 65536
Tue Jul 31 20:06:20 2007  processing polynomials in batches of 6
Tue Jul 31 20:06:20 2007  using a sieve bound of 1885601 (70588 primes)
Tue Jul 31 20:06:20 2007  using large prime bound of 220615317 (27 bits)
Tue Jul 31 20:06:20 2007  using double large prime bound of 1043624286913572 (42-50 bits)
Tue Jul 31 20:06:20 2007  using trial factoring cutoff of 50 bits
Tue Jul 31 20:06:20 2007  polynomial 'A' values have 12 factors
Tue Jul 31 22:12:14 2007  71029 relations (18147 full + 52882 combined from 923968 partial), need 70684
Tue Jul 31 22:12:15 2007  begin with 942115 relations
Tue Jul 31 22:12:16 2007  reduce to 179413 relations in 13 passes
Tue Jul 31 22:12:16 2007  attempting to read 179413 relations
Tue Jul 31 22:12:18 2007  recovered 179413 relations
Tue Jul 31 22:12:18 2007  recovered 159146 polynomials
Tue Jul 31 22:12:18 2007  attempting to build 71029 cycles
Tue Jul 31 22:12:18 2007  found 71029 cycles in 5 passes
Tue Jul 31 22:12:19 2007  distribution of cycle lengths:
Tue Jul 31 22:12:19 2007     length 1 : 18147
Tue Jul 31 22:12:19 2007     length 2 : 13037
Tue Jul 31 22:12:19 2007     length 3 : 12364
Tue Jul 31 22:12:19 2007     length 4 : 9648
Tue Jul 31 22:12:19 2007     length 5 : 7028
Tue Jul 31 22:12:19 2007     length 6 : 4488
Tue Jul 31 22:12:19 2007     length 7 : 2773
Tue Jul 31 22:12:19 2007     length 9+: 3544
Tue Jul 31 22:12:19 2007  largest cycle: 18 relations
Tue Jul 31 22:12:19 2007  matrix is 70588 x 71029 with weight 4271043 (avg 60.13/col)
Tue Jul 31 22:12:20 2007  filtering completed in 3 passes
Tue Jul 31 22:12:20 2007  matrix is 66489 x 66553 with weight 4008580 (avg 60.23/col)
Tue Jul 31 22:12:21 2007  saving the first 48 matrix rows for later
Tue Jul 31 22:12:21 2007  matrix is 66441 x 66553 with weight 3003773 (avg 45.13/col)
Tue Jul 31 22:12:21 2007  matrix includes 64 packed rows
Tue Jul 31 22:12:21 2007  using block size 21845 for processor cache size 512 kB
Tue Jul 31 22:12:21 2007  commencing Lanczos iteration
Tue Jul 31 22:13:01 2007  lanczos halted after 1053 iterations
Tue Jul 31 22:13:02 2007  recovered 19 nontrivial dependencies
Tue Jul 31 22:13:02 2007  prp35 factor: 94998794192060872628935849323365693
Tue Jul 31 22:13:02 2007  prp58 factor: 1664577444559100089652031980780871295487207378438987754367
Tue Jul 31 22:13:02 2007  elapsed time 02:06:42

AMD 64 3400+

Jul 31, 2007

By Sinkiti Sibata / Msieve v. 1.23

7·10¹¹⁵+3 = 7(0)₁₁₄3_<116> = 71 · 571 · 1753 · 41759 · 101687624751179_<15> · C90

C90 = P45 · P46

P45 = 229383234010881253145836095413674027664523319_<45>

P46 = 1011211039809810274754617373533701326457880829_<46>

Tue Jul 31 07:34:45 2007  Msieve v. 1.23
Tue Jul 31 07:34:45 2007  random seeds: f6cd87d8 a53fdc24
Tue Jul 31 07:34:45 2007  factoring 231954858579080269057677376740414939630659505325131391785225954643473927231021865193551451 (90 digits)
Tue Jul 31 07:34:46 2007  commencing quadratic sieve (89-digit input)
Tue Jul 31 07:34:46 2007  using multiplier of 11
Tue Jul 31 07:34:46 2007  using 64kb Pentium 2 sieve core
Tue Jul 31 07:34:46 2007  sieve interval: 18 blocks of size 65536
Tue Jul 31 07:34:46 2007  processing polynomials in batches of 6
Tue Jul 31 07:34:46 2007  using a sieve bound of 1575269 (59601 primes)
Tue Jul 31 07:34:46 2007  using large prime bound of 126021520 (26 bits)
Tue Jul 31 07:34:46 2007  using double large prime bound of 380890718607520 (42-49 bits)
Tue Jul 31 07:34:46 2007  using trial factoring cutoff of 49 bits
Tue Jul 31 07:34:46 2007  polynomial 'A' values have 12 factors
Tue Jul 31 17:16:16 2007  59785 relations (16189 full + 43596 combined from 628261 partial), need 59697
Tue Jul 31 17:16:20 2007  begin with 644450 relations
Tue Jul 31 17:16:21 2007  reduce to 144357 relations in 9 passes
Tue Jul 31 17:16:21 2007  attempting to read 144357 relations
Tue Jul 31 17:16:29 2007  recovered 144357 relations
Tue Jul 31 17:16:29 2007  recovered 122313 polynomials
Tue Jul 31 17:16:29 2007  attempting to build 59785 cycles
Tue Jul 31 17:16:30 2007  found 59785 cycles in 6 passes
Tue Jul 31 17:16:34 2007  distribution of cycle lengths:
Tue Jul 31 17:16:34 2007     length 1 : 16189
Tue Jul 31 17:16:34 2007     length 2 : 11643
Tue Jul 31 17:16:34 2007     length 3 : 10503
Tue Jul 31 17:16:34 2007     length 4 : 7913
Tue Jul 31 17:16:34 2007     length 5 : 5683
Tue Jul 31 17:16:34 2007     length 6 : 3388
Tue Jul 31 17:16:34 2007     length 7 : 2104
Tue Jul 31 17:16:34 2007     length 9+: 2362
Tue Jul 31 17:16:34 2007  largest cycle: 22 relations
Tue Jul 31 17:16:35 2007  matrix is 59601 x 59785 with weight 3535144 (avg 59.13/col)
Tue Jul 31 17:16:41 2007  filtering completed in 3 passes
Tue Jul 31 17:16:41 2007  matrix is 55625 x 55687 with weight 3317745 (avg 59.58/col)
Tue Jul 31 17:16:43 2007  saving the first 48 matrix rows for later
Tue Jul 31 17:16:43 2007  matrix is 55577 x 55687 with weight 2590949 (avg 46.53/col)
Tue Jul 31 17:16:43 2007  matrix includes 64 packed rows
Tue Jul 31 17:16:43 2007  using block size 5461 for processor cache size 128 kB
Tue Jul 31 17:16:44 2007  commencing Lanczos iteration
Tue Jul 31 17:19:46 2007  lanczos halted after 879 iterations
Tue Jul 31 17:19:47 2007  recovered 16 nontrivial dependencies
Tue Jul 31 17:19:50 2007  prp45 factor: 229383234010881253145836095413674027664523319
Tue Jul 31 17:19:50 2007  prp46 factor: 1011211039809810274754617373533701326457880829
Tue Jul 31 17:19:50 2007  elapsed time 09:45:05

Jul 30, 2007 (2nd)

The factor table of 700...003 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Jul 30, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp

(7·10¹⁶³-1)/3 = 2(3)₁₆₃_<164> = 31 · 26480968333_<11> · C152

C152 = P73 · P79

P73 = 6005499498342026296996247513568027884866123915015309416115316591128827611_<73>

P79 = 4732951939505968237884782724690167133167712747934122360855348805147547921808661_<79>

Number: n
N=28423740498380012646351441222833046018885664846683919488791556370619977774011134692143246359762495624861587748954770936198932245142948442069275595738871
  ( 152 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=6005499498342026296996247513568027884866123915015309416115316591128827611 (pp73)
 r2=4732951939505968237884782724690167133167712747934122360855348805147547921808661 (pp79)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 62.00 hours.
Scaled time: 84.63 units (timescale=1.365).
Factorization parameters were as follows:
name: KA_2_3_163
n: 28423740498380012646351441222833046018885664846683919488791556370619977774011134692143246359762495624861587748954770936198932245142948442069275595738871
skew: 0.17
deg: 5
c5: 7000
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2600001)
Primes: RFBsize:250150, AFBsize:250186, largePrimes:7515166 encountered
Relations: rels:7038514, finalFF:567391
Max relations in full relation-set: 28
Initial matrix: 500403 x 567391 with sparse part having weight 42599784.
Pruned matrix : 449316 x 451882 with weight 30245743.
Total sieving time: 56.37 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 5.04 hours.
Total square root time: 0.30 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 62.00 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 29, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

(2·10¹⁶⁰+1)/3 = (6)₁₅₉7_<160> = 227 · 419 · 1458595001_<10> · 16026242851179144358700459_<26> · C121

C121 = P48 · P74

P48 = 161463735175025949280548404486238854502944749577_<48>

P74 = 18570663712910018221335055151517350281831147548443709556829543800274598713_<74>

Number: 66667_160
N=2998488727765767306056724256898840427400661293190185342767414314752818203241712663724341297601486372223255855543951494401
  ( 121 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=161463735175025949280548404486238854502944749577 (pp48)
 r2=18570663712910018221335055151517350281831147548443709556829543800274598713 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 25.89 hours.
Scaled time: 55.06 units (timescale=2.127).
Factorization parameters were as follows:
n: 2998488727765767306056724256898840427400661293190185342767414314752818203241712663724341297601486372223255855543951494401
m: 100000000000000000000000000000000
c5: 2
c0: 1
skew: 0.87
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3500001)
Primes: RFBsize:283146, AFBsize:282707, largePrimes:5745066 encountered
Relations: rels:5888263, finalFF:750273
Max relations in full relation-set: 28
Initial matrix: 565918 x 750273 with sparse part having weight 47378726.
Pruned matrix : 416316 x 419209 with weight 29586910.
Total sieving time: 24.83 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.93 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 25.89 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

(83·10¹⁵⁸+61)/9 = 9(2)₁₅₇9_<159> = 117545651888135840815842818880953169751_<39> · C121

C121 = P53 · P69

P53 = 19948874429255659337544510594592376405101429806260627_<53>

P69 = 393287929414931017949697007530034379610754908774038875145063023078177_<69>

Number: 92229_158
N=7845651518440422046274124148055206572053296058018576850355756519442414234698093136206369834368093919414710356459458036979
  ( 121 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=19948874429255659337544510594592376405101429806260627 (pp53)
 r2=393287929414931017949697007530034379610754908774038875145063023078177 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 38.31 hours.
Scaled time: 82.06 units (timescale=2.142).
Factorization parameters were as follows:
n: 7845651518440422046274124148055206572053296058018576850355756519442414234698093136206369834368093919414710356459458036979
m: 20000000000000000000000000000000
c5: 10375
c0: 244
skew: 0.47
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4200001)
Primes: RFBsize:283146, AFBsize:283188, largePrimes:5761581 encountered
Relations: rels:5805318, finalFF:660921
Max relations in full relation-set: 28
Initial matrix: 566401 x 660921 with sparse part having weight 47281694.
Pruned matrix : 502096 x 504992 with weight 33891197.
Total sieving time: 36.70 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.46 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 38.31 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 29, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(10¹⁶³-7)/3 = (3)₁₆₂1_<163> = 401 · 340687 · C155

C155 = P34 · P58 · P65

P34 = 1169754593539985501873975459730137_<34>

P58 = 1658788489453091556494815237092230110842898508302882101211_<58>

P65 = 12574566972385656776513038298834533485077579778495931368800832559_<65>

Number: n
N=24399381113601954464601318101902556137967969424530421893773531937366173816979720120115908479199970449421545694400908832051620423776210184232870562715436013
  ( 155 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=1169754593539985501873975459730137 (pp34)
 r2=1658788489453091556494815237092230110842898508302882101211 (pp58)
 r3=12574566972385656776513038298834533485077579778495931368800832559 (pp65)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 42.87 hours.
Scaled time: 62.21 units (timescale=1.451).
Factorization parameters were as follows:
name: KA_3_162_1
n: 24399381113601954464601318101902556137967969424530421893773531937366173816979720120115908479199970449421545694400908832051620423776210184232870562715436013
skew: 0.37
deg: 5
c5: 1000
c0: -7
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2000001)
Primes: RFBsize:250150, AFBsize:249886, largePrimes:7373909 encountered
Relations: rels:6949423, finalFF:611249
Max relations in full relation-set: 28
Initial matrix: 500102 x 611249 with sparse part having weight 41187658.
Pruned matrix : 405991 x 408555 with weight 24372265.
Total sieving time: 38.29 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 4.21 hours.
Total square root time: 0.14 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 42.87 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(16·10¹⁶³-7)/9 = 1(7)₁₆₃_<164> = 257 · 423277 · C156

C156 = P41 · P51 · P64

P41 = 73711078007185859471835668366940479393171_<41>

P51 = 821912260604473840932297229077014953449618054109223_<51>

P64 = 2697500027586692927181515435498036599615808525035592363867652721_<64>

Number: n
N=163425446216914956342510976477755726884460633328290330485790994496146586807310687393666786552509784278911484101296929939309989227903639425547667346331647893
  ( 156 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=73711078007185859471835668366940479393171 (pp41)
 r2=821912260604473840932297229077014953449618054109223 (pp51)
 r3=2697500027586692927181515435498036599615808525035592363867652721 (pp64)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 61.71 hours.
Scaled time: 73.69 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_1_7_163
n: 163425446216914956342510976477755726884460633328290330485790994496146586807310687393666786552509784278911484101296929939309989227903639425547667346331647893
type: snfs
skew: 0.43
deg: 5
c5: 500
c0: -7
m: 200000000000000000000000000000000
rlim: 3600000
alim: 3600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2600001)
Primes: RFBsize:256726, AFBsize:256456, largePrimes:7276877 encountered
Relations: rels:6788820, finalFF:601944
Max relations in full relation-set: 28
Initial matrix: 513248 x 601944 with sparse part having weight 36488675.
Pruned matrix : 437144 x 439774 with weight 22807094.
Total sieving time: 56.01 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 5.06 hours.
Total square root time: 0.35 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3600000,3600000,28,28,48,48,2.3,2.3,100000
total time: 61.71 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Jul 28, 2007 (5th)

By honeycrack7 / GGNFS-0.77.1-20060513-k8

4·10¹⁷⁰+3 = 4(0)₁₆₉3_<171> = 13 · 2332022449008725190543961_<25> · 9091674957193157331925985427613_<31> · C115

C115 = P52 · P63

P52 = 5519848976962319518553726010848147162459426482482457_<52>

P63 = 262913457234491688131920560141939578410279343647748980394630731_<63>

Jul 28, 2007 (4th)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

7·10¹⁵⁰-3 = 6(9)₁₄₉7_<151> = 23537 · 117047527 · C139

C139 = P55 · P84

P55 = 8764729519896434388185150658193376696083145995054647761_<55>

P84 = 289898636097657769901727571746993680083346617528438604091309287391756698440245150523_<84>

Number: 69997_150
N=2540883133582855129103294851665209412058385608097038665067689287721635183644657611078834087886540221297369512376354576518671195152189929003
  ( 139 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=8764729519896434388185150658193376696083145995054647761 (pp55)
 r2=289898636097657769901727571746993680083346617528438604091309287391756698440245150523 (pp84)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 26.99 hours.
Scaled time: 18.41 units (timescale=0.682).
Factorization parameters were as follows:
name: 69997_150
n: 2540883133582855129103294851665209412058385608097038665067689287721635183644657611078834087886540221297369512376354576518671195152189929003
m: 1000000000000000000000000000000
c5: 7
c0: -3
skew: 0.84
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:175733, largePrimes:5394959 encountered
Relations: rels:5312038, finalFF:400934
Max relations in full relation-set: 0
Initial matrix: 352100 x 400934 with sparse part having weight 23256659.
Pruned matrix : 317140 x 318964 with weight 17341814.
Total sieving time: 23.86 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.81 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 26.99 hours.
 --------- CPU info (if available) ----------

Jul 28, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

(2·10¹⁵⁹+43)/9 = (2)₁₅₈7_<159> = 239 · 809 · 4027 · 238547 · 885263 · C139

C139 = P45 · P94

P45 = 347764084623597453108213934934669011761877139_<45>

P94 = 3886229406208272471593857319229809807058694766986913068964477873900842341708025811926593810169_<94>

Number: 22227_159
N=1351491012087326549211979087569214053838808220524355993937154678565591119267140370025719121273819964452615804361909214924166342965666826491
  ( 139 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=347764084623597453108213934934669011761877139 (pp45)
 r2=3886229406208272471593857319229809807058694766986913068964477873900842341708025811926593810169 (pp94)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 29.92 hours.
Scaled time: 63.91 units (timescale=2.136).
Factorization parameters were as follows:
n: 1351491012087326549211979087569214053838808220524355993937154678565591119267140370025719121273819964452615804361909214924166342965666826491
m: 100000000000000000000000000000000
c5: 1
c0: 215
skew: 2.93
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:283892, largePrimes:5618226 encountered
Relations: rels:5629970, finalFF:640876
Max relations in full relation-set: 28
Initial matrix: 567102 x 640876 with sparse part having weight 39940913.
Pruned matrix : 509180 x 512079 with weight 28084715.
Total sieving time: 27.43 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 2.35 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 29.92 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

2·10¹⁵⁹-9 = 1(9)₁₅₈1_<160> = 11 · 24691 · 52861 · 266261 · 4151011 · C138

C138 = P47 · P91

P47 = 40930808775623536636245772098276860041853369431_<47>

P91 = 3079296349757713797324715535825813229817563878384139018839754824005144136790174117702778331_<91>

Number: 19991_159
N=126038090055408555107408847579488891171318490786133096772283218499151669830811145264505896403808824896321957494548755525749518542444599661
  ( 138 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=40930808775623536636245772098276860041853369431 (pp47)
 r2=3079296349757713797324715535825813229817563878384139018839754824005144136790174117702778331 (pp91)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 23.56 hours.
Scaled time: 50.48 units (timescale=2.143).
Factorization parameters were as follows:
n: 126038090055408555107408847579488891171318490786133096772283218499151669830811145264505896403808824896321957494548755525749518542444599661
m: 100000000000000000000000000000000
c5: 1
c0: -45
skew: 2.14
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3300001)
Primes: RFBsize:283146, AFBsize:283177, largePrimes:5644839 encountered
Relations: rels:5726943, finalFF:702143
Max relations in full relation-set: 28
Initial matrix: 566387 x 702143 with sparse part having weight 41923918.
Pruned matrix : 452126 x 455021 with weight 25213445.
Total sieving time: 22.45 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.97 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 23.56 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 28, 2007 (2nd)

By JMB / GMP-ECM B1=1000000

(25·10¹⁹⁷-7)/9 = 2(7)₁₉₇_<198> = 1373 · C195

C195 = P32 · C163

P32 = 85030629703280968207735306809773_<32>

C163 = [2379312940877966056839041692231255679976556971431892634670943410004573553981330698167952823566726167898725398615761464958869155626448416241982456084785127904775513_<163>]

Jul 28, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(2·10¹⁶²+1)/3 = (6)₁₆₁7_<162> = 89 · 5942153001947_<13> · C148

C148 = P54 · P94

P54 = 260109084099025462382032890421450150382266857071125187_<54>

P94 = 4846401432771397426216214806428116706548778140446303082763979669092372351100444829939195019827_<94>

Number: n
N=1260593037854372908702191537268240612213565622246104193999268784722069543835151571262530708956084288244937923573974982203746499701928418153664082649
  ( 148 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=260109084099025462382032890421450150382266857071125187 (pp54)
 r2=4846401432771397426216214806428116706548778140446303082763979669092372351100444829939195019827 (pp94)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 41.90 hours.
Scaled time: 55.51 units (timescale=1.325).
Factorization parameters were as follows:
name: KA_6_161_7
n: 1260593037854372908702191537268240612213565622246104193999268784722069543835151571262530708956084288244937923573974982203746499701928418153664082649
skew: 0.35
deg: 5
c5: 200
c0: 1
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:250150, AFBsize:249566, largePrimes:7143893 encountered
Relations: rels:6652480, finalFF:561530
Max relations in full relation-set: 48
Initial matrix: 499781 x 561530 with sparse part having weight 37610274.
Pruned matrix : 446875 x 449437 with weight 24206431.
Total sieving time: 36.44 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 5.14 hours.
Total square root time: 0.09 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 41.90 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 27, 2007 (6th)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp

9·10¹⁶¹+1 = 9(0)₁₆₀1_<162> = 19² · 268115868282277_<15> · C145

C145 = P43 · P103

P43 = 1452612416148001223786387377375980929408933_<43>

P103 = 6401224184307784221531476143753944364302696193784598490179821129689892756268275790197304471135782300801_<103>

Number: n
N=9298497728672348738654088152725043047653335440887426945669034198013979457141066603768096625347093326453497719648788386059162812868886287742455333
  ( 145 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=1452612416148001223786387377375980929408933 (pp43)
 r2=6401224184307784221531476143753944364302696193784598490179821129689892756268275790197304471135782300801 (pp103)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 50.93 hours.
Scaled time: 54.65 units (timescale=1.073).
Factorization parameters were as follows:
name: KA_9_0_160_1
n: 9298497728672348738654088152725043047653335440887426945669034198013979457141066603768096625347093326453497719648788386059162812868886287742455333
skew: 0.41
deg: 5
c5: 90
c0: 1
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2000001)
Primes: RFBsize:250150, AFBsize:249956, largePrimes:7360513 encountered
Relations: rels:6909886, finalFF:585073
Max relations in full relation-set: 28
Initial matrix: 500173 x 585073 with sparse part having weight 41263807.
Pruned matrix : 430599 x 433163 with weight 26317605.
Total sieving time: 45.72 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 4.79 hours.
Total square root time: 0.16 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 50.93 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 27, 2007 (5th)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

5·10¹⁶³-3 = 4(9)₁₆₂7_<164> = 2833 · 184967 · 13315699 · C148

C148 = P35 · P113

P35 = 74998792236344109387450078891725779_<35>

P113 = 95545654112791421636906751022948221950213818775035727503822215288586505310116495426553720942470582028517007755987_<113>

Number: 49997_163
N=7165808661890840897859714216746508466161349306048122768370338285750348690423700476081529989454370863114686016738935169566343753929497072942549488873
  ( 148 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=74998792236344109387450078891725779 (pp35)
 r2=95545654112791421636906751022948221950213818775035727503822215288586505310116495426553720942470582028517007755987 (pp113)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 96.02 hours.
Scaled time: 65.49 units (timescale=0.682).
Factorization parameters were as follows:
name: 49997_163
n: 7165808661890840897859714216746508466161349306048122768370338285750348690423700476081529989454370863114686016738935169566343753929497072942549488873
m: 500000000000000000000000000000000
c5: 8
c0: -15
skew: 1.13
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4550001)
Primes: RFBsize:315948, AFBsize:315761, largePrimes:5791399 encountered
Relations: rels:5931578, finalFF:709466
Max relations in full relation-set: 0
Initial matrix: 631774 x 709466 with sparse part having weight 36626735.
Pruned matrix : 573328 x 576550 with weight 28530803.
Total sieving time: 82.87 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 12.59 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 96.02 hours.
 --------- CPU info (if available) ----------

Jul 27, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

6·10¹⁶²-1 = 5(9)₁₆₂_<163> = 33413 · 15377792567_<11> · C149

C149 = P40 · P109

P40 = 8461863041793557423309640118101540415199_<40>

P109 = 1379989523873218126548187496324337406517253315539049102957670242333680936574239687581847686601665035459375931_<109>

Number: n
N=11677282350125072565528496755056693390894578124346913826602577065368169930338426882409563592311243405998642515404383594961811857506465947731167175269
  ( 149 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=8461863041793557423309640118101540415199 (pp40)
 r2=1379989523873218126548187496324337406517253315539049102957670242333680936574239687581847686601665035459375931 (pp109)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 42.45 hours.
Scaled time: 61.47 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_5_9_162
n: 11677282350125072565528496755056693390894578124346913826602577065368169930338426882409563592311243405998642515404383594961811857506465947731167175269
skew: 0.28
deg: 5
c5: 600
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1900001)
Primes: RFBsize:250150, AFBsize:249916, largePrimes:7325134 encountered
Relations: rels:6881070, finalFF:592491
Max relations in full relation-set: 28
Initial matrix: 500132 x 592491 with sparse part having weight 39869074.
Pruned matrix : 421848 x 424412 with weight 24612582.
Total sieving time: 37.71 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 4.45 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 42.45 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(13·10¹⁶¹-1)/3 = 4(3)₁₆₁_<162> = 35591 · 56617483129_<11> · C147

C147 = P28 · P56 · P64

P28 = 6916321829686376333181913823_<28>

P56 = 11574884111412367178608580326121743923707807455418638553_<56>

P64 = 2686207161095289004338174437326230035207838243702836292283105613_<64>

Number: n
N=215045989550297315654863919994251904257815223605138461618086564897394811789556878090551491142316445311255103555809184394301856619887795350638801947
  ( 147 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=6916321829686376333181913823 (pp28)
 r2=11574884111412367178608580326121743923707807455418638553 (pp56)
 r3=2686207161095289004338174437326230035207838243702836292283105613 (pp64)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 61.29 hours.
Scaled time: 58.97 units (timescale=0.962).
Factorization parameters were as follows:
name: KA_4_3_161
n: 215045989550297315654863919994251904257815223605138461618086564897394811789556878090551491142316445311255103555809184394301856619887795350638801947
type: snfs
skew: 1
deg: 5
c5: 130
c0: -1
m: 100000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [1750000, 3750001)
Primes: RFBsize:250150, AFBsize:250361, largePrimes:7677203 encountered
Relations: rels:7173676, finalFF:581835
Max relations in full relation-set: 48
Initial matrix: 500578 x 581835 with sparse part having weight 54017180.
Pruned matrix : 461516 x 464082 with weight 37017683.
Total sieving time: 53.03 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 7.72 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.3,2.3,100000
total time: 61.29 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 2400+ stepping 01
Memory: 901612k/917504k available (1069k kernel code, 15504k reserved, 459k data, 96k init, 0k highmem)
sisfb: Memory heap starting at 12288K, size 19960K
Calibrating delay loop... 4010.80 BogoMIPS

Jul 27, 2007 (3rd)

By JMB / GMP-ECM B1=1000000

(25·10¹⁸⁵-7)/9 = 2(7)₁₈₅_<186> = 809 · 1498561 · 4617297143_<10> · C167

C167 = P32 · P135

P32 = 54832091297347447631038216522501_<32>

P135 = 905006956151265763655758125706409102912355176390129079383960741381669849617325066992415304569102339104861501591003320417505261613287411_<135>

Jul 27, 2007 (2nd)

By Jo Yeong Uk / Msieve v. 1.25, GGNFS-0.77.1-20050930-nocona

(25·10¹⁶⁵-7)/9 = 2(7)₁₆₅_<166> = 296987 · 1840206433618866165991_<22> · 26841431788288106581500307455836598045271854373_<47> · C93

C93 = P44 · P49

P44 = 47762472444603047641362563601969990683449099_<44>

P49 = 3964615152987551810337697840608378229741533181603_<49>

Fri Jul 27 00:00:02 2007  
Fri Jul 27 00:00:02 2007  
Fri Jul 27 00:00:02 2007  Msieve v. 1.25
Fri Jul 27 00:00:02 2007  random seeds: 2bd8376f a00d4807
Fri Jul 27 00:00:02 2007  factoring 189359821998023639433196029818337369944098310651646127033896205015214673371291949815173725697 (93 digits)
Fri Jul 27 00:00:02 2007  commencing quadratic sieve (92-digit input)
Fri Jul 27 00:00:02 2007  using multiplier of 1
Fri Jul 27 00:00:02 2007  using 32kb Intel Core sieve core
Fri Jul 27 00:00:02 2007  sieve interval: 36 blocks of size 32768
Fri Jul 27 00:00:02 2007  processing polynomials in batches of 6
Fri Jul 27 00:00:02 2007  using a sieve bound of 1888763 (70588 primes)
Fri Jul 27 00:00:02 2007  using large prime bound of 220985271 (27 bits)
Fri Jul 27 00:00:02 2007  using double large prime bound of 1046776511774331 (42-50 bits)
Fri Jul 27 00:00:02 2007  using trial factoring cutoff of 50 bits
Fri Jul 27 00:00:02 2007  polynomial 'A' values have 12 factors
Fri Jul 27 01:44:58 2007  70722 relations (18185 full + 52537 combined from 929745 partial), need 70684
Fri Jul 27 01:44:59 2007  begin with 947930 relations
Fri Jul 27 01:44:59 2007  reduce to 179343 relations in 10 passes
Fri Jul 27 01:44:59 2007  attempting to read 179343 relations
Fri Jul 27 01:45:01 2007  recovered 179343 relations
Fri Jul 27 01:45:01 2007  recovered 160005 polynomials
Fri Jul 27 01:45:01 2007  attempting to build 70722 cycles
Fri Jul 27 01:45:01 2007  found 70722 cycles in 6 passes
Fri Jul 27 01:45:01 2007  distribution of cycle lengths:
Fri Jul 27 01:45:01 2007     length 1 : 18185
Fri Jul 27 01:45:01 2007     length 2 : 12896
Fri Jul 27 01:45:01 2007     length 3 : 12122
Fri Jul 27 01:45:01 2007     length 4 : 9485
Fri Jul 27 01:45:01 2007     length 5 : 6891
Fri Jul 27 01:45:01 2007     length 6 : 4485
Fri Jul 27 01:45:01 2007     length 7 : 2866
Fri Jul 27 01:45:01 2007     length 9+: 3792
Fri Jul 27 01:45:01 2007  largest cycle: 24 relations
Fri Jul 27 01:45:01 2007  matrix is 70588 x 70722 with weight 4300045 (avg 60.80/col)
Fri Jul 27 01:45:02 2007  filtering completed in 3 passes
Fri Jul 27 01:45:02 2007  matrix is 66700 x 66763 with weight 4091463 (avg 61.28/col)
Fri Jul 27 01:45:03 2007  saving the first 48 matrix rows for later
Fri Jul 27 01:45:03 2007  matrix is 66652 x 66763 with weight 3180982 (avg 47.65/col)
Fri Jul 27 01:45:03 2007  matrix includes 64 packed rows
Fri Jul 27 01:45:03 2007  using block size 26705 for processor cache size 4096 kB
Fri Jul 27 01:45:03 2007  commencing Lanczos iteration
Fri Jul 27 01:45:24 2007  lanczos halted after 1056 iterations
Fri Jul 27 01:45:24 2007  recovered 17 nontrivial dependencies
Fri Jul 27 01:45:25 2007  prp44 factor: 47762472444603047641362563601969990683449099
Fri Jul 27 01:45:25 2007  prp49 factor: 3964615152987551810337697840608378229741533181603
Fri Jul 27 01:45:25 2007  elapsed time 01:45:23

(25·10¹⁷⁶-7)/9 = 2(7)₁₇₆_<177> = 53 · 170174087 · 9924073470733_<13> · 5048202952542749191_<19> · 250364392061117480432331832411240313552347_<42> · C94

C94 = P37 · P57

P37 = 3963347185486060546396209546732592561_<37>

P57 = 619536279901870322724589710902400805635161682525735259507_<57>

Fri Jul 27 01:51:19 2007  
Fri Jul 27 01:51:19 2007  
Fri Jul 27 01:51:19 2007  Msieve v. 1.25
Fri Jul 27 01:51:19 2007  random seeds: a432810d 7a7c1870
Fri Jul 27 01:51:19 2007  factoring 2455437371255581962526922265114020960306360460563718242524031556201268139958057995992232727427 (94 digits)
Fri Jul 27 01:51:19 2007  commencing quadratic sieve (94-digit input)
Fri Jul 27 01:51:19 2007  using multiplier of 3
Fri Jul 27 01:51:19 2007  using 32kb Intel Core sieve core
Fri Jul 27 01:51:19 2007  sieve interval: 36 blocks of size 32768
Fri Jul 27 01:51:19 2007  processing polynomials in batches of 6
Fri Jul 27 01:51:19 2007  using a sieve bound of 2023097 (75294 primes)
Fri Jul 27 01:51:19 2007  using large prime bound of 271094998 (28 bits)
Fri Jul 27 01:51:19 2007  using double large prime bound of 1512232961643520 (42-51 bits)
Fri Jul 27 01:51:19 2007  using trial factoring cutoff of 51 bits
Fri Jul 27 01:51:19 2007  polynomial 'A' values have 12 factors
Fri Jul 27 03:46:55 2007  75609 relations (19298 full + 56311 combined from 1057051 partial), need 75390
Fri Jul 27 03:46:55 2007  begin with 1076349 relations
Fri Jul 27 03:46:56 2007  reduce to 193033 relations in 11 passes
Fri Jul 27 03:46:56 2007  attempting to read 193033 relations
Fri Jul 27 03:46:58 2007  recovered 193033 relations
Fri Jul 27 03:46:58 2007  recovered 172661 polynomials
Fri Jul 27 03:46:58 2007  attempting to build 75609 cycles
Fri Jul 27 03:46:58 2007  found 75609 cycles in 5 passes
Fri Jul 27 03:46:58 2007  distribution of cycle lengths:
Fri Jul 27 03:46:58 2007     length 1 : 19298
Fri Jul 27 03:46:58 2007     length 2 : 13639
Fri Jul 27 03:46:58 2007     length 3 : 12851
Fri Jul 27 03:46:58 2007     length 4 : 10149
Fri Jul 27 03:46:58 2007     length 5 : 7572
Fri Jul 27 03:46:58 2007     length 6 : 4979
Fri Jul 27 03:46:58 2007     length 7 : 3073
Fri Jul 27 03:46:58 2007     length 9+: 4048
Fri Jul 27 03:46:58 2007  largest cycle: 19 relations
Fri Jul 27 03:46:58 2007  matrix is 75294 x 75609 with weight 4735754 (avg 62.63/col)
Fri Jul 27 03:46:59 2007  filtering completed in 3 passes
Fri Jul 27 03:46:59 2007  matrix is 71057 x 71120 with weight 4477233 (avg 62.95/col)
Fri Jul 27 03:47:00 2007  saving the first 48 matrix rows for later
Fri Jul 27 03:47:00 2007  matrix is 71009 x 71120 with weight 3452561 (avg 48.55/col)
Fri Jul 27 03:47:00 2007  matrix includes 64 packed rows
Fri Jul 27 03:47:00 2007  using block size 28448 for processor cache size 4096 kB
Fri Jul 27 03:47:00 2007  commencing Lanczos iteration
Fri Jul 27 03:47:26 2007  lanczos halted after 1125 iterations
Fri Jul 27 03:47:26 2007  recovered 15 nontrivial dependencies
Fri Jul 27 03:47:26 2007  prp37 factor: 3963347185486060546396209546732592561
Fri Jul 27 03:47:26 2007  prp57 factor: 619536279901870322724589710902400805635161682525735259507
Fri Jul 27 03:47:26 2007  elapsed time 01:56:07

(7·10¹⁸¹-1)/3 = 2(3)₁₈₁_<182> = C182

C182 = P50 · P59 · P74

P50 = 63260551995570788106768735871476130074461634746477_<50>

P59 = 25995503880899966863964451990659560723251183499345255736491_<59>

P74 = 14188796769082230791752762485216295330686733826011471336380633628674520219_<74>

Number: 23333_181
N=23333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333
  ( 182 digits)
SNFS difficulty: 181 digits.
Divisors found:
 r1=63260551995570788106768735871476130074461634746477 (pp50)
 r2=25995503880899966863964451990659560723251183499345255736491 (pp59)
 r3=14188796769082230791752762485216295330686733826011471336380633628674520219 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 251.75 hours.
Scaled time: 538.99 units (timescale=2.141).
Factorization parameters were as follows:
n: 23333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333
m: 1000000000000000000000000000000000000
c5: 70
c0: -1
skew: 0.43
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [5000000, 9100001)
Primes: RFBsize:664579, AFBsize:665975, largePrimes:11133286 encountered
Relations: rels:11498215, finalFF:1574842
Max relations in full relation-set: 28
Initial matrix: 1330621 x 1574842 with sparse part having weight 97445326.
Pruned matrix : 1107698 x 1114415 with weight 66130008.
Total sieving time: 240.97 hours.
Total relation processing time: 0.46 hours.
Matrix solve time: 10.19 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,181,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000
total time: 251.75 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 27, 2007

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000

4·10¹⁹⁴+1 = 4(0)₁₉₃1_<195> = 721324202162977116296517293557_<30> · 230366834312643340988031253121778481_<36> · C130

C130 = P46 · P84

P46 = 4539551603725680577678687090612374940158174209_<46>

P84 = 530269411486144259272416902466941069870793165414892485082648513501276740375531374317_<84>

Jul 26, 2007 (5th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

(8·10¹⁵⁸+1)/9 = (8)₁₅₇9_<158> = 251 · 19051 · 661553 · 16802878173815484403_<20> · C127

C127 = P36 · P91

P36 = 507720820294334799136631537333312339_<36>

P91 = 3293689718850709442805545468432778915791702568309037103083241191944222576426385744129092889_<91>

Number: 88889_158
N=1672274845849899157699286610421044576382314630035217679398866050298573807484823525552765996029264801596675892531763861780857371
  ( 127 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=507720820294334799136631537333312339 (pp36)
 r2=3293689718850709442805545468432778915791702568309037103083241191944222576426385744129092889 (pp91)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 26.23 hours.
Scaled time: 56.17 units (timescale=2.141).
Factorization parameters were as follows:
n: 1672274845849899157699286610421044576382314630035217679398866050298573807484823525552765996029264801596675892531763861780857371
m: 100000000000000000000000000000000
c5: 2
c0: 25
skew: 1.66
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3500001)
Primes: RFBsize:283146, AFBsize:282402, largePrimes:5682679 encountered
Relations: rels:5768719, finalFF:704676
Max relations in full relation-set: 28
Initial matrix: 565613 x 704676 with sparse part having weight 43802932.
Pruned matrix : 450587 x 453479 with weight 27244630.
Total sieving time: 25.05 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.04 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 26.23 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 26, 2007 (4th)

By Alfred Reich

10⁵¹⁵+1 is divisible by 896048585318577702680084550566846611_<36>

Reference: Factorizations of numbers of the form 10^n+1 (Alfred Reich)

Jul 26, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

6·10¹⁶¹-1 = 5(9)₁₆₁_<162> = 43 · 836569 · 2898421 · C148

C148 = P43 · P48 · P58

P43 = 8293782204604425278695261694855447366239429_<43>

P48 = 373661139043910874867543028013950188940119372163_<48>

P58 = 1856902068363473523911678753942645197496692067981158293791_<58>

Number: n
N=5754658547595349311495950603756779150156168225617883200618038320893662324167945261296559539792048549985733231130607693324550635705623295348791018257
  ( 148 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=8293782204604425278695261694855447366239429 (pp43)
 r2=373661139043910874867543028013950188940119372163 (pp48)
 r3=1856902068363473523911678753942645197496692067981158293791 (pp58)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 38.23 hours.
Scaled time: 50.61 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_5_9_161
n: 5754658547595349311495950603756779150156168225617883200618038320893662324167945261296559539792048549985733231130607693324550635705623295348791018257
skew: 0.44
deg: 5
c5: 60
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:250150, AFBsize:249771, largePrimes:7114930 encountered
Relations: rels:6634553, finalFF:568518
Max relations in full relation-set: 48
Initial matrix: 499988 x 568518 with sparse part having weight 37166803.
Pruned matrix : 440914 x 443477 with weight 23182215.
Total sieving time: 33.28 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 4.57 hours.
Total square root time: 0.15 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 38.23 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

6·10¹⁶³+1 = 6(0)₁₆₂1_<164> = 17 · 353 · 383 · C158

C158 = P55 · P103

P55 = 5215147241069255739103596758994562191897609456843465301_<55>

P103 = 5005670690155230684429614037038784632521687552228111599112073609027731095334283017297356948767263632947_<103>

Number: n
N=26105309689464288588977555089817493429076006914426359749441237600521758122993426247931698067728485635335799124863001510192165535509094872351561945941994872047
  ( 158 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=5215147241069255739103596758994562191897609456843465301 (pp55)
 r2=5005670690155230684429614037038784632521687552228111599112073609027731095334283017297356948767263632947 (pp103)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 63.28 hours.
Scaled time: 75.62 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_6_0_162_1
n: 26105309689464288588977555089817493429076006914426359749441237600521758122993426247931698067728485635335799124863001510192165535509094872351561945941994872047
type: snfs
skew: 0.35
deg: 5
c5: 375
c0: 2
m: 200000000000000000000000000000000
rlim: 3600000
alim: 3600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2500001)
Primes: RFBsize:256726, AFBsize:256771, largePrimes:7311903 encountered
Relations: rels:6805144, finalFF:587598
Max relations in full relation-set: 28
Initial matrix: 513563 x 587598 with sparse part having weight 35738792.
Pruned matrix : 452305 x 454936 with weight 23525858.
Total sieving time: 57.84 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 5.04 hours.
Total square root time: 0.12 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3600000,3600000,28,28,48,48,2.3,2.3,100000
total time: 63.28 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Jul 26, 2007 (2nd)

By JMB / GMP-ECM B1=1000000

(25·10¹⁷⁶-7)/9 = 2(7)₁₇₆_<177> = 53 · 170174087 · 9924073470733_<13> · 5048202952542749191_<19> · C135

C135 = P42 · C94

P42 = 250364392061117480432331832411240313552347_<42>

C94 = [2455437371255581962526922265114020960306360460563718242524031556201268139958057995992232727427_<94>]

Jul 26, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs

7·10¹⁶⁰-3 = 6(9)₁₅₉7_<161> = 1023557 · 676040311822727_<15> · 225167822909311193771939915964703697_<36> · C105

C105 = P47 · P59

P47 = 26553121374225817669622704350957054548498613613_<47>

P59 = 16919655045991966846784423102442420227389002548091598746443_<59>

Number: 69997_160
N=449269654046257004984956784811621039356018734468246305859975642850924126367108968544894530278674215128559
  ( 105 digits)
Divisors found:
 r1=26553121374225817669622704350957054548498613613 (pp47)
 r2=16919655045991966846784423102442420227389002548091598746443 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.63 hours.
Scaled time: 18.49 units (timescale=2.142).
Factorization parameters were as follows:
name: 69997_160
n: 449269654046257004984956784811621039356018734468246305859975642850924126367108968544894530278674215128559
skew: 10958.86
# norm 7.52e+14
c5: 43560
c4: -563864382
c3: -51657033522313
c2: 36279037644759719
c1: 357816660151572433929
c0: 516503811917770537490127
# alpha -6.49
Y1: 32038029803
Y0: -100619974011831009902
# Murphy_E 2.05e-09
# M 112706527664659458380579445234447723037480698246914182616771058378695853459900351089940084316930206294864
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1320001)
Primes: RFBsize:135072, AFBsize:135315, largePrimes:4535175 encountered
Relations: rels:4601948, finalFF:406094
Max relations in full relation-set: 28
Initial matrix: 270467 x 406094 with sparse part having weight 36895626.
Pruned matrix : 194220 x 195636 with weight 16421677.
Polynomial selection time: 0.43 hours.
Total sieving time: 7.88 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 8.63 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 25, 2007 (4th)

By Alban Nonymous

10¹¹⁴²+1 is divisible by 72902178953713285322996186513081_<32>

10¹¹⁷⁴+1 is divisible by 56360262697642563914567399981_<29>

10¹³⁴⁸+1 is divisible by 28060177869481210079003327188873_<32>

10¹³⁴⁸+1 is divisible by 87621827832372981614062571297033_<32>

10¹³⁸²+1 is divisible by 897720822084629349764719120861_<30>

10¹⁴¹⁵+1 is divisible by 21279344764661594183530203415321_<32>

10¹⁴³⁹+1 is divisible by 6652742443560007068799568102809_<31>

10¹⁴⁴⁸+1 is divisible by 3741284323572778169733000409441_<31>

10¹⁴⁵⁴+1 is divisible by 24474149875167364484471358364249_<32>

10¹⁷⁶⁸+1 is divisible by 54377311669469461225374918721_<29>

10¹⁸²⁸+1 is divisible by 99257142543720996230422229080081_<32>

Reference: Factorizations of numbers of the form 10^n+1 (Alfred Reich)

Jul 25, 2007 (3rd)

By JMB / GMP-ECM B1=3000000

(25·10¹⁷¹-7)/9 = 2(7)₁₇₁_<172> = 17 · 2087 · 21787 · 105991859 · 5704794863611639_<16> · 514082498989493831_<18> · C122

C122 = P39 · P83

P39 = 197487969842997416603481017802302838281_<39>

P83 = 58538648152060113017157905351021224725745777751121568986210159879682035562955814559_<83>

(25·10¹⁶⁵-7)/9 = 2(7)₁₆₅_<166> = 296987 · 1840206433618866165991_<22> · C139

C139 = P47 · C93

P47 = 26841431788288106581500307455836598045271854373_<47>

C93 = [189359821998023639433196029818337369944098310651646127033896205015214673371291949815173725697_<93>]

(25·10¹⁶¹-7)/9 = 2(7)₁₆₁_<162> = 145934700643261_<15> · 253469408840513_<15> · C133

C133 = P37 · P97

P37 = 2540772921047677915010225799850512679_<37>

P97 = 2955612696837122473621797379554555189784507453027799522994334517349252054962930031497122170904691_<97>

Jul 25, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp

7·10¹⁵⁸-3 = 6(9)₁₅₇7_<159> = 1303 · 2473 · 133346505599_<12> · C142

C142 = P65 · P77

P65 = 42315979991490290739022320497289947523549183832673097091435256957_<65>

P77 = 38498469586434182358752612193019411923606426698177641577645805015090636763441_<77>

Number: n
N=1629100468722546348836181865908396777509268424093637341521060707834668285197254554652258415454552586334588148334243116907405481886978658509037
  ( 142 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=42315979991490290739022320497289947523549183832673097091435256957 (pp65)
 r2=38498469586434182358752612193019411923606426698177641577645805015090636763441 (pp77)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.97 hours.
Scaled time: 51.83 units (timescale=1.441).
Factorization parameters were as follows:
name: KA_6_9_157_7
n: 1629100468722546348836181865908396777509268424093637341521060707834668285197254554652258415454552586334588148334243116907405481886978658509037
skew: 0.21
deg: 5
c5: 7000
c0: -3
m: 10000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1600001)
Primes: RFBsize:250150, AFBsize:249771, largePrimes:7127717 encountered
Relations: rels:6646443, finalFF:562655
Max relations in full relation-set: 28
Initial matrix: 499988 x 562655 with sparse part having weight 34901852.
Pruned matrix : 443280 x 445843 with weight 23027628.
Total sieving time: 31.37 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 4.32 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 35.97 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

7·10¹⁵⁹-3 = 6(9)₁₅₈7_<160> = 11480647 · C153

C153 = P37 · P117

P37 = 2123843629199706450095966417930509967_<37>

P117 = 287084098820217654683647609855563415797505527535490938568019121616173404487170471297898238166611115453129796922918453_<117>

Number: n
N=609721734323858228547572275325597938861808049668280890441104930758693303609108441362233330577971781555516862420732908171464552476876956499054452244721051
  ( 153 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=2123843629199706450095966417930509967 (pp37)
 r2=287084098820217654683647609855563415797505527535490938568019121616173404487170471297898238166611115453129796922918453 (pp117)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 52.22 hours.
Scaled time: 71.22 units (timescale=1.364).
Factorization parameters were as follows:
name: KA_6_9_158_7
n: 609721734323858228547572275325597938861808049668280890441104930758693303609108441362233330577971781555516862420732908171464552476876956499054452244721051
skew: 1.34
deg: 5
c5: 7
c0: -30
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2100001)
Primes: RFBsize:250150, AFBsize:249671, largePrimes:7451024 encountered
Relations: rels:7012972, finalFF:594936
Max relations in full relation-set: 28
Initial matrix: 499886 x 594936 with sparse part having weight 41833194.
Pruned matrix : 422235 x 424798 with weight 26496990.
Total sieving time: 46.74 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 4.28 hours.
Total square root time: 0.93 hours, sqrts: 7.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 52.22 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 25, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

(7·10¹⁵⁸-43)/9 = (7)₁₅₇3_<158> = 89 · 517482230513_<12> · 5274627333364848091_<19> · C126

C126 = P46 · P81

P46 = 2933276055435097150496053520245973899417083587_<46>

P81 = 109150408258221546428199289249059666027298203143441744801893598785485031825721717_<81>

Number: 77773_158
N=320168278984806550631540855094563858596255377566714042276093831735771608620605463361630935228187638716394639828145755590158879
  ( 126 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=2933276055435097150496053520245973899417083587 (pp46)
 r2=109150408258221546428199289249059666027298203143441744801893598785485031825721717 (pp81)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 33.67 hours.
Scaled time: 72.19 units (timescale=2.144).
Factorization parameters were as follows:
n: 320168278984806550631540855094563858596255377566714042276093831735771608620605463361630935228187638716394639828145755590158879
m: 20000000000000000000000000000000
c5: 875
c0: -172
skew: 0.72
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3900001)
Primes: RFBsize:283146, AFBsize:283557, largePrimes:5672154 encountered
Relations: rels:5680276, finalFF:635478
Max relations in full relation-set: 28
Initial matrix: 566770 x 635478 with sparse part having weight 40948383.
Pruned matrix : 518482 x 521379 with weight 30154788.
Total sieving time: 31.82 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 1.67 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 33.67 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 24, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

3·10¹⁶³-1 = 2(9)₁₆₃_<164> = 997 · 2287 · C158

C158 = P50 · P108

P50 = 45747879641691574163746483574403221719068934066339_<50>

P108 = 287600053136766851692762111657822054428122201049566171614253119368688303514147608918518033049860541686054719_<108>

Number: n
N=13157092615844911209360481970616703630787421293175547631087403004816811606660821993746872449442775199231274935431567987741098240063434729198526931910730003741
  ( 158 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=45747879641691574163746483574403221719068934066339 (pp50)
 r2=287600053136766851692762111657822054428122201049566171614253119368688303514147608918518033049860541686054719 (pp108)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 63.42 hours.
Scaled time: 82.76 units (timescale=1.305).
Factorization parameters were as follows:
name: KA_2_9_163
n: 13157092615844911209360481970616703630787421293175547631087403004816811606660821993746872449442775199231274935431567987741098240063434729198526931910730003741
skew: 0.20
deg: 5
c5: 3000
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 3600000
alim: 3600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2600001)
Primes: RFBsize:256726, AFBsize:256576, largePrimes:7639847 encountered
Relations: rels:7209577, finalFF:633047
Max relations in full relation-set: 48
Initial matrix: 513369 x 633047 with sparse part having weight 51694938.
Pruned matrix : 421670 x 424300 with weight 31990993.
Total sieving time: 56.77 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 5.99 hours.
Total square root time: 0.37 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3600000,3600000,28,28,48,48,2.5,2.5,100000
total time: 63.42 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁴⁹-3 = 6(9)₁₄₈7_<150> = 73 · 139 · C146

C146 = P44 · P50 · P53

P44 = 79426057057573470993450111694681586724818267_<44>

P50 = 10135149856645968832942226206178100278444840800939_<50>

P53 = 85697312347290420035372811292253154086540948455681127_<53>

Number: n
N=68985907164679215531684241647777668276337833842515029072632305114812259781216122992017345028087119345619394895042869813738050655366118064452547551
  ( 146 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=79426057057573470993450111694681586724818267 (pp44)
 r2=10135149856645968832942226206178100278444840800939 (pp50)
 r3=85697312347290420035372811292253154086540948455681127 (pp53)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 28.79 hours.
Scaled time: 27.70 units (timescale=0.962).
Factorization parameters were as follows:
name: KA_6_9_148_7
n: 68985907164679215531684241647777668276337833842515029072632305114812259781216122992017345028087119345619394895042869813738050655366118064452547551
type: snfs
skew: 1
deg: 5
c5: 7
c0: -30
m: 1000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2400001)
Primes: RFBsize:216816, AFBsize:216451, largePrimes:7557334 encountered
Relations: rels:7186983, finalFF:648300
Max relations in full relation-set: 48
Initial matrix: 433332 x 648300 with sparse part having weight 55843030.
Pruned matrix : 303102 x 305332 with weight 30614410.
Total sieving time: 24.47 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 3.92 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 28.79 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 2400+ stepping 01
Memory: 901612k/917504k available (1069k kernel code, 15504k reserved, 459k data, 96k init, 0k highmem)
sisfb: Memory heap starting at 12288K, size 19960K
Calibrating delay loop... 4010.80 BogoMIPS

Jul 24, 2007

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000

7·10¹⁶⁰-3 = 6(9)₁₅₉7_<161> = 1023557 · 676040311822727_<15> · C141

C141 = P36 · C105

P36 = 225167822909311193771939915964703697_<36>

C105 = [449269654046257004984956784811621039356018734468246305859975642850924126367108968544894530278674215128559_<105>]

Jul 23, 2007 (5th)

By Bruce Dodson

10²⁷¹+1 is divisible by 256031814642414583920091086688834271205176259587307504943_<57>, cofactor is prime.

Reference: ECMNET (Paul Zimmermann)

Jul 23, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp

(73·10¹⁶²-1)/9 = 8(1)₁₆₂_<163> = 1423 · 19441 · C156

C156 = P39 · P55 · P63

P39 = 543595994789336592839503974042022463653_<39>

P55 = 3924592279844824544604200287483373227338892292932056637_<55>

P63 = 137431427308481583890246932087896925834997509780593354650152457_<63>

Number: n
N=293195196143710420631604545613173914028188035172354414497687928953357773201281912052952080614926879909460680811214235894339953893730003460064788025275209177
  ( 156 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=543595994789336592839503974042022463653 (pp39)
 r2=3924592279844824544604200287483373227338892292932056637 (pp55)
 r3=137431427308481583890246932087896925834997509780593354650152457 (pp63)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 69.55 hours.
Scaled time: 100.51 units (timescale=1.445).
Factorization parameters were as follows:
name: KA_8_1_162
n: 293195196143710420631604545613173914028188035172354414497687928953357773201281912052952080614926879909460680811214235894339953893730003460064788025275209177
skew: 0.17
deg: 5
c5: 7300
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3200001)
Primes: RFBsize:250150, AFBsize:251141, largePrimes:7701069 encountered
Relations: rels:7215982, finalFF:564079
Max relations in full relation-set: 28
Initial matrix: 501358 x 564079 with sparse part having weight 45743064.
Pruned matrix : 462725 x 465295 with weight 34374223.
Total sieving time: 62.01 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 7.00 hours.
Total square root time: 0.28 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 69.55 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

7·10¹⁴⁰-3 = 6(9)₁₃₉7_<141> = 991 · 1057391 · 345418457 · C124

C124 = P59 · P66

P59 = 11250180495689321348084945885182355115543862335246134474303_<59>

P66 = 171903114767847828998563831031206474014001920428664101581017239147_<66>

Number: n
N=1933941068909484585739512229673477136075976625781953413961591541199884613868795341283880692719104589317952297566427277139541
  ( 124 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=11250180495689321348084945885182355115543862335246134474303 (pp59)
 r2=171903114767847828998563831031206474014001920428664101581017239147 (pp66)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.58 hours.
Scaled time: 8.26 units (timescale=0.963).
Factorization parameters were as follows:
name: KA_6_9_139_7
n: 1933941068909484585739512229673477136075976625781953413961591541199884613868795341283880692719104589317952297566427277139541
type: snfs
skew: 1
deg: 5
c5: 7
c0: -3
m: 10000000000000000000000000000
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [1250000, 1850001)
Primes: RFBsize:183072, AFBsize:182526, largePrimes:6512840 encountered
Relations: rels:5911205, finalFF:420901
Max relations in full relation-set: 48
Initial matrix: 365663 x 420901 with sparse part having weight 26924881.
Pruned matrix : 322386 x 324278 with weight 16005615.
Total sieving time: 6.02 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.27 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.3,2.3,100000
total time: 8.58 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 2400+ stepping 01
Memory: 901612k/917504k available (1069k kernel code, 15504k reserved, 459k data, 96k init, 0k highmem)
sisfb: Memory heap starting at 12288K, size 19960K
Calibrating delay loop... 4010.80 BogoMIPS

(2·10¹⁶¹+7)/9 = (2)₁₆₀3_<161> = 1714933083439_<13> · C149

C149 = P32 · P117

P32 = 21393514829134244932337814471241_<32>

P117 = 605700824976428319254861005827037748162874928762405763234457258027843650353567084980102064536103816470993229797108377_<117>

Number: n
N=12958069581152065089700334183735480199819753791816814760004627272433457888819522067048753782066853574073171870347608059491626405404996336087026685857
  ( 149 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=21393514829134244932337814471241 (pp32)
 r2=605700824976428319254861005827037748162874928762405763234457258027843650353567084980102064536103816470993229797108377 (pp117)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 37.29 hours.
Scaled time: 50.87 units (timescale=1.364).
Factorization parameters were as follows:
name: KA_2_160_3
n: 12958069581152065089700334183735480199819753791816814760004627272433457888819522067048753782066853574073171870347608059491626405404996336087026685857
skew: 0.81
deg: 5
c5: 20
c0: 7
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:250150, AFBsize:249316, largePrimes:7126735 encountered
Relations: rels:6696335, finalFF:602076
Max relations in full relation-set: 28
Initial matrix: 499532 x 602076 with sparse part having weight 35432862.
Pruned matrix : 408966 x 411527 with weight 19865620.
Total sieving time: 33.82 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.16 hours.
Total square root time: 0.12 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 37.29 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁴⁶-3 = 6(9)₁₄₅7_<147> = 17 · C146

C146 = P58 · P89

P58 = 2772341545407390176277168504286752739988576758255116308281_<58>

P89 = 14852596591660026569344293574475374603014785217941966344202020052222211474146804385683861_<89>

Number: n
N=41176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941
  ( 146 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=2772341545407390176277168504286752739988576758255116308281 (pp58)
 r2=14852596591660026569344293574475374603014785217941966344202020052222211474146804385683861 (pp89)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 12.83 hours.
Scaled time: 18.57 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_6_9_145_7
n: 41176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941
skew: 0.53
deg: 5
c5: 70
c0: -3
m: 100000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:183072, AFBsize:182426, largePrimes:7031056 encountered
Relations: rels:6506072, finalFF:476292
Max relations in full relation-set: 28
Initial matrix: 365565 x 476292 with sparse part having weight 34230439.
Pruned matrix : 282716 x 284607 with weight 19056754.
Total sieving time: 10.50 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.04 hours.
Total square root time: 0.11 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 12.83 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(86·10¹⁶²+31)/9 = 9(5)₁₆₁9_<163> = 13 · 137 · 191 · 733 · C155

C155 = P56 · P100

P56 = 15748989216219619926851701365192338858672015860064422379_<56>

P100 = 2433335515280598540281314498084827557020483327676703163289609599551700916484623909357190520150067147_<100>

Number: n
N=38322574789598358592787335737630181268537088962417700159555639086291479506619682708714377535238568925490441405819861474435299782420863402913266182619482713
  ( 155 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=15748989216219619926851701365192338858672015860064422379 (pp56)
 r2=2433335515280598540281314498084827557020483327676703163289609599551700916484623909357190520150067147 (pp100)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 72.01 hours.
Scaled time: 86.12 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_9_5_161_9
n: 38322574789598358592787335737630181268537088962417700159555639086291479506619682708714377535238568925490441405819861474435299782420863402913266182619482713
type: snfs
skew: 0.32
deg: 5
c5: 8600
c0: 31
m: 100000000000000000000000000000000
rlim: 3600000
alim: 3600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2800001)
Primes: RFBsize:256726, AFBsize:257352, largePrimes:7397949 encountered
Relations: rels:6878522, finalFF:577657
Max relations in full relation-set: 28
Initial matrix: 514145 x 577657 with sparse part having weight 36827281.
Pruned matrix : 463389 x 466023 with weight 25709396.
Total sieving time: 65.41 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 5.74 hours.
Total square root time: 0.55 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3600000,3600000,28,28,48,48,2.3,2.3,100000
total time: 72.01 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Jul 23, 2007 (3rd)

By Sinkiti Sibata / Msieve v. 1.23, GGNFS-0.77.1-20060722-pentium4

7·10¹⁴⁵-3 = 6(9)₁₄₄7_<146> = 135899 · 2882653 · 4137260381_<10> · 769330598837417_<15> · 213310674409584473_<18> · C93

C93 = P41 · P52

P41 = 38419676520928330018576887493317188578379_<41>

P52 = 6850105473822077822398812945194215058951502092829389_<52>

Sun Jul 22 08:36:10 2007  Msieve v. 1.23
Sun Jul 22 08:36:10 2007  random seeds: 3eab88d0 395fcfcd
Sun Jul 22 08:36:10 2007  factoring 263178836438484716512595291995766692784822600963980076573334298726819222124062974186701180431 (93 digits)
Sun Jul 22 08:36:11 2007  commencing quadratic sieve (93-digit input)
Sun Jul 22 08:36:11 2007  using multiplier of 1
Sun Jul 22 08:36:11 2007  using 64kb Pentium 2 sieve core
Sun Jul 22 08:36:12 2007  sieve interval: 18 blocks of size 65536
Sun Jul 22 08:36:12 2007  processing polynomials in batches of 6
Sun Jul 22 08:36:12 2007  using a sieve bound of 1923127 (71422 primes)
Sun Jul 22 08:36:12 2007  using large prime bound of 232698367 (27 bits)
Sun Jul 22 08:36:12 2007  using double large prime bound of 1148756443608092 (42-51 bits)
Sun Jul 22 08:36:12 2007  using trial factoring cutoff of 51 bits
Sun Jul 22 08:36:12 2007  polynomial 'A' values have 12 factors
Mon Jul 23 02:26:32 2007  71761 relations (17892 full + 53869 combined from 964161 partial), need 71518
Mon Jul 23 02:26:37 2007  begin with 982053 relations
Mon Jul 23 02:26:39 2007  reduce to 183833 relations in 10 passes
Mon Jul 23 02:26:39 2007  attempting to read 183833 relations
Mon Jul 23 02:26:48 2007  recovered 183833 relations
Mon Jul 23 02:26:48 2007  recovered 165542 polynomials
Mon Jul 23 02:26:49 2007  attempting to build 71761 cycles
Mon Jul 23 02:26:49 2007  found 71761 cycles in 6 passes
Mon Jul 23 02:26:55 2007  distribution of cycle lengths:
Mon Jul 23 02:26:55 2007     length 1 : 17892
Mon Jul 23 02:26:55 2007     length 2 : 12817
Mon Jul 23 02:26:55 2007     length 3 : 12407
Mon Jul 23 02:26:55 2007     length 4 : 9896
Mon Jul 23 02:26:55 2007     length 5 : 7008
Mon Jul 23 02:26:55 2007     length 6 : 4784
Mon Jul 23 02:26:55 2007     length 7 : 2999
Mon Jul 23 02:26:55 2007     length 9+: 3958
Mon Jul 23 02:26:55 2007  largest cycle: 20 relations
Mon Jul 23 02:26:57 2007  matrix is 71422 x 71761 with weight 4423886 (avg 61.65/col)
Mon Jul 23 02:27:03 2007  filtering completed in 3 passes
Mon Jul 23 02:27:03 2007  matrix is 67649 x 67713 with weight 4191481 (avg 61.90/col)
Mon Jul 23 02:27:06 2007  saving the first 48 matrix rows for later
Mon Jul 23 02:27:07 2007  matrix is 67601 x 67713 with weight 3220413 (avg 47.56/col)
Mon Jul 23 02:27:07 2007  matrix includes 64 packed rows
Mon Jul 23 02:27:07 2007  using block size 5461 for processor cache size 128 kB
Mon Jul 23 02:27:07 2007  commencing Lanczos iteration
Mon Jul 23 02:31:49 2007  lanczos halted after 1071 iterations
Mon Jul 23 02:31:50 2007  recovered 17 nontrivial dependencies
Mon Jul 23 02:31:51 2007  prp41 factor: 38419676520928330018576887493317188578379
Mon Jul 23 02:31:51 2007  prp52 factor: 6850105473822077822398812945194215058951502092829389
Mon Jul 23 02:31:51 2007  elapsed time 17:55:41

5·10¹⁶¹-3 = 4(9)₁₆₀7_<162> = 509 · 1747 · C156

C156 = P44 · P49 · P64

P44 = 84102469602460672319344905855931567246447997_<44>

P49 = 2165440703043832390582601658352828177598414559503_<49>

P64 = 3087480849537780573910857739142506288073610114206777292982835929_<64>

Number: 49997_161
N=562288649753773800272822452860531047892373454127929664437379599942871473185016581892281238789370045534134857060602346093162232645804258324402315279744226139
  ( 156 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=84102469602460672319344905855931567246447997 (pp44)
 r2=2165440703043832390582601658352828177598414559503 (pp49)
 r3=3087480849537780573910857739142506288073610114206777292982835929 (pp64)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 84.32 hours.
Scaled time: 57.59 units (timescale=0.683).
Factorization parameters were as follows:
name: 49997_161
n: 562288649753773800272822452860531047892373454127929664437379599942871473185016581892281238789370045534134857060602346093162232645804258324402315279744226139
m: 100000000000000000000000000000000
c5: 50
c0: -3
skew: 0.57
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4250001)
Primes: RFBsize:315948, AFBsize:315546, largePrimes:5795947 encountered
Relations: rels:5955594, finalFF:716832
Max relations in full relation-set: 0
Initial matrix: 631559 x 716832 with sparse part having weight 35018298.
Pruned matrix : 561436 x 564657 with weight 26268658.
Total sieving time: 72.28 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 11.50 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 84.32 hours.
 --------- CPU info (if available) ----------

Jul 23, 2007 (2nd)

By JMB / GMP-ECM B1=1000000

(25·10¹⁷³-7)/9 = 2(7)₁₇₃_<174> = 6169017583_<10> · 20358471981247_<14> · C151

C151 = P33 · P119

P33 = 147538874768229210393236316231919_<33>

P119 = 14990973816674434798810951647946982968321498302818159656670508001237850390226986288400829699930440359734410720309273583_<119>

(25·10¹⁶⁸-7)/9 = 2(7)₁₆₈_<169> = 467 · 1951 · 669181 · 754597 · 1164052117_<10> · 947954614376246137517748334624309_<33> · C109

C109 = P30 · P79

P30 = 927132501806373661426134175901_<30>

P79 = 5901506603211846125449705047676356701978336662915489305427354655975488018446161_<79>

(25·10¹⁸⁰-7)/9 = 2(7)₁₈₀_<181> = 29 · 1431838763_<10> · C170

C170 = P38 · P133

P38 = 18470961602412156590684680364912916293_<38>

P133 = 3621728413595020127934729686179752937236914591769684906994555969901118223512872261753854263218760544399218998367476041945127627646307_<133>

Jul 23, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, GMP-ECM 6.1.2 B1=1000000

7·10¹⁴²-3 = 6(9)₁₄₁7_<143> = 41 · 684820152391010899426909_<24> · C118

C118 = P42 · P76

P42 = 293996872467290101398339992619243102794207_<42>

P76 = 8479982205197969383707708914235563099398323494880780373423205897700123689959_<76>

Number: 69997_142
N=2493088246906476884084912070409326850502294819795549558679381121592194090497586991463738201828121886276619548249267513
  ( 118 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=293996872467290101398339992619243102794207 (pp42)
 r2=8479982205197969383707708914235563099398323494880780373423205897700123689959 (pp76)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 7.68 hours.
Scaled time: 16.37 units (timescale=2.132).
Factorization parameters were as follows:
n: 2493088246906476884084912070409326850502294819795549558679381121592194090497586991463738201828121886276619548249267513
m: 10000000000000000000000000000
c5: 700
c0: -3
skew: 0.34
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 1250001)
Primes: RFBsize:114155, AFBsize:114337, largePrimes:2621896 encountered
Relations: rels:2599825, finalFF:287405
Max relations in full relation-set: 28
Initial matrix: 228559 x 287405 with sparse part having weight 18474157.
Pruned matrix : 199501 x 200707 with weight 10381351.
Total sieving time: 7.49 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000
total time: 7.68 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

7·10¹⁵³-3 = 6(9)₁₅₂7_<154> = 23² · 10303 · 4132288063902465163_<19> · 73545936976938384659_<20> · C109

C109 = P33 · P77

P33 = 368950902030040136294932320283019_<33>

P77 = 11454095970935197036364142614850850481119263863106296451412205403591388218697_<77>

7·10¹⁴³-3 = 6(9)₁₄₂7_<144> = 1390760561015147597115111631999_<31> · C114

C114 = P48 · P67

P48 = 176985412377038489455150177398295039807447995083_<48>

P67 = 2843859925569024851779496154354305448575151654276681477679351507241_<67>

Number: 69997_143
N=503321721669367848389014004967846324275133410824146226320877399025698826072432114856210091439057067468359606896003
  ( 114 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=176985412377038489455150177398295039807447995083 (pp48)
 r2=2843859925569024851779496154354305448575151654276681477679351507241 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.45 hours.
Scaled time: 22.29 units (timescale=2.133).
Factorization parameters were as follows:
n: 503321721669367848389014004967846324275133410824146226320877399025698826072432114856210091439057067468359606896003
m: 20000000000000000000000000000
c5: 875
c0: -12
skew: 0.42
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 1450001)
Primes: RFBsize:114155, AFBsize:114347, largePrimes:2712236 encountered
Relations: rels:2714874, finalFF:310280
Max relations in full relation-set: 28
Initial matrix: 228569 x 310280 with sparse part having weight 22031944.
Pruned matrix : 197851 x 199057 with weight 11694112.
Total sieving time: 10.24 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000
total time: 10.45 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

7·10¹⁴⁸-3 = 6(9)₁₄₇7_<149> = 311 · 7912579919_<10> · C137

C137 = P30 · P43 · P65

P30 = 301037510767131424181611457969_<30>

P43 = 5434594245435338312688573491110293470744533_<43>

P65 = 17387286194393844709918894508724977643672044365413394191742373729_<65>

Number: 69997_148
N=28445890993355795785465713412766066538152730750893507917803289805207609319238261618681814513715015288973371527222324093744020519559325733
  ( 137 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=301037510767131424181611457969 (pp30)
 r2=5434594245435338312688573491110293470744533 (pp43)
 r3=17387286194393844709918894508724977643672044365413394191742373729 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 12.60 hours.
Scaled time: 27.00 units (timescale=2.143).
Factorization parameters were as follows:
n: 28445890993355795785465713412766066538152730750893507917803289805207609319238261618681814513715015288973371527222324093744020519559325733
m: 200000000000000000000000000000
c5: 875
c0: -12
skew: 0.42
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1725001)
Primes: RFBsize:135072, AFBsize:135518, largePrimes:3840968 encountered
Relations: rels:3910546, finalFF:354284
Max relations in full relation-set: 28
Initial matrix: 270657 x 354284 with sparse part having weight 33819268.
Pruned matrix : 244258 x 245675 with weight 20068683.
Total sieving time: 12.20 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.31 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 12.60 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 22, 2007 (6th)

By JMB / GMP-ECM B1=1000000

(25·10¹⁶²-7)/9 = 2(7)₁₆₂_<163> = 31 · 193 · 419 · 5655980505619_<13> · C144

C144 = P30 · P114

P30 = 757834905954475759153120346779_<30>

P114 = 258512748121660648679500730489730055051223230946990605506285956104708110213970081444008373211813972771066168890501_<114>

(25·10¹⁶⁸-7)/9 = 2(7)₁₆₈_<169> = 467 · 1951 · 669181 · 754597 · 1164052117_<10> · C142

C142 = P33 · C109

P33 = 947954614376246137517748334624309_<33>

C109 = [5471478581462633018677789162246038606727580138540073007104958991038578407898337844421297328962275304272166061_<109>]

Jul 22, 2007 (5th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

7·10¹³¹-3 = 6(9)₁₃₀7_<132> = 23 · 43 · 200357 · 686073298051849_<15> · C109

C109 = P49 · P61

P49 = 3492650375317905457798484924118526607821958419517_<49>

P61 = 1474251565366503210694631337567966010127470661351122913594633_<61>

Number: 69997_131
N=5149045283090327070069279376634643521531392220622868283592793023104111216823296932910173748751679693893652261
  ( 109 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=3492650375317905457798484924118526607821958419517 (pp49)
 r2=1474251565366503210694631337567966010127470661351122913594633 (pp61)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.06 hours.
Scaled time: 6.56 units (timescale=2.144).
Factorization parameters were as follows:
n: 5149045283090327070069279376634643521531392220622868283592793023104111216823296932910173748751679693893652261
m: 100000000000000000000000000
c5: 70
c0: -3
skew: 0.53
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 1150001)
Primes: RFBsize:78498, AFBsize:78021, largePrimes:1557428 encountered
Relations: rels:1555267, finalFF:175874
Max relations in full relation-set: 28
Initial matrix: 156586 x 175874 with sparse part having weight 11502732.
Pruned matrix : 150400 x 151246 with weight 8326009.
Total sieving time: 2.95 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 3.06 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

5·10¹⁵⁸-1 = 4(9)₁₅₈_<159> = 929 · 2039 · 195480696444471195235091_<24> · C130

C130 = P55 · P75

P55 = 3914379888823857856496565940348441055481401908952110819_<55>

P75 = 344961172633478712235231612125560933379158026766703661954210221883077707201_<75>

Number: 49999_158
N=1350309076581584038910089762282315799270660996144707824782483833075965830415212667287719844360646971845236733069095577551786307619
  ( 130 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=3914379888823857856496565940348441055481401908952110819 (pp55)
 r2=344961172633478712235231612125560933379158026766703661954210221883077707201 (pp75)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.89 hours.
Scaled time: 53.09 units (timescale=2.133).
Factorization parameters were as follows:
n: 1350309076581584038910089762282315799270660996144707824782483833075965830415212667287719844360646971845236733069095577551786307619
m: 100000000000000000000000000000000
c5: 1
c0: -20
skew: 1.82
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3400001)
Primes: RFBsize:283146, AFBsize:282402, largePrimes:5586780 encountered
Relations: rels:5610115, finalFF:652381
Max relations in full relation-set: 28
Initial matrix: 565612 x 652381 with sparse part having weight 39533074.
Pruned matrix : 493839 x 496731 with weight 26115813.
Total sieving time: 23.41 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 1.35 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 24.89 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

7·10¹³⁶-3 = 6(9)₁₃₅7_<137> = 1911173014322791_<16> · C122

C122 = P40 · P82

P40 = 6688529150867410750543674810071273572433_<40>

P82 = 5476050080158143153708958738926903788962439257212131688978965251785087525399823499_<82>

Number: 69997_136
N=36626720592747561803500026700296649794252768847574024237934710155034041818228816099980837330026827983143189237441392003067
  ( 122 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=6688529150867410750543674810071273572433 (pp40)
 r2=5476050080158143153708958738926903788962439257212131688978965251785087525399823499 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.99 hours.
Scaled time: 10.69 units (timescale=2.143).
Factorization parameters were as follows:
n: 36626720592747561803500026700296649794252768847574024237934710155034041818228816099980837330026827983143189237441392003067
m: 1000000000000000000000000000
c5: 70
c0: -3
skew: 0.53
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [700000, 1650001)
Primes: RFBsize:107126, AFBsize:106428, largePrimes:1903120 encountered
Relations: rels:2018723, finalFF:271339
Max relations in full relation-set: 28
Initial matrix: 213621 x 271339 with sparse part having weight 20879664.
Pruned matrix : 192022 x 193154 with weight 12401408.
Total sieving time: 4.80 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,45,45,2.3,2.3,50000
total time: 4.99 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 22, 2007 (4th)

By Yousuke Koide

(10⁸⁵³-1)/9 is divisible by 446687009597873860118984450851524186409_<39>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jul 22, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

7·10¹³²-3 = 6(9)₁₃₁7_<133> = 41 · 761 · 823 · 8863 · 6082088060418354263973053_<25> · C97

C97 = P35 · P63

P35 = 27212650857151474320206035877612519_<35>

P63 = 185834091366309855618215438086593893231210033409435324983518879_<63>

Number: n
N=5057038245707377286077394752451829803112566267314143247542799158823686682115360518604401883246201
  ( 97 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=27212650857151474320206035877612519 (pp35)
 r2=185834091366309855618215438086593893231210033409435324983518879 (pp63)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 5.60 hours.
Scaled time: 5.40 units (timescale=0.963).
Factorization parameters were as follows:
name: KA_6_9_131_7
n: 5057038245707377286077394752451829803112566267314143247542799158823686682115360518604401883246201
type: snfs
skew: 1
deg: 5
c5: 700
c0: -3
m: 100000000000000000000000000
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [1250000, 1750001)
Primes: RFBsize:183072, AFBsize:183021, largePrimes:5616253 encountered
Relations: rels:5027789, finalFF:431914
Max relations in full relation-set: 48
Initial matrix: 366160 x 431914 with sparse part having weight 16649644.
Pruned matrix : 301469 x 303363 with weight 9063422.
Total sieving time: 4.17 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.20 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.2,2.2,50000
total time: 5.60 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 2400+ stepping 01
Memory: 901612k/917504k available (1069k kernel code, 15504k reserved, 459k data, 96k init, 0k highmem)
sisfb: Memory heap starting at 12288K, size 19960K
Calibrating delay loop... 4010.80 BogoMIPS

Jul 22, 2007 (2nd)

By Jo Yeong Uk / Msieve v. 1.25, GGNFS-0.77.1-20050930-nocona

7·10¹¹⁶-3 = 6(9)₁₁₅7_<117> = 257 · 271861 · 9968346863_<10> · 5492745356335264771_<19> · C81

C81 = P35 · P46

P35 = 38690791643388328103740921502952607_<35>

P46 = 4729310014865205650831153297596976512403898451_<46>

Sat Jul 21 23:59:36 2007  
Sat Jul 21 23:59:36 2007  
Sat Jul 21 23:59:36 2007  Msieve v. 1.25
Sat Jul 21 23:59:36 2007  random seeds: 59986908 0149e5dc
Sat Jul 21 23:59:36 2007  factoring 182980748402139428556729916605951877285225472985237924125874449528521933893711757 (81 digits)
Sat Jul 21 23:59:36 2007  commencing quadratic sieve (80-digit input)
Sat Jul 21 23:59:36 2007  using multiplier of 7
Sat Jul 21 23:59:36 2007  using 32kb Intel Core sieve core
Sat Jul 21 23:59:36 2007  sieve interval: 12 blocks of size 32768
Sat Jul 21 23:59:36 2007  processing polynomials in batches of 17
Sat Jul 21 23:59:36 2007  using a sieve bound of 1305643 (50294 primes)
Sat Jul 21 23:59:36 2007  using large prime bound of 129258657 (26 bits)
Sat Jul 21 23:59:36 2007  using trial factoring cutoff of 27 bits
Sat Jul 21 23:59:36 2007  polynomial 'A' values have 10 factors
Sun Jul 22 00:11:15 2007  50465 relations (25708 full + 24757 combined from 274294 partial), need 50390
Sun Jul 22 00:11:15 2007  begin with 300002 relations
Sun Jul 22 00:11:15 2007  reduce to 72144 relations in 2 passes
Sun Jul 22 00:11:15 2007  attempting to read 72144 relations
Sun Jul 22 00:11:16 2007  recovered 72144 relations
Sun Jul 22 00:11:16 2007  recovered 61871 polynomials
Sun Jul 22 00:11:16 2007  attempting to build 50465 cycles
Sun Jul 22 00:11:16 2007  found 50465 cycles in 1 passes
Sun Jul 22 00:11:16 2007  distribution of cycle lengths:
Sun Jul 22 00:11:16 2007     length 1 : 25708
Sun Jul 22 00:11:16 2007     length 2 : 24757
Sun Jul 22 00:11:16 2007  largest cycle: 2 relations
Sun Jul 22 00:11:16 2007  matrix is 50294 x 50465 with weight 1573880 (avg 31.19/col)
Sun Jul 22 00:11:16 2007  filtering completed in 4 passes
Sun Jul 22 00:11:16 2007  matrix is 42972 x 43036 with weight 1314047 (avg 30.53/col)
Sun Jul 22 00:11:16 2007  saving the first 48 matrix rows for later
Sun Jul 22 00:11:16 2007  matrix is 42924 x 43036 with weight 1004755 (avg 23.35/col)
Sun Jul 22 00:11:16 2007  matrix includes 64 packed rows
Sun Jul 22 00:11:16 2007  commencing Lanczos iteration
Sun Jul 22 00:11:41 2007  lanczos halted after 680 iterations
Sun Jul 22 00:11:41 2007  recovered 9 nontrivial dependencies
Sun Jul 22 00:11:41 2007  prp35 factor: 38690791643388328103740921502952607
Sun Jul 22 00:11:41 2007  prp46 factor: 4729310014865205650831153297596976512403898451
Sun Jul 22 00:11:41 2007  elapsed time 00:12:05

7·10¹²⁷-3 = 6(9)₁₂₆7_<128> = 41² · 151 · 2347 · 39819539 · 55136742586585039706768971261_<29> · C83

C83 = P33 · P50

P33 = 996661217419669522960891631306797_<33>

P50 = 53697664591766885637251106829273235075760230423267_<50>

Sun Jul 22 00:13:13 2007  
Sun Jul 22 00:13:13 2007  
Sun Jul 22 00:13:13 2007  Msieve v. 1.25
Sun Jul 22 00:13:13 2007  random seeds: 103aacd2 23967dbd
Sun Jul 22 00:13:13 2007  factoring 53518379764623465702863279224822425408675308236078968242775516646260859391644045799 (83 digits)
Sun Jul 22 00:13:13 2007  commencing quadratic sieve (83-digit input)
Sun Jul 22 00:13:13 2007  using multiplier of 5
Sun Jul 22 00:13:13 2007  using 32kb Intel Core sieve core
Sun Jul 22 00:13:13 2007  sieve interval: 12 blocks of size 32768
Sun Jul 22 00:13:13 2007  processing polynomials in batches of 17
Sun Jul 22 00:13:13 2007  using a sieve bound of 1372627 (52647 primes)
Sun Jul 22 00:13:13 2007  using large prime bound of 122163803 (26 bits)
Sun Jul 22 00:13:13 2007  using trial factoring cutoff of 27 bits
Sun Jul 22 00:13:13 2007  polynomial 'A' values have 11 factors
Sun Jul 22 00:33:32 2007  52785 relations (26977 full + 25808 combined from 279646 partial), need 52743
Sun Jul 22 00:33:33 2007  begin with 306623 relations
Sun Jul 22 00:33:33 2007  reduce to 75331 relations in 2 passes
Sun Jul 22 00:33:33 2007  attempting to read 75331 relations
Sun Jul 22 00:33:33 2007  recovered 75331 relations
Sun Jul 22 00:33:33 2007  recovered 68714 polynomials
Sun Jul 22 00:33:33 2007  attempting to build 52785 cycles
Sun Jul 22 00:33:33 2007  found 52785 cycles in 1 passes
Sun Jul 22 00:33:33 2007  distribution of cycle lengths:
Sun Jul 22 00:33:33 2007     length 1 : 26977
Sun Jul 22 00:33:33 2007     length 2 : 25808
Sun Jul 22 00:33:33 2007  largest cycle: 2 relations
Sun Jul 22 00:33:33 2007  matrix is 52647 x 52785 with weight 1723884 (avg 32.66/col)
Sun Jul 22 00:33:33 2007  filtering completed in 4 passes
Sun Jul 22 00:33:33 2007  matrix is 45365 x 45429 with weight 1454573 (avg 32.02/col)
Sun Jul 22 00:33:34 2007  saving the first 48 matrix rows for later
Sun Jul 22 00:33:34 2007  matrix is 45317 x 45429 with weight 1108107 (avg 24.39/col)
Sun Jul 22 00:33:34 2007  matrix includes 64 packed rows
Sun Jul 22 00:33:34 2007  commencing Lanczos iteration
Sun Jul 22 00:34:03 2007  lanczos halted after 718 iterations
Sun Jul 22 00:34:03 2007  recovered 10 nontrivial dependencies
Sun Jul 22 00:34:03 2007  prp33 factor: 996661217419669522960891631306797
Sun Jul 22 00:34:03 2007  prp50 factor: 53697664591766885637251106829273235075760230423267
Sun Jul 22 00:34:03 2007  elapsed time 00:20:50

7·10¹³⁴-3 = 6(9)₁₃₃7_<135> = 127 · 186103 · 284041 · 67139650373_<11> · 224080515702813399469184201_<27> · C85

C85 = P40 · P46

P40 = 1657367916841120248990423676418651639587_<40>

P46 = 4181747575834472305239024549045571460403317707_<46>

Sun Jul 22 01:59:47 2007  
Sun Jul 22 01:59:47 2007  
Sun Jul 22 01:59:47 2007  Msieve v. 1.25
Sun Jul 22 01:59:47 2007  random seeds: 7b30c364 1c9cc3ef
Sun Jul 22 01:59:47 2007  factoring 6930694268516183887694709958969040895366115620435867716462445489842053938330019267009 (85 digits)
Sun Jul 22 01:59:47 2007  commencing quadratic sieve (85-digit input)
Sun Jul 22 01:59:48 2007  using multiplier of 1
Sun Jul 22 01:59:48 2007  using 32kb Intel Core sieve core
Sun Jul 22 01:59:48 2007  sieve interval: 12 blocks of size 32768
Sun Jul 22 01:59:48 2007  processing polynomials in batches of 17
Sun Jul 22 01:59:48 2007  using a sieve bound of 1434241 (54497 primes)
Sun Jul 22 01:59:48 2007  using large prime bound of 116173521 (26 bits)
Sun Jul 22 01:59:48 2007  using double large prime bound of 328997602795950 (41-49 bits)
Sun Jul 22 01:59:48 2007  using trial factoring cutoff of 49 bits
Sun Jul 22 01:59:48 2007  polynomial 'A' values have 11 factors
Sun Jul 22 02:21:27 2007  54900 relations (16114 full + 38786 combined from 570398 partial), need 54593
Sun Jul 22 02:21:27 2007  begin with 586512 relations
Sun Jul 22 02:21:27 2007  reduce to 128737 relations in 9 passes
Sun Jul 22 02:21:27 2007  attempting to read 128737 relations
Sun Jul 22 02:21:28 2007  recovered 128737 relations
Sun Jul 22 02:21:28 2007  recovered 106037 polynomials
Sun Jul 22 02:21:28 2007  attempting to build 54900 cycles
Sun Jul 22 02:21:28 2007  found 54900 cycles in 5 passes
Sun Jul 22 02:21:28 2007  distribution of cycle lengths:
Sun Jul 22 02:21:28 2007     length 1 : 16114
Sun Jul 22 02:21:28 2007     length 2 : 11199
Sun Jul 22 02:21:28 2007     length 3 : 9754
Sun Jul 22 02:21:28 2007     length 4 : 6903
Sun Jul 22 02:21:28 2007     length 5 : 4674
Sun Jul 22 02:21:28 2007     length 6 : 2887
Sun Jul 22 02:21:28 2007     length 7 : 1597
Sun Jul 22 02:21:28 2007     length 9+: 1772
Sun Jul 22 02:21:28 2007  largest cycle: 19 relations
Sun Jul 22 02:21:29 2007  matrix is 54497 x 54900 with weight 2829346 (avg 51.54/col)
Sun Jul 22 02:21:29 2007  filtering completed in 3 passes
Sun Jul 22 02:21:29 2007  matrix is 49646 x 49710 with weight 2569219 (avg 51.68/col)
Sun Jul 22 02:21:29 2007  saving the first 48 matrix rows for later
Sun Jul 22 02:21:30 2007  matrix is 49598 x 49710 with weight 1887856 (avg 37.98/col)
Sun Jul 22 02:21:30 2007  matrix includes 64 packed rows
Sun Jul 22 02:21:30 2007  commencing Lanczos iteration
Sun Jul 22 02:22:14 2007  lanczos halted after 786 iterations
Sun Jul 22 02:22:14 2007  recovered 15 nontrivial dependencies
Sun Jul 22 02:22:15 2007  prp40 factor: 1657367916841120248990423676418651639587
Sun Jul 22 02:22:15 2007  prp46 factor: 4181747575834472305239024549045571460403317707
Sun Jul 22 02:22:15 2007  elapsed time 00:22:28

7·10¹²⁶-3 = 6(9)₁₂₅7_<127> = C127

C127 = P49 · P79

P49 = 3733064887567996534792974929164593204373697227583_<49>

P79 = 1875134831787061276782822033581045574929236611892954682370632550609251043832259_<79>

Number: 69997_126
N=6999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997
  ( 127 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=3733064887567996534792974929164593204373697227583 (pp49)
 r2=1875134831787061276782822033581045574929236611892954682370632550609251043832259 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.18 hours.
Scaled time: 4.65 units (timescale=2.128).
Factorization parameters were as follows:
n: 6999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997
m: 10000000000000000000000000
c5: 70
c0: -3
skew: 0.53
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 950001)
Primes: RFBsize:78498, AFBsize:78021, largePrimes:1558333 encountered
Relations: rels:1597125, finalFF:213619
Max relations in full relation-set: 28
Initial matrix: 156586 x 213619 with sparse part having weight 11148790.
Pruned matrix : 132114 x 132960 with weight 5515036.
Total sieving time: 2.10 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 2.18 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

7·10¹⁰⁹-3 = 6(9)₁₀₈7_<110> = 23 · 73 · 8689 · C103

C103 = P42 · P62

P42 = 228859484167433722234911564635934681814193_<42>

P62 = 20965664506503249718202161151414441563687134934979206768443859_<62>

Number: 69997_109
N=4798191164185807622283101367066353705790409115027790780495023898762004988610807815924387635993589890787
  ( 103 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=228859484167433722234911564635934681814193 (pp42)
 r2=20965664506503249718202161151414441563687134934979206768443859 (pp62)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.61 hours.
Scaled time: 1.31 units (timescale=2.143).
Factorization parameters were as follows:
n: 4798191164185807622283101367066353705790409115027790780495023898762004988610807815924387635993589890787
m: 10000000000000000000000
c5: 7
c0: -30
skew: 1.34
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 300001)
Primes: RFBsize:30757, AFBsize:30494, largePrimes:983606 encountered
Relations: rels:888199, finalFF:73849
Max relations in full relation-set: 28
Initial matrix: 61316 x 73849 with sparse part having weight 3415148.
Pruned matrix : 56457 x 56827 with weight 2004983.
Total sieving time: 0.58 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.61 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

7·10¹²¹-3 = 6(9)₁₂₀7_<122> = 47653 · 1369371443767_<13> · C106

C106 = P35 · P71

P35 = 36358147136114613307985190682380569_<35>

P71 = 29504263852952324258374435890140498246794971645497980237929073951677863_<71>

Number: 69997_121
N=1072720366308388454659014573709742439750797378507314566568561935551101727969483113552373319637988658644047
  ( 106 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=36358147136114613307985190682380569 (pp35)
 r2=29504263852952324258374435890140498246794971645497980237929073951677863 (pp71)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.34 hours.
Scaled time: 2.86 units (timescale=2.142).
Factorization parameters were as follows:
n: 1072720366308388454659014573709742439750797378507314566568561935551101727969483113552373319637988658644047
m: 1000000000000000000000000
c5: 70
c0: -3
skew: 0.53
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 540001)
Primes: RFBsize:49098, AFBsize:48796, largePrimes:2105450 encountered
Relations: rels:2178868, finalFF:179576
Max relations in full relation-set: 28
Initial matrix: 97961 x 179576 with sparse part having weight 18093782.
Pruned matrix : 84353 x 84906 with weight 6257540.
Total sieving time: 1.27 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 1.34 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

7·10¹²³-3 = 6(9)₁₂₂7_<124> = 173 · 61027 · 713562389 · C108

C108 = P54 · P55

P54 = 135311009685237351278540689388809518241159030458513113_<54>

P55 = 6866964940815089427027581044049877493885455562590216551_<55>

Number: 69997_123
N=929175959614815900163066670327570369604706388965383155597477001152268117687211419282352024355512064143133263
  ( 108 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=135311009685237351278540689388809518241159030458513113 (pp54)
 r2=6866964940815089427027581044049877493885455562590216551 (pp55)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.38 hours.
Scaled time: 2.94 units (timescale=2.131).
Factorization parameters were as follows:
n: 929175959614815900163066670327570369604706388965383155597477001152268117687211419282352024355512064143133263
m: 2000000000000000000000000
c5: 875
c0: -12
skew: 0.42
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 540001)
Primes: RFBsize:49098, AFBsize:49241, largePrimes:2087615 encountered
Relations: rels:2138687, finalFF:167675
Max relations in full relation-set: 28
Initial matrix: 98406 x 167675 with sparse part having weight 16330556.
Pruned matrix : 86136 x 86692 with weight 6130758.
Total sieving time: 1.31 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 1.38 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

7·10¹²⁴-3 = 6(9)₁₂₃7_<125> = 12435393851_<11> · C115

C115 = P49 · P67

P49 = 1653859776119932304506498458736364717902994881823_<49>

P67 = 3403610153505365266823631691628573931926592430091798145981178781689_<67>

Number: 69997_124
N=5629093926475911824338727170724976501590661199557369773249492232749066308603561735312182192338670303366493671339047
  ( 115 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=1653859776119932304506498458736364717902994881823 (pp49)
 r2=3403610153505365266823631691628573931926592430091798145981178781689 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.76 hours.
Scaled time: 3.78 units (timescale=2.145).
Factorization parameters were as follows:
n: 5629093926475911824338727170724976501590661199557369773249492232749066308603561735312182192338670303366493671339047
m: 10000000000000000000000000
c5: 7
c0: -30
skew: 1.34
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 850001)
Primes: RFBsize:78498, AFBsize:77956, largePrimes:1482727 encountered
Relations: rels:1490685, finalFF:186596
Max relations in full relation-set: 28
Initial matrix: 156519 x 186596 with sparse part having weight 8875261.
Pruned matrix : 140381 x 141227 with weight 5293869.
Total sieving time: 1.69 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 1.76 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

7·10¹³⁰-3 = 6(9)₁₂₉7_<131> = 17 · 6967 · 22159 · C122

C122 = P56 · P67

P56 = 12377339630211913014729356379781933602404602590397460483_<56>

P67 = 2154893656072748577302512740902433579438090282103291765000036292359_<67>

Number: 69997_130
N=26671850648201471139952050436640275593130415064623068809555644373410921858636706510104666244043064581907285529588537349397
  ( 122 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=12377339630211913014729356379781933602404602590397460483 (pp56)
 r2=2154893656072748577302512740902433579438090282103291765000036292359 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.95 hours.
Scaled time: 4.18 units (timescale=2.143).
Factorization parameters were as follows:
n: 26671850648201471139952050436640275593130415064623068809555644373410921858636706510104666244043064581907285529588537349397
m: 100000000000000000000000000
c5: 7
c0: -3
skew: 0.84
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 900001)
Primes: RFBsize:78498, AFBsize:78031, largePrimes:1497101 encountered
Relations: rels:1513263, finalFF:193250
Max relations in full relation-set: 28
Initial matrix: 156594 x 193250 with sparse part having weight 9535488.
Pruned matrix : 138779 x 139625 with weight 5365586.
Total sieving time: 1.88 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 1.95 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 22, 2007

By Kenichiro Yamaguchi / Msieve v. 1.25

7·10¹³⁷-3 = 6(9)₁₃₆7_<138> = 19 · 41 · 83 · 14431 · 32687 · 220474522090692269_<18> · 3088175041540998887_<19> · C89

C89 = P41 · P48

P41 = 53204897233454695830562193693392037137397_<41>

P48 = 633576518273911287795959707919898837003414686923_<48>

C89=P41*P48
P41=53204897233454695830562193693392037137397
P48=633576518273911287795959707919898837003414686923

Sun Jul 22 01:55:34 2007  Msieve v. 1.25
Sun Jul 22 01:55:34 2007  random seeds: 1d6eae68 a4f7c8cb
Sun Jul 22 01:55:34 2007  factoring 33709373544293481213343982315692544285548550722517329478640267756974328368014399890159431 (89 digits)
Sun Jul 22 01:55:34 2007  commencing quadratic sieve (89-digit input)
Sun Jul 22 01:55:34 2007  using multiplier of 5
Sun Jul 22 01:55:34 2007  using 32kb Pentium M sieve core
Sun Jul 22 01:55:34 2007  sieve interval: 32 blocks of size 32768
Sun Jul 22 01:55:34 2007  processing polynomials in batches of 7
Sun Jul 22 01:55:34 2007  using a sieve bound of 1556189 (58911 primes)
Sun Jul 22 01:55:34 2007  using large prime bound of 124495120 (26 bits)
Sun Jul 22 01:55:34 2007  using double large prime bound of 372626841652480 (42-49 bits)
Sun Jul 22 01:55:34 2007  using trial factoring cutoff of 49 bits
Sun Jul 22 01:55:34 2007  polynomial 'A' values have 11 factors
Sun Jul 22 03:49:04 2007  59251 relations (15409 full + 43842 combined from 635927 partial), need 59007
Sun Jul 22 03:49:06 2007  begin with 651336 relations
Sun Jul 22 03:49:07 2007  reduce to 146490 relations in 10 passes
Sun Jul 22 03:49:07 2007  attempting to read 146490 relations
Sun Jul 22 03:49:13 2007  recovered 146490 relations
Sun Jul 22 03:49:13 2007  recovered 128156 polynomials
Sun Jul 22 03:49:13 2007  attempting to build 59251 cycles
Sun Jul 22 03:49:13 2007  found 59251 cycles in 5 passes
Sun Jul 22 03:49:13 2007  distribution of cycle lengths:
Sun Jul 22 03:49:13 2007     length 1 : 15409
Sun Jul 22 03:49:13 2007     length 2 : 11060
Sun Jul 22 03:49:13 2007     length 3 : 10314
Sun Jul 22 03:49:14 2007     length 4 : 8027
Sun Jul 22 03:49:14 2007     length 5 : 5815
Sun Jul 22 03:49:14 2007     length 6 : 3624
Sun Jul 22 03:49:14 2007     length 7 : 2227
Sun Jul 22 03:49:14 2007     length 9+: 2775
Sun Jul 22 03:49:15 2007  largest cycle: 18 relations
Sun Jul 22 03:49:15 2007  matrix is 58911 x 59251 with weight 3663344 (avg 61.83/col)
Sun Jul 22 03:49:17 2007  filtering completed in 4 passes
Sun Jul 22 03:49:17 2007  matrix is 55380 x 55444 with weight 3442544 (avg 62.09/col)
Sun Jul 22 03:49:18 2007  saving the first 48 matrix rows for later
Sun Jul 22 03:49:18 2007  matrix is 55332 x 55444 with weight 2837873 (avg 51.18/col)
Sun Jul 22 03:49:18 2007  matrix includes 64 packed rows
Sun Jul 22 03:49:18 2007  using block size 22177 for processor cache size 2048 kB
Sun Jul 22 03:49:18 2007  commencing Lanczos iteration
Sun Jul 22 03:50:16 2007  lanczos halted after 876 iterations
Sun Jul 22 03:50:16 2007  recovered 19 nontrivial dependencies
Sun Jul 22 03:50:17 2007  prp41 factor: 53204897233454695830562193693392037137397
Sun Jul 22 03:50:17 2007  prp48 factor: 633576518273911287795959707919898837003414686923
Sun Jul 22 03:50:17 2007  elapsed time 01:54:43

7·10¹⁷⁶-3 = 6(9)₁₇₅7_<177> = 127 · 1427 · 1823167117_<10> · 3122832099875424913_<19> · 4959902390670157503819923_<25> · 96538958547137354194163712683_<29> · C91

C91 = P42 · P49

P42 = 226468883271578475618379567962241702278977_<42>

P49 = 6256204756417669062376992564657832577417523732181_<49>

C91=P42*P49
P42=226468883271578475618379567962241702278977
P49=6256204756417669062376992564657832577417523732181

Sun Jul 22 11:36:57 2007  Msieve v. 1.25
Sun Jul 22 11:36:57 2007  random seeds: afc45a78 7d8aa159
Sun Jul 22 11:36:57 2007  factoring 1416835704704247144924541052389267917368021881114236322739410829329143705256446130294658837 (91 digits)
Sun Jul 22 11:36:58 2007  commencing quadratic sieve (90-digit input)
Sun Jul 22 11:36:58 2007  using multiplier of 5
Sun Jul 22 11:36:58 2007  using 32kb Pentium M sieve core
Sun Jul 22 11:36:58 2007  sieve interval: 36 blocks of size 32768
Sun Jul 22 11:36:58 2007  processing polynomials in batches of 6
Sun Jul 22 11:36:58 2007  using a sieve bound of 1652491 (62295 primes)
Sun Jul 22 11:36:58 2007  using large prime bound of 145419208 (27 bits)
Sun Jul 22 11:36:58 2007  using double large prime bound of 492854925172808 (42-49 bits)
Sun Jul 22 11:36:58 2007  using trial factoring cutoff of 49 bits
Sun Jul 22 11:36:58 2007  polynomial 'A' values have 12 factors
Sun Jul 22 14:18:41 2007  62560 relations (15701 full + 46859 combined from 707243 partial), need 62391
Sun Jul 22 14:18:54 2007  begin with 722944 relations
Sun Jul 22 14:18:55 2007  reduce to 155793 relations in 10 passes
Sun Jul 22 14:18:55 2007  attempting to read 155793 relations
Sun Jul 22 14:19:06 2007  recovered 155793 relations
Sun Jul 22 14:19:06 2007  recovered 138792 polynomials
Sun Jul 22 14:19:06 2007  attempting to build 62560 cycles
Sun Jul 22 14:19:06 2007  found 62560 cycles in 5 passes
Sun Jul 22 14:19:06 2007  distribution of cycle lengths:
Sun Jul 22 14:19:06 2007     length 1 : 15701
Sun Jul 22 14:19:06 2007     length 2 : 11811
Sun Jul 22 14:19:06 2007     length 3 : 11050
Sun Jul 22 14:19:06 2007     length 4 : 8666
Sun Jul 22 14:19:06 2007     length 5 : 6156
Sun Jul 22 14:19:06 2007     length 6 : 3886
Sun Jul 22 14:19:06 2007     length 7 : 2377
Sun Jul 22 14:19:06 2007     length 9+: 2913
Sun Jul 22 14:19:06 2007  largest cycle: 17 relations
Sun Jul 22 14:19:07 2007  matrix is 62295 x 62560 with weight 3738751 (avg 59.76/col)
Sun Jul 22 14:19:08 2007  filtering completed in 3 passes
Sun Jul 22 14:19:08 2007  matrix is 59024 x 59088 with weight 3551902 (avg 60.11/col)
Sun Jul 22 14:19:09 2007  saving the first 48 matrix rows for later
Sun Jul 22 14:19:09 2007  matrix is 58976 x 59088 with weight 2711102 (avg 45.88/col)
Sun Jul 22 14:19:09 2007  matrix includes 64 packed rows
Sun Jul 22 14:19:09 2007  using block size 23635 for processor cache size 2048 kB
Sun Jul 22 14:19:09 2007  commencing Lanczos iteration
Sun Jul 22 14:20:07 2007  lanczos halted after 934 iterations
Sun Jul 22 14:20:07 2007  recovered 17 nontrivial dependencies
Sun Jul 22 14:20:08 2007  prp42 factor: 226468883271578475618379567962241702278977
Sun Jul 22 14:20:08 2007  prp49 factor: 6256204756417669062376992564657832577417523732181
Sun Jul 22 14:20:08 2007  elapsed time 02:43:11

Jul 21, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

2·10¹⁵⁸-3 = 1(9)₁₅₇7_<159> = 571 · 8308493 · 627908707 · 19547338624799_<14> · C127

C127 = P48 · P79

P48 = 765613002593259893435771444351052001550447832917_<48>

P79 = 4486195411014709158764439342476979691484480174887014872203008588690204116766979_<79>

Number: 19997_158
N=3434689538847075156669170246694359027751302650612112051029535669072282263120505215768659729098715953969223080215754614814847743
  ( 127 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=765613002593259893435771444351052001550447832917 (pp48)
 r2=4486195411014709158764439342476979691484480174887014872203008588690204116766979 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.75 hours.
Scaled time: 53.09 units (timescale=2.145).
Factorization parameters were as follows:
n: 3434689538847075156669170246694359027751302650612112051029535669072282263120505215768659729098715953969223080215754614814847743
m: 20000000000000000000000000000000
c5: 125
c0: -6
skew: 0.54
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3400001)
Primes: RFBsize:283146, AFBsize:282582, largePrimes:5753873 encountered
Relations: rels:5897488, finalFF:751668
Max relations in full relation-set: 28
Initial matrix: 565793 x 751668 with sparse part having weight 45568672.
Pruned matrix : 412610 x 415502 with weight 27462155.
Total sieving time: 23.64 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.98 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 24.75 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 21, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon

(28·10¹⁶⁰+17)/9 = 3(1)₁₅₉3_<161> = 3 · 601 · 604411 · 92915322557_<11> · C141

C141 = P50 · P91

P50 = 40211844589201070870193753925177566929720034091471_<50>

P91 = 7640927890799418264376357335504587466320927492331080493247053896348840184348910650404572763_<91>

Number: n
N=307255804862118138238800959977993782051356232749794701698253135356472234511279752884270077185205828579676440295689321401915567074990617204373
  ( 141 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=40211844589201070870193753925177566929720034091471 (pp50)
 r2=7640927890799418264376357335504587466320927492331080493247053896348840184348910650404572763 (pp91)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 43.45 hours.
Scaled time: 59.31 units (timescale=1.365).
Factorization parameters were as follows:
name: KA_3_1_159_3
n: 307255804862118138238800959977993782051356232749794701698253135356472234511279752884270077185205828579676440295689321401915567074990617204373
skew: 0.91
deg: 5
c5: 28
c0: 17
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:250150, AFBsize:251161, largePrimes:7385460 encountered
Relations: rels:7003197, finalFF:646856
Max relations in full relation-set: 28
Initial matrix: 501377 x 646856 with sparse part having weight 41926338.
Pruned matrix : 377245 x 379815 with weight 22916317.
Total sieving time: 40.00 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 2.85 hours.
Total square root time: 0.33 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 43.45 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(2·10¹⁶⁰+61)/9 = (2)₁₅₉9_<160> = 3 · 10103 · 15613457 · 416632441 · C140

C140 = P49 · P91

P49 = 2936151587344808656346302770353734642204342157279_<49>

P91 = 3838709524601464946084217929761401324614789430983800435309597156231900651034036787115571447_<91>

Number: n
N=11271033064014227117251631716765959674881912246034154599682541233752667463468895884880810622635796812902030044764864707565008915372835612713
  ( 140 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=2936151587344808656346302770353734642204342157279 (pp49)
 r2=3838709524601464946084217929761401324614789430983800435309597156231900651034036787115571447 (pp91)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 43.68 hours.
Scaled time: 57.78 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_2_159_9
n: 11271033064014227117251631716765959674881912246034154599682541233752667463468895884880810622635796812902030044764864707565008915372835612713
skew: 1.98
deg: 5
c5: 2
c0: 61
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1800001)
Primes: RFBsize:250150, AFBsize:250287, largePrimes:7344485 encountered
Relations: rels:6910066, finalFF:610929
Max relations in full relation-set: 48
Initial matrix: 500504 x 610929 with sparse part having weight 44987741.
Pruned matrix : 407031 x 409597 with weight 25737146.
Total sieving time: 38.85 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 4.52 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 43.68 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 21, 2007

The factor table of 699...997 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Jul 20, 2007 (4th)

By Bruce Dodson / Jul 17, 2007

10³²²+1 is divisible by 1009805096139614383066323378818605356821967673241_<49>, cofactor is prime.

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jul 20, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs

2·10¹⁸⁹+3 = 2(0)₁₈₈3_<190> = 211 · 617 · 186762743 · 3025939986458771807_<19> · 299721566142829669823_<21> · 6007634365195440036739_<22> · C116

C116 = P57 · P59

P57 = 419817276608201618522516989479656415256109781516871114787_<57>

P59 = 35960856659366982010140181518614170249139085672467809368871_<59>

Number: 20003_189
N=15096988907233357495521287258396184736155032772962973177413972069504983979832606332318573583018636209111156665595477
  ( 116 digits)
Divisors found:
 r1=419817276608201618522516989479656415256109781516871114787 (pp57)
 r2=35960856659366982010140181518614170249139085672467809368871 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 26.59 hours.
Scaled time: 56.99 units (timescale=2.143).
Factorization parameters were as follows:
name: 20003_189
n: 15096988907233357495521287258396184736155032772962973177413972069504983979832606332318573583018636209111156665595477
skew: 41912.62
# norm 2.16e+15
c5: 6360
c4: -1373737086
c3: -45296079427237
c2: 3778123322489630234
c1: -16523333732336258468648
c0: -33305705182922434771711568
# alpha -4.95
Y1: 311998665473
Y0: -18840262728057601590579
# Murphy_E 5.40e-10
# M 9806237666384931345996401187694326584755524337853627549119046455930816589581929721798263470708982718933220092999579
type: gnfs
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1800000, 3225001)
Primes: RFBsize:256726, AFBsize:256878, largePrimes:7669673 encountered
Relations: rels:7649278, finalFF:642547
Max relations in full relation-set: 28
Initial matrix: 513683 x 642547 with sparse part having weight 57962084.
Pruned matrix : 414171 x 416803 with weight 36292501.
Total sieving time: 25.12 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.19 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000
total time: 26.59 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 20, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=3000000

5·10¹⁸⁵+3 = 5(0)₁₈₄3_<186> = 7 · 505752502245677956259_<21> · C165

C165 = P38 · P127

P38 = 18507977608619856746602644452748137837_<38>

P127 = 7630885880694883788242610766381704283225279287936847958869670360168616422552526506424965632629458726936822609309848264083247763_<127>

Jul 20, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(4·10¹⁶⁰-13)/9 = (4)₁₅₉3_<160> = 3² · 305111482118759_<15> · C145

C145 = P46 · P100

P46 = 1599713742434510285313677046167755092936978823_<46>

P100 = 1011752171645268180409456572991158703185507059827665215709520041736230600671785104494834474709153811_<100>

Number: n
N=1618513852918894982244660695192826276506442011651985662185105820561633856669307795206595456944773683156646273494967998942230092499261817156744453
  ( 145 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=1599713742434510285313677046167755092936978823 (pp46)
 r2=1011752171645268180409456572991158703185507059827665215709520041736230600671785104494834474709153811 (pp100)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 43.16 hours.
Scaled time: 56.97 units (timescale=1.320).
Factorization parameters were as follows:
name: KA_4_159_3
n: 1618513852918894982244660695192826276506442011651985662185105820561633856669307795206595456944773683156646273494967998942230092499261817156744453
skew: 1.27
deg: 5
c5: 4
c0: -13
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1800001)
Primes: RFBsize:250150, AFBsize:250321, largePrimes:7367990 encountered
Relations: rels:6945136, finalFF:621444
Max relations in full relation-set: 48
Initial matrix: 500535 x 621444 with sparse part having weight 45008824.
Pruned matrix : 398253 x 400819 with weight 25062427.
Total sieving time: 38.50 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 4.36 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 43.16 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(2·10¹⁶⁰-17)/3 = (6)₁₅₉1_<160> = 727 · 1583 · 95988095509_<11> · C143

C143 = P45 · P99

P45 = 101750434942955870404274154756703815926783363_<45>

P99 = 593116172250912842488653172573804937639666230962446807900778437541739835324711444191625551399818163_<99>

Number: n
N=60349828498231515075105017277191802863759950651617645337907466391569953750527359884165767483560724325965640457676728648881641211444679693622169
  ( 143 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=101750434942955870404274154756703815926783363 (pp45)
 r2=593116172250912842488653172573804937639666230962446807900778437541739835324711444191625551399818163 (pp99)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 40.20 hours.
Scaled time: 58.17 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_6_159_1
n: 60349828498231515075105017277191802863759950651617645337907466391569953750527359884165767483560724325965640457676728648881641211444679693622169
skew: 1.53
deg: 5
c5: 2
c0: -17
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1900001)
Primes: RFBsize:250150, AFBsize:249961, largePrimes:7392335 encountered
Relations: rels:6971314, finalFF:612340
Max relations in full relation-set: 28
Initial matrix: 500176 x 612340 with sparse part having weight 42132816.
Pruned matrix : 405751 x 408315 with weight 24833572.
Total sieving time: 35.40 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 4.23 hours.
Total square root time: 0.36 hours, sqrts: 5.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 40.20 hours.
 --------- CPU info (if available) ----------

5·10¹⁶⁶+3 = 5(0)₁₆₅3_<167> = 58411 · C166

C162 = P69 · P94

P69 = 205212516206615635610167665320053000460472202204809200220862876866413_<69>

P94 = 4171300883176815364229387134807678863679793387097531618573030009987940624111825593896704727821_<94>

Number: n
N=856003150091592337059800380065398640666997654551368749036996456146958620807724572426426529249627638629710157333378986834671551591309856020270154594168906541576073
  ( 162 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=205212516206615635610167665320053000460472202204809200220862876866413 (pp69)
 r2=4171300883176815364229387134807678863679793387097531618573030009987940624111825593896704727821 (pp94)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 80.81 hours.
Scaled time: 96.49 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_5_0_165_3
n: 856003150091592337059800380065398640666997654551368749036996456146958620807724572426426529249627638629710157333378986834671551591309856020270154594168906541576073
type: snfs
skew: 0.57
deg: 5
c5: 50
c0: 3
m: 1000000000000000000000000000000000
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3000001)
Primes: RFBsize:283146, AFBsize:283047, largePrimes:7663698 encountered
Relations: rels:7215429, finalFF:636030
Max relations in full relation-set: 28
Initial matrix: 566258 x 636030 with sparse part having weight 42205013.
Pruned matrix : 510577 x 513472 with weight 29645883.
Total sieving time: 71.79 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 7.83 hours.
Total square root time: 0.87 hours, sqrts: 6.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000
total time: 80.81 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Jul 19, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp

(25·10¹⁶⁰-7)/9 = 2(7)₁₆₀_<161> = 3 · 27947 · 7306883 · 138621983 · C141

C141 = P69 · P72

P69 = 883323744340659477525559747044983470768166295315797627245668926714929_<69>

P72 = 370302704851532106577899935747396428452827041176147028833284274712784437_<72>

Number: n
N=327097171788929430479622084869129690697740912748786682229340262241719606549744366710334791145444653101642953787249946765260803343440926759973
  ( 141 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=883323744340659477525559747044983470768166295315797627245668926714929 (pp69)
 r2=370302704851532106577899935747396428452827041176147028833284274712784437 (pp72)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 36.41 hours.
Scaled time: 49.70 units (timescale=1.365).
Factorization parameters were as follows:
name: KA_2_7_160
n: 327097171788929430479622084869129690697740912748786682229340262241719606549744366710334791145444653101642953787249946765260803343440926759973
skew: 0.78
deg: 5
c5: 25
c0: -7
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:250150, AFBsize:250196, largePrimes:7112312 encountered
Relations: rels:6671455, finalFF:592115
Max relations in full relation-set: 28
Initial matrix: 500410 x 592115 with sparse part having weight 34549711.
Pruned matrix : 418302 x 420868 with weight 20091437.
Total sieving time: 33.04 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 3.04 hours.
Total square root time: 0.10 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 36.41 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 19, 2007 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

5·10¹⁶¹+3 = 5(0)₁₆₀3_<162> = 7² · 1447 · 180463 · 26314542158435393005535533221629_<32> · C121

C121 = P59 · P63

P59 = 11706943567107084998551285511603272813010623152246453284257_<59>

P63 = 126846321501220363453898438705886991913400990993746411945018359_<63>

Number: 50003_161
N=1484982727509908854740212306941041004792973008825939876458829727780821383869898582890053749715127694042906997885710674263
  ( 121 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=11706943567107084998551285511603272813010623152246453284257 (pp59)
 r2=126846321501220363453898438705886991913400990993746411945018359 (pp63)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 80.52 hours.
Scaled time: 54.99 units (timescale=0.683).
Factorization parameters were as follows:
name: 50003_161
n: 1484982727509908854740212306941041004792973008825939876458829727780821383869898582890053749715127694042906997885710674263
m: 100000000000000000000000000000000
c5: 50
c0: 3
skew: 0.57
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4150001)
Primes: RFBsize:315948, AFBsize:315546, largePrimes:5714501 encountered
Relations: rels:5824294, finalFF:708200
Max relations in full relation-set: 0
Initial matrix: 631559 x 708200 with sparse part having weight 36699917.
Pruned matrix : 568992 x 572213 with weight 27259397.
Total sieving time: 67.88 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 12.11 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 80.52 hours.
 --------- CPU info (if available) ----------

Jul 19, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

5·10¹⁵⁷-3 = 4(9)₁₅₆7_<158> = 170751714607368696896080865604341002901_<39> · C120

C120 = P50 · P70

P50 = 35723845046279761616907730154034566105895929934169_<50>

P70 = 8196845212810478814820742135146474925279643255860336587608186692950513_<70>

Number: 49997_157
N=292822828250781602016000167325285828040891795200764250827620597365088252659542353359323090342351116997142479928464778697
  ( 120 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=35723845046279761616907730154034566105895929934169 (pp50)
 r2=8196845212810478814820742135146474925279643255860336587608186692950513 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.71 hours.
Scaled time: 53.00 units (timescale=2.145).
Factorization parameters were as follows:
n: 292822828250781602016000167325285828040891795200764250827620597365088252659542353359323090342351116997142479928464778697
m: 50000000000000000000000000000000
c5: 4
c0: -75
skew: 1.8
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3400001)
Primes: RFBsize:283146, AFBsize:282917, largePrimes:5641286 encountered
Relations: rels:5700798, finalFF:682263
Max relations in full relation-set: 28
Initial matrix: 566127 x 682263 with sparse part having weight 40514085.
Pruned matrix : 469219 x 472113 with weight 25366768.
Total sieving time: 23.34 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 1.24 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 24.71 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 18, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs

5·10¹⁹⁶+3 = 5(0)₁₉₅3_<197> = 53 · 4831 · 81435758513_<11> · 620177514568967_<15> · 8335212300603379_<16> · 35165888307807931_<17> · 1724266535012524133_<19> · C115

C115 = P47 · P69

P47 = 18149768500139575450781954504934682959012295193_<47>

P69 = 421514178392323250396382121254673947852157285795193589239114535798571_<69>

Number: 50003_196
N=7650384757347202203321962443218518173640546585406568276655144521369399383167952622184566026725961406618337839569203
  ( 115 digits)
Divisors found:
 r1=18149768500139575450781954504934682959012295193 (pp47)
 r2=421514178392323250396382121254673947852157285795193589239114535798571 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 23.37 hours.
Scaled time: 49.86 units (timescale=2.134).
Factorization parameters were as follows:
name: 50003_196
n: 7650384757347202203321962443218518173640546585406568276655144521369399383167952622184566026725961406618337839569203
skew: 19553.70
# norm 3.28e+15
c5: 16920
c4: -3549394118
c3: -96775513274836
c2: -922030925486182961
c1: 11391841096341814490596
c0: -17247691065672184548477665
# alpha -5.74
Y1: 678599985437
Y0: -13522515818159374759236
# Murphy_E 6.05e-10
# M 1884377264941917291735930955710612016215991487489349721733252967878467057857630059934213163822258669912389565149551
type: gnfs
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1800000, 2925001)
Primes: RFBsize:256726, AFBsize:255896, largePrimes:7598169 encountered
Relations: rels:7604204, finalFF:692093
Max relations in full relation-set: 28
Initial matrix: 512710 x 692093 with sparse part having weight 60076442.
Pruned matrix : 368783 x 371410 with weight 33519290.
Polynomial selection time: 1.33 hours.
Total sieving time: 20.87 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.88 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000
total time: 23.37 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 18, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp

(25·10¹⁵⁹-1)/3 = 8(3)₁₅₉_<160> = 13 · 67 · 2236664243479_<13> · C145

C145 = P68 · P77

P68 = 85262497941625226303736633385477406332679270895304586298374767884871_<68>

P77 = 50169728633912464831848958683943349449579452577543046686850278491362296324547_<77>

Number: n
N=4277596384380857709493007778877230054219181915921345009085918406957522336511160704245123636854674964203757729951971401133102929893914016547228437
  ( 145 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=85262497941625226303736633385477406332679270895304586298374767884871 (pp68)
 r2=50169728633912464831848958683943349449579452577543046686850278491362296324547 (pp77)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 32.10 hours.
Scaled time: 42.47 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_8_3_159
n: 4277596384380857709493007778877230054219181915921345009085918406957522336511160704245123636854674964203757729951971401133102929893914016547228437
skew: 0.83
deg: 5
c5: 5
c0: -2
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:250150, AFBsize:249566, largePrimes:6976915 encountered
Relations: rels:6496813, finalFF:566255
Max relations in full relation-set: 48
Initial matrix: 499781 x 566255 with sparse part having weight 34478584.
Pruned matrix : 438189 x 440751 with weight 21194488.
Total sieving time: 27.82 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 4.02 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 32.10 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(67·10¹⁶⁰+23)/9 = 7(4)₁₅₉7_<161> = 61 · 173 · 401199361 · C149

C149 = P59 · P91

P59 = 10926374007313810829354105515688558278231191096957190128523_<59>

P91 = 1609237188318111563993645016667268783331795663193421462542500398194843294512175283899466533_<91>

Number: n
N=17583127386041774296839855493344250162140468475916165432870626962320083118392473075736410533833904510381392754713628615579892796163624551333407220759
  ( 149 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=10926374007313810829354105515688558278231191096957190128523 (pp59)
 r2=1609237188318111563993645016667268783331795663193421462542500398194843294512175283899466533 (pp91)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 36.67 hours.
Scaled time: 53.17 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_7_4_159_7
n: 17583127386041774296839855493344250162140468475916165432870626962320083118392473075736410533833904510381392754713628615579892796163624551333407220759
skew: 0.81
deg: 5
c5: 67
c0: 23
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1600001)
Primes: RFBsize:250150, AFBsize:249876, largePrimes:7232989 encountered
Relations: rels:6812085, finalFF:613709
Max relations in full relation-set: 28
Initial matrix: 500091 x 613709 with sparse part having weight 37971848.
Pruned matrix : 402209 x 404773 with weight 21189373.
Total sieving time: 32.31 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.89 hours.
Total square root time: 0.28 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 36.67 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(34·10¹⁵⁹-7)/9 = 3(7)₁₅₉_<160>= 3² · 71 · 9849193859_<10> · C147

C147 = P38 · P110

P38 = 15789711189493102093850282846783373661_<38>

P110 = 38015497418106844664862291991531816509233084067775500201987562671218032336050381463628044115703545766523286857_<110>

Number: n
N=600253724956827777777889593571298375324011458737641410037337583447615653917558424232237914428509235194183545143746268503264957812846753488921273477
  ( 147 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=15789711189493102093850282846783373661 (pp38)
 r2=38015497418106844664862291991531816509233084067775500201987562671218032336050381463628044115703545766523286857 (pp110)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 45.27 hours.
Scaled time: 61.80 units (timescale=1.365).
Factorization parameters were as follows:
name: KA_3_7_159
n: 600253724956827777777889593571298375324011458737641410037337583447615653917558424232237914428509235194183545143746268503264957812846753488921273477
skew: 1.16
deg: 5
c5: 17
c0: -35
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2000001)
Primes: RFBsize:250150, AFBsize:249491, largePrimes:7263434 encountered
Relations: rels:6782000, finalFF:559844
Max relations in full relation-set: 28
Initial matrix: 499706 x 559844 with sparse part having weight 36936566.
Pruned matrix : 449732 x 452294 with weight 25239638.
Total sieving time: 40.93 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 3.98 hours.
Total square root time: 0.14 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 45.27 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 17, 2007 (2nd)

By Yousuke Koide

10⁸⁶³+1 is divisible by 1584705713225403483147160166143_<31>

10¹³²⁹+1 is divisible by558143308808597896050937412527393543_<36>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jul 17, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs

5·10¹⁷⁹-3 = 4(9)₁₇₈7_<180> = 1900472818297_<13> · 143368179663990121285177_<24> · 806484427355480910242618688187_<30> · C115

C115 = P33 · P82

P33 = 621517573913879824531937479098749_<33>

P82 = 3661054312333149079554418503387457027608632989634573487936702648419063794797276451_<82>

Number: 49997_179
N=2275409594168246455928757421586717932537118162223751052838379676300521807658832201602602122092595306083443281259799
  ( 115 digits)
Divisors found:
 r1=621517573913879824531937479098749 (pp33)
 r2=3661054312333149079554418503387457027608632989634573487936702648419063794797276451 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 25.17 hours.
Scaled time: 53.93 units (timescale=2.143).
Factorization parameters were as follows:
name: 49997_179
n: 2275409594168246455928757421586717932537118162223751052838379676300521807658832201602602122092595306083443281259799
skew: 48196.28
# norm 2.56e+15
c5: 17100
c4: -244455031
c3: -4688970535978
c2: 2873460003022738472
c1: -73570840875606184789656
c0: -1602366182681329256539047600
# alpha -5.29
Y1: 1286465858737
Y0: -10587973502887367643287
# Murphy_E 5.24e-10
# M 1767462674691911687831046393184802436937077927791968598803245797389906802841504982740536471287350721141060325879747
type: gnfs
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1800000, 3075001)
Primes: RFBsize:256726, AFBsize:256075, largePrimes:7543117 encountered
Relations: rels:7471856, finalFF:627137
Max relations in full relation-set: 28
Initial matrix: 512887 x 627137 with sparse part having weight 54070246.
Pruned matrix : 419748 x 422376 with weight 33364516.
Polynomial selection time: 1.32 hours.
Total sieving time: 22.33 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.22 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000
total time: 25.17 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 16, 2007 (4th)

By Robert Backstrom / GMP-ECM 5.0 B1=891500, GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon

5·10¹⁵¹+3 = 5(0)₁₅₀3_<152> = 443 · 947 · C147

C147 = P35 · P40 · P73

P35 = 16270985621257205906905273044911329_<35>

P40 = 1985841848915255165882503532099473704607_<40>

P73 = 3688567872296026104787199609577180339676172266118012744852132484083849981_<73>

Number: n
N=7324912443369749282814026596498825470913846589987658708241984849562150308735119605514615544006418914029296562467
  ( 112 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=1985841848915255165882503532099473704607 (pp40)
 r2=3688567872296026104787199609577180339676172266118012744852132484083849981 (pp73)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 19.96 hours.
Scaled time: 27.26 units (timescale=1.366).
Factorization parameters were as follows:
name: KA_5_0_150_3

n: 7324912443369749282814026596498825470913846589987658708241984849562150308735119605514615544006418914029296562467

# n: 119183545043037178115040725017341205803761909415738425490023145444447357819989940908798367662167090562808536402230162494845311676888642046524488643

skew: 0.57
deg: 5
c5: 50
c0: 3
m: 1000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 800001)
Primes: RFBsize:216816, AFBsize:216516, largePrimes:6804261 encountered
Relations: rels:6450784, finalFF:626071
Max relations in full relation-set: 28
Initial matrix: 433397 x 626071 with sparse part having weight 36162324.
Pruned matrix : 263684 x 265914 with weight 16092660.
Total sieving time: 17.97 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 1.70 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 19.96 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

5·10¹⁵⁷+3 = 5(0)₁₅₆3_<158> = 53 · 149 · C154

C154 = P77 · P78

P77 = 13437119575793745653860491268913351112372015271429983467581637225087533319599_<77>

P78 = 471196096929417376262628665137399248660726397583286864726053838970722199918901_<78>

Number: n
N=6331518298087881473977459794858807141952640243130302646574648600734456122578194250981385336203621628466506268203115107002659237685196910219070533113840699
  ( 154 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=13437119575793745653860491268913351112372015271429983467581637225087533319599 (pp77)
 r2=471196096929417376262628665137399248660726397583286864726053838970722199918901 (pp78)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 29.27 hours.
Scaled time: 38.69 units (timescale=1.322).
Factorization parameters were as follows:
name: KA_5_0_156_3
n: 6331518298087881473977459794858807141952640243130302646574648600734456122578194250981385336203621628466506268203115107002659237685196910219070533113840699
skew: 0.36
deg: 5
c5: 500
c0: 3
m: 10000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:250150, AFBsize:249916, largePrimes:7074187 encountered
Relations: rels:6675409, finalFF:633608
Max relations in full relation-set: 48
Initial matrix: 500132 x 633608 with sparse part having weight 36398161.
Pruned matrix : 379352 x 381916 with weight 17859403.
Total sieving time: 26.08 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 2.92 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 29.27 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

5·10¹⁵⁸+3 = 5(0)₁₅₇3_<159> = 23535093831695777_<17> · C143

C143 = P43 · P100

P43 = 3336615942677038549001641449007892174836007_<43>

P100 = 6367190586858022590177464026314548769045456613292917746979423848926661873487443619330012203341779877_<100>

Number: n
N=21244869622173647341125524581467461321857532311440306649055866165271370428262898974355677169015308439811677066930201131833443993338133967631139
  ( 143 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=3336615942677038549001641449007892174836007 (pp43)
 r2=6367190586858022590177464026314548769045456613292917746979423848926661873487443619330012203341779877 (pp100)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 29.31 hours.
Scaled time: 42.38 units (timescale=1.446).
Factorization parameters were as follows:
name: KA_5_0_157_3
n: 21244869622173647341125524581467461321857532311440306649055866165271370428262898974355677169015308439811677066930201131833443993338133967631139
skew: 1.13
deg: 5
c5: 8
c0: 15
m: 50000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:250150, AFBsize:249771, largePrimes:7121193 encountered
Relations: rels:6715214, finalFF:623828
Max relations in full relation-set: 28
Initial matrix: 499986 x 623828 with sparse part having weight 35936151.
Pruned matrix : 388924 x 391487 with weight 18826913.
Total sieving time: 25.99 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.08 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 29.31 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

5·10¹⁵²+3 = 5(0)₁₅₁3_<153> = 14869 · C149

C149 = P57 · P93

P57 = 135268966532217716081858222979343678676268459159986363363_<57>

P93 = 248593672856895851344394797338957581879512075361661154360125070884478563005695290561420504349_<93>

Number: n
N=33627009213800524581343735288183468962270495662115811419732329006658147824332503867106059587060326854529558141098930661107001143318313269217835765687
  ( 149 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=135268966532217716081858222979343678676268459159986363363 (pp57)
 r2=248593672856895851344394797338957581879512075361661154360125070884478563005695290561420504349 (pp93)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 24.70 hours.
Scaled time: 29.56 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_5_0_151_3
n: 33627009213800524581343735288183468962270495662115811419732329006658147824332503867106059587060326854529558141098930661107001143318313269217835765687
type: snfs
skew: 0.36
deg: 5
c5: 500
c0: 3
m: 1000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1000001)
Primes: RFBsize:216816, AFBsize:216936, largePrimes:6041357 encountered
Relations: rels:5535427, finalFF:506590
Max relations in full relation-set: 28
Initial matrix: 433818 x 506590 with sparse part having weight 22617044.
Pruned matrix : 360584 x 362817 with weight 12620042.
Total sieving time: 22.48 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 1.96 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 24.70 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Jul 16, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs, GGNFS-0.77.1-20050930-nocona

(7·10¹⁶⁰-1)/3 = 2(3)₁₆₀_<161> = 767759 · 101791091 · 144095279191_<12> · 35667897961095649947526145377069_<32> · C104

C104 = P50 · P54

P50 = 62240253527047472580312971081891307447294255689341_<50>

P54 = 933347736560011308158563114276369605838717858921125863_<54>

Number: 23333_160
N=58091799752391019095159666661111369201684177850360308694417611514513839600421435152360645238364888526283
  ( 104 digits)
Divisors found:
 r1=62240253527047472580312971081891307447294255689341 (pp50)
 r2=933347736560011308158563114276369605838717858921125863 (pp54)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.76 hours.
Scaled time: 14.49 units (timescale=2.143).
Factorization parameters were as follows:
name: 23333_160
n: 58091799752391019095159666661111369201684177850360308694417611514513839600421435152360645238364888526283
skew: 3825.25
# norm 1.63e+14
c5: 583440
c4: 2326542356
c3: -1039085397060
c2: -24696191837440549
c1: -63642552109250830002
c0: 197660511380706138491336
# alpha -5.58
Y1: 23540119783
Y0: -39776221118266163853
# Murphy_E 2.00e-09
# M 24646029232970984534273208895494097189591808184433543572167780495792969620406958018181523786806597925930
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1800001)
Primes: RFBsize:135072, AFBsize:135103, largePrimes:4502987 encountered
Relations: rels:4540682, finalFF:378476
Max relations in full relation-set: 28
Initial matrix: 270263 x 378476 with sparse part having weight 34673689.
Pruned matrix : 213384 x 214799 with weight 18092350.
Polynomial selection time: 0.39 hours.
Total sieving time: 6.00 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 6.76 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

(8·10¹⁵⁷+1)/9 = (8)₁₅₆9_<157> = 3 · 167 · 643 · 386810729226965311961660138063_<30> · C122

C122 = P57 · P66

P57 = 584698862250581133160768195196298297489539613970663689401_<57>

P66 = 122002299998521265446868714174191654500476089207312611183964015921_<66>

Number: 88889_157
N=71334606001089460171433505241882854150874389311670197254671100147853471919307059160203441539544459417073704994902162953321
  ( 122 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=584698862250581133160768195196298297489539613970663689401 (pp57)
 r2=122002299998521265446868714174191654500476089207312611183964015921 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 19.80 hours.
Scaled time: 42.41 units (timescale=2.142).
Factorization parameters were as follows:
n: 71334606001089460171433505241882854150874389311670197254671100147853471919307059160203441539544459417073704994902162953321
m: 20000000000000000000000000000000
c5: 25
c0: 1
skew: 0.53
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2700001)
Primes: RFBsize:216816, AFBsize:216556, largePrimes:5671234 encountered
Relations: rels:5704347, finalFF:614436
Max relations in full relation-set: 28
Initial matrix: 433436 x 614436 with sparse part having weight 47552480.
Pruned matrix : 325242 x 327473 with weight 29562975.
Total sieving time: 19.05 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.62 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 19.80 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 16, 2007 (2nd)

By JMB / GMP-ECM B1=1000000

5·10¹⁸⁰+3 = 5(0)₁₇₉3_<181> = 3636511 · 10065320359_<11> · 170781899320909_<15> · C150

C150 = P35 · P116

P35 = 28365504652386968928074018263317721_<35>

P116 = 28198443896462682489337688478809235310463625892214771261649188513799597672988910349570886709139480460830651399289823_<116>

Jul 16, 2007

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000

(89·10¹⁵⁹+1)/9 = 9(8)₁₅₈9_<160> = 11 · 1607 · 117727 · 9898242372013_<13> · C138

C138 = P36 · P102

P36 = 748314670082521201732646760076033103_<36>

P102 = 641535236229688185049707266010883443210404427579829424348071950643837839950313319024896633402043943969_<102>

Jul 15, 2007 (5th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, GGNFS-0.77.1-20050930-nocona gnfs, GMP-ECM 6.1.2 B1=1000000

5·10¹⁴⁹+3 = 5(0)₁₄₈3_<150> = 7 · 1931 · C146

C146 = P70 · P76

P70 = 5243209539041849099760187057760329315540666673453359958582230909941313_<70>

P76 = 7054926221581529213954354507669417037749392705948230321975121930804768049743_<76>

Number: 50003_149
N=36990456462232743952060368424946363838129762521269512465783827772434711844344159206924613449729969667825700969149959310497891543981652733594732559
  ( 146 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=5243209539041849099760187057760329315540666673453359958582230909941313 (pp70)
 r2=7054926221581529213954354507669417037749392705948230321975121930804768049743 (pp76)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.32 hours.
Scaled time: 22.11 units (timescale=2.143).
Factorization parameters were as follows:
n: 36990456462232743952060368424946363838129762521269512465783827772434711844344159206924613449729969667825700969149959310497891543981652733594732559
m: 1000000000000000000000000000000
c5: 1
c0: 6
skew: 1.43
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1575001)
Primes: RFBsize:135072, AFBsize:135038, largePrimes:3902867 encountered
Relations: rels:4084643, finalFF:460007
Max relations in full relation-set: 28
Initial matrix: 270174 x 460007 with sparse part having weight 43534247.
Pruned matrix : 208806 x 210220 with weight 19236951.
Total sieving time: 10.03 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 10.32 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

5·10¹⁶⁵+3 = 5(0)₁₆₄3_<166> = 107 · 3347 · 76127449 · 526115281 · 8629342554611_<13> · 669110924591646330515236469_<27> · C104

C104 = P44 · P60

P44 = 90824126989341694860705521906459719377905473_<44>

P60 = 664708541046310574292268644887995665738412289611807142993429_<60>

Number: 50003_165
N=60371572942890158021797115986528632028025448079180506843525853489532798120896719516288434944161422136917
  ( 104 digits)
Divisors found:
 r1=90824126989341694860705521906459719377905473 (pp44)
 r2=664708541046310574292268644887995665738412289611807142993429 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.17 hours.
Scaled time: 13.22 units (timescale=2.141).
Factorization parameters were as follows:
name: 50003_165
n: 60371572942890158021797115986528632028025448079180506843525853489532798120896719516288434944161422136917
skew: 7512.98
# norm 2.02e+14
c5: 166500
c4: -1914787896
c3: -27411196426603
c2: 131255323836306125
c1: 909402917800101582079
c0: -10830259771894865408765
# alpha -5.96
Y1: 44183744759
Y0: -51509164741546869936
# Murphy_E 2.11e-09
# M 17593451203521667606384512745223636260136127566053466928071642609603807329680876842845993513292579249217
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1680001)
Primes: RFBsize:135072, AFBsize:134796, largePrimes:4380469 encountered
Relations: rels:4317631, finalFF:327814
Max relations in full relation-set: 28
Initial matrix: 269947 x 327814 with sparse part having weight 26520107.
Pruned matrix : 232660 x 234073 with weight 15995712.
Polynomial selection time: 0.39 hours.
Total sieving time: 5.42 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 6.17 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

(71·10¹⁵⁹-17)/9 = 7(8)₁₅₈7_<160> = 3² · 11 · 19 · 1109 · 3623 · 5261 · 267040418211849516599855437_<27> · C120

C120 = P35 · P86

P35 = 40952345579027162659509811761961327_<35>

P86 = 18142748524569935341717716457506943467605125808300221525169648512901304619161112676899_<86>

(7·10¹⁶⁰-1)/3 = 2(3)₁₆₀_<161> = 767759 · 101791091 · 144095279191_<12> · C136

C136 = P32 · C104

P32 = 35667897961095649947526145377069_<32>

C104 = [58091799752391019095159666661111369201684177850360308694417611514513839600421435152360645238364888526283_<104>]

Jul 15, 2007 (4th)

By suberi / GMP-ECM 6.1.2 B1=1000000

5·10¹⁷³+3 = 5(0)₁₇₂3_<174> = 7 · 313 · 169061906987_<12> · C160

C160 = P32 · P128

P32 = 59249254073379949902901368057587_<32>

P128 = 22782373957682117221393919745453826568924577598689253992144435924521117243880060681895434415464594199441242777852408944634407357_<128>

Jul 15, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp

(19·10¹⁵⁷-1)/9 = 2(1)₁₅₇_<158> = 3 · 7 · 4129 · 4139 · 136082245808735331544874467_<27> · C123

C123 = P61 · P62

P61 = 6186192101868302643109806651993561689864386250254698505182203_<61>

P62 = 69875771724775887872374741822268114523219808403456062141215761_<62>

Number: n
N=432264947155761060829306720543648014786687216349608237446155217915853935721724780996199161863813705702775908099453240301483
  ( 123 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=6186192101868302643109806651993561689864386250254698505182203 (pp61)
 r2=69875771724775887872374741822268114523219808403456062141215761 (pp62)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 45.81 hours.
Scaled time: 54.75 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_2_1_157
n: 432264947155761060829306720543648014786687216349608237446155217915853935721724780996199161863813705702775908099453240301483
type: snfs
skew: 0.22
deg: 5
c5: 1900
c0: -1
m: 10000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1800001)
Primes: RFBsize:250150, AFBsize:249896, largePrimes:6865713 encountered
Relations: rels:6360045, finalFF:568119
Max relations in full relation-set: 28
Initial matrix: 500113 x 568119 with sparse part having weight 30885928.
Pruned matrix : 436560 x 439124 with weight 19548005.
Total sieving time: 41.67 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 3.79 hours.
Total square root time: 0.11 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.3,2.3,100000
total time: 45.81 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

5·10¹³⁶+3 = 5(0)₁₃₅3_<137> = 229 · 82132721813_<11> · C124

C124 = P58 · P66

P58 = 5824999790723064946307734440392437977214744000689735893063_<58>

P66 = 456375574500296265791802787296814526424506695836333278231520021053_<66>

Number: n
N=2658387625955344283447253598161736872225766192093870684024282834889948633340957531901645111619482902526329350996955516655339
  ( 124 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=5824999790723064946307734440392437977214744000689735893063 (pp58)
 r2=456375574500296265791802787296814526424506695836333278231520021053 (pp66)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 5.26 hours.
Scaled time: 6.96 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_5_0_135_3
n: 2658387625955344283447253598161736872225766192093870684024282834889948633340957531901645111619482902526329350996955516655339
skew: 0.57
deg: 5
c5: 50
c0: 3
m: 1000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 500001)
Primes: RFBsize:183072, AFBsize:182856, largePrimes:5537962 encountered
Relations: rels:5074935, finalFF:454061
Max relations in full relation-set: 48
Initial matrix: 365993 x 454061 with sparse part having weight 18698401.
Pruned matrix : 276551 x 278444 with weight 8183715.
Total sieving time: 4.18 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.82 hours.
Total square root time: 0.13 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,75000
total time: 5.26 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(73·10¹⁷⁸-1)/9 = 8(1)₁₇₈_<179> = 3 · C179

C179 = P76 · P104

P76 = 1916119867312670924752148611535640415033386450801802237208935853302075657931_<76>

P104 = 14110305674642407281721016340336939892095295727428257624280415428343597811358551505074904645162638085927_<104>

Number: n
N=27037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037
  ( 179 digits)
SNFS difficulty: 179 digits.
Divisors found:
 r1=1916119867312670924752148611535640415033386450801802237208935853302075657931 (pp76)
 r2=14110305674642407281721016340336939892095295727428257624280415428343597811358551505074904645162638085927 (pp104)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 432.02 hours.
Scaled time: 590.57 units (timescale=1.367).
Factorization parameters were as follows:
name: KA_8_1_178
n: 27037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037
skew: 0.11
deg: 5
c5: 73000
c0: -1
m: 100000000000000000000000000000000000
type: snfs
rlim: 5500000
alim: 5500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 17500001)
Primes: RFBsize:380800, AFBsize:380932, largePrimes:10269650 encountered
Relations: rels:10024620, finalFF:853883
Max relations in full relation-set: 28
Initial matrix: 761799 x 853883 with sparse part having weight 106544632.
Pruned matrix : 703884 x 707756 with weight 90829890.
Total sieving time: 405.67 hours.
Total relation processing time: 1.62 hours.
Matrix solve time: 24.13 hours.
Total square root time: 0.60 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,179,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000
total time: 432.02 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

5·10¹³⁷+3 = 5(0)₁₃₆3_<138> = 7 · 3343 · 1231884389_<10> · C125

C125 = P56 · P70

P56 = 14133656423605033089328341238732583072598888641345800951_<56>

P70 = 1227188017945406154897963678957290689881567366655657179710045847933577_<70>

Number: n
N=17344653812805218322201570213942926988367052498223811015981967787777496609303098136878312186566884764798888346267889311431727
  ( 125 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=14133656423605033089328341238732583072598888641345800951 (pp56)
 r2=1227188017945406154897963678957290689881567366655657179710045847933577 (pp70)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.48 hours.
Scaled time: 7.74 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_5_0_136_3
n: 17344653812805218322201570213942926988367052498223811015981967787777496609303098136878312186566884764798888346267889311431727
type: snfs
skew: 0.36
deg: 5
c5: 500
c0: 3
m: 1000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 700001)
Primes: RFBsize:148933, AFBsize:148735, largePrimes:5741066 encountered
Relations: rels:5246168, finalFF:473203
Max relations in full relation-set: 28
Initial matrix: 297734 x 473203 with sparse part having weight 21419198.
Pruned matrix : 149345 x 150897 with weight 8231855.
Total sieving time: 5.80 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.48 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,75000
total time: 6.48 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

5·10¹⁴⁴+3 = 5(0)₁₄₃3_<145> = 53 · C143

C143 = P67 · P77

P67 = 8915485535218874463020966252542555006448848732763244901456195853393_<67>

P77 = 10581546262269091742312886939766011985159784242637011168380827339866200032807_<77>

Number: n
N=94339622641509433962264150943396226415094339622641509433962264150943396226415094339622641509433962264150943396226415094339622641509433962264151
  ( 143 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=8915485535218874463020966252542555006448848732763244901456195853393 (pp67)
 r2=10581546262269091742312886939766011985159784242637011168380827339866200032807 (pp77)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.42 hours.
Scaled time: 9.79 units (timescale=1.320).
Factorization parameters were as follows:
name: KA_5_0_143_3
n: 94339622641509433962264150943396226415094339622641509433962264150943396226415094339622641509433962264150943396226415094339622641509433962264151
skew: 1.43
deg: 5
c5: 1
c0: 6
m: 100000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 800001)
Primes: RFBsize:183072, AFBsize:183151, largePrimes:6364163 encountered
Relations: rels:5878097, finalFF:499432
Max relations in full relation-set: 48
Initial matrix: 366287 x 499432 with sparse part having weight 26509055.
Pruned matrix : 248154 x 250049 with weight 10949064.
Total sieving time: 6.14 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.04 hours.
Total square root time: 0.08 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 7.42 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

5·10¹⁵⁴+3 = 5(0)₁₅₃3_<155> = 31 · 4021 · C150

C150 = P36 · P115

P36 = 167160802616143494509108495516497129_<36>

P115 = 2399605173928420299498820740137566306845129879546122780196166540333527775067120892884179276851300720910497809301857_<115>

Number: n
N=401119926835725345163697042141659513361304762898011247402748473738678390065061652132754650985551660235377173067203632542057424328725802440413634868553
  ( 150 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=167160802616143494509108495516497129 (pp36)
 r2=2399605173928420299498820740137566306845129879546122780196166540333527775067120892884179276851300720910497809301857 (pp115)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 18.03 hours.
Scaled time: 26.12 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_5_0_153_3
n: 401119926835725345163697042141659513361304762898011247402748473738678390065061652132754650985551660235377173067203632542057424328725802440413634868553
skew: 1.43
deg: 5
c5: 1
c0: 6
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 800001)
Primes: RFBsize:216816, AFBsize:216821, largePrimes:6423682 encountered
Relations: rels:5914055, finalFF:487619
Max relations in full relation-set: 28
Initial matrix: 433701 x 487619 with sparse part having weight 27166609.
Pruned matrix : 381771 x 384003 with weight 17076701.
Total sieving time: 15.26 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 2.48 hours.
Total square root time: 0.15 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 18.03 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jul 15, 2007 (2nd)

By Jo Yeong Uk / Msieve v. 1.21, GGNFS-0.77.1-20050930-nocona gnfs

5·10¹⁶⁰+3 = 5(0)₁₅₉3_<161> = 2207 · 7760503636757_<13> · 120355074834623_<15> · 82551714075637674821552052888550681_<35> · C96

C96 = P43 · P54

P43 = 1770092901260328461943147499208826822490849_<43>

P54 = 165993545605717346668480035353143215370070055379374031_<54>

Sat Jul 14 21:15:30 2007  
Sat Jul 14 21:15:30 2007  
Sat Jul 14 21:15:30 2007  Msieve v. 1.21
Sat Jul 14 21:15:30 2007  random seeds: 7cf136d0 06e41b3c
Sat Jul 14 21:15:30 2007  factoring 293823996731712864770458618120875378669709169546409049689172378069092682226620668855969845742319 (96 digits)
Sat Jul 14 21:15:30 2007  commencing quadratic sieve (96-digit input)
Sat Jul 14 21:15:30 2007  using multiplier of 1
Sat Jul 14 21:15:30 2007  using 32kb Intel Core sieve core
Sat Jul 14 21:15:30 2007  sieve interval: 36 blocks of size 32768
Sat Jul 14 21:15:30 2007  processing polynomials in batches of 6
Sat Jul 14 21:15:30 2007  using a sieve bound of 2258261 (83529 primes)
Sat Jul 14 21:15:30 2007  using large prime bound of 338739150 (28 bits)
Sat Jul 14 21:15:30 2007  using double large prime bound of 2258175411908100 (43-52 bits)
Sat Jul 14 21:15:30 2007  using trial factoring cutoff of 52 bits
Sat Jul 14 21:15:30 2007  polynomial 'A' values have 12 factors
Sun Jul 15 00:30:57 2007  83772 relations (20431 full + 63341 combined from 1261659 partial), need 83625
Sun Jul 15 00:30:57 2007  begin with 1282090 relations
Sun Jul 15 00:30:58 2007  reduce to 219241 relations in 10 passes
Sun Jul 15 00:30:58 2007  attempting to read 219241 relations
Sun Jul 15 00:31:00 2007  recovered 219241 relations
Sun Jul 15 00:31:00 2007  recovered 203549 polynomials
Sun Jul 15 00:31:00 2007  attempting to build 83772 cycles
Sun Jul 15 00:31:00 2007  found 83772 cycles in 6 passes
Sun Jul 15 00:31:00 2007  distribution of cycle lengths:
Sun Jul 15 00:31:00 2007     length 1 : 20431
Sun Jul 15 00:31:00 2007     length 2 : 14459
Sun Jul 15 00:31:00 2007     length 3 : 13979
Sun Jul 15 00:31:00 2007     length 4 : 11430
Sun Jul 15 00:31:00 2007     length 5 : 8505
Sun Jul 15 00:31:00 2007     length 6 : 5874
Sun Jul 15 00:31:00 2007     length 7 : 3781
Sun Jul 15 00:31:00 2007     length 9+: 5313
Sun Jul 15 00:31:00 2007  largest cycle: 25 relations
Sun Jul 15 00:31:00 2007  matrix is 83529 x 83772 with weight 5702285 (avg 68.07/col)
Sun Jul 15 00:31:01 2007  filtering completed in 3 passes
Sun Jul 15 00:31:01 2007  matrix is 82006 x 82070 with weight 5508650 (avg 67.12/col)
Sun Jul 15 00:31:02 2007  saving the first 48 matrix rows for later
Sun Jul 15 00:31:02 2007  matrix is 81958 x 82070 with weight 4517163 (avg 55.04/col)
Sun Jul 15 00:31:02 2007  matrix includes 32 packed rows
Sun Jul 15 00:31:02 2007  using block size 32828 for processor cache size 4096 kB
Sun Jul 15 00:31:40 2007  lanczos halted after 1298 iterations
Sun Jul 15 00:31:40 2007  recovered 16 nontrivial dependencies
Sun Jul 15 00:31:40 2007  prp43 factor: 1770092901260328461943147499208826822490849
Sun Jul 15 00:31:40 2007  prp54 factor: 165993545605717346668480035353143215370070055379374031
Sun Jul 15 00:31:40 2007  elapsed time 03:16:10

5·10¹⁵⁶+3 = 5(0)₁₅₅3_<157> = 17 · 19 · 353 · 9781 · 2903959 · 3738923 · 48999199953669556762469285191647229_<35> · C100

C100 = P44 · P57

P44 = 16220542161012079506892689114089790259652611_<44>

P57 = 519539008028015605717126723388083053475004321678810798119_<57>

Number: 50003_156
N=8427204384008820376729101935985157281095142510409891407641557472295423610841518758316232116592238709
  ( 100 digits)
Divisors found:
 r1=16220542161012079506892689114089790259652611 (pp44)
 r2=519539008028015605717126723388083053475004321678810798119 (pp57)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.73 hours.
Scaled time: 7.99 units (timescale=2.143).
Factorization parameters were as follows:
name: 50003_156
n: 8427204384008820376729101935985157281095142510409891407641557472295423610841518758316232116592238709
skew: 3444.23
# norm 9.10e+13
c5: 173280
c4: -628911052
c3: 10329441200556
c2: -274954422866913
c1: -77119095993536940626
c0: -44666410367268089640360
# alpha -6.59
Y1: 27461304337
Y0: -8657410638244314449
# Murphy_E 3.57e-09
# M 7478100621744003382968441551055951149169645585010492469244137615838640289772215551370324908911734284
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [750000, 1250001)
Primes: RFBsize:114155, AFBsize:113396, largePrimes:3918665 encountered
Relations: rels:3901134, finalFF:350563
Max relations in full relation-set: 28
Initial matrix: 227632 x 350563 with sparse part having weight 27724694.
Pruned matrix : 160476 x 161678 with weight 11045630.
Polynomial selection time: 0.25 hours.
Total sieving time: 3.27 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,48,48,2.5,2.5,50000
total time: 3.73 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

5·10¹⁵⁹+3 = 5(0)₁₅₈3_<160> = C160

C160 = P44 · P116

P44 = 83066365779588590821426749068056416859826527_<44>

P116 = 60192834405048939466899798943567903902651745875844194867985009267232595787118690954252254004124505688435636777703389_<116>

Number: 50003_159
N=5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
  ( 160 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=83066365779588590821426749068056416859826527 (pp44)
 r2=60192834405048939466899798943567903902651745875844194867985009267232595787118690954252254004124505688435636777703389 (pp116)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.58 hours.
Scaled time: 51.97 units (timescale=2.114).
Factorization parameters were as follows:
n: 5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
m: 100000000000000000000000000000000
c5: 1
c0: 6
skew: 1.43
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3400001)
Primes: RFBsize:283146, AFBsize:283322, largePrimes:5636652 encountered
Relations: rels:5694712, finalFF:681230
Max relations in full relation-set: 28
Initial matrix: 566532 x 681230 with sparse part having weight 41699472.
Pruned matrix : 471507 x 474403 with weight 26271016.
Total sieving time: 23.28 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 1.18 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 24.58 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 15, 2007

By JMB / GGNFS

5·10¹⁴⁵+3 = 5(0)₁₄₄3_<146> = 10903 · 323797439456498340561904697913457873787_<39> · C104

C104 = P46 · P58

P46 = 2465188889777582684991267296272427043966702509_<46>

P58 = 5745136880246153704523428561631148137811827694096870119147_<58>

Jul 14, 2007 (8th)

By JMB / GMP-ECM B1=1000000

5·10¹⁷⁸+3 = 5(0)₁₇₇3_<179> = 61 · 5813 · C174

C174 = P34 · C141

P34 = 1266095772152669053113048638910331_<34>

C141 = [111371299677925599229304910106423605557497863192994526047063490147240879819809490792264436773201047749707743497289808646191385677866285614841_<141>]

5·10¹⁷²+3 = 5(0)₁₇₁3_<173> = 17 · 9089719 · 870832992287_<12> · 13385200156201_<14> · 47347314846917_<14> · 724273923844727_<15> · C111

C111 = P36 · P76

P36 = 199380097814707075827853407010411667_<36>

P76 = 4060045237533688631179618384328067264911276818684333348445532508588775649451_<76>

5·10¹⁷⁹+3 = 5(0)₁₇₈3_<180> = 7 · 6581 · 274649101458389267214457_<24> · 17442996660668102907927206569_<29> · C124

C124 = P38 · P86

P38 = 58420054131152676580667221137068677907_<38>

P86 = 38780985245897447564182837100518071852832635692767107596372080155550102208945138108939_<86>

5·10¹⁴⁵+3 = 5(0)₁₄₄3_<146> = 10903 · C142

C142 = P39 · C104

P39 = 323797439456498340561904697913457873787_<39>

C104 = [14162847607434260658361502210554839882035030992737898227692191559764168402119735000385403725547533839823_<104>]

Jul 14, 2007 (7th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, GMP-ECM 6.1.2 B1=1000000

5·10¹³⁰+3 = 5(0)₁₂₉3_<131> = 349 · C129

C129 = P45 · P84

P45 = 223050252687486781077222133508703494233225969_<45>

P84 = 642305820856559171936319435779114051384175861818268799381835937621892642342986131663_<84>

Number: 50003_130
N=143266475644699140401146131805157593123209169054441260744985673352435530085959885386819484240687679083094555873925501432664756447
  ( 129 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=223050252687486781077222133508703494233225969 (pp45)
 r2=642305820856559171936319435779114051384175861818268799381835937621892642342986131663 (pp84)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.97 hours.
Scaled time: 4.23 units (timescale=2.144).
Factorization parameters were as follows:
n: 143266475644699140401146131805157593123209169054441260744985673352435530085959885386819484240687679083094555873925501432664756447
m: 100000000000000000000000000
c5: 5
c0: 3
skew: 0.9
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 900001)
Primes: RFBsize:78498, AFBsize:78421, largePrimes:1491823 encountered
Relations: rels:1505178, finalFF:190379
Max relations in full relation-set: 28
Initial matrix: 156984 x 190379 with sparse part having weight 9500964.
Pruned matrix : 140981 x 141829 with weight 5530242.
Total sieving time: 1.90 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 1.97 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

5·10¹³¹+3 = 5(0)₁₃₀3_<132> = 7 · 53 · 4048842607_<10> · C120

C120 = P48 · P72

P48 = 523541404697611061806834745219853229328170446317_<48>

P72 = 635790693115827427508005325491084683125703813484245526914108384957137147_<72>

Number: 50003_131
N=332862752567528046530685118837102160591749923555522639241418808436225983242944407127183464433987927779293409445570037599
  ( 120 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=523541404697611061806834745219853229328170446317 (pp48)
 r2=635790693115827427508005325491084683125703813484245526914108384957137147 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.42 hours.
Scaled time: 5.12 units (timescale=2.118).
Factorization parameters were as follows:
n: 332862752567528046530685118837102160591749923555522639241418808436225983242944407127183464433987927779293409445570037599
m: 100000000000000000000000000
c5: 50
c0: 3
skew: 0.57
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 1000001)
Primes: RFBsize:78498, AFBsize:78466, largePrimes:1559164 encountered
Relations: rels:1595536, finalFF:210853
Max relations in full relation-set: 28
Initial matrix: 157029 x 210853 with sparse part having weight 10838743.
Pruned matrix : 135540 x 136389 with weight 5520586.
Total sieving time: 2.34 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 2.42 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

5·10¹³²+3 = 5(0)₁₃₁3_<133> = 16187 · C129

C129 = P59 · P71

P59 = 18572566704029876782615951371188489713635855833627934104693_<59>

P71 = 16631511131550278291805996309948604657716454712748581690326108061640533_<71>

Number: 50003_132
N=308889849879532958546982146166676962994995984431951566071538889232099833199481065052202384629641069994439982702168406746154321369
  ( 129 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=18572566704029876782615951371188489713635855833627934104693 (pp59)
 r2=16631511131550278291805996309948604657716454712748581690326108061640533 (pp71)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.52 hours.
Scaled time: 5.41 units (timescale=2.144).
Factorization parameters were as follows:
n: 308889849879532958546982146166676962994995984431951566071538889232099833199481065052202384629641069994439982702168406746154321369
m: 500000000000000000000000000
c5: 4
c0: 75
skew: 1.8
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [700000, 1150001)
Primes: RFBsize:107126, AFBsize:106673, largePrimes:1795749 encountered
Relations: rels:1865223, finalFF:245894
Max relations in full relation-set: 28
Initial matrix: 213863 x 245894 with sparse part having weight 12440753.
Pruned matrix : 192707 x 193840 with weight 7862026.
Total sieving time: 2.38 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,45,45,2.3,2.3,50000
total time: 2.52 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

5·10¹³³+3 = 5(0)₁₃₂3_<134> = 11057031539_<11> · C124

C124 = P42 · P82

P42 = 886544732452880113982144287654486535090287_<42>

P82 = 5100711993689431955514377563639991758308507294250704290195426082082810455667928671_<82>

Number: 50003_133
N=4522009349764594173325890157795994688624718772270474935469929475797618053624329089471361776496421369211037031120835260918577
  ( 124 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=886544732452880113982144287654486535090287 (pp42)
 r2=5100711993689431955514377563639991758308507294250704290195426082082810455667928671 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.78 hours.
Scaled time: 5.91 units (timescale=2.128).
Factorization parameters were as follows:
n: 4522009349764594173325890157795994688624718772270474935469929475797618053624329089471361776496421369211037031120835260918577
m: 1000000000000000000000000000
c5: 1
c0: 60
skew: 2.27
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [700000, 1200001)
Primes: RFBsize:107126, AFBsize:106993, largePrimes:1858990 encountered
Relations: rels:1990762, finalFF:296586
Max relations in full relation-set: 28
Initial matrix: 214183 x 296586 with sparse part having weight 15830089.
Pruned matrix : 168876 x 170010 with weight 7418709.
Total sieving time: 2.66 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,45,45,2.3,2.3,50000
total time: 2.78 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

(19·10¹⁶⁰-1)/9 = 2(1)₁₆₀_<161> = 3² · 15418862204910161_<17> · C144

C144 = P33 · P111

P33 = 198440143099519652057552815018259_<33>

P111 = 766631611792914428985345616031997540862285764082560979052617179307561469122129221254517402352149820216246478021_<111>

Jul 14, 2007 (6th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(89·10¹⁵⁸+1)/9 = 9(8)₁₅₇9_<159> = 19 · 1301 · 153009010613_<12> · C144

C144 = P63 · P81

P63 = 424900550000295550092866554354772812998171689914130662333763053_<63>

P81 = 615335965218209178221823895527708916744280900160476438475349268969266385168270279_<81>

Number: n
N=261456590056179812443165367795872934768914215004307843412220192729070446047275621879186181977133609132560926795382217178649634421230505048201787
  ( 144 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=424900550000295550092866554354772812998171689914130662333763053 (pp63)
 r2=615335965218209178221823895527708916744280900160476438475349268969266385168270279 (pp81)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 33.67 hours.
Scaled time: 48.65 units (timescale=1.445).
Factorization parameters were as follows:
name: KA_9_8_157_9
n: 261456590056179812443165367795872934768914215004307843412220192729070446047275621879186181977133609132560926795382217178649634421230505048201787
skew: 0.10
deg: 5
c5: 89000
c0: 1
m: 10000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:250150, AFBsize:249496, largePrimes:6906833 encountered
Relations: rels:6429793, finalFF:563547
Max relations in full relation-set: 28
Initial matrix: 499713 x 563547 with sparse part having weight 31998849.
Pruned matrix : 438837 x 441399 with weight 20235550.
Total sieving time: 28.59 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 4.48 hours.
Total square root time: 0.40 hours, sqrts: 6.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 33.67 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(7·10¹⁵⁷-61)/9 = (7)₁₅₆1_<157> = 536746193918741_<15> · 74325871959677983_<17> · C126

C126 = P57 · P69

P57 = 664828967518681180559161523946360773815099210144871733241_<57>

P69 = 293249047514706248599001187604405935292797388117330624974946437107177_<69>

Number: n
N=194960461485038834727296645467655591808226295435757088586794057750949454544474226631511051570795485756565910575024330070570657
  ( 126 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=664828967518681180559161523946360773815099210144871733241 (pp57)
 r2=293249047514706248599001187604405935292797388117330624974946437107177 (pp69)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 43.28 hours.
Scaled time: 57.26 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_7_156_1
n: 194960461485038834727296645467655591808226295435757088586794057750949454544474226631511051570795485756565910575024330070570657
skew: 0.61
deg: 5
c5: 700
c0: -61
m: 10000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1800001)
Primes: RFBsize:250150, AFBsize:249972, largePrimes:7243078 encountered
Relations: rels:6755304, finalFF:568264
Max relations in full relation-set: 48
Initial matrix: 500189 x 568264 with sparse part having weight 39667025.
Pruned matrix : 443449 x 446013 with weight 25263932.
Total sieving time: 37.86 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 5.05 hours.
Total square root time: 0.09 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 43.28 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 14, 2007 (5th)

By Jo Yeong Uk / Msieve v. 1.21, GMP-ECM 6.1.2 B1=1000000

5·10¹⁶⁸+3 = 5(0)₁₆₇3_<169> = 30261601 · 890150258236321_<15> · 498727304848409587637_<21> · 142978063635046612431340573579_<30> · C97

C97 = P44 · P54

P44 = 12718944880656352612135685179437522176294183_<44>

P54 = 204659137232336784991399810699824456814839775637627027_<54>

Sat Jul 14 01:19:05 2007  
Sat Jul 14 01:19:05 2007  
Sat Jul 14 01:19:05 2007  Msieve v. 1.21
Sat Jul 14 01:19:05 2007  random seeds: 2c6b3972 03752bf5
Sat Jul 14 01:19:05 2007  factoring 2603048285780775881221905377785187247573247246016520013086521779141708972201219207045854783683941 (97 digits)
Sat Jul 14 01:19:05 2007  commencing quadratic sieve (97-digit input)
Sat Jul 14 01:19:06 2007  using multiplier of 61
Sat Jul 14 01:19:06 2007  using 32kb Intel Core sieve core
Sat Jul 14 01:19:06 2007  sieve interval: 36 blocks of size 32768
Sat Jul 14 01:19:06 2007  processing polynomials in batches of 6
Sat Jul 14 01:19:06 2007  using a sieve bound of 2361367 (87059 primes)
Sat Jul 14 01:19:06 2007  using large prime bound of 354205050 (28 bits)
Sat Jul 14 01:19:06 2007  using double large prime bound of 2447138225130900 (43-52 bits)
Sat Jul 14 01:19:06 2007  using trial factoring cutoff of 52 bits
Sat Jul 14 01:19:06 2007  polynomial 'A' values have 13 factors
Sat Jul 14 05:43:47 2007  87427 relations (21313 full + 66114 combined from 1303942 partial), need 87155
Sat Jul 14 05:43:48 2007  begin with 1325255 relations
Sat Jul 14 05:43:48 2007  reduce to 228294 relations in 12 passes
Sat Jul 14 05:43:48 2007  attempting to read 228294 relations
Sat Jul 14 05:43:50 2007  recovered 228294 relations
Sat Jul 14 05:43:50 2007  recovered 215876 polynomials
Sat Jul 14 05:43:51 2007  attempting to build 87427 cycles
Sat Jul 14 05:43:51 2007  found 87427 cycles in 6 passes
Sat Jul 14 05:43:51 2007  distribution of cycle lengths:
Sat Jul 14 05:43:51 2007     length 1 : 21313
Sat Jul 14 05:43:51 2007     length 2 : 15209
Sat Jul 14 05:43:51 2007     length 3 : 14610
Sat Jul 14 05:43:51 2007     length 4 : 12030
Sat Jul 14 05:43:51 2007     length 5 : 8885
Sat Jul 14 05:43:51 2007     length 6 : 6060
Sat Jul 14 05:43:51 2007     length 7 : 3877
Sat Jul 14 05:43:51 2007     length 9+: 5443
Sat Jul 14 05:43:51 2007  largest cycle: 25 relations
Sat Jul 14 05:43:51 2007  matrix is 87059 x 87427 with weight 5727486 (avg 65.51/col)
Sat Jul 14 05:43:51 2007  filtering completed in 3 passes
Sat Jul 14 05:43:51 2007  matrix is 85635 x 85699 with weight 5541486 (avg 64.66/col)
Sat Jul 14 05:43:53 2007  saving the first 48 matrix rows for later
Sat Jul 14 05:43:53 2007  matrix is 85587 x 85699 with weight 4247055 (avg 49.56/col)
Sat Jul 14 05:43:53 2007  matrix includes 32 packed rows
Sat Jul 14 05:43:53 2007  using block size 34279 for processor cache size 4096 kB
Sat Jul 14 05:44:30 2007  lanczos halted after 1355 iterations
Sat Jul 14 05:44:30 2007  recovered 14 nontrivial dependencies
Sat Jul 14 05:44:30 2007  prp44 factor: 12718944880656352612135685179437522176294183
Sat Jul 14 05:44:30 2007  prp54 factor: 204659137232336784991399810699824456814839775637627027
Sat Jul 14 05:44:30 2007  elapsed time 04:25:25

5·10¹²⁷+3 = 5(0)₁₂₆3_<128> = 1063 · 19759 · 9528013351973_<13> · C108

C108 = P36 · P73

P36 = 231486198826356536297596881484840829_<36>

P73 = 1079305320539789652825036330387473369897040690627974500945419108513238427_<73>

5·10¹²⁶+3 = 5(0)₁₂₅3_<127> = 23 · 32869 · C121

C121 = P40 · P82

P40 = 1771845148714035530042375961149100976639_<40>

P82 = 3732758672015730547173100481173208742246650750942529540645311897013388939508906671_<82>

5·10¹⁷⁷+3 = 5(0)₁₇₆3_<178> = C178

C178 = P30 · C149

P30 = 176218992155079534631185354899_<30>

C149 = [28373786155806670640998399527341074498848269897625772403660234914777229704006772677455191720133985486886631783071384944023777763803864984794834905297_<149>]

Jul 14, 2007 (4th)

By JMB / GMP-ECM B1=1000000

5·10¹⁸⁷+3 = 5(0)₁₈₆3_<188> = 43951 · 881623824379321_<15> · C169

C169 = P34 · P135

P34 = 7538781648531214385240912695837561_<34>

P135 = 171165708092478089670945899225361876860032835861904429144861641040302889862809476562441735553451758084446668158294751605231000217623613_<135>

5·10¹⁵⁶+3 = 5(0)₁₅₅3_<157> = 17 · 19 · 353 · 9781 · 2903959 · 3738923 · C135

C135 = P35 · C100

P35 = 48999199953669556762469285191647229_<35>

C100 = [8427204384008820376729101935985157281095142510409891407641557472295423610841518758316232116592238709_<100>]

5·10¹⁶¹+3 = 5(0)₁₆₀3_<162> = 7² · 1447 · 180463 · C152

C152 = P32 · C121

P32 = 26314542158435393005535533221629_<32>

C121 = [1484982727509908854740212306941041004792973008825939876458829727780821383869898582890053749715127694042906997885710674263_<121>]

Jul 14, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

5·10¹²⁸+3 = 5(0)₁₂₇3_<129> = 824220383604228418854258476629_<30> · C99

C99 = P39 · P60

P39 = 778977109190834486013530928931812523699_<39>

P60 = 778756989881128479103802248680558442310201163296540906795693_<60>

Number: n
N=606633868739757406203256446479850116767816318805314527242598676929677564111420625371388633713628407
  ( 99 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=778977109190834486013530928931812523699 (pp39)
 r2=778756989881128479103802248680558442310201163296540906795693 (pp60)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.38 hours.
Scaled time: 3.45 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_5_0_127_3
n: 606633868739757406203256446479850116767816318805314527242598676929677564111420625371388633713628407
skew: 1.13
deg: 5
c5: 8
c0: 15
m: 50000000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 400001)
Primes: RFBsize:78498, AFBsize:78351, largePrimes:5398510 encountered
Relations: rels:4800608, finalFF:256002
Max relations in full relation-set: 28
Initial matrix: 156914 x 256002 with sparse part having weight 19788163.
Pruned matrix : 117925 x 118773 with weight 6523826.
Total sieving time: 2.01 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.18 hours.
Total square root time: 0.04 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000
total time: 2.38 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jul 14, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

5·10¹¹⁰+3 = 5(0)₁₀₉3_<111> = 181 · 140869 · 11063288894785937_<17> · C88

C88 = P31 · P57

P31 = 6039261878537983804809377055481_<31>

P57 = 293499849169094259922144875395852639709254512750131598291_<57>

Number: 50003_110
N=1772522450443559105303400406863312386769861079139349751622786142722504963484025911782971
  ( 88 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=6039261878537983804809377055481 (pp31)
 r2=293499849169094259922144875395852639709254512750131598291 (pp57)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.51 hours.
Scaled time: 1.08 units (timescale=2.144).
Factorization parameters were as follows:
n: 1772522450443559105303400406863312386769861079139349751622786142722504963484025911782971
m: 10000000000000000000000
c5: 5
c0: 3
skew: 0.9
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 280001)
Primes: RFBsize:30757, AFBsize:30494, largePrimes:1050943 encountered
Relations: rels:988188, finalFF:104048
Max relations in full relation-set: 28
Initial matrix: 61316 x 104048 with sparse part having weight 4750487.
Pruned matrix : 47929 x 48299 with weight 1555471.
Total sieving time: 0.48 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.51 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

5·10¹¹⁴+3 = 5(0)₁₁₃3_<115> = 316469363851_<12> · C104

C104 = P31 · P32 · P42

P31 = 1081354250785203149101117499513_<31>

P32 = 33280544906954346861035663714839_<32>

P42 = 439015556833735689338180321004768868727479_<42>

Number: 50003_114
N=15799317631118626468490249640104333120774198019987032630994473961208379779282675169509041640621008750953
  ( 104 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=1081354250785203149101117499513 (pp31)
 r2=33280544906954346861035663714839 (pp32)
 r3=439015556833735689338180321004768868727479 (pp42)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.54 hours.
Scaled time: 1.15 units (timescale=2.143).
Factorization parameters were as follows:
n: 15799317631118626468490249640104333120774198019987032630994473961208379779282675169509041640621008750953
m: 100000000000000000000000
c5: 1
c0: 6
skew: 1.43
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 300001)
Primes: RFBsize:30757, AFBsize:30754, largePrimes:976509 encountered
Relations: rels:884427, finalFF:74434
Max relations in full relation-set: 28
Initial matrix: 61575 x 74434 with sparse part having weight 3217169.
Pruned matrix : 56872 x 57243 with weight 1876427.
Total sieving time: 0.51 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.54 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

5·10¹¹⁹+3 = 5(0)₁₁₈3_<120> = 7² · 71843 · C114

C114 = P47 · P67

P47 = 90543020753040293576959578835244863827338385803_<47>

P67 = 1568680455115318344001740770037613906724896970510571219229245382643_<67>

Number: 50003_119
N=142033067002394961575794383842091044900345339199109623109575386464873660166570699657728715137628621594650693817329
  ( 114 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=90543020753040293576959578835244863827338385803 (pp47)
 r2=1568680455115318344001740770037613906724896970510571219229245382643 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.79 hours.
Scaled time: 1.69 units (timescale=2.143).
Factorization parameters were as follows:
n: 142033067002394961575794383842091044900345339199109623109575386464873660166570699657728715137628621594650693817329
m: 1000000000000000000000000
c5: 1
c0: 6
skew: 1.43
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 420001)
Primes: RFBsize:49098, AFBsize:49231, largePrimes:1971794 encountered
Relations: rels:2027062, finalFF:202354
Max relations in full relation-set: 28
Initial matrix: 98393 x 202354 with sparse part having weight 16943511.
Pruned matrix : 76211 x 76766 with weight 4142003.
Total sieving time: 0.74 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 0.79 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 14, 2007

By JMB / GMP-ECM B1=1000000

5·10¹⁶⁰+3 = 5(0)₁₅₉3_<161> = 2207 · 7760503636757_<13> · 120355074834623_<15> · C131

C131 = P35 · C96

P35 = 82551714075637674821552052888550681_<35>

C96 = [293823996731712864770458618120875378669709169546409049689172378069092682226620668855969845742319_<96>]

Jul 13, 2007 (6th)

By Bruce Dodson / Jul 12, 2007

10³³⁷+1 is divisible by 1687858617956114857563779160203327248258725852773131_<52>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jul 13, 2007 (5th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, Msieve v. 1.21, GGNFS-0.77.1-20050930-nocona gnfs

5·10¹²³+3 = 5(0)₁₂₂3_<124> = C124

C124 = P47 · P78

P47 = 29103572282156559112182740936226932631374490509_<47>

P78 = 171800215847231475291585450337672992777067604341481417436023086954002453065167_<78>

Number: 50003_123
N=5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
  ( 124 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=29103572282156559112182740936226932631374490509 (pp47)
 r2=171800215847231475291585450337672992777067604341481417436023086954002453065167 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.06 hours.
Scaled time: 2.26 units (timescale=2.129).
Factorization parameters were as follows:
n: 5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
m: 10000000000000000000000000
c5: 1
c0: 60
skew: 2.27
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 480001)
Primes: RFBsize:49098, AFBsize:48986, largePrimes:1922445 encountered
Relations: rels:1871417, finalFF:110397
Max relations in full relation-set: 28
Initial matrix: 98148 x 110397 with sparse part having weight 9157899.
Pruned matrix : 94827 x 95381 with weight 6835596.
Total sieving time: 0.99 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 1.06 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

5·10¹³⁵+3 = 5(0)₁₃₄3_<136> = 29 · 97 · 293 · 12415969 · 8179360663_<10> · 3544624710199_<13> · 502246085292724499_<18> · C83

C83 = P33 · P51

P33 = 103888204664039275506234925332227_<33>

P51 = 322982960901345113517889401979443805784667940709243_<51>

Fri Jul 13 23:04:56 2007  
Fri Jul 13 23:04:56 2007  
Fri Jul 13 23:04:56 2007  Msieve v. 1.21
Fri Jul 13 23:04:56 2007  random seeds: d29e7421 231acc36
Fri Jul 13 23:04:56 2007  factoring 33554119945116336385337462642964476014723803391219875848421325898095952849784674161 (83 digits)
Fri Jul 13 23:04:56 2007  commencing quadratic sieve (83-digit input)
Fri Jul 13 23:04:56 2007  using multiplier of 1
Fri Jul 13 23:04:56 2007  using 32kb Intel Core sieve core
Fri Jul 13 23:04:56 2007  sieve interval: 12 blocks of size 32768
Fri Jul 13 23:04:56 2007  processing polynomials in batches of 17
Fri Jul 13 23:04:56 2007  using a sieve bound of 1372829 (52647 primes)
Fri Jul 13 23:04:56 2007  using large prime bound of 122181781 (26 bits)
Fri Jul 13 23:04:56 2007  using trial factoring cutoff of 27 bits
Fri Jul 13 23:04:56 2007  polynomial 'A' values have 10 factors
Fri Jul 13 23:21:48 2007  52748 relations (27073 full + 25675 combined from 277937 partial), need 52743
Fri Jul 13 23:21:48 2007  begin with 305010 relations
Fri Jul 13 23:21:48 2007  reduce to 75223 relations in 2 passes
Fri Jul 13 23:21:48 2007  attempting to read 75223 relations
Fri Jul 13 23:21:48 2007  recovered 75223 relations
Fri Jul 13 23:21:48 2007  recovered 67365 polynomials
Fri Jul 13 23:21:48 2007  attempting to build 52748 cycles
Fri Jul 13 23:21:48 2007  found 52748 cycles in 1 passes
Fri Jul 13 23:21:48 2007  distribution of cycle lengths:
Fri Jul 13 23:21:48 2007     length 1 : 27073
Fri Jul 13 23:21:48 2007     length 2 : 25675
Fri Jul 13 23:21:48 2007  largest cycle: 2 relations
Fri Jul 13 23:21:48 2007  matrix is 52647 x 52748 with weight 1615124 (avg 30.62/col)
Fri Jul 13 23:21:48 2007  filtering completed in 4 passes
Fri Jul 13 23:21:48 2007  matrix is 45423 x 45487 with weight 1365016 (avg 30.01/col)
Fri Jul 13 23:21:49 2007  saving the first 48 matrix rows for later
Fri Jul 13 23:21:49 2007  matrix is 45375 x 45487 with weight 1103284 (avg 24.25/col)
Fri Jul 13 23:21:49 2007  matrix includes 32 packed rows
Fri Jul 13 23:22:10 2007  lanczos halted after 719 iterations
Fri Jul 13 23:22:10 2007  recovered 9 nontrivial dependencies
Fri Jul 13 23:22:11 2007  prp33 factor: 103888204664039275506234925332227
Fri Jul 13 23:22:11 2007  prp51 factor: 322982960901345113517889401979443805784667940709243
Fri Jul 13 23:22:11 2007  elapsed time 00:17:15

5·10¹²⁴+3 = 5(0)₁₂₃3_<125> = 17 · 31 · 139 · 199 · 353 · 17749 · 4211985913711273004737734377_<28> · C84

C84 = P33 · P52

P33 = 128040753937687879477084697015491_<33>

P52 = 1015097562328485295738336683852546474132803693053831_<52>

Fri Jul 13 23:24:22 2007  
Fri Jul 13 23:24:22 2007  
Fri Jul 13 23:24:22 2007  Msieve v. 1.21
Fri Jul 13 23:24:22 2007  random seeds: 1a661020 c160427d
Fri Jul 13 23:24:22 2007  factoring 129973857200848371297919511176220553709357372754369950897383608306308229333303896021 (84 digits)
Fri Jul 13 23:24:23 2007  commencing quadratic sieve (83-digit input)
Fri Jul 13 23:24:23 2007  using multiplier of 1
Fri Jul 13 23:24:23 2007  using 32kb Intel Core sieve core
Fri Jul 13 23:24:23 2007  sieve interval: 12 blocks of size 32768
Fri Jul 13 23:24:23 2007  processing polynomials in batches of 17
Fri Jul 13 23:24:23 2007  using a sieve bound of 1388659 (53235 primes)
Fri Jul 13 23:24:23 2007  using large prime bound of 120813333 (26 bits)
Fri Jul 13 23:24:23 2007  using trial factoring cutoff of 27 bits
Fri Jul 13 23:24:23 2007  polynomial 'A' values have 11 factors
Fri Jul 13 23:45:21 2007  53475 relations (27195 full + 26280 combined from 283677 partial), need 53331
Fri Jul 13 23:45:21 2007  begin with 310872 relations
Fri Jul 13 23:45:21 2007  reduce to 76468 relations in 2 passes
Fri Jul 13 23:45:21 2007  attempting to read 76468 relations
Fri Jul 13 23:45:21 2007  recovered 76468 relations
Fri Jul 13 23:45:21 2007  recovered 69986 polynomials
Fri Jul 13 23:45:21 2007  attempting to build 53475 cycles
Fri Jul 13 23:45:21 2007  found 53475 cycles in 1 passes
Fri Jul 13 23:45:21 2007  distribution of cycle lengths:
Fri Jul 13 23:45:21 2007     length 1 : 27195
Fri Jul 13 23:45:21 2007     length 2 : 26280
Fri Jul 13 23:45:21 2007  largest cycle: 2 relations
Fri Jul 13 23:45:21 2007  matrix is 53235 x 53475 with weight 1691816 (avg 31.64/col)
Fri Jul 13 23:45:22 2007  filtering completed in 4 passes
Fri Jul 13 23:45:22 2007  matrix is 46232 x 46296 with weight 1435739 (avg 31.01/col)
Fri Jul 13 23:45:22 2007  saving the first 48 matrix rows for later
Fri Jul 13 23:45:22 2007  matrix is 46184 x 46296 with weight 1076659 (avg 23.26/col)
Fri Jul 13 23:45:22 2007  matrix includes 32 packed rows
Fri Jul 13 23:45:47 2007  lanczos halted after 732 iterations
Fri Jul 13 23:45:47 2007  recovered 12 nontrivial dependencies
Fri Jul 13 23:45:47 2007  prp33 factor: 128040753937687879477084697015491
Fri Jul 13 23:45:47 2007  prp52 factor: 1015097562328485295738336683852546474132803693053831
Fri Jul 13 23:45:47 2007  elapsed time 00:21:25

5·10¹⁶⁵-3 = 4(9)₁₆₄7_<166> = 19 · 57057317 · 98215463 · 2605629635761_<13> · 3946732535812616137099_<22> · C115

C115 = P34 · P81

P34 = 7543512127570632979961763022705421_<34>

P81 = 605342568468243602479097354297941125861779312424902349610895360925921457852332187_<81>

Number: 49997_165
N=4566409006574951863433979568362754800728318400898293602723291780776693632787788274495993362803824147636639137685727
  ( 115 digits)
Divisors found:
 r1=7543512127570632979961763022705421 (pp34)
 r2=605342568468243602479097354297941125861779312424902349610895360925921457852332187 (pp81)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 27.02 hours.
Scaled time: 57.56 units (timescale=2.130).
Factorization parameters were as follows:
name: 49997_165
n: 4566409006574951863433979568362754800728318400898293602723291780776693632787788274495993362803824147636639137685727
skew: 37063.96
# norm 4.73e+15
c5: 62160
c4: -3621719066
c3: -306726077373988
c2: 4532051020693653061
c1: 228973543810823218638998
c0: 1468727302885487696151709760
# alpha -5.55
Y1: 1746324969367
Y0: -9401858279023299564901
# Murphy_E 5.17e-10
# M 1002986331347959461341605441671137184505700766449988056152747414018476686730995147030702035468882560833614505929064
type: gnfs
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1800000, 3150001)
Primes: RFBsize:256726, AFBsize:256682, largePrimes:7522227 encountered
Relations: rels:7394243, finalFF:577903
Max relations in full relation-set: 28
Initial matrix: 513492 x 577903 with sparse part having weight 50045594.
Pruned matrix : 462271 x 464902 with weight 35767881.
Polynomial selection time: 1.34 hours.
Total sieving time: 23.99 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.38 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000
total time: 27.02 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

Jul 13, 2007 (4th)

The factor table of 500...003 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Jul 13, 2007 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 gnfs

5·10¹⁵⁸-3 = 4(9)₁₅₇7_<159> = 7 · 2111 · 80552352457081_<14> · 5710039315042630712188991_<25> · C116

C116 = P54 · P63

P54 = 467341027637686776935113873903056598872599949645184321_<54>

P63 = 157410063903105298144279249626151629802510455702264743972251571_<63>

Number: 49997_158
N=73564181024991174831410187304979775278602449566930735136444638612241727301463214510006040339766493271745851676818291
  ( 116 digits)
Divisors found:
 r1=467341027637686776935113873903056598872599949645184321 (pp54)
 r2=157410063903105298144279249626151629802510455702264743972251571 (pp63)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 75.59 hours.
Scaled time: 51.55 units (timescale=0.682).
Factorization parameters were as follows:
name: 49997_158
n: 73564181024991174831410187304979775278602449566930735136444638612241727301463214510006040339766493271745851676818291
skew: 42822.68
# norm 5.10e+15
c5: 37680
c4: 38633798
c3: -353231884823776
c2: 649944449545850313
c1: 316689536566344976014916
c0: 2229243313064835235066218784
# alpha -5.41
Y1: 756740286929
Y0: -18118035169349655294225
# Murphy_E 4.48e-10
# M 18062748841787132536527980613922191917491498627232287844155502604722767071327377360711903467081749263690925827819192
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3690001)
Primes: RFBsize:315948, AFBsize:316005, largePrimes:7444584 encountered
Relations: rels:7386540, finalFF:708105
Max relations in full relation-set: 0
Initial matrix: 632036 x 708105 with sparse part having weight 58435719.
Pruned matrix : 566947 x 570171 with weight 38719113.
Total sieving time: 58.58 hours.
Total relation processing time: 0.57 hours.
Matrix solve time: 15.99 hours.
Time per square root: 0.46 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 75.59 hours.
 --------- CPU info (if available) ----------

Jul 13, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000

(7·10¹⁵⁸-61)/9 = (7)₁₅₇1_<158> = 469891 · 36460481 · 4181947377644793050081_<22> · C124

C124 = P35 · P89

P35 = 19452134249342894566208338343315587_<35>

P89 = 55807194183615693406796837297244974493029600283991480615392292095590717453155106764298483_<89>

Jul 13, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GMP-ECM 5.0 B1=1221000

(64·10¹⁵⁷-1)/9 = 7(1)₁₅₇_<158> = 8564115301768762508376928872997_<31> · C127

C127 = P57 · P71

P57 = 311235374037474312294580186612322910045517898252957252213_<57>

P71 = 26678782543165187104805765400094072904958914109911757415689580416168751_<71>

Number: n
N=8303380863686457181005966020913589977121038158477222397503411687450746021165003481262209392026801408206039035454342249876195963
  ( 127 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=311235374037474312294580186612322910045517898252957252213 (pp57)
 r2=26678782543165187104805765400094072904958914109911757415689580416168751 (pp71)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 29.20 hours.
Scaled time: 42.30 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_7_1_157
n: 8303380863686457181005966020913589977121038158477222397503411687450746021165003481262209392026801408206039035454342249876195963
skew: 0.35
deg: 5
c5: 200
c0: -1
m: 20000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:250150, AFBsize:249566, largePrimes:7196272 encountered
Relations: rels:6819995, finalFF:650477
Max relations in full relation-set: 28
Initial matrix: 499781 x 650477 with sparse part having weight 38973134.
Pruned matrix : 364784 x 367346 with weight 19461875.
Total sieving time: 25.94 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.83 hours.
Total square root time: 0.23 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 29.20 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(13·10¹⁶⁰-1)/3 = 4(3)₁₆₀_<161> = 61 · 10722039721_<11> · C149

C149 = P40 · P46 · P65

P40 = 1478358147879228767608167158274095081731_<40>

P46 = 1068416170500962398505260990592751451937327749_<46>

P65 = 41946404360747518012731992568602333958344340144878162072473881247_<65>

Number: n
N=44816216713394732869400742251936381608859550861620422044292600609519547873818196195562696333410057367543823003
  ( 110 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=1068416170500962398505260990592751451937327749 (pp46)
 r2=41946404360747518012731992568602333958344340144878162072473881247 (pp65)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 41.22 hours.
Scaled time: 49.26 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_4_3_160

n: 44816216713394732869400742251936381608859550861620422044292600609519547873818196195562696333410057367543823003

# n: 66254419135368374354145868844236142720498084646190457527394820437684299192700760966498827238982222849523472761840642307270779277283858346731482858193

type: snfs
skew: 0.60
deg: 5
c5: 13
c0: -1
m: 100000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:250150, AFBsize:249271, largePrimes:6713157 encountered
Relations: rels:6239590, finalFF:580304
Max relations in full relation-set: 28
Initial matrix: 499486 x 580304 with sparse part having weight 30086204.
Pruned matrix : 422637 x 425198 with weight 17790023.
Total sieving time: 37.50 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 3.33 hours.
Total square root time: 0.09 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.3,2.3,100000
total time: 41.22 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Jul 12, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(2·10¹⁶⁴+61)/9 = (2)₁₆₃9_<164> = 8599 · C160

C160 = P65 · P96

P65 = 22651222927647321814936310172131574319011957238861315512443742367_<65>

P96 = 114090079554391502386878822975570247933855139052610776246086403516712638744974826517502878472813_<96>

Number: n
N=2584279825819539739763021539972348205863730924784535669522295874197258079104805468336111434146089338553578581488803607654636844077476709178069801398095385768371
  ( 160 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=22651222927647321814936310172131574319011957238861315512443742367 (pp65)
 r2=114090079554391502386878822975570247933855139052610776246086403516712638744974826517502878472813 (pp96)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 61.85 hours.
Scaled time: 81.83 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_2_163_9
n: 2584279825819539739763021539972348205863730924784535669522295874197258079104805468336111434146089338553578581488803607654636844077476709178069801398095385768371
skew: 3.14
deg: 5
c5: 1
c0: 305
m: 1000000000000000000000000000000000
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2500001)
Primes: RFBsize:283146, AFBsize:282858, largePrimes:7623038 encountered
Relations: rels:7210159, finalFF:669993
Max relations in full relation-set: 48
Initial matrix: 566068 x 669993 with sparse part having weight 44463704.
Pruned matrix : 477178 x 480072 with weight 26963646.
Total sieving time: 55.32 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 6.10 hours.
Total square root time: 0.18 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000
total time: 61.85 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 12, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000, GGNFS-0.77.1-20050930-pentium3 gnfs

(43·10¹⁶⁰-7)/9 = 4(7)₁₆₀_<161> = 5007179 · 7008751163_<10> · C145

C145 = P28 · C117

P28 = 4421264001211142317908244507_<28>

C117 = [307925559846392608191890342655880287652240774038193999902100985083530393790025178760683643373658220133542015572724043_<117>]

5·10¹⁷¹-3 = 4(9)₁₇₀7_<172> = 46000847 · 6121638571_<10> · 958447987411_<12> · 6312681043024475375491430161_<28> · C115

C115 = P45 · P71

P45 = 241198112402284085400049735671995479639288153_<45>

P71 = 12166907050378837298642013658257125610939904245160777794608634185199787_<71>

Number: 49997_171
N=2934635014325417516096701273747698164950838782296104637022869061437943116969747674977296282584317681872004767223411
  ( 115 digits)
Divisors found:
 r1=241198112402284085400049735671995479639288153 (pp45)
 r2=12166907050378837298642013658257125610939904245160777794608634185199787 (pp71)
Version: GGNFS-0.77.1-20050930-pentium3
Total time: 26.09 hours.
Scaled time: 7.75 units (timescale=0.297).
Factorization parameters were as follows:
name: 49997_171
n: 2934635014325417516096701273747698164950838782296104637022869061437943116969747674977296282584317681872004767223411
skew: 74056.80
# norm 1.29e+16
c5: 33600
c4: -3746392840
c3: -544442683811411
c2: 17054315618171851220
c1: 1217441680378892041663324
c0: -19655107573523269710901021680
# alpha -6.40
Y1: 1547472681557
Y0: -9732950247591089513527
# Murphy_E 5.29e-10
# M 1529526105085601883212096215779823540361348901810900877749446168933591385261591139256845661451207162190541862940240
type: gnfs
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1800000, 3150000)
Primes: RFBsize:256726, AFBsize:257300, largePrimes:7660466 encountered
Relations: rels:7701963, finalFF:702520
Max relations in full relation-set: 28
Initial matrix: 514107 x 702520 with sparse part having weight 63078489.
Pruned matrix : 368728 x 371362 with weight 37331473.
Total sieving time: 23.97 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.93 hours.
Time per square root: 1.02 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000
total time: 26.09 hours.
 --------- CPU info (if available) ----------

Jul 12, 2007

By Jo Yeong Uk / Msieve v. 1.21

5·10¹⁵⁹-3 = 4(9)₁₅₈7_<160> = 23 · 10611966307_<11> · 4368534516821_<13> · 5006536233163_<13> · 3603669365157562557541028774720347_<34> · C90

C90 = P42 · P49

P42 = 191027376246576260076013368620556928804243_<42>

P49 = 1360606753360105851237415658886311322045879676319_<49>

Thu Jul 12 08:25:38 2007  
Thu Jul 12 08:25:38 2007  
Thu Jul 12 08:25:38 2007  Msieve v. 1.21
Thu Jul 12 08:25:38 2007  random seeds: 3396b730 2c6be133
Thu Jul 12 08:25:38 2007  factoring 259913138197753528521831503031382370167660110953871390680307688669870475962297396553821517 (90 digits)
Thu Jul 12 08:25:38 2007  commencing quadratic sieve (90-digit input)
Thu Jul 12 08:25:38 2007  using multiplier of 29
Thu Jul 12 08:25:38 2007  using 32kb Intel Core sieve core
Thu Jul 12 08:25:38 2007  sieve interval: 36 blocks of size 32768
Thu Jul 12 08:25:38 2007  processing polynomials in batches of 6
Thu Jul 12 08:25:38 2007  using a sieve bound of 1584931 (59872 primes)
Thu Jul 12 08:25:38 2007  using large prime bound of 126794480 (26 bits)
Thu Jul 12 08:25:38 2007  using double large prime bound of 385106280791040 (42-49 bits)
Thu Jul 12 08:25:38 2007  using trial factoring cutoff of 49 bits
Thu Jul 12 08:25:38 2007  polynomial 'A' values have 12 factors
Thu Jul 12 09:21:20 2007  60317 relations (16443 full + 43874 combined from 635017 partial), need 59968
Thu Jul 12 09:21:20 2007  begin with 651460 relations
Thu Jul 12 09:21:20 2007  reduce to 145915 relations in 10 passes
Thu Jul 12 09:21:20 2007  attempting to read 145915 relations
Thu Jul 12 09:21:22 2007  recovered 145915 relations
Thu Jul 12 09:21:22 2007  recovered 124747 polynomials
Thu Jul 12 09:21:22 2007  attempting to build 60317 cycles
Thu Jul 12 09:21:22 2007  found 60317 cycles in 6 passes
Thu Jul 12 09:21:22 2007  distribution of cycle lengths:
Thu Jul 12 09:21:22 2007     length 1 : 16443
Thu Jul 12 09:21:22 2007     length 2 : 11820
Thu Jul 12 09:21:22 2007     length 3 : 10631
Thu Jul 12 09:21:22 2007     length 4 : 7828
Thu Jul 12 09:21:22 2007     length 5 : 5627
Thu Jul 12 09:21:22 2007     length 6 : 3460
Thu Jul 12 09:21:22 2007     length 7 : 2063
Thu Jul 12 09:21:22 2007     length 9+: 2445
Thu Jul 12 09:21:22 2007  largest cycle: 20 relations
Thu Jul 12 09:21:22 2007  matrix is 59872 x 60317 with weight 3587835 (avg 59.48/col)
Thu Jul 12 09:21:22 2007  filtering completed in 3 passes
Thu Jul 12 09:21:22 2007  matrix is 58252 x 58316 with weight 3393360 (avg 58.19/col)
Thu Jul 12 09:21:23 2007  saving the first 48 matrix rows for later
Thu Jul 12 09:21:23 2007  matrix is 58204 x 58316 with weight 2649013 (avg 45.43/col)
Thu Jul 12 09:21:23 2007  matrix includes 32 packed rows
Thu Jul 12 09:21:23 2007  using block size 23326 for processor cache size 4096 kB
Thu Jul 12 09:21:39 2007  lanczos halted after 922 iterations
Thu Jul 12 09:21:39 2007  recovered 17 nontrivial dependencies
Thu Jul 12 09:21:39 2007  prp42 factor: 191027376246576260076013368620556928804243
Thu Jul 12 09:21:39 2007  prp49 factor: 1360606753360105851237415658886311322045879676319
Thu Jul 12 09:21:39 2007  elapsed time 00:56:01

Jul 11, 2007 (4th)

By Maksym Voznyy

(10²⁷⁰³⁴³-1)/9 is PRP.

Jul 11, 2007 (3rd)

By Jo Yeong Uk / Msieve v. 1.21

(2·10¹⁵⁸+61)/9 = (2)₁₅₇9_<158> = 313251391 · 4232920182402397664794465973_<28> · 8180004382945353667194983565175097_<34> · C88

C88 = P37 · P52

P37 = 1173816789875564874460017932751680269_<37>

P52 = 1745422399702334476184140689167794733731023214569971_<52>

Wed Jul 11 19:35:21 2007  
Wed Jul 11 19:35:21 2007  
Wed Jul 11 19:35:21 2007  Msieve v. 1.21
Wed Jul 11 19:35:21 2007  random seeds: 5b524611 d566dca2
Wed Jul 11 19:35:21 2007  factoring 2048806118195499354913542723718755940102140970322140966978079897796843232293172520602199 (88 digits)
Wed Jul 11 19:35:21 2007  commencing quadratic sieve (88-digit input)
Wed Jul 11 19:35:21 2007  using multiplier of 35
Wed Jul 11 19:35:21 2007  using 32kb Intel Core sieve core
Wed Jul 11 19:35:21 2007  sieve interval: 25 blocks of size 32768
Wed Jul 11 19:35:21 2007  processing polynomials in batches of 9
Wed Jul 11 19:35:21 2007  using a sieve bound of 1516987 (57667 primes)
Wed Jul 11 19:35:21 2007  using large prime bound of 121358960 (26 bits)
Wed Jul 11 19:35:21 2007  using double large prime bound of 355901048223760 (42-49 bits)
Wed Jul 11 19:35:21 2007  using trial factoring cutoff of 49 bits
Wed Jul 11 19:35:21 2007  polynomial 'A' values have 11 factors
Wed Jul 11 20:23:35 2007  57807 relations (15424 full + 42383 combined from 616759 partial), need 57763
Wed Jul 11 20:23:36 2007  begin with 632183 relations
Wed Jul 11 20:23:36 2007  reduce to 141408 relations in 12 passes
Wed Jul 11 20:23:36 2007  attempting to read 141408 relations
Wed Jul 11 20:23:37 2007  recovered 141408 relations
Wed Jul 11 20:23:37 2007  recovered 123274 polynomials
Wed Jul 11 20:23:37 2007  attempting to build 57807 cycles
Wed Jul 11 20:23:37 2007  found 57807 cycles in 5 passes
Wed Jul 11 20:23:37 2007  distribution of cycle lengths:
Wed Jul 11 20:23:37 2007     length 1 : 15424
Wed Jul 11 20:23:37 2007     length 2 : 11026
Wed Jul 11 20:23:37 2007     length 3 : 10054
Wed Jul 11 20:23:37 2007     length 4 : 7830
Wed Jul 11 20:23:37 2007     length 5 : 5352
Wed Jul 11 20:23:37 2007     length 6 : 3440
Wed Jul 11 20:23:37 2007     length 7 : 2150
Wed Jul 11 20:23:37 2007     length 9+: 2531
Wed Jul 11 20:23:37 2007  largest cycle: 17 relations
Wed Jul 11 20:23:37 2007  matrix is 57667 x 57807 with weight 3502421 (avg 60.59/col)
Wed Jul 11 20:23:38 2007  filtering completed in 4 passes
Wed Jul 11 20:23:38 2007  matrix is 56148 x 56212 with weight 3349462 (avg 59.59/col)
Wed Jul 11 20:23:38 2007  saving the first 48 matrix rows for later
Wed Jul 11 20:23:39 2007  matrix is 56100 x 56212 with weight 2776045 (avg 49.39/col)
Wed Jul 11 20:23:39 2007  matrix includes 32 packed rows
Wed Jul 11 20:23:39 2007  using block size 22484 for processor cache size 4096 kB
Wed Jul 11 20:23:54 2007  lanczos halted after 888 iterations
Wed Jul 11 20:23:54 2007  recovered 19 nontrivial dependencies
Wed Jul 11 20:23:55 2007  prp37 factor: 1173816789875564874460017932751680269
Wed Jul 11 20:23:55 2007  prp52 factor: 1745422399702334476184140689167794733731023214569971
Wed Jul 11 20:23:55 2007  elapsed time 00:48:34

(23·10¹⁵⁷+1)/3 = 7(6)₁₅₆7_<158> = 7² · 11 · 103 · 3931093 · 187918820385783433750403_<24> · 20896654878601350360268149361_<29> · C95

C95 = P41 · P55

P41 = 78193602897564757645098493674472199158583_<41>

P55 = 1144060525373511021818728474775835114113368172612932063_<55>

Wed Jul 11 20:25:41 2007  
Wed Jul 11 20:25:41 2007  
Wed Jul 11 20:25:41 2007  Msieve v. 1.21
Wed Jul 11 20:25:41 2007  random seeds: 124ff28c e04ddd07
Wed Jul 11 20:25:41 2007  factoring 89458214411835630370906446629114652455106051226197501160191146683705663732977188286693142346729 (95 digits)
Wed Jul 11 20:25:41 2007  commencing quadratic sieve (95-digit input)
Wed Jul 11 20:25:42 2007  using multiplier of 6
Wed Jul 11 20:25:42 2007  using 32kb Intel Core sieve core
Wed Jul 11 20:25:42 2007  sieve interval: 36 blocks of size 32768
Wed Jul 11 20:25:42 2007  processing polynomials in batches of 6
Wed Jul 11 20:25:42 2007  using a sieve bound of 2196599 (81150 primes)
Wed Jul 11 20:25:42 2007  using large prime bound of 329489850 (28 bits)
Wed Jul 11 20:25:42 2007  using double large prime bound of 2148402323041500 (43-51 bits)
Wed Jul 11 20:25:42 2007  using trial factoring cutoff of 51 bits
Wed Jul 11 20:25:42 2007  polynomial 'A' values have 12 factors
Wed Jul 11 23:02:25 2007  81576 relations (20604 full + 60972 combined from 1201596 partial), need 81246
Wed Jul 11 23:02:25 2007  begin with 1222200 relations
Wed Jul 11 23:02:26 2007  reduce to 209892 relations in 12 passes
Wed Jul 11 23:02:26 2007  attempting to read 209892 relations
Wed Jul 11 23:02:28 2007  recovered 209892 relations
Wed Jul 11 23:02:28 2007  recovered 192187 polynomials
Wed Jul 11 23:02:28 2007  attempting to build 81576 cycles
Wed Jul 11 23:02:28 2007  found 81576 cycles in 6 passes
Wed Jul 11 23:02:28 2007  distribution of cycle lengths:
Wed Jul 11 23:02:28 2007     length 1 : 20604
Wed Jul 11 23:02:28 2007     length 2 : 14493
Wed Jul 11 23:02:28 2007     length 3 : 13853
Wed Jul 11 23:02:28 2007     length 4 : 11006
Wed Jul 11 23:02:28 2007     length 5 : 8296
Wed Jul 11 23:02:28 2007     length 6 : 5403
Wed Jul 11 23:02:28 2007     length 7 : 3318
Wed Jul 11 23:02:28 2007     length 9+: 4603
Wed Jul 11 23:02:28 2007  largest cycle: 19 relations
Wed Jul 11 23:02:28 2007  matrix is 81150 x 81576 with weight 5566718 (avg 68.24/col)
Wed Jul 11 23:02:29 2007  filtering completed in 4 passes
Wed Jul 11 23:02:29 2007  matrix is 79471 x 79535 with weight 5325669 (avg 66.96/col)
Wed Jul 11 23:02:30 2007  saving the first 48 matrix rows for later
Wed Jul 11 23:02:30 2007  matrix is 79423 x 79535 with weight 4374458 (avg 55.00/col)
Wed Jul 11 23:02:30 2007  matrix includes 32 packed rows
Wed Jul 11 23:02:30 2007  using block size 31814 for processor cache size 4096 kB
Wed Jul 11 23:03:05 2007  lanczos error: not all columns used
Wed Jul 11 23:03:05 2007  lanczos halted after 1257 iterations
Wed Jul 11 23:03:05 2007  linear algebra failed; retrying...
Wed Jul 11 23:03:40 2007  lanczos halted after 1258 iterations
Wed Jul 11 23:03:40 2007  recovered 18 nontrivial dependencies
Wed Jul 11 23:03:41 2007  prp41 factor: 78193602897564757645098493674472199158583
Wed Jul 11 23:03:41 2007  prp55 factor: 1144060525373511021818728474775835114113368172612932063
Wed Jul 11 23:03:41 2007  elapsed time 02:38:00

5·10¹⁵⁹-3 = 4(9)₁₅₈7_<160> = 23 · 10611966307_<11> · 4368534516821_<13> · 5006536233163_<13> · C123

C123 = P34 · C90

P34 = 3603669365157562557541028774720347_<34>

C90 = [259913138197753528521831503031382370167660110953871390680307688669870475962297396553821517_<90>]

Jul 11, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000, GGNFS-0.77.1-20050930-nocona gnfs

(7·10¹⁵⁷-1)/3 = 2(3)₁₅₇_<158> = 61 · 1279 · 14635063 · 3987383581_<10> · 4581360201133_<13> · C124

C124 = P42 · P83

P42 = 111804472216234621446149216648206991096293_<42>

P83 = 10005531849149209867385888327748278326019822739848288047545094990750961458768022501_<83>

(7·10¹⁵⁹-61)/9 = (7)₁₅₈1_<159> = 3³ · 43 · 263 · 349831 · 17126917 · 28619057539265783684510425072387757_<35> · C107

C107 = P33 · P74

P33 = 797403209935797539434823436791693_<33>

P74 = 18629310032851632076163322531678663673503016373642711951312754825678195311_<74>

Number: 77771_159
N=14855071619085049328530992857412182242694733285669768452444236785568599716426578493792762350613756076351523
  ( 107 digits)
Divisors found:
 r1=797403209935797539434823436791693 (pp33)
 r2=18629310032851632076163322531678663673503016373642711951312754825678195311 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.49 hours.
Scaled time: 22.36 units (timescale=2.132).
Factorization parameters were as follows:
name: 77771_159
n: 14855071619085049328530992857412182242694733285669768452444236785568599716426578493792762350613756076351523
skew: 17252.59
# norm 4.53e+14
c5: 24360
c4: 1552062034
c3: -12155455866301
c2: -501419086915678603
c1: 4107034064874536958069
c0: -110865863932083856105047
# alpha -5.86
Y1: 159151859009
Y0: -227528404968347614694
# Murphy_E 1.61e-09
# M 13177898755741697868442278760361905096607553508203604547219497232778306454584708936145593728319772417207638
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1440001)
Primes: RFBsize:135072, AFBsize:135225, largePrimes:4558581 encountered
Relations: rels:4599743, finalFF:363106
Max relations in full relation-set: 28
Initial matrix: 270381 x 363106 with sparse part having weight 34524026.
Pruned matrix : 218438 x 219853 with weight 18421094.
Polynomial selection time: 0.54 hours.
Total sieving time: 9.58 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 10.49 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129)
Total of 4 processors activated (19246.12 BogoMIPS).

(23·10¹⁵⁷+1)/3 = 7(6)₁₅₆7_<158> = 7² · 11 · 103 · 3931093 · 187918820385783433750403_<24> · C124

C124 = P29 · C95

P29 = 20896654878601350360268149361_<29>

C95 = [89458214411835630370906446629114652455106051226197501160191146683705663732977188286693142346729_<95>]

3·10¹⁵⁹-1 = 2(9)₁₅₉_<160> = 1321 · 6967 · 398760584767619777_<18> · C135

C135 = P34 · P102

P34 = 1365996837467415111026906770750469_<34>

P102 = 598426350404332450433128876484310209991358869759713755798077815328602741567697247226824883321819832989_<102>

(2·10¹⁵⁸+61)/9 = (2)₁₅₇9_<158> = 313251391 · 4232920182402397664794465973_<28> · C122

C122 = P34 · C88

P34 = 8180004382945353667194983565175097_<34>

C88 = [2048806118195499354913542723718755940102140970322140966978079897796843232293172520602199_<88>]

Jul 11, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

5·10¹⁵⁶-3 = 4(9)₁₅₅7_<157> = 1973 · 2053063 · C148

C148 = P53 · P95

P53 = 88666131158617287229707084514778242205719232955907723_<53>

P95 = 13921399093960280961780774878816447259601802769512930326480215435970153126193617396031190315661_<95>

Number: n
N=1234356597976538139280142028842356943894606126781952641732207333922863854916604980909466777183418645194248264906713195221843429918982863975157749903
  ( 148 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=88666131158617287229707084514778242205719232955907723 (pp53)
 r2=13921399093960280961780774878816447259601802769512930326480215435970153126193617396031190315661 (pp95)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 33.75 hours.
Scaled time: 40.30 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_4_9_155_7
n: 1234356597976538139280142028842356943894606126781952641732207333922863854916604980909466777183418645194248264906713195221843429918982863975157749903
type: snfs
skew: 0.57
deg: 5
c5: 50
c0: -3
m: 10000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:250150, AFBsize:250256, largePrimes:6432804 encountered
Relations: rels:5951628, finalFF:565359
Max relations in full relation-set: 28
Initial matrix: 500471 x 565359 with sparse part having weight 25798180.
Pruned matrix : 434020 x 436586 with weight 15831361.
Total sieving time: 30.40 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 3.06 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.3,2.3,100000
total time: 33.75 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

5·10¹⁶²-3 = 4(9)₁₆₁7_<163> = C163

C163 = P49 · P114

P49 = 8544406184158733288717788329856875808280189100763_<49>

P114 = 585178172974730942884427619934926129351771486625491327311590996532550927049973737667478017100778019085012646208519_<114>

Number: n
N=4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997
  ( 163 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=8544406184158733288717788329856875808280189100763 (pp49)
 r2=585178172974730942884427619934926129351771486625491327311590996532550927049973737667478017100778019085012646208519 (pp114)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 43.47 hours.
Scaled time: 63.03 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_4_9_161_7
n: 4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997
skew: 0.36
deg: 5
c5: 500
c0: -3
m: 100000000000000000000000000000000
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1900001)
Primes: RFBsize:283146, AFBsize:282917, largePrimes:7337299 encountered
Relations: rels:6908627, finalFF:639847
Max relations in full relation-set: 28
Initial matrix: 566129 x 639847 with sparse part having weight 37255811.
Pruned matrix : 497961 x 500855 with weight 23972880.
Total sieving time: 37.76 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 5.18 hours.
Total square root time: 0.30 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000
total time: 43.47 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jul 10, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

5·10¹⁵⁰-3 = 4(9)₁₄₉7_<151> = 67 · 3116051 · 28212754553911189_<17> · C126

C126 = P61 · P65

P61 = 9067846705098386264105687808083859986016022518939144596253611_<61>

P65 = 93614039200569581281008047873083290213666429881740082969167944179_<65>

Number: n
N=848877756915836047327005956367688030754050414861578135676328925892022810228355445983559089497621983270454716296031158175180369
  ( 126 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=9067846705098386264105687808083859986016022518939144596253611 (pp61)
 r2=93614039200569581281008047873083290213666429881740082969167944179 (pp65)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 15.95 hours.
Scaled time: 21.05 units (timescale=1.320).
Factorization parameters were as follows:
name: KA_4_9_149_7
n: 848877756915836047327005956367688030754050414861578135676328925892022810228355445983559089497621983270454716296031158175180369
skew: 0.90
deg: 5
c5: 5
c0: -3
m: 1000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 700001)
Primes: RFBsize:250150, AFBsize:249871, largePrimes:6181244 encountered
Relations: rels:5785296, finalFF:582205
Max relations in full relation-set: 48
Initial matrix: 500086 x 582205 with sparse part having weight 24719108.
Pruned matrix : 412540 x 415104 with weight 13084779.
Total sieving time: 13.54 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 2.16 hours.
Total square root time: 0.10 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 15.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jul 10, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

5·10¹⁴⁶-3 = 4(9)₁₄₅7_<147> = 7 · 797 · 239329 · 93483761128799642385893_<23> · C115

C115 = P45 · P71

P45 = 128452413621408811962701715902967521602390963_<45>

P71 = 31184577944989473183131805515755584538817242291977209687873566291246313_<71>

Number: 49997_146
N=4005734304798850622326249951143037423616711644650164979183042659808685924415865726837714445893729270428277958269419
  ( 115 digits)
Divisors found:
 r1=128452413621408811962701715902967521602390963 (pp45)
 r2=31184577944989473183131805515755584538817242291977209687873566291246313 (pp71)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 62.55 hours.
Scaled time: 41.60 units (timescale=0.665).
Factorization parameters were as follows:
name: 49997_146
n: 4005734304798850622326249951143037423616711644650164979183042659808685924415865726837714445893729270428277958269419
skew: 36021.67
# norm 2.21e+16
c5: 39600
c4: -5544913316
c3: 808385282931308
c2: 4256940067114749501
c1: -289150373904486983283538
c0: -1001954365526770591150788255
# alpha -6.85
Y1: 195581790739
Y0: -10022997639641682506218
# Murphy_E 5.45e-10
# M 830918682632186915924213558878628963560867949599055263643356419771358536458349787830192216066526682747955092642640
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2950001)
Primes: RFBsize:250150, AFBsize:250336, largePrimes:7615163 encountered
Relations: rels:7554461, finalFF:563033
Max relations in full relation-set: 0
Initial matrix: 500568 x 563033 with sparse part having weight 41679643.
Pruned matrix : 450560 x 453126 with weight 30186049.
Polynomial selection time: 2.62 hours.
Total sieving time: 50.83 hours.
Total relation processing time: 0.45 hours.
Matrix solve time: 8.26 hours.
Time per square root: 0.40 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 62.55 hours.
 --------- CPU info (if available) ----------

Jul 9, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

5·10¹⁴⁹-3 = 4(9)₁₄₈7_<150> = 29 · 6983106863_<10> · C139

C139 = P48 · P92

P48 = 208747880384388120276325252490914165886057736101_<48>

P92 = 11827725694599174236257190431349303144204489375682681972938043512380134113838243183754907011_<92>

Number: n
N=2469012668515542318460277664481179790737291307383604284844296502512716634601796579368377536357106844920154402705397083070678261616432704111
  ( 139 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=208747880384388120276325252490914165886057736101 (pp48)
 r2=11827725694599174236257190431349303144204489375682681972938043512380134113838243183754907011 (pp92)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 12.93 hours.
Scaled time: 18.71 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_4_9_148_7
n: 2469012668515542318460277664481179790737291307383604284844296502512716634601796579368377536357106844920154402705397083070678261616432704111
skew: 1.43
deg: 5
c5: 1
c0: -6
m: 1000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 600001)
Primes: RFBsize:250150, AFBsize:250351, largePrimes:5947139 encountered
Relations: rels:5574191, finalFF:579093
Max relations in full relation-set: 28
Initial matrix: 500565 x 579093 with sparse part having weight 22226434.
Pruned matrix : 404909 x 407475 with weight 11698567.
Total sieving time: 10.91 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 1.85 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 12.93 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jul 9, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(5·10¹⁷⁹-17)/3 = 1(6)₁₇₈1_<180> = 11 · C179

C179 = P88 · P91

P88 = 1639019173770832049695358993053022960848462753158292470147701013746739785573856983124029_<88>

P91 = 9244257415644875817165595378275105183625338529342101678091693130990885547247677848761743419_<91>

Number: n
N=15151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151
  ( 179 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=1639019173770832049695358993053022960848462753158292470147701013746739785573856983124029 (pp88)
 r2=9244257415644875817165595378275105183625338529342101678091693130990885547247677848761743419 (pp91)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 227.13 hours.
Scaled time: 330.25 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_1_6_178_1
n: 15151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151
skew: 2.02
deg: 5
c5: 1
c0: -34
m: 1000000000000000000000000000000000000
type: snfs
rlim: 5500000
alim: 5500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3200001)
Primes: RFBsize:380800, AFBsize:380652, largePrimes:8184922 encountered
Relations: rels:7889387, finalFF:860871
Max relations in full relation-set: 28
Initial matrix: 761516 x 860871 with sparse part having weight 49715353.
Pruned matrix : 669290 x 673161 with weight 32998412.
Total sieving time: 216.42 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 10.21 hours.
Total square root time: 0.20 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000
total time: 227.13 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

P88 is the largest factor found by GGNFS so far in our tables. Congratulations!

(4·10¹⁷⁴+23)/9 = (4)₁₇₃7_<174> = 3 · C174

C174 = P66 · P108

P66 = 431698729585373966167026238230882951903861668583514905584774408843_<66>

P108 = 343174853190875443246946483687163515522963880644358945766137050568648583698244978599326968646362907761905343_<108>

Number: n
N=148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148149
  ( 174 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=431698729585373966167026238230882951903861668583514905584774408843 (pp66)
 r2=343174853190875443246946483687163515522963880644358945766137050568648583698244978599326968646362907761905343 (pp108)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 219.68 hours.
Scaled time: 290.86 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_4_173_7
n: 148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148149
skew: 2.25
deg: 5
c5: 2
c0: 115
m: 100000000000000000000000000000000000
type: snfs
rlim: 5500000
alim: 5500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 8500001)
Primes: RFBsize:380800, AFBsize:380192, largePrimes:9150545 encountered
Relations: rels:8710774, finalFF:854421
Max relations in full relation-set: 48
Initial matrix: 761057 x 854421 with sparse part having weight 74383121.
Pruned matrix : 692647 x 696516 with weight 56412545.
Total sieving time: 199.12 hours.
Total relation processing time: 0.62 hours.
Matrix solve time: 19.49 hours.
Total square root time: 0.45 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000
total time: 219.68 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(7·10¹⁷⁴-61)/9 = (7)₁₇₃1_<174> = 3 · C174

C174 = P66 · P108

P66 = 592183130436863192470465165361108333811673611186266348002248596759_<66>

P108 = 437802507254807238882928297138447646164159872834322448723319030478316704747682896028097705022390728332298223_<108>

Number: n
N=259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259257
  ( 174 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=592183130436863192470465165361108333811673611186266348002248596759 (pp66)
 r2=437802507254807238882928297138447646164159872834322448723319030478316704747682896028097705022390728332298223 (pp108)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 333.18 hours.
Scaled time: 397.82 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_7_173_1
n: 259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259257
type: snfs
skew: 2.44
deg: 5
c5: 7
c0: -610
m: 100000000000000000000000000000000000
rlim: 5500000
alim: 5500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 11600001)
Primes: RFBsize:380800, AFBsize:381368, largePrimes:8890149 encountered
Relations: rels:8648810, finalFF:860116
Max relations in full relation-set: 28
Initial matrix: 762233 x 860116 with sparse part having weight 86306908.
Pruned matrix : 693173 x 697048 with weight 70123858.
Total sieving time: 307.41 hours.
Total relation processing time: 0.72 hours.
Matrix solve time: 24.26 hours.
Total square root time: 0.79 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.6,2.6,100000
total time: 333.18 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Jul 8, 2007

By Yousuke Koide

10¹²⁷⁸+1 is divisible by 40006639726526214492389221911263641_<35>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jul 7, 2007 (3rd)

By Torbjörn Granlund

(10⁸⁵⁷-1)/9 is divisible by 600675575158100017424925351819839677_<36>, cofactor is probably prime

10⁵³¹+1 is divisible by 216300405364911283995901633078340436727_<39>

10⁸⁴¹+1 is divisible by 1630777462352881403814023114519396413_<37>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jul 7, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

5·10¹⁴⁷-3 = 4(9)₁₄₆7_<148> = 19 · 139 · 601 · 13681 · 40487 · 354995006736248519_<18> · C116

C116 = P47 · P70

P47 = 10067361505415681618873296936552921933923299611_<47>

P70 = 1591313628803614731260135467601813388393486021881617569796951585055279_<70>

Number: 49997_147
N=16020329569660849975695435240487629364228641450318647485024030704932582906631343798326668419485613524001679514196469
  ( 116 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=10067361505415681618873296936552921933923299611 (pp47)
 r2=1591313628803614731260135467601813388393486021881617569796951585055279 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 9.23 hours.
Scaled time: 19.79 units (timescale=2.144).
Factorization parameters were as follows:
n: 16020329569660849975695435240487629364228641450318647485024030704932582906631343798326668419485613524001679514196469
m: 500000000000000000000000000000
c5: 4
c0: -75
skew: 1.8
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1500001)
Primes: RFBsize:135072, AFBsize:134758, largePrimes:3616122 encountered
Relations: rels:3602120, finalFF:311536
Max relations in full relation-set: 28
Initial matrix: 269894 x 311536 with sparse part having weight 26078125.
Pruned matrix : 251458 x 252871 with weight 18101350.
Total sieving time: 8.87 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 9.23 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹⁴⁸-3 = 4(9)₁₄₇7_<149> = 17 · 61 · 3907 · 184094837 · C134

C134 = P42 · P46 · P47

P42 = 856199339682423221681610853181988817318913_<42>

P46 = 1556144666064391456467500163826224366444427919_<46>

P47 = 50313134072976025481264005755700033644273942497_<47>

Number: 49997_148
N=67035712232671026578085702644158591186552652917191706966233004080754358180856116346537407110225442792919527957856093621681551793501359
  ( 134 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=856199339682423221681610853181988817318913 (pp42)
 r2=1556144666064391456467500163826224366444427919 (pp46)
 r3=50313134072976025481264005755700033644273942497 (pp47)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.81 hours.
Scaled time: 22.89 units (timescale=2.117).
Factorization parameters were as follows:
n: 67035712232671026578085702644158591186552652917191706966233004080754358180856116346537407110225442792919527957856093621681551793501359
m: 1000000000000000000000000000000
c5: 1
c0: -60
skew: 2.27
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1575001)
Primes: RFBsize:135072, AFBsize:134688, largePrimes:3788068 encountered
Relations: rels:3897704, finalFF:405595
Max relations in full relation-set: 28
Initial matrix: 269824 x 405595 with sparse part having weight 37011153.
Pruned matrix : 222190 x 223603 with weight 17763617.
Total sieving time: 10.40 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.33 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 10.81 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Total of 4 processors activated (19246.09 BogoMIPS).

Jul 7, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060513-k8, GGNFS-0.77.1-20060722-pentium4

(32·10¹⁸⁶-23)/9 = 3(5)₁₈₅3_<187> = C187

C187 = P77 · P111

P77 = 22505468127454808181216964200487999120781593821049054585465704599969960629843_<77>

P111 = 157986296282283153038019270956995707149770776451983434848501382962868901158389576269567185495417338509918446971_<111>

Number: 35553_186
N=3555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553
  ( 187 digits)
SNFS difficulty: 187 digits.
Divisors found:
 r1=22505468127454808181216964200487999120781593821049054585465704599969960629843 (pp77)
 r2=157986296282283153038019270956995707149770776451983434848501382962868901158389576269567185495417338509918446971 (pp111)
Version: GGNFS-0.77.1-20060513-k8
Total time: 935.90 hours.
Scaled time: 1881.16 units (timescale=2.010).
Factorization parameters were as follows:
name: 35553_186
n: 3555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553
m: 20000000000000000000000000000000000000
c5: 10
c0: -23
skew: 1.18
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 14600001)
Primes: RFBsize:501962, AFBsize:502936, largePrimes:6862780 encountered
Relations: rels:7364860, finalFF:1143693
Max relations in full relation-set: 28
Initial matrix: 1004964 x 1143693 with sparse part having weight 105432265.
Pruned matrix : 897970 x 903058 with weight 86536058.
Total sieving time: 920.03 hours.
Total relation processing time: 0.64 hours.
Matrix solve time: 14.83 hours.
Time per square root: 0.40 hours.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 935.90 hours.
 --------- CPU info (if available) ----------

3·10¹⁶⁴-1 = 2(9)₁₆₄_<165> = 13 · 2591 · C160

C160 = P47 · P50 · P65

P47 = 20864331285956384714363476632186247632145067881_<47>

P50 = 16745773198975668201316866017478902963614694091371_<50>

P65 = 25491818321127692702503378138106307806982680946323585329451086103_<65>

Number: 29999_164
N=8906570079862245049431463943235460024344624884956803135112668111510257399875308018881928569307959504794703559659175251610604756108422646438856396401745687735653
  ( 160 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=20864331285956384714363476632186247632145067881 (pp47)
 r2=16745773198975668201316866017478902963614694091371 (pp50)
 r3=25491818321127692702503378138106307806982680946323585329451086103 (pp65)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 125.82 hours.
Scaled time: 85.56 units (timescale=0.680).
Factorization parameters were as follows:
name: 29999_164
n: 8906570079862245049431463943235460024344624884956803135112668111510257399875308018881928569307959504794703559659175251610604756108422646438856396401745687735653
m: 1000000000000000000000000000000000
c5: 3
c0: -10
skew: 1.27
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 5400001)
Primes: RFBsize:348513, AFBsize:348501, largePrimes:5894099 encountered
Relations: rels:6079819, finalFF:784956
Max relations in full relation-set: 0
Initial matrix: 697079 x 784956 with sparse part having weight 43312634.
Pruned matrix : 626895 x 630444 with weight 33519435.
Total sieving time: 107.99 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 17.17 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 125.82 hours.
 --------- CPU info (if available) ----------

Jul 6, 2007 (4th)

By Alban Nonymous

10¹⁰⁶³+1 is divisible by 2928852075918417027638457828557_<31>

10¹²¹⁷+1 is divisible by 1097021863038561688666089244771_<31>

10¹²⁴⁹+1 is divisible by 83933507135165614961893401401_<29>, cofactor is probably prime

10¹⁴²⁰+1 is divisible by 33233412196028093809254651841_<29>

10¹⁴⁸⁰+1 is divisible by 2922137698079622949054068972641_<31>

10¹⁶⁴³+1 is divisible by 1393949954184795816301811495623_<31>

10¹⁷⁰⁶+1 is divisible by 2585176909735148567915152915961_<31>

10¹⁷³⁷+1 is divisible by 5337159554189680210862121006289_<31>

10¹⁸⁴¹+1 is divisible by 1221836164173949226042017629809_<31>

10¹⁹²⁵+1 is divisible by 1358137502639759693901685682201_<31>

10¹⁹³⁹+1 is divisible by 8672844768252056198113722386329_<31>, cofactor is probably prime

10¹⁹⁴¹+1 is divisible by 315539166618894730521025791493_<30>

10¹⁹⁴²+1 is divisible by 817080761838450112158972131041_<30>

Reference: Factorizations of numbers of the form 10^n+1 (Alfred Reich)

Jul 6, 2007 (3rd)

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000, GGNFS-0.77.1-20050930-nocona

5·10¹⁵⁷-3 = 4(9)₁₅₆7_<158> = C158

C158 = P39 · C120

P39 = 170751714607368696896080865604341002901_<39>

C120 = [292822828250781602016000167325285828040891795200764250827620597365088252659542353359323090342351116997142479928464778697_<120>]

5·10¹⁴³-3 = 4(9)₁₄₂7_<144> = 409 · C142

C142 = P61 · P81

P61 = 2935742145013115478236491256387688161775892870102820487172343_<61>

P81 = 416417323846778387561709274459675711946255835461780664134795831916578834221071331_<81>

Number: 49997_143
N=1222493887530562347188264058679706601466992665036674816625916870415647921760391198044009779951100244498777506112469437652811735941320293398533
  ( 142 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=2935742145013115478236491256387688161775892870102820487172343 (pp61)
 r2=416417323846778387561709274459675711946255835461780664134795831916578834221071331 (pp81)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.13 hours.
Scaled time: 17.41 units (timescale=2.143).
Factorization parameters were as follows:
n: 1222493887530562347188264058679706601466992665036674816625916870415647921760391198044009779951100244498777506112469437652811735941320293398533
m: 100000000000000000000000000000
c5: 1
c0: -60
skew: 2.27
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 1300001)
Primes: RFBsize:114155, AFBsize:113882, largePrimes:2653193 encountered
Relations: rels:2644766, finalFF:300265
Max relations in full relation-set: 28
Initial matrix: 228101 x 300265 with sparse part having weight 19434761.
Pruned matrix : 195584 x 196788 with weight 10280185.
Total sieving time: 7.95 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000
total time: 8.13 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Total of 4 processors activated (19246.09 BogoMIPS).

Jul 6, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, Msieve v. 1.21, GMP-ECM 6.1.2

5·10¹²⁰-3 = 4(9)₁₁₉7_<121> = 109 · C119

C119 = P38 · P81

P38 = 71651015110439976712949381761124614909_<38>

P81 = 640208091432102618875345096934692490876535014728092248096211914729816834699112037_<81>

Number: 49997_120
N=45871559633027522935779816513761467889908256880733944954128440366972477064220183486238532110091743119266055045871559633
  ( 119 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=71651015110439976712949381761124614909 (pp38)
 r2=640208091432102618875345096934692490876535014728092248096211914729816834699112037 (pp81)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.93 hours.
Scaled time: 1.99 units (timescale=2.125).
Factorization parameters were as follows:
n: 45871559633027522935779816513761467889908256880733944954128440366972477064220183486238532110091743119266055045871559633
m: 1000000000000000000000000
c5: 5
c0: -3
skew: 0.9
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 450001)
Primes: RFBsize:49098, AFBsize:48956, largePrimes:2046876 encountered
Relations: rels:2149382, finalFF:235375
Max relations in full relation-set: 28
Initial matrix: 98119 x 235375 with sparse part having weight 21516547.
Pruned matrix : 73294 x 73848 with weight 4654054.
Total sieving time: 0.88 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 0.93 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹²⁸-3 = 4(9)₁₂₇7_<129> = 7 · 1871 · 142184699 · C117

C117 = P52 · P65

P52 = 9755302500995483441296854824102920959702641390257253_<52>

P65 = 27523557876492693925945733984595465953928510734994989947908285283_<65>

Number: 49997_128
N=268500632988843114399137334497132172339031733517253072560760156230954193300391203370973608509515917709832913483907599
  ( 117 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=9755302500995483441296854824102920959702641390257253 (pp52)
 r2=27523557876492693925945733984595465953928510734994989947908285283 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.77 hours.
Scaled time: 3.76 units (timescale=2.128).
Factorization parameters were as follows:
n: 268500632988843114399137334497132172339031733517253072560760156230954193300391203370973608509515917709832913483907599
m: 100000000000000000000000000
c5: 1
c0: -60
skew: 2.27
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 850001)
Primes: RFBsize:78498, AFBsize:78351, largePrimes:1470489 encountered
Relations: rels:1481355, finalFF:188290
Max relations in full relation-set: 28
Initial matrix: 156913 x 188290 with sparse part having weight 8758854.
Pruned matrix : 139088 x 139936 with weight 5115713.
Total sieving time: 1.69 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 1.77 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹⁵⁴-3 = 4(9)₁₅₃7_<155> = 223 · 421 · 2256879067_<10> · 7689247183_<10> · 7976152762042959475996039114316239979_<37> · C94

C94 = P46 · P49

P46 = 2921647769384774308532275896959632201186400323_<46>

P49 = 1316950995804027485247023644858332723329794421707_<49>

Fri Jul  6 00:56:55 2007  
Fri Jul  6 00:56:55 2007  
Fri Jul  6 00:56:55 2007  Msieve v. 1.21
Fri Jul  6 00:56:55 2007  random seeds: d977a1fa f013ce09
Fri Jul  6 00:56:55 2007  factoring 3847666939279894172268033897682969407262717898287172366419424639735420453122353902836783011361 (94 digits)
Fri Jul  6 00:56:55 2007  commencing quadratic sieve (94-digit input)
Fri Jul  6 00:56:55 2007  using multiplier of 1
Fri Jul  6 00:56:55 2007  using 32kb Intel Core sieve core
Fri Jul  6 00:56:55 2007  sieve interval: 36 blocks of size 32768
Fri Jul  6 00:56:55 2007  processing polynomials in batches of 6
Fri Jul  6 00:56:55 2007  using a sieve bound of 2025281 (75006 primes)
Fri Jul  6 00:56:55 2007  using large prime bound of 271387654 (28 bits)
Fri Jul  6 00:56:55 2007  using double large prime bound of 1515172741378278 (42-51 bits)
Fri Jul  6 00:56:55 2007  using trial factoring cutoff of 51 bits
Fri Jul  6 00:56:55 2007  polynomial 'A' values have 12 factors
Fri Jul  6 03:02:27 2007  75317 relations (18669 full + 56648 combined from 1068446 partial), need 75102
Fri Jul  6 03:02:28 2007  begin with 1087115 relations
Fri Jul  6 03:02:28 2007  reduce to 195099 relations in 11 passes
Fri Jul  6 03:02:28 2007  attempting to read 195099 relations
Fri Jul  6 03:02:30 2007  recovered 195099 relations
Fri Jul  6 03:02:30 2007  recovered 176930 polynomials
Fri Jul  6 03:02:30 2007  attempting to build 75317 cycles
Fri Jul  6 03:02:30 2007  found 75316 cycles in 5 passes
Fri Jul  6 03:02:30 2007  distribution of cycle lengths:
Fri Jul  6 03:02:30 2007     length 1 : 18669
Fri Jul  6 03:02:30 2007     length 2 : 13325
Fri Jul  6 03:02:30 2007     length 3 : 12721
Fri Jul  6 03:02:30 2007     length 4 : 10305
Fri Jul  6 03:02:30 2007     length 5 : 7536
Fri Jul  6 03:02:30 2007     length 6 : 4964
Fri Jul  6 03:02:30 2007     length 7 : 3344
Fri Jul  6 03:02:30 2007     length 9+: 4452
Fri Jul  6 03:02:30 2007  largest cycle: 19 relations
Fri Jul  6 03:02:30 2007  matrix is 75006 x 75316 with weight 4694209 (avg 62.33/col)
Fri Jul  6 03:02:30 2007  filtering completed in 3 passes
Fri Jul  6 03:02:30 2007  matrix is 73619 x 73683 with weight 4526930 (avg 61.44/col)
Fri Jul  6 03:02:32 2007  saving the first 48 matrix rows for later
Fri Jul  6 03:02:32 2007  matrix is 73571 x 73683 with weight 3487432 (avg 47.33/col)
Fri Jul  6 03:02:32 2007  matrix includes 32 packed rows
Fri Jul  6 03:02:32 2007  using block size 29473 for processor cache size 4096 kB
Fri Jul  6 03:02:58 2007  lanczos halted after 1165 iterations
Fri Jul  6 03:02:58 2007  recovered 15 nontrivial dependencies
Fri Jul  6 03:02:59 2007  prp46 factor: 2921647769384774308532275896959632201186400323
Fri Jul  6 03:02:59 2007  prp49 factor: 1316950995804027485247023644858332723329794421707
Fri Jul  6 03:02:59 2007  elapsed time 02:06:04

5·10¹⁷⁵-3 = 4(9)₁₇₄7_<176> = C176

C176 = P38 · C138

P38 = 82494503209048359090450275383194039527_<38>

C138 = [606100989217373462581008360915327251534574087696954550955083284282765441327791625110225200206880593890686186829406312682705912893389087611_<138>]

5·10¹⁴²-3 = 4(9)₁₄₁7_<143> = 71 · 2143 · 2343611 · 1711248061_<10> · 2674951691_<10> · 1461605018313863471_<19> · C95

C95 = P34 · P61

P34 = 8731327716744500293395495818364077_<34>

P61 = 2400295605687202500809285138795364428820556768937793554302027_<61>

Fri Jul  6 08:21:10 2007  
Fri Jul  6 08:21:10 2007  
Fri Jul  6 08:21:10 2007  Msieve v. 1.21
Fri Jul  6 08:21:10 2007  random seeds: 58e36f1b b3909a7e
Fri Jul  6 08:21:10 2007  factoring 20957767550316699204490665365600675841056124504326905194322448749729894011632283651292705084079 (95 digits)
Fri Jul  6 08:21:10 2007  commencing quadratic sieve (95-digit input)
Fri Jul  6 08:21:10 2007  using multiplier of 39
Fri Jul  6 08:21:10 2007  using 32kb Intel Core sieve core
Fri Jul  6 08:21:10 2007  sieve interval: 36 blocks of size 32768
Fri Jul  6 08:21:10 2007  processing polynomials in batches of 6
Fri Jul  6 08:21:10 2007  using a sieve bound of 2128177 (78814 primes)
Fri Jul  6 08:21:10 2007  using large prime bound of 310713842 (28 bits)
Fri Jul  6 08:21:10 2007  using double large prime bound of 1933076650188010 (43-51 bits)
Fri Jul  6 08:21:10 2007  using trial factoring cutoff of 51 bits
Fri Jul  6 08:21:10 2007  polynomial 'A' values have 12 factors
Fri Jul  6 10:59:50 2007  78971 relations (19724 full + 59247 combined from 1157803 partial), need 78910
Fri Jul  6 10:59:51 2007  begin with 1177527 relations
Fri Jul  6 10:59:51 2007  reduce to 203965 relations in 11 passes
Fri Jul  6 10:59:51 2007  attempting to read 203965 relations
Fri Jul  6 10:59:53 2007  recovered 203965 relations
Fri Jul  6 10:59:53 2007  recovered 187676 polynomials
Fri Jul  6 10:59:53 2007  attempting to build 78971 cycles
Fri Jul  6 10:59:53 2007  found 78971 cycles in 6 passes
Fri Jul  6 10:59:53 2007  distribution of cycle lengths:
Fri Jul  6 10:59:53 2007     length 1 : 19724
Fri Jul  6 10:59:53 2007     length 2 : 13855
Fri Jul  6 10:59:53 2007     length 3 : 13538
Fri Jul  6 10:59:53 2007     length 4 : 10684
Fri Jul  6 10:59:53 2007     length 5 : 7791
Fri Jul  6 10:59:53 2007     length 6 : 5465
Fri Jul  6 10:59:53 2007     length 7 : 3347
Fri Jul  6 10:59:53 2007     length 9+: 4567
Fri Jul  6 10:59:53 2007  largest cycle: 21 relations
Fri Jul  6 10:59:54 2007  matrix is 78814 x 78971 with weight 5395208 (avg 68.32/col)
Fri Jul  6 10:59:54 2007  filtering completed in 3 passes
Fri Jul  6 10:59:54 2007  matrix is 77248 x 77312 with weight 5215318 (avg 67.46/col)
Fri Jul  6 10:59:55 2007  saving the first 48 matrix rows for later
Fri Jul  6 10:59:55 2007  matrix is 77200 x 77312 with weight 4324622 (avg 55.94/col)
Fri Jul  6 10:59:55 2007  matrix includes 32 packed rows
Fri Jul  6 10:59:55 2007  using block size 30924 for processor cache size 4096 kB
Fri Jul  6 11:00:30 2007  lanczos halted after 1222 iterations
Fri Jul  6 11:00:30 2007  recovered 18 nontrivial dependencies
Fri Jul  6 11:00:31 2007  prp34 factor: 8731327716744500293395495818364077
Fri Jul  6 11:00:31 2007  prp61 factor: 2400295605687202500809285138795364428820556768937793554302027
Fri Jul  6 11:00:31 2007  elapsed time 02:39:21

5·10¹³⁷-3 = 4(9)₁₃₆7_<138> = 23 · 163 · 39461 · 93871607 · C122

C122 = P31 · P37 · P54

P31 = 5891496177752933541219267704741_<31>

P37 = 7812216930943689316265896059629904893_<37>

P54 = 782262172768407880210825956642975867414150295248290803_<54>

Number: 49997_137
N=36004121990432414722179291080937945766418689524785810698872912601379557840153318452414515762972516047917479488800024533539
  ( 122 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=5891496177752933541219267704741 (pp31)
 r2=7812216930943689316265896059629904893 (pp37)
 r3=782262172768407880210825956642975867414150295248290803 (pp54)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.00 hours.
Scaled time: 8.58 units (timescale=2.145).
Factorization parameters were as follows:
n: 36004121990432414722179291080937945766418689524785810698872912601379557840153318452414515762972516047917479488800024533539
m: 5000000000000000000000000000
c5: 4
c0: -75
skew: 1.8
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [700000, 1450001)
Primes: RFBsize:107126, AFBsize:106673, largePrimes:1867994 encountered
Relations: rels:1987379, finalFF:283262
Max relations in full relation-set: 28
Initial matrix: 213863 x 283262 with sparse part having weight 17166479.
Pruned matrix : 184846 x 185979 with weight 9061365.
Total sieving time: 3.84 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,45,45,2.3,2.3,50000
total time: 4.00 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Total of 4 processors activated (19246.09 BogoMIPS).

Jul 6, 2007

By Kenichiro Yamaguchi / Msieve v. 1.25

5·10¹²²-3 = 4(9)₁₂₁7_<123> = 7 · 2446494083906698889244510653_<28> · C95

C95 = P43 · P52

P43 = 6303845095126307972819884509608992783019357_<43>

P52 = 4631506328102789383103305306718062753677381160084451_<52>

Thu Jul 05 23:38:40 2007  
Thu Jul 05 23:38:40 2007  
Thu Jul 05 23:38:40 2007  Msieve v. 1.25
Thu Jul 05 23:38:40 2007  random seeds: c91b51d8 af500c75
Thu Jul 05 23:38:40 2007  factoring 29196298449457225683898977265132542300678896172777155830274719264937835884224090396632887718007 (95 digits)
Thu Jul 05 23:38:41 2007  commencing quadratic sieve (95-digit input)
Thu Jul 05 23:38:41 2007  using multiplier of 7
Thu Jul 05 23:38:41 2007  using 32kb Pentium M sieve core
Thu Jul 05 23:38:41 2007  sieve interval: 36 blocks of size 32768
Thu Jul 05 23:38:41 2007  processing polynomials in batches of 6
Thu Jul 05 23:38:41 2007  using a sieve bound of 2115527 (78824 primes)
Thu Jul 05 23:38:41 2007  using large prime bound of 308866942 (28 bits)
Thu Jul 05 23:38:41 2007  using double large prime bound of 1912443258076426 (43-51 bits)
Thu Jul 05 23:38:41 2007  using trial factoring cutoff of 51 bits
Thu Jul 05 23:38:41 2007  polynomial 'A' values have 12 factors
Fri Jul 06 04:10:53 2007  79253 relations (19388 full + 59865 combined from 1166604 partial), need 78920
Fri Jul 06 04:10:55 2007  begin with 1185992 relations
Fri Jul 06 04:10:56 2007  reduce to 206355 relations in 10 passes
Fri Jul 06 04:10:56 2007  attempting to read 206355 relations
Fri Jul 06 04:11:00 2007  recovered 206355 relations
Fri Jul 06 04:11:00 2007  recovered 189200 polynomials
Fri Jul 06 04:11:00 2007  attempting to build 79253 cycles
Fri Jul 06 04:11:00 2007  found 79252 cycles in 5 passes
Fri Jul 06 04:11:00 2007  distribution of cycle lengths:
Fri Jul 06 04:11:00 2007     length 1 : 19388
Fri Jul 06 04:11:00 2007     length 2 : 13782
Fri Jul 06 04:11:00 2007     length 3 : 13535
Fri Jul 06 04:11:00 2007     length 4 : 10814
Fri Jul 06 04:11:00 2007     length 5 : 8041
Fri Jul 06 04:11:00 2007     length 6 : 5414
Fri Jul 06 04:11:00 2007     length 7 : 3423
Fri Jul 06 04:11:00 2007     length 9+: 4855
Fri Jul 06 04:11:00 2007  largest cycle: 23 relations
Fri Jul 06 04:11:01 2007  matrix is 78824 x 79252 with weight 5331274 (avg 67.27/col)
Fri Jul 06 04:11:02 2007  filtering completed in 4 passes
Fri Jul 06 04:11:02 2007  matrix is 75026 x 75090 with weight 5058349 (avg 67.36/col)
Fri Jul 06 04:11:02 2007  saving the first 48 matrix rows for later
Fri Jul 06 04:11:02 2007  matrix is 74978 x 75090 with weight 4132765 (avg 55.04/col)
Fri Jul 06 04:11:02 2007  matrix includes 64 packed rows
Fri Jul 06 04:11:02 2007  using block size 30036 for processor cache size 2048 kB
Fri Jul 06 04:11:02 2007  commencing Lanczos iteration
Fri Jul 06 04:11:51 2007  lanczos halted after 1187 iterations
Fri Jul 06 04:11:51 2007  recovered 17 nontrivial dependencies
Fri Jul 06 04:11:52 2007  prp43 factor: 6303845095126307972819884509608992783019357
Fri Jul 06 04:11:52 2007  prp52 factor: 4631506328102789383103305306718062753677381160084451
Fri Jul 06 04:11:52 2007  elapsed time 04:33:12

Jul 5, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

5·10¹⁰⁶-3 = 4(9)₁₀₅7_<107> = C107

C107 = P53 · P54

P53 = 51379467791652406382241099912651400334898984400190777_<53>

P54 = 973151380289763769238966237755432094392232133691333861_<54>

Number: 49997_106
N=49999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997
  ( 107 digits)
SNFS difficulty: 106 digits.
Divisors found:
 r1=51379467791652406382241099912651400334898984400190777 (pp53)
 r2=973151380289763769238966237755432094392232133691333861 (pp54)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.45 hours.
Scaled time: 0.96 units (timescale=2.145).
Factorization parameters were as follows:
n: 49999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997
m: 1000000000000000000000
c5: 50
c0: -3
skew: 0.57
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 260001)
Primes: RFBsize:30757, AFBsize:30789, largePrimes:1045486 encountered
Relations: rels:987914, finalFF:108071
Max relations in full relation-set: 28
Initial matrix: 61611 x 108071 with sparse part having weight 4604823.
Pruned matrix : 46229 x 46601 with weight 1394879.
Total sieving time: 0.43 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,106,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.45 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹¹³-3 = 4(9)₁₁₂7_<114> = C114

C114 = P48 · P66

P48 = 907436158859512909422687304965377963070381712507_<48>

P66 = 551002949483974443730009627016215019549109574303626681725606916071_<66>

Number: 49997_113
N=499999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997
  ( 114 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=907436158859512909422687304965377963070381712507 (pp48)
 r2=551002949483974443730009627016215019549109574303626681725606916071 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.63 hours.
Scaled time: 1.34 units (timescale=2.143).
Factorization parameters were as follows:
n: 499999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997
m: 100000000000000000000000
c5: 1
c0: -60
skew: 2.27
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 320001)
Primes: RFBsize:30757, AFBsize:30699, largePrimes:1057310 encountered
Relations: rels:986957, finalFF:96871
Max relations in full relation-set: 28
Initial matrix: 61520 x 96871 with sparse part having weight 4430990.
Pruned matrix : 51748 x 52119 with weight 1665807.
Total sieving time: 0.60 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.63 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹²³-3 = 4(9)₁₂₂7_<124> = C124

C124 = P59 · P66

P59 = 41339256942088911622012358254358042113678371404430757997789_<59>

P66 = 120950408155723983526356287938613353278226690610618708055828192673_<66>

Number: 49997_123
N=4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997
  ( 124 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=41339256942088911622012358254358042113678371404430757997789 (pp59)
 r2=120950408155723983526356287938613353278226690610618708055828192673 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.04 hours.
Scaled time: 2.23 units (timescale=2.145).
Factorization parameters were as follows:
n: 4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997
m: 10000000000000000000000000
c5: 1
c0: -60
skew: 2.27
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 480001)
Primes: RFBsize:49098, AFBsize:48986, largePrimes:1922284 encountered
Relations: rels:1871231, finalFF:110151
Max relations in full relation-set: 28
Initial matrix: 98148 x 110151 with sparse part having weight 9092255.
Pruned matrix : 94832 x 95386 with weight 6810840.
Total sieving time: 0.97 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 1.04 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10¹¹⁸-3 = 4(9)₁₁₇7_<119> = 2887441 · C113

C113 = P56 · P57

P56 = 63010830359033312483466077306764627266644155646127728707_<56>

P57 = 274815790254415776711435696262112720520718579760139674831_<57>

Number: 49997_118
N=17316371139704672753486564747123837335550752379009649028326466237751697783608392344640115590240631756631564073517
  ( 113 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=63010830359033312483466077306764627266644155646127728707 (pp56)
 r2=274815790254415776711435696262112720520718579760139674831 (pp57)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.78 hours.
Scaled time: 1.68 units (timescale=2.145).
Factorization parameters were as follows:
n: 17316371139704672753486564747123837335550752379009649028326466237751697783608392344640115590240631756631564073517
m: 1000000000000000000000000
c5: 1
c0: -60
skew: 2.27
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 420001)
Primes: RFBsize:49098, AFBsize:48986, largePrimes:1903519 encountered
Relations: rels:1888791, finalFF:147578
Max relations in full relation-set: 28
Initial matrix: 98148 x 147578 with sparse part having weight 11914433.
Pruned matrix : 85032 x 85586 with weight 4763073.
Total sieving time: 0.73 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 0.78 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Total of 4 processors activated (19246.09 BogoMIPS).

Jul 5, 2007

The factor table of 499...997 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Jul 2, 2007 (2nd)

By Torbjörn Granlund

10⁷⁹⁹+1 is divisible by 84381206263904600374587469219832511232219_<41>

10⁸⁹¹+1 is divisible by 22663213771462227811088536403512441819_<38>

10⁹⁴⁴+1 is divisible by 4859846047732923587514032493793_<31>

(10⁸¹⁵-1)/9 is divisible by 3664950640511701126041972679226717351_<37>

Reference: Factoring and Prime Identification (Torbjörn Granlund)

Jul 2, 2007

By suberi / GMP-ECM 6.1.2 B1=11000000

4·10¹⁹⁵-3 = 3(9)₁₉₄7_<196> = 7 · 101197 · C190

C190 = P37 · P154

P37 = 3771194733060677910727165656242155763_<37>

P154 = 1497322513815848534027864445072580097326790638319429568818602330439582708603315019200778229678277949703995368212735241456117614079298626340503579378845661_<154>

Jul 1, 2007

By Torbjörn Granlund

(10⁵⁰⁷-1)/9 is divisible by 82638297310634344310411757401076652003_<38>

10⁶⁸⁰+1 is divisible by 1516395051122929541850783680941040161_<37>

10⁶⁹¹+1 is divisible by 26578194229497643738821679856668807_<35>

10⁷⁵⁹+1 is divisible by 2832165561296805799533565929552471103_<37>

By Yousuke Koide

10¹²³³+1 is divisible by 14881155992657195128437244984378939_<35>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

June 2007

Jun 30, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

9·10¹⁶²+1 = 9(0)₁₆₁1_<163> = 17 · 233 · 5693 · 199673 · 3207278521_<10> · 118788802665563673626749_<24> · C118

C118 = P51 · P68

P51 = 152599297155465124131657187052166911440245078117469_<51>

P68 = 34380518818628962059427663768446076926280486458367419362075072569669_<68>

Number: 90001_162
N=5246443007563021739957261207032237060105169135561012564450700562709375031236031853655679900656876972792186038868447761
  ( 118 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=152599297155465124131657187052166911440245078117469 (pp51)
 r2=34380518818628962059427663768446076926280486458367419362075072569669 (pp68)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 87.52 hours.
Scaled time: 59.60 units (timescale=0.681).
Factorization parameters were as follows:
name: 90001_162
n: 5246443007563021739957261207032237060105169135561012564450700562709375031236031853655679900656876972792186038868447761
m: 100000000000000000000000000000000
c5: 900
c0: 1
skew: 0.26
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4350001)
Primes: RFBsize:315948, AFBsize:315061, largePrimes:5796639 encountered
Relations: rels:5953554, finalFF:716636
Max relations in full relation-set: 0
Initial matrix: 631072 x 716636 with sparse part having weight 34710609.
Pruned matrix : 561549 x 564768 with weight 26227273.
Total sieving time: 75.30 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 11.66 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 87.52 hours.
 --------- CPU info (if available) ----------

Jun 29, 2007

100...001 was updated.

Reference: Factorizations of numbers of the form 10^n+1 (Alfred Reich)

Jun 27, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(46·10¹⁶⁴-1)/9 = 5(1)₁₆₄_<165> = 7 · 149 · C162

C162 = P65 · P97

P65 = 92242528670324886100687746039495178044373011581100025580286480497_<65>

P97 = 5312510652925782344961262133689200030431493691271417414388712363170017984463868615627801357604941_<97>

Number: n
N=490039416213912858208160221583040374986683711515926281026952167891765207201448812187067220624267604133375945456482369234047086396079684670288697134334718227335677
  ( 162 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=92242528670324886100687746039495178044373011581100025580286480497 (pp65)
 r2=5312510652925782344961262133689200030431493691271417414388712363170017984463868615627801357604941 (pp97)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 58.95 hours.
Scaled time: 85.31 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_5_1_164
n: 490039416213912858208160221583040374986683711515926281026952167891765207201448812187067220624267604133375945456482369234047086396079684670288697134334718227335677
skew: 0.74
deg: 5
c5: 23
c0: -5
m: 1000000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2600001)
Primes: RFBsize:315948, AFBsize:316461, largePrimes:6886645 encountered
Relations: rels:6655180, finalFF:711185
Max relations in full relation-set: 28
Initial matrix: 632474 x 711185 with sparse part having weight 40763719.
Pruned matrix : 559689 x 562915 with weight 26736168.
Total sieving time: 51.88 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 6.55 hours.
Total square root time: 0.26 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000
total time: 58.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jun 26, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp

(4·10¹⁶⁴-13)/9 = (4)₁₆₃3_<164> = 367 · C162

C162 = P79 · P84

P79 = 1024998888971229736671457541060040483691797694445518916330624823174235310567513_<79>

P84 = 118148448512489899718403228417122472387954784945079796830310415633311893761115829533_<84>

Number: n
N=121102028458976687859521646987587042082954889494399031183772328186497123826824099303663336360884044807750529821374508023009385407205570693309112927641537995761429
  ( 162 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=1024998888971229736671457541060040483691797694445518916330624823174235310567513 (pp79)
 r2=118148448512489899718403228417122472387954784945079796830310415633311893761115829533 (pp84)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 72.53 hours.
Scaled time: 98.93 units (timescale=1.364).
Factorization parameters were as follows:
name: KA_4_163_3
n: 121102028458976687859521646987587042082954889494399031183772328186497123826824099303663336360884044807750529821374508023009385407205570693309112927641537995761429
skew: 2.01
deg: 5
c5: 2
c0: -65
m: 1000000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2900001)
Primes: RFBsize:315948, AFBsize:315216, largePrimes:6629143 encountered
Relations: rels:6530594, finalFF:741465
Max relations in full relation-set: 28
Initial matrix: 631229 x 741465 with sparse part having weight 44081270.
Pruned matrix : 534485 x 537705 with weight 27414349.
Total sieving time: 66.44 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 5.63 hours.
Total square root time: 0.15 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000
total time: 72.53 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jun 26, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

(73·10¹⁵⁷-1)/9 = 8(1)₁₅₇_<158> = 3 · 557 · 12503 · 21121 · 198623 · 24027128221834955244829_<23> · C119

C119 = P48 · P71

P48 = 709366404715725202134278510977230883791091516457_<48>

P71 = 54296667246476640184537223444832866376469118179207748377776959859458053_<71>

Number: 81111_157
N=38516231632679209057909219312447870443031509684067141874491405901558633307604267425485343175874835928384687741950678221
  ( 119 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=709366404715725202134278510977230883791091516457 (pp48)
 r2=54296667246476640184537223444832866376469118179207748377776959859458053 (pp71)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 81.74 hours.
Scaled time: 55.66 units (timescale=0.681).
Factorization parameters were as follows:
name: 81111_157
n: 38516231632679209057909219312447870443031509684067141874491405901558633307604267425485343175874835928384687741950678221
m: 10000000000000000000000000000000
c5: 7300
c0: -1
skew: 0.17
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4000001)
Primes: RFBsize:283146, AFBsize:284167, largePrimes:5778061 encountered
Relations: rels:5850073, finalFF:638910
Max relations in full relation-set: 0
Initial matrix: 567380 x 638910 with sparse part having weight 36945897.
Pruned matrix : 516655 x 519555 with weight 28801074.
Total sieving time: 70.46 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 10.71 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 81.74 hours.
 --------- CPU info (if available) ----------

Jun 25, 2007 (2nd)

By Alfred Reich / GMP-ECM / Jun 24, 2007

10¹⁵⁰⁶+1 is divisible by 104384225205357273799356477841_<30>

Reference: Factorizations of numbers of the form 10^n+1 (Alfred Reich)

Jun 25, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(5·10¹⁷³-41)/9 = (5)₁₇₂1_<173> = 3 · 179 · C171

C171 = P42 · P129

P42 = 114384483875150871829057541898587264239841_<42>

P129 = 904453184672326204317688425492042339266607258173108466450183893916706681010256982023307530563855324688384934286035740785881630103_<129>

Number: n
N=103455410717980550382785019656528036416304572729153734740326919097868818539209600662114628595075522449824125801779433064349265466583902338092282226360438650941444237533623
  ( 171 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=114384483875150871829057541898587264239841 (pp42)
 r2=904453184672326204317688425492042339266607258173108466450183893916706681010256982023307530563855324688384934286035740785881630103 (pp129)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 204.90 hours.
Scaled time: 268.42 units (timescale=1.310).
Factorization parameters were as follows:
name: KA_5_172_1
n: 103455410717980550382785019656528036416304572729153734740326919097868818539209600662114628595075522449824125801779433064349265466583902338092282226360438650941444237533623
skew: 1.91
deg: 5
c5: 8
c0: -205
m: 50000000000000000000000000000000000
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 8100001)
Primes: RFBsize:348513, AFBsize:348437, largePrimes:8931314 encountered
Relations: rels:8460683, finalFF:782229
Max relations in full relation-set: 48
Initial matrix: 697015 x 782229 with sparse part having weight 77788583.
Pruned matrix : 641763 x 645312 with weight 59397651.
Total sieving time: 185.11 hours.
Total relation processing time: 0.60 hours.
Matrix solve time: 19.04 hours.
Total square root time: 0.14 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,174,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000
total time: 204.90 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jun 24, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(8·10¹⁶⁴+1)/9 = (8)₁₆₃9_<164> = 881 · C162

C162 = P57 · P105

P57 = 438099651139842378074782985862900871663962476527603599689_<57>

P105 = 230302504990454513418307626464605022752045200943246897387527811045552664240151617880164349500151770360321_<105>

Number: n
N=100895447092949930634380123596922688863665027115651406230293857989658216672972632109976037331315424391474334720645730861394879556060032791020305208727456173540169
  ( 162 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=438099651139842378074782985862900871663962476527603599689 (pp57)
 r2=230302504990454513418307626464605022752045200943246897387527811045552664240151617880164349500151770360321 (pp105)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 45.31 hours.
Scaled time: 65.87 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_8_163_9
n: 100895447092949930634380123596922688863665027115651406230293857989658216672972632109976037331315424391474334720645730861394879556060032791020305208727456173540169
skew: 1.05
deg: 5
c5: 4
c0: 5
m: 1000000000000000000000000000000000
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2000001)
Primes: RFBsize:283146, AFBsize:283197, largePrimes:5489253 encountered
Relations: rels:5506229, finalFF:648965
Max relations in full relation-set: 28
Initial matrix: 566407 x 648965 with sparse part having weight 37677844.
Pruned matrix : 491814 x 494710 with weight 23543322.
Total sieving time: 39.96 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 5.09 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.5,2.5,100000
total time: 45.31 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jun 24, 2007 (2nd)

By JMB / GMP-ECM 6.0.1 B1=1000000

(7·10¹⁵⁹-61)/9 = (7)₁₅₈1_<159> = 3³ · 43 · 263 · 349831 · 17126917 · C141

C141 = P35 · C107

P35 = 28619057539265783684510425072387757_<35>

C107 = [14855071619085049328530992857412182242694733285669768452444236785568599716426578493792762350613756076351523_<107>]

Jun 24, 2007

11...11 (Repunit) and 100...001 were updated.

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Reference: Factorizations of numbers of the form 10^n+1 (Alfred Reich)

Jun 23, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp

(16·10¹⁶³-61)/9 = 1(7)₁₆₂1_<164> = 11 · 347 · C160

C160 = P42 · P48 · P71

P42 = 646634560597002933420775479995833343960443_<42>

P48 = 398763057690552657144449211172587774514959984401_<48>

P71 = 18062650687187667320018671801554696018440996733928315494676273037001241_<71>

Number: n
N=4657526271359124385060984484615608534916892265595435624254068058102640235205076703635781445579716473088231013303059412569499024830436934183331877856373533606963
  ( 160 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=646634560597002933420775479995833343960443 (pp42)
 r2=398763057690552657144449211172587774514959984401 (pp48)
 r3=18062650687187667320018671801554696018440996733928315494676273037001241 (pp71)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 57.05 hours.
Scaled time: 77.82 units (timescale=1.364).
Factorization parameters were as follows:
name: KA_1_7_162_1
n: 4657526271359124385060984484615608534916892265595435624254068058102640235205076703635781445579716473088231013303059412569499024830436934183331877856373533606963
skew: 0.66
deg: 5
c5: 500
c0: -61
m: 200000000000000000000000000000000
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2300001)
Primes: RFBsize:283146, AFBsize:283473, largePrimes:5594710 encountered
Relations: rels:5651279, finalFF:678375
Max relations in full relation-set: 28
Initial matrix: 566685 x 678375 with sparse part having weight 40831702.
Pruned matrix : 469314 x 472211 with weight 24216609.
Total sieving time: 52.65 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.92 hours.
Total square root time: 0.26 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.5,2.5,100000
total time: 57.05 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jun 22, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(25·10¹⁶³-7)/9 = 2(7)₁₆₃_<164> = 3³ · 53 · C161

C161 = P52 · P109

P52 = 5784099087847801999595098935811677620966410670797411_<52>

P109 = 3356001460754311479240774153689287838703249898666255530643269682857515657144061974783366037668112153528135197_<109>

Number: n
N=19411444987964904107461759453373709138908300333876853792996350648342262598027797189222765742681885239537231151486916686078111654631570774128426120040375805574967
  ( 161 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=5784099087847801999595098935811677620966410670797411 (pp52)
 r2=3356001460754311479240774153689287838703249898666255530643269682857515657144061974783366037668112153528135197 (pp109)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 55.82 hours.
Scaled time: 81.11 units (timescale=1.453).
Factorization parameters were as follows:
name: KA_2_7_163
n: 19411444987964904107461759453373709138908300333876853792996350648342262598027797189222765742681885239537231151486916686078111654631570774128426120040375805574967
skew: 0.97
deg: 5
c5: 8
c0: -7
m: 500000000000000000000000000000000
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2100001)
Primes: RFBsize:283146, AFBsize:282602, largePrimes:5499517 encountered
Relations: rels:5503640, finalFF:637582
Max relations in full relation-set: 28
Initial matrix: 565813 x 637582 with sparse part having weight 38094152.
Pruned matrix : 501050 x 503943 with weight 25009807.
Total sieving time: 41.68 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 13.81 hours.
Total square root time: 0.14 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.5,2.5,100000
total time: 55.82 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jun 21, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon

(55·10¹⁶³-1)/9 = 6(1)₁₆₃_<164> = 503 · C162

C162 = P43 · P44 · P76

P43 = 1487407993549019848776612935809194872068909_<43>

P44 = 11413058107787456233245536501918521595780953_<44>

P76 = 7156819357030125486732946829220674112434544047932731153794325074222174276381_<76>

Number: n
N=121493262646344157278550916721890876960459465429644356085707974375966423680141373978352109564833222884912745747735807377954495250717914733819306383918709962447537
  ( 162 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=1487407993549019848776612935809194872068909 (pp43)
 r2=11413058107787456233245536501918521595780953 (pp44)
 r3=7156819357030125486732946829220674112434544047932731153794325074222174276381 (pp76)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 63.80 hours.
Scaled time: 87.34 units (timescale=1.369).
Factorization parameters were as follows:
name: KA_6_1_163
n: 121493262646344157278550916721890876960459465429644356085707974375966423680141373978352109564833222884912745747735807377954495250717914733819306383918709962447537
skew: 0.56
deg: 5
c5: 88
c0: -5
m: 500000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2600001)
Primes: RFBsize:250150, AFBsize:250657, largePrimes:7570457 encountered
Relations: rels:7122095, finalFF:594860
Max relations in full relation-set: 28
Initial matrix: 500873 x 594860 with sparse part having weight 44530909.
Pruned matrix : 429195 x 431763 with weight 29739754.
Total sieving time: 58.27 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 4.83 hours.
Total square root time: 0.42 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 63.80 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(16·10¹⁷³-1)/3 = 5(3)₁₇₃_<174> = 67 · C172

C172 = P68 · P104

P68 = 96371276020696526133446288272274025697919084102770639532241766004453_<68>

P104 = 82599290303737453966408350950661246292450859283670030355136080034796461939594945728788702602573657900283_<104>

Number: n
N=7960199004975124378109452736318407960199004975124378109452736318407960199004975124378109452736318407960199004975124378109452736318407960199004975124378109452736318407960199
  ( 172 digits)
SNFS difficulty: 174 digits.
Divisors found:
 r1=96371276020696526133446288272274025697919084102770639532241766004453 (pp68)
 r2=82599290303737453966408350950661246292450859283670030355136080034796461939594945728788702602573657900283 (pp104)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 172.53 hours.
Scaled time: 206.34 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_5_3_173
n: 7960199004975124378109452736318407960199004975124378109452736318407960199004975124378109452736318407960199004975124378109452736318407960199004975124378109452736318407960199
type: snfs
skew: 0.29
deg: 5
c5: 500
c0: -1
m: 20000000000000000000000000000000000
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 6100001)
Primes: RFBsize:348513, AFBsize:348381, largePrimes:8606327 encountered
Relations: rels:8178018, finalFF:784475
Max relations in full relation-set: 28
Initial matrix: 696960 x 784475 with sparse part having weight 56036078.
Pruned matrix : 632811 x 636359 with weight 42788642.
Total sieving time: 158.37 hours.
Total relation processing time: 0.66 hours.
Matrix solve time: 13.29 hours.
Total square root time: 0.20 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,174,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.6,2.6,100000
total time: 172.53 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Jun 21, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

(8·10¹⁵⁷-53)/9 = (8)₁₅₆3_<157> = 3² · 99259 · 298883603 · 412769895811232603033399_<24> · C119

C119 = P41 · P78

P41 = 91704661940135167282070266149538417976081_<41>

P78 = 879495360224213103544482307466419072309436217083572482010934548798414923507149_<78>

Number: 88883_157
N=80653824687278864260499882306813850511268547403444054213087351371389500573348614528160269592553396427774786594914503069
  ( 119 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=91704661940135167282070266149538417976081 (pp41)
 r2=879495360224213103544482307466419072309436217083572482010934548798414923507149 (pp78)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 62.70 hours.
Scaled time: 42.70 units (timescale=0.681).
Factorization parameters were as follows:
name: 88883_157
n: 80653824687278864260499882306813850511268547403444054213087351371389500573348614528160269592553396427774786594914503069
m: 20000000000000000000000000000000
c5: 25
c0: -53
skew: 1.16
type: snfs
 Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3000001)
Primes: RFBsize:216816, AFBsize:217081, largePrimes:5636168 encountered
Relations: rels:5570899, finalFF:488151
Max relations in full relation-set: 0
Initial matrix: 433961 x 488151 with sparse part having weight 34548626.
Pruned matrix : 409449 x 411682 with weight 26681522.
Total sieving time: 55.38 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 6.84 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 62.70 hours.
 --------- CPU info (if available) ----------

Jun 20, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=203500, B1=1024000

(14·10¹⁶²-41)/9 = 1(5)₁₆₁1_<163> = 3 · 214219 · 10324063 · C150

C150 = P36 · P41 · P74

P36 = 110021344519261749564662722162683047_<36>

P41 = 34504949858484862052592280714802542174189_<41>

P74 = 61758578210491351731564901830521726152917416595997540856609496672738529267_<74>

Jun 19, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(34·10¹⁶⁰-7)/9 = 3(7)₁₆₀_<161> = 37 · 739 · 1061 · 6359 · C150

C150 = P40 · P111

P40 = 1122510875599841509819333162942527354919_<40>

P111 = 182429672649887044863888718305726909178631224196066040957083526804690245217425139299330145938851723157067710419_<111>

Number: n
N=204779291581617165659482935465497566962336896463508396519683855623161916137193553474407168443864391313760716948157646481601056640075903959403527201061
  ( 150 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=1122510875599841509819333162942527354919 (pp40)
 r2=182429672649887044863888718305726909178631224196066040957083526804690245217425139299330145938851723157067710419 (pp111)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 40.46 hours.
Scaled time: 58.47 units (timescale=1.445).
Factorization parameters were as follows:
name: KA_3_7_160
n: 204779291581617165659482935465497566962336896463508396519683855623161916137193553474407168443864391313760716948157646481601056640075903959403527201061
skew: 0.73
deg: 5
c5: 34
c0: -7
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1800001)
Primes: RFBsize:250150, AFBsize:249466, largePrimes:7231529 encountered
Relations: rels:6757696, finalFF:567845
Max relations in full relation-set: 28
Initial matrix: 499682 x 567845 with sparse part having weight 37971589.
Pruned matrix : 441964 x 444526 with weight 24954498.
Total sieving time: 35.43 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 4.60 hours.
Total square root time: 0.22 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 40.46 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jun 18, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp

(17·10¹⁶²-71)/9 = 1(8)₁₆₁1_<163> = 3 · 1439 · C159

C159 = P70 · P90

P70 = 2583124372509618337040968830299059261714173907429069612978604367206603_<70>

P90 = 169386598202867977225527166176651263517709056741805060006511940185061380465616968087449231_<90>

Number: n
N=437546650194322188762772501479937199186677991403495225593905232543175559158880910097032404190152626566803078269374308290222119270069235322883689805163050472293
  ( 159 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=2583124372509618337040968830299059261714173907429069612978604367206603 (pp70)
 r2=169386598202867977225527166176651263517709056741805060006511940185061380465616968087449231 (pp90)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 57.94 hours.
Scaled time: 78.51 units (timescale=1.355).
Factorization parameters were as follows:
name: KA_1_8_161_1
n: 437546650194322188762772501479937199186677991403495225593905232543175559158880910097032404190152626566803078269374308290222119270069235322883689805163050472293
skew: 0.53
deg: 5
c5: 1700
c0: -71
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2400001)
Primes: RFBsize:250150, AFBsize:250202, largePrimes:7459585 encountered
Relations: rels:6986844, finalFF:572535
Max relations in full relation-set: 28
Initial matrix: 500419 x 572535 with sparse part having weight 41248883.
Pruned matrix : 442792 x 445358 with weight 28101844.
Total sieving time: 52.51 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 4.81 hours.
Total square root time: 0.34 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 57.94 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jun 17, 2007 (3rd)

By suberi / GMP-ECM 6.1.2 B1=11000000

4·10¹⁶⁶-3 = 3(9)₁₆₅7_<167> = 37 · 109 · 467 · 21467 · C156

C156 = P35 · P122

P35 = 10558902718487179894422921589845289_<35>

P122 = 93696796766281288719136025075673968299994681684211285870697078809182558148593470010534568057803410687480015936158750023029_<122>

Jun 17, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(83·10¹⁶¹+61)/9 = 9(2)₁₆₀9_<162> = 7 · 11 · 12377 · 19541 · C152

C152 = P55 · P98

P55 = 1253925579802704887847319737479996409450417957300062431_<55>

P98 = 39492162932172239037026100445899515906877612660361618281345600460588359473016205661201392275400531_<98>

Number: n
N=49520233302386964779546750368695160262255294423154139840175164473697688657347976477513615143791891804577561756279764230158227764030719676476471830550861
  ( 152 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=1253925579802704887847319737479996409450417957300062431 (pp55)
 r2=39492162932172239037026100445899515906877612660361618281345600460588359473016205661201392275400531 (pp98)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 65.76 hours.
Scaled time: 95.42 units (timescale=1.451).
Factorization parameters were as follows:
name: KA_9_2_160_9
n: 49520233302386964779546750368695160262255294423154139840175164473697688657347976477513615143791891804577561756279764230158227764030719676476471830550861
skew: 0.59
deg: 5
c5: 830
c0: 61
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2900001)
Primes: RFBsize:250150, AFBsize:249517, largePrimes:7668454 encountered
Relations: rels:7187894, finalFF:565601
Max relations in full relation-set: 28
Initial matrix: 499734 x 565601 with sparse part having weight 45402229.
Pruned matrix : 454050 x 456612 with weight 33560178.
Total sieving time: 58.49 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 6.82 hours.
Total square root time: 0.19 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 65.76 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jun 17, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060513-k8

4·10¹⁸⁰+3 = 4(0)₁₇₉3_<181> = 7 · C180

C180 = P86 · P94

P86 = 83826283922298951250679670902394172492665030066721447476491438645405060824416416839171_<86>

P94 = 6816818600216674079721080459803918316770769056707557617751767138646831184079876164364702748599_<94>

Number: 40003_180
N=571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429
  ( 180 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=83826283922298951250679670902394172492665030066721447476491438645405060824416416839171 (pp86)
 r2=6816818600216674079721080459803918316770769056707557617751767138646831184079876164364702748599 (pp94)
Version: GGNFS-0.77.1-20060513-k8
Total time: 402.02 hours.
Scaled time: 805.24 units (timescale=2.003).
Factorization parameters were as follows:
name: 40003_180
n: 571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429
m: 1000000000000000000000000000000000000
c5: 4
c0: 3
skew: 1
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 8200001)
Primes: RFBsize:501962, AFBsize:502056, largePrimes:6501623 encountered
Relations: rels:7055323, finalFF:1224296
Max relations in full relation-set: 28
Initial matrix: 1004085 x 1224296 with sparse part having weight 64791188.
Pruned matrix : 810729 x 815813 with weight 46491843.
Total sieving time: 393.70 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 7.71 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 402.02 hours.
 --------- CPU info (if available) ----------

P86 is the largest factor found by GGNFS so far in our tables. Congratulations!

Jun 16, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GMP-ECM 5.0 B1=555500, GGNFS-0.77.1-20051202-athlon

(64·10¹⁶¹-1)/9 = 7(1)₁₆₁_<162>= 3 · 7001 · 16644197 · C151

C151 = P60 · P91

P60 = 242234408783777373086114783431817508160131008952509616569639_<60>

P91 = 8397643833649287842181389119448886552064945552482189671050550356474674679669138218340127239_<91>

Number: n
N=2034198289220768944122855330305356229027758545561694863312919801308175051845084868498046294285027792142932415919483934510480134883453891368081964296721
  ( 151 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=242234408783777373086114783431817508160131008952509616569639 (pp60)
 r2=8397643833649287842181389119448886552064945552482189671050550356474674679669138218340127239 (pp91)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 38.61 hours.
Scaled time: 52.75 units (timescale=1.366).
Factorization parameters were as follows:
name: KA_7_1_161
n: 2034198289220768944122855330305356229027758545561694863312919801308175051845084868498046294285027792142932415919483934510480134883453891368081964296721
skew: 0.55
deg: 5
c5: 20
c0: -1
m: 200000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:250150, AFBsize:249621, largePrimes:7178047 encountered
Relations: rels:6706081, finalFF:569137
Max relations in full relation-set: 28
Initial matrix: 499837 x 569137 with sparse part having weight 35817686.
Pruned matrix : 439711 x 442274 with weight 23181566.
Total sieving time: 34.90 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.38 hours.
Total square root time: 0.12 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 38.61 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(4·10¹⁷¹-7)/3 = 1(3)₁₇₀1_<172> = 11 · 509 · C168

C168 = P31 · P62 · P76

P31 = 1579581662729255260822279089299_<31>

P62 = 15140952069917912762805059248526017411056580054721603176641137_<62>

P76 = 9957103032241894992392055264616753554079600537545293015777629476295758102863_<76>

Number: n
N=150760019766408845647399019187174726946819254572510064535376429497480082829008432013771344824709618636211004729226783886499508955683275231
  ( 138 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=15140952069917912762805059248526017411056580054721603176641137 (pp62)
 r2=9957103032241894992392055264616753554079600537545293015777629476295758102863 (pp76)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 92.21 hours.
Scaled time: 122.09 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_1_3_170_1

n: 150760019766408845647399019187174726946819254572510064535376429497480082829008432013771344824709618636211004729226783886499508955683275231

# n: 238137762695719473715544442459963088646782163481574090611418705721259748764660356015955230100613204738941477644817526939334404953265464070965053283324403167232243853069

skew: 0.71
deg: 5
c5: 40
c0: -7
m: 10000000000000000000000000000000000
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3700001)
Primes: RFBsize:348513, AFBsize:348246, largePrimes:8112542 encountered
Relations: rels:7771094, finalFF:817458
Max relations in full relation-set: 48
Initial matrix: 696825 x 817458 with sparse part having weight 48005762.
Pruned matrix : 589738 x 593286 with weight 30161766.
Total sieving time: 83.41 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 8.15 hours.
Total square root time: 0.31 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000
total time: 92.21 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jun 14, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

(4·10¹⁷⁷+41)/9 = (4)₁₇₆9_<177> = C177

C177 = P42 · P136

P42 = 168147754451668131804909254590792523405537_<42>

P136 = 2643177994816423045994801272196432548527495305343780758343199586659007613587966246673472391393843105829320609766702837229594492464461377_<136>

Number: 44449_177
N=444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449
  ( 177 digits)
SNFS difficulty: 177 digits.
Divisors found:
 r1=168147754451668131804909254590792523405537 (pp42)
 r2=2643177994816423045994801272196432548527495305343780758343199586659007613587966246673472391393843105829320609766702837229594492464461377 (pp136)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 183.14 hours.
Scaled time: 391.19 units (timescale=2.136).
Factorization parameters were as follows:
n: 444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449
m: 200000000000000000000000000000000000
c5: 25
c0: 82
skew: 1.27
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [5000000, 7900001)
Primes: RFBsize:664579, AFBsize:665706, largePrimes:10888385 encountered
Relations: rels:11167090, finalFF:1501554
Max relations in full relation-set: 28
Initial matrix: 1330349 x 1501554 with sparse part having weight 84723705.
Pruned matrix : 1171071 x 1177786 with weight 56372503.
Total sieving time: 173.41 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 9.37 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,177,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000
total time: 183.14 hours.
 --------- CPU info (if available) ----------

Jun 14, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=235000, GGNFS-0.77.1-20051202-athlon, GMP-ECM 5.0 B1=148000, GGNFS-0.77.1-20060513-athlon-xp

8·10¹⁷³-3 = 7(9)₁₇₂7_<174> = 11 · 17 · C172

C172 = P32 · P141

P32 = 16714781670858896574412244553011_<32>

P141 = 255945602554216888346456751285955406140848117378586326431440585310105420050084687172161632857854573720137957976799629434184623898942614879421_<141>

(5·10¹⁶⁰-41)/9 = (5)₁₅₉1_<160> = 7 · 13 · 38339629 · C151

C151 = P59 · P92

P59 = 93930422496056102672951745999929180207457761507108874860957_<59>

P92 = 16952428477316522540754897578493590824200183248034476666556039573794818514422723747420375637_<92>

Number: n
N=1592348769208513991125215662625766411590734512586468952556897748021011107359699830430311416447197781962393273577322854377674078720220820343907085304609
  ( 151 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=93930422496056102672951745999929180207457761507108874860957 (pp59)
 r2=16952428477316522540754897578493590824200183248034476666556039573794818514422723747420375637 (pp92)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 34.68 hours.
Scaled time: 50.01 units (timescale=1.442).
Factorization parameters were as follows:
name: KA_5_159_1
n: 1592348769208513991125215662625766411590734512586468952556897748021011107359699830430311416447197781962393273577322854377674078720220820343907085304609
skew: 1.52
deg: 5
c5: 5
c0: -41
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1600001)
Primes: RFBsize:250150, AFBsize:250147, largePrimes:7174417 encountered
Relations: rels:6714797, finalFF:578820
Max relations in full relation-set: 28
Initial matrix: 500362 x 578820 with sparse part having weight 36630150.
Pruned matrix : 431983 x 434548 with weight 22708070.
Total sieving time: 30.10 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 4.13 hours.
Total square root time: 0.14 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 34.68 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(16·10¹⁶¹-1)/3 = 5(3)₁₆₁_<162> = 371464902031_<12> · C151

C151 = P38 · P53 · P61

P38 = 21296628673706037218941669897405375529_<38>

P53 = 18789442466366541078334745181943959375398817645988163_<53>

P61 = 3588031028791720530702891116571104480395193265875079747911009_<61>

Number: n
N=67417102583019983171184801555027292869246270062017192633036181651915613927135668150787776143695353707888791386467
  ( 113 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=18789442466366541078334745181943959375398817645988163 (pp53)
 r2=3588031028791720530702891116571104480395193265875079747911009 (pp61)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 35.56 hours.
Scaled time: 48.54 units (timescale=1.365).
Factorization parameters were as follows:
name: KA_5_3_161

n: 67417102583019983171184801555027292869246270062017192633036181651915613927135668150787776143695353707888791386467

# n: 1435756999967724720152252411207919472795542416216408834314647200422664077480544169773101373842224239920853631269279030738644813825332397365358703566043

skew: 0.72
deg: 5
c5: 5
c0: -1
m: 200000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:250150, AFBsize:249616, largePrimes:7109746 encountered
Relations: rels:6650928, finalFF:579476
Max relations in full relation-set: 28
Initial matrix: 499831 x 579476 with sparse part having weight 35607840.
Pruned matrix : 430167 x 432730 with weight 21710821.
Total sieving time: 31.47 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 3.37 hours.
Total square root time: 0.34 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 35.56 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jun 13, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=11000000

4·10¹⁷⁹-3 = 3(9)₁₇₈7_<180> = 13 · 751609465955754276518902944827_<30> · C149

C149 = P31 · P118

P31 = 5440737829768967253704195829959_<31>

P118 = 7524308589497537700550163236387070963072198888286762101154838011070880004644191216696466958842086243668442125836776933_<118>

Jun 13, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(25·10¹⁷¹-1)/3 = 8(3)₁₇₁_<172> = 13 · 479 · C169

C169 = P68 · P101

P68 = 29118448070168224831416797259913943918883957045985714959238024271677_<68>

P101 = 45959115678209855991045867600068525726469370895875466784175162434036104055601120929335967260638369027_<101>

Number: n
N=1338258123226807986724479417590064771693164177506557464803811359134949949146191317381296504469782131577538675659761254750816337455168352871901932444729939510732830148279
  ( 169 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=29118448070168224831416797259913943918883957045985714959238024271677 (pp68)
 r2=45959115678209855991045867600068525726469370895875466784175162434036104055601120929335967260638369027 (pp101)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 134.87 hours.
Scaled time: 158.06 units (timescale=1.172).
Factorization parameters were as follows:
name: KA_8_3_171
n: 1338258123226807986724479417590064771693164177506557464803811359134949949146191317381296504469782131577538675659761254750816337455168352871901932444729939510732830148279
type: snfs
skew: 0.33
deg: 5
c5: 250
c0: -1
m: 10000000000000000000000000000000000
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4800000)
Primes: RFBsize:348513, AFBsize:348111, largePrimes:8295364 encountered
Relations: rels:7898851, finalFF:788404
Max relations in full relation-set: 28
Initial matrix: 696690 x 788404 with sparse part having weight 47562588.
Pruned matrix : 621809 x 625356 with weight 34416063.
Total sieving time: 122.44 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 10.69 hours.
Total square root time: 1.30 hours, sqrts: 7.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.6,2.6,100000
total time: 134.87 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Jun 12, 2007 (2nd)

By honeycrack7 / GGNFS-0.77.1-20060513-pentium4

2·10¹⁶⁶+3 = 2(0)₁₆₅3_<167> = 79 · 729941 · 1137496712761_<13> · 3151934443985899535720514258097_<31> · C116

C116 = P38 · P39 · P41

P38 = 29139773847805639821445881025078673003_<38>

P39 = 245334893549794309989767836564265608087_<39>

P41 = 13531387192579406360450949532177073435621_<41>

Number: 20003_166
N=96735931896521673246753209867323320086123873399038844839615081198086925909914926262118324884197380820104433849572081
  ( 116 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=29139773847805639821445881025078673003 (pp38)
 r2=245334893549794309989767836564265608087 (pp39)
 r3=13531387192579406360450949532177073435621 (pp41)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 149.93 hours.
Scaled time: 223.25 units (timescale=1.489).
Factorization parameters were as follows:
n: 96735931896521673246753209867323320086123873399038844839615081198086925909914926262118324884197380820104433849572081
m: 1000000000000000000000000000000000
c5: 20
c0: 3
skew: 1
type: snfsFactor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 6300001)
Primes: RFBsize:348513, AFBsize:348151, largePrimes:6025351 encountered
Relations: rels:6221740, finalFF:823022
Max relations in full relation-set: 28
Initial matrix: 696730 x 823022 with sparse part having weight 62738206.
Pruned matrix : 600136 x 603683 with weight 46382057.
Total sieving time: 130.43 hours.
Total relation processing time: 0.54 hours.
Matrix solve time: 18.63 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 149.93 hours.
 --------- CPU info (if available) ----------

Jun 12, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GMP-ECM 5.0 B1=1739000

(7·10¹⁷⁰-1)/3 = 2(3)₁₇₀_<171> = 311 · C168

C168 = P74 · P95

P74 = 11932010618769729868493135550576478670582273449378145996805715014527203523_<74>

P95 = 62878585748162680828932573824793216019304952212408377491474470576966134103734657544119040624561_<95>

Number: n
N=750267952840300107181136120042872454448017148981779206859592711682743837084673097534833869239013933547695605573419078242229367631296891747052518756698821007502679528403
  ( 168 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=11932010618769729868493135550576478670582273449378145996805715014527203523 (pp74)
 r2=62878585748162680828932573824793216019304952212408377491474470576966134103734657544119040624561 (pp95)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 89.70 hours.
Scaled time: 118.41 units (timescale=1.320).
Factorization parameters were as follows:
name: KA_2_3_170
n: 750267952840300107181136120042872454448017148981779206859592711682743837084673097534833869239013933547695605573419078242229367631296891747052518756698821007502679528403
skew: 0.68
deg: 5
c5: 7
c0: -1
m: 10000000000000000000000000000000000
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3600001)
Primes: RFBsize:348513, AFBsize:348031, largePrimes:8026856 encountered
Relations: rels:7665683, finalFF:795791
Max relations in full relation-set: 48
Initial matrix: 696611 x 795791 with sparse part having weight 46042124.
Pruned matrix : 608294 x 611841 with weight 29860162.
Total sieving time: 80.68 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 8.40 hours.
Total square root time: 0.21 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000
total time: 89.70 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(65·10¹⁶¹+43)/9 = 7(2)₁₆₀7_<162> = 11 · 3407 · C158

C158 = P44 · P114

P44 = 52947769774827685110950551656087356218398433_<44>

P114 = 363963939109135155217567052297823083527155953215564045576179453409875651685542451308909281653467079298253731913847_<114>

Number: n
N=19271078854289890392033039523500339467465971721915367351234683198287542285194178355317187134034800603629485343603335971988745689949094704011052704918275801751
  ( 158 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=52947769774827685110950551656087356218398433 (pp44)
 r2=363963939109135155217567052297823083527155953215564045576179453409875651685542451308909281653467079298253731913847 (pp114)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 51.24 hours.
Scaled time: 74.29 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_7_2_160_7
n: 19271078854289890392033039523500339467465971721915367351234683198287542285194178355317187134034800603629485343603335971988745689949094704011052704918275801751
skew: 0.58
deg: 5
c5: 650
c0: 43
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2300001)
Primes: RFBsize:250150, AFBsize:249736, largePrimes:7540584 encountered
Relations: rels:7113733, finalFF:609923
Max relations in full relation-set: 28
Initial matrix: 499953 x 609923 with sparse part having weight 44644601.
Pruned matrix : 412583 x 415146 with weight 28053407.
Total sieving time: 45.96 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 4.95 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 51.24 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(83·10¹⁵⁹+61)/9 = 9(2)₁₅₈9_<160> = 11 · 67 · 151901 · C152

C152 = P38 · P115

P38 = 79242765343021762777586110766574321493_<38>

P115 = 1039555880362478945347803022950014270999726058613258831222612147118945027723605412596578155237411757742769127379669_<115>

Jun 11, 2007 (2nd)

By suberi / Msieve v. 1.23

4·10¹⁸⁴+3 = 4(0)₁₈₃3_<185> = 643 · 44017 · 49859134658930905291_<20> · 3260581655841388369657396033_<28> · 5986920270178566508580072759197219_<34> · C97

C97 = P48 · P49

P48 = 598460262591086976314911215354850882063724060041_<48>

P49 = 2426330557371719231339466672548563551076810498249_<49>

Thu Jun 07 01:51:11 2007  
Thu Jun 07 01:51:11 2007  
Thu Jun 07 01:51:11 2007  Msieve v. 1.23
Thu Jun 07 01:51:11 2007  random seeds: 37e514e8 67c1b05e
Thu Jun 07 01:51:11 2007  factoring 1451242577945435488202684730983697729965218073649465682642517742785018455031453318180555507115689620266670700586067 (115 digits)
Thu Jun 07 01:51:12 2007  commencing quadratic sieve (114-digit input)
Thu Jun 07 01:51:14 2007  using multiplier of 3
Thu Jun 07 01:51:14 2007  using 64kb Pentium 4 sieve core
Thu Jun 07 01:51:14 2007  sieve interval: 35 blocks of size 65536
Thu Jun 07 01:51:14 2007  processing polynomials in batches of 3
Thu Jun 07 01:51:14 2007  using a sieve bound of 9160121 (306250 primes)
Thu Jun 07 01:51:14 2007  using large prime bound of 1374018150 (30 bits)
Thu Jun 07 01:51:14 2007  using double large prime bound of 28079309877748350 (47-55 bits)
Thu Jun 07 01:51:14 2007  using trial factoring cutoff of 55 bits
Thu Jun 07 01:51:14 2007  polynomial 'A' values have 15 factors
Thu Jun 07 17:03:36 2007  2573 relations (2507 full + 66 combined from 147158 partial), need 306346
Thu Jun 07 17:03:36 2007  c115 factor: 1451242577945435488202684730983697729965218073649465682642517742785018455031453318180555507115689620266670700586067
Thu Jun 07 17:03:36 2007  elapsed time 15:12:25
Sun Jun 10 22:09:11 2007  
Sun Jun 10 22:09:11 2007  
Sun Jun 10 22:09:11 2007  Msieve v. 1.23
Sun Jun 10 22:09:11 2007  random seeds: c6371880 07cdeec2
Sun Jun 10 22:09:11 2007  factoring 1452062422497457515275178568841712183672090367974976058364101164379409367802639948011198401368209 (97 digits)
Sun Jun 10 22:09:11 2007  commencing quadratic sieve (96-digit input)
Sun Jun 10 22:09:12 2007  using multiplier of 1
Sun Jun 10 22:09:12 2007  using 64kb Pentium 4 sieve core
Sun Jun 10 22:09:12 2007  sieve interval: 18 blocks of size 65536
Sun Jun 10 22:09:12 2007  processing polynomials in batches of 6
Sun Jun 10 22:09:12 2007  using a sieve bound of 2328947 (85882 primes)
Sun Jun 10 22:09:12 2007  using large prime bound of 349342050 (28 bits)
Sun Jun 10 22:09:12 2007  using double large prime bound of 2386995188843550 (43-52 bits)
Sun Jun 10 22:09:12 2007  using trial factoring cutoff of 52 bits
Sun Jun 10 22:09:12 2007  polynomial 'A' values have 12 factors
Mon Jun 11 07:51:47 2007  86181 relations (21034 full + 65147 combined from 1292570 partial), need 85978
Mon Jun 11 07:51:49 2007  begin with 1313604 relations
Mon Jun 11 07:51:52 2007  reduce to 225635 relations in 14 passes
Mon Jun 11 07:51:52 2007  attempting to read 225635 relations
Mon Jun 11 07:51:57 2007  recovered 225635 relations
Mon Jun 11 07:51:57 2007  recovered 210860 polynomials
Mon Jun 11 07:51:57 2007  attempting to build 86181 cycles
Mon Jun 11 07:51:57 2007  found 86181 cycles in 6 passes
Mon Jun 11 07:51:57 2007  distribution of cycle lengths:
Mon Jun 11 07:51:57 2007     length 1 : 21034
Mon Jun 11 07:51:57 2007     length 2 : 15162
Mon Jun 11 07:51:57 2007     length 3 : 14263
Mon Jun 11 07:51:57 2007     length 4 : 11625
Mon Jun 11 07:51:57 2007     length 5 : 8916
Mon Jun 11 07:51:57 2007     length 6 : 6072
Mon Jun 11 07:51:57 2007     length 7 : 3792
Mon Jun 11 07:51:57 2007     length 9+: 5317
Mon Jun 11 07:51:57 2007  largest cycle: 20 relations
Mon Jun 11 07:51:58 2007  matrix is 85882 x 86181 with weight 5832332 (avg 67.68/col)
Mon Jun 11 07:52:00 2007  filtering completed in 3 passes
Mon Jun 11 07:52:00 2007  matrix is 82073 x 82137 with weight 5580342 (avg 67.94/col)
Mon Jun 11 07:52:01 2007  saving the first 48 matrix rows for later
Mon Jun 11 07:52:02 2007  matrix is 82025 x 82137 with weight 4657748 (avg 56.71/col)
Mon Jun 11 07:52:02 2007  matrix includes 64 packed rows
Mon Jun 11 07:52:02 2007  using block size 21845 for processor cache size 512 kB
Mon Jun 11 07:52:02 2007  commencing Lanczos iteration
Mon Jun 11 07:53:56 2007  lanczos halted after 1299 iterations
Mon Jun 11 07:53:57 2007  recovered 17 nontrivial dependencies
Mon Jun 11 07:53:59 2007  prp48 factor: 598460262591086976314911215354850882063724060041
Mon Jun 11 07:53:59 2007  prp49 factor: 2426330557371719231339466672548563551076810498249
Mon Jun 11 07:53:59 2007  elapsed time 09:44:48

Jun 11, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=166500, B1=621000

(34·10¹⁶¹-43)/9 = 3(7)₁₆₀3_<162> = 11² · 62134973 · C152

C152 = P31 · P33 · P89

P31 = 4307682285413506208225521446163_<31>

P33 = 119609608489188908704802685341489_<33>

P89 = 97522581802448847543848204896401695824467527895737868563689707593989646588087900743901683_<89>

Jun 10, 2007 (4th)

By suberi / GGNFS-0.77.1-20060722-pentium4, GMP-ECM 6.1.2 B1=11000000

(4·10¹⁷¹-1)/3 = 1(3)₁₇₁_<172> = 43 · 563075957 · C161

C161 = P62 · P100

P62 = 10565196783884673236263834339911427983584335421440205826081601_<62>

P100 = 5212255627583432316510330673884890259823438206542422559981296851838922765444865400476740562332250083_<100>

Number: 13333_171
N=55068506393329268228781801372382135819242644394692096548700842559697060441144881140842260739500877847149902384753995071567447570857215517700565083852457497022883
  ( 161 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=10565196783884673236263834339911427983584335421440205826081601 (pp62)
 r2=5212255627583432316510330673884890259823438206542422559981296851838922765444865400476740562332250083 (pp100)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 182.70 hours.
Scaled time: 124.78 units (timescale=0.683).
Factorization parameters were as follows:
n: 55068506393329268228781801372382135819242644394692096548700842559697060441144881140842260739500877847149902384753995071567447570857215517700565083852457497022883
m: 10000000000000000000000000000000000
c5: 40
c0: -1
skew: 1
type: snfs
Factor base limits: 8400000/8400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [4200000, 
)
Primes: RFBsize:564877, AFBsize:564646, largePrimes:6291159 encountered
Relations: rels:6883739, finalFF:1293233
Max relations in full relation-set: 32
Initial matrix: 1129589 x 1293233 with sparse part having weight 43585609.
Pruned matrix : 977490 x 983201 with weight 30378877.
Total sieving time: 140.70 hours.
Total relation processing time: 0.70 hours.
Matrix solve time: 41.01 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,8400000,8400000,27,27,48,48,2.6,2.6,100000
total time: 182.70 hours.
 --------- CPU info (if available) ----------

4·10¹⁷⁵+3 = 4(0)₁₇₄3_<176> = 17 · 6883 · 19412177 · 169757677820354209_<18> · C147

C147 = P31 · P116

P31 = 7869296226745426570552208159293_<31>

P116 = 13182377316446225748087882274614574555076488881805882086115583209285537401151576878380413502502112486527863046837877_<116>

4·10¹⁸⁴+3 = 4(0)₁₈₃3_<185> = 643 · 44017 · 49859134658930905291_<20> · 3260581655841388369657396033_<28> · C130

C130 = P34 · C97

P34 = 5986920270178566508580072759197219_<34>

C97 = [1452062422497457515275178568841712183672090367974976058364101164379409367802639948011198401368209_<97>]

Jun 10, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(65·10¹⁶⁰+43)/9 = 7(2)₁₅₉7_<161> = 1291 · 297457 · C153

C153 = P32 · P34 · P88

P32 = 17352541246944072825111665711753_<32>

P34 = 2342545412736254376314836515222427_<34>

P88 = 4626678339400851524807725560482691036987427405150010526072468457028149806517927931218291_<88>

Number: n
N=188070384038043145789855963382740207328959180189136326467303443069361466091139927156978142277394156582511341411629330403090273249350352884837936146356521
  ( 153 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=17352541246944072825111665711753 (pp32)
 r2=2342545412736254376314836515222427 (pp34)
 r3=4626678339400851524807725560482691036987427405150010526072468457028149806517927931218291 (pp88)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 39.23 hours.
Scaled time: 56.69 units (timescale=1.445).
Factorization parameters were as follows:
name: KA_7_2_159_7
n: 188070384038043145789855963382740207328959180189136326467303443069361466091139927156978142277394156582511341411629330403090273249350352884837936146356521
skew: 0.92
deg: 5
c5: 65
c0: 43
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:250150, AFBsize:250296, largePrimes:7171287 encountered
Relations: rels:6695030, finalFF:564527
Max relations in full relation-set: 28
Initial matrix: 500512 x 564527 with sparse part having weight 35787677.
Pruned matrix : 445479 x 448045 with weight 23699811.
Total sieving time: 34.25 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 4.54 hours.
Total square root time: 0.23 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 39.23 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jun 10, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000

(5·10¹⁸⁴-17)/3 = 1(6)₁₈₃1_<185> = C185

C185 = P42 · C143

P42 = 650396194789255960015809850516619718777599_<42>

C143 = [25625406175795767517350994169187890818937242743959519616955167305594370202781899645404855476406496245046648724032900205007202467374194220379739_<143>]

Jun 10, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GMP-ECM 5.0 B1=367500

6·10¹⁶⁰+1 = 6(0)₁₅₉1_<161> = 31 · 670853 · C154

C154 = P41 · P114

P41 = 27432596289301964073885280181487235430291_<41>

P114 = 105170824355437139403715973975995678497668642440971399521069843399452536718803322806044637013799975195072495150977_<114>

Number: n
N=2885108765955793497955395545286278042836460061944246907992871665601660822478151672379743016630295863576285617689525078880075789883875814724662289604044307
  ( 154 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=27432596289301964073885280181487235430291 (pp41)
 r2=105170824355437139403715973975995678497668642440971399521069843399452536718803322806044637013799975195072495150977 (pp114)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 33.19 hours.
Scaled time: 45.33 units (timescale=1.366).
Factorization parameters were as follows:
name: KA_6_0_159_1
n: 2885108765955793497955395545286278042836460061944246907992871665601660822478151672379743016630295863576285617689525078880075789883875814724662289604044307
skew: 0.70
deg: 5
c5: 6
c0: 1
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:250150, AFBsize:250351, largePrimes:7044823 encountered
Relations: rels:6590876, finalFF:582384
Max relations in full relation-set: 28
Initial matrix: 500567 x 582384 with sparse part having weight 34717814.
Pruned matrix : 426273 x 428839 with weight 20692604.
Total sieving time: 29.74 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 2.86 hours.
Total square root time: 0.33 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 33.19 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(8·10¹⁶⁰-17)/9 = (8)₁₅₉7_<160> = 6934331 · C154

C154 = P33 · P121

P33 = 968995160047131185467992972361627_<33>

P121 = 1322882591846643298048151628358822882762642650753662322011497085867674561864363575653354158395684834292581003964206621551_<121>

Jun 9, 2007 (2nd)

By Alexander Mkrtychyan / GGNFS-0.77.1-20060513-pentium4

10¹⁷⁹+7 = 1(0)₁₇₈7_<180> = 167 · C177

C177 = P53 · P124

P53 = 60950560869098197619847712489744585923674505423726671_<53>

P124 = 9824395160130058065900701752890082125561413858734478820643602889430506537378449350699284748319422251954897604377774555118351_<124>

Number: 10007_109
N=598802395209580838323353293413173652694610778443113772455089820359281437125748502994011976047904191616766467065868263473053892215568862275449101796407185628742514970059880239521
  ( 177 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=60950560869098197619847712489744585923674505423726671 (pp53)
 r2=9824395160130058065900701752890082125561413858734478820643602889430506537378449350699284748319422251954897604377774555118351 (pp124)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 409.50 hours.
Scaled time: 819.00 units (timescale=2.000).
Factorization parameters were as follows:
n: 598802395209580838323353293413173652694610778443113772455089820359281437125748502994011976047904191616766467065868263473053892215568862275449101796407185628742514970059880239521
m: 1000000000000000000000000000000000000
c5: 1
c0: 70
skew: 2.34
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 8700001)
Primes: RFBsize:501962, AFBsize:503466, largePrimes:6469967 encountered
Relations: rels:6943936, finalFF:1154759
Max relations in full relation-set: 28
Initial matrix: 1005492 x 1154759 with sparse part having weight 64569777.
Pruned matrix : 877696 x 882787 with weight 48153746.
Total sieving time: 382.49 hours.
Total relation processing time: 0.69 hours.
Matrix solve time: 26.02 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 409.50 hours.

Jun 9, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(8·10¹⁶¹+1)/9 = (8)₁₆₀9_<161> = 2874007 · C155

C155 = P65 · P91

P65 = 20551810746861218705246366224186858134216473117184809940650521769_<65>

P91 = 1504906659159028468961208577641797976861017330391535785231117565171524456762298528051525783_<91>

Number: n
N=30928556850727534375834466961593652655991752591030184995683339981040021436582753239254075890869051080560655867883720843021220508122940858838857695506270127
  ( 155 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=20551810746861218705246366224186858134216473117184809940650521769 (pp65)
 r2=1504906659159028468961208577641797976861017330391535785231117565171524456762298528051525783 (pp91)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.08 hours.
Scaled time: 50.90 units (timescale=1.451).
Factorization parameters were as follows:
name: KA_8_160_9
n: 30928556850727534375834466961593652655991752591030184995683339981040021436582753239254075890869051080560655867883720843021220508122940858838857695506270127
skew: 0.83
deg: 5
c5: 5
c0: 2
m: 200000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1600001)
Primes: RFBsize:250150, AFBsize:249566, largePrimes:7153402 encountered
Relations: rels:6692688, finalFF:576485
Max relations in full relation-set: 28
Initial matrix: 499781 x 576485 with sparse part having weight 35524689.
Pruned matrix : 433288 x 435850 with weight 22114077.
Total sieving time: 30.66 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 4.16 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 35.08 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jun 8, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GMP-ECM 5.0 B1=807000, GGNFS-0.77.1-20051202-athlon

8·10¹⁶¹-1 = 7(9)₁₆₁_<162> = 11448961 · C155

C155 = P43 · P50 · P64

P43 = 4539588034558524737970606694078211509057811_<43>

P50 = 11816947682969491809277478418090336975083252421299_<50>

P64 = 1302573251363958712781218721583539351026194452662047110920669831_<64>

Number: n
N=69875336285973897544065352305768182807156038002051015808334048827662178253555060585847047605455202441514125168213954087187474915846075464839123829664543359
  ( 155 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=4539588034558524737970606694078211509057811 (pp43)
 r2=11816947682969491809277478418090336975083252421299 (pp50)
 r3=1302573251363958712781218721583539351026194452662047110920669831 (pp64)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 39.71 hours.
Scaled time: 54.29 units (timescale=1.367).
Factorization parameters were as follows:
name: KA_7_9_161
n: 69875336285973897544065352305768182807156038002051015808334048827662178253555060585847047605455202441514125168213954087187474915846075464839123829664543359
skew: 0.83
deg: 5
c5: 5
c0: -2
m: 200000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:250150, AFBsize:249566, largePrimes:7182966 encountered
Relations: rels:6717273, finalFF:574042
Max relations in full relation-set: 28
Initial matrix: 499781 x 574042 with sparse part having weight 36072684.
Pruned matrix : 435510 x 438072 with weight 22844668.
Total sieving time: 35.55 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 3.71 hours.
Total square root time: 0.24 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 39.71 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(2·10¹⁷¹-11)/9 = (2)₁₇₀1_<171> = 13 · 23 · C168

C168 = P32 · P39 · P98

P32 = 27851033920037562716463233492393_<32>

P39 = 275686147181721751471622993232321660739_<39>

P98 = 96796584127055481810278948284165150853864843387232107130793898378385677491078494178075979521903877_<98>

Number: n
N=26685477338339329039543211617052433617893367389355907405472169844555157404025928817956271993597584603028709449313596895296724931762785103
  ( 137 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=275686147181721751471622993232321660739 (pp39)
 r2=96796584127055481810278948284165150853864843387232107130793898378385677491078494178075979521903877 (pp98)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 109.28 hours.
Scaled time: 144.57 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_2_170_1
n: 26685477338339329039543211617052433617893367389355907405472169844555157404025928817956271993597584603028709449313596895296724931762785103

# n: 743218134522482348569305091044221479004087699739873652917131178000743218134522482348569305091044221479004087699739873652917131178000743218134522482348569305091044221479

skew: 0.89
deg: 5
c5: 20
c0: -11
m: 10000000000000000000000000000000000
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 4300001)
Primes: RFBsize:348513, AFBsize:348817, largePrimes:8249964 encountered
Relations: rels:7870823, finalFF:800899
Max relations in full relation-set: 48
Initial matrix: 697396 x 800899 with sparse part having weight 47329242.
Pruned matrix : 610868 x 614418 with weight 32155254.
Total sieving time: 98.90 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 9.69 hours.
Total square root time: 0.33 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000
total time: 109.28 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jun 8, 2007

By suberi / GMP-ECM 6.1.2 B1=11000000

4·10¹⁶³+3 = 4(0)₁₆₂3_<164> = 1316989799426812351_<19> · C146

C146 = P40 · P106

P40 = 9122825587223042642884812944337703070033_<40>

P106 = 3329263796544560932998781161768664065173476621162459775686753155158211188126981055831370511645586167117741_<106>

4·10¹⁶⁹+3 = 4(0)₁₆₈3_<170> = 23 · 43 · 2695744223_<10> · C158

C158 = P37 · P122

P37 = 1095863878505531791352248008590604473_<37>

P122 = 13690786705166299346121105341688039593329430814257896520268003985603036085194932170203623925361810203165403423559971573513_<122>

4·10¹⁷⁶+3 = 4(0)₁₇₅3_<177> = 13² · 14479 · 1727839 · C164

C164 = P38 · C127

P38 = 30175961085952909008534878737421283007_<38>

C127 = [3135236706631199341096636684750581017076426724373352960266683033160613553116178668067537726925834017042340630910117649030813861_<127>]

Jun 7, 2007 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-k8

2·10¹⁷¹+3 = 2(0)₁₇₀3_<172> = 8627 · C168

C168 = P41 · P127

P41 = 41713247973026961742658321646485423054431_<41>

P127 = 5557713951456074967962531890753686473889384220379793822875068616831334165905093911472798378503095080109303609626110094430409519_<127>

Number: 20003_171
N=231830300220238785209226845948765503651327228468760867045322823693056682508403848382983655963834473165642749507360612031992581430392952358873304740929639503883157528689
  ( 168 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=41713247973026961742658321646485423054431 (pp41)
 r2=5557713951456074967962531890753686473889384220379793822875068616831334165905093911472798378503095080109303609626110094430409519 (pp127)
Version: GGNFS-0.77.1-20060513-k8
Total time: 206.25 hours.
Scaled time: 413.12 units (timescale=2.003).
Factorization parameters were as follows:
name: 20003_171
n: 231830300220238785209226845948765503651327228468760867045322823693056682508403848382983655963834473165642749507360612031992581430392952358873304740929639503883157528689
m: 10000000000000000000000000000000000
c5: 20
c0: 3
skew: 1
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 9300001)
Primes: RFBsize:412849, AFBsize:412656, largePrimes:6353030 encountered
Relations: rels:6686637, finalFF:976860
Max relations in full relation-set: 28
Initial matrix: 825571 x 976860 with sparse part having weight 78469523.
Pruned matrix : 705516 x 709707 with weight 60130180.
Total sieving time: 198.00 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 7.61 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 206.25 hours.
 --------- CPU info (if available) ----------

Jun 7, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(13·10¹⁷¹-1)/3 = 4(3)₁₇₁_<172> = 7 · C171

C171 = P80 · P92

P80 = 41301678601887909281508978574307473779381336266973146191783297973077225039301321_<80>

P92 = 14988437274298150142827003772114850577864102899199141349041142889289160609017099225061284139_<92>

Number: n
N=619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619
  ( 171 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=41301678601887909281508978574307473779381336266973146191783297973077225039301321 (pp80)
 r2=14988437274298150142827003772114850577864102899199141349041142889289160609017099225061284139 (pp92)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 136.44 hours.
Scaled time: 163.05 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_4_3_171
n: 619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619
type: snfs
skew: 0.38
deg: 5
c5: 130
c0: -1
m: 10000000000000000000000000000000000
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4800000)
Primes: RFBsize:348513, AFBsize:349036, largePrimes:8355279 encountered
Relations: rels:7958858, finalFF:790913
Max relations in full relation-set: 28
Initial matrix: 697616 x 790913 with sparse part having weight 49108257.
Pruned matrix : 622652 x 626204 with weight 35955650.
Total sieving time: 124.32 hours.
Total relation processing time: 0.58 hours.
Matrix solve time: 11.17 hours.
Total square root time: 0.38 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.6,2.6,100000
total time: 136.44 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(4·10¹⁶¹-13)/9 = (4)₁₆₀3_<161> = 7 · 77867 · C155

C155 = P54 · P102

P54 = 319550413044553780518507753936684693865291403825034473_<54>

P102 = 255168238619378957640510165325532105096040257500576497491031577087931802511480908975140897813777669839_<102>

Number: n
N=81539116046673805416276552958330861678878168533606652450321783929088692338849658381680932954257982832346811953063638630053157388228727820596006091787359847
  ( 155 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=319550413044553780518507753936684693865291403825034473 (pp54)
 r2=255168238619378957640510165325532105096040257500576497491031577087931802511480908975140897813777669839 (pp102)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 40.78 hours.
Scaled time: 58.92 units (timescale=1.445).
Factorization parameters were as follows:
name: KA_4_160_3
n: 81539116046673805416276552958330861678878168533606652450321783929088692338849658381680932954257982832346811953063638630053157388228727820596006091787359847
skew: 0.80
deg: 5
c5: 40
c0: -13
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1800001)
Primes: RFBsize:250150, AFBsize:250286, largePrimes:7303690 encountered
Relations: rels:6857429, finalFF:592319
Max relations in full relation-set: 28
Initial matrix: 500502 x 592319 with sparse part having weight 38801200.
Pruned matrix : 421594 x 424160 with weight 23783758.
Total sieving time: 35.81 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 4.32 hours.
Total square root time: 0.43 hours, sqrts: 6.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 40.78 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jun 6, 2007 (3rd)

By suberi / Msieve 1.22

4·10¹⁵⁹+3 = 4(0)₁₅₈3_<160> = 17 · 29 · 409 · 4108499 · 39134819 · 417437569 · 3210493232143522115233150147270451_<34> · C98

C98 = P46 · P53

P46 = 2111007970395248522288822270407200076593257339_<46>

P53 = 43610401448779057354383384061999544768111674794916639_<53>

Wed Jun 06 13:02:36 2007  
Wed Jun 06 13:02:36 2007  
Wed Jun 06 13:02:36 2007  Msieve v. 1.22
Wed Jun 06 13:02:36 2007  random seeds: 1e082aa8 9c72287f
Wed Jun 06 13:02:36 2007  factoring 92061905050509083573242674474131090797477960189592323155314191961704503438069174058130179979963621 (98 digits)
Wed Jun 06 13:02:37 2007  commencing quadratic sieve (98-digit input)
Wed Jun 06 13:02:37 2007  using multiplier of 5
Wed Jun 06 13:02:37 2007  using 64kb Opteron sieve core
Wed Jun 06 13:02:37 2007  sieve interval: 18 blocks of size 65536
Wed Jun 06 13:02:37 2007  processing polynomials in batches of 6
Wed Jun 06 13:02:37 2007  using a sieve bound of 2542703 (92941 primes)
Wed Jun 06 13:02:37 2007  using large prime bound of 381405450 (28 bits)
Wed Jun 06 13:02:37 2007  using double large prime bound of 2795737419206850 (43-52 bits)
Wed Jun 06 13:02:37 2007  using trial factoring cutoff of 52 bits
Wed Jun 06 13:02:37 2007  polynomial 'A' values have 13 factors
Wed Jun 06 21:05:02 2007  93287 relations (22735 full + 70552 combined from 1389878 partial), need 93037
Wed Jun 06 21:05:26 2007  begin with 1412613 relations
Wed Jun 06 21:05:28 2007  reduce to 242711 relations in 10 passes
Wed Jun 06 21:05:28 2007  attempting to read 242711 relations
Wed Jun 06 21:05:33 2007  recovered 242711 relations
Wed Jun 06 21:05:33 2007  recovered 229853 polynomials
Wed Jun 06 21:05:34 2007  attempting to build 93287 cycles
Wed Jun 06 21:05:34 2007  found 93287 cycles in 6 passes
Wed Jun 06 21:05:34 2007  distribution of cycle lengths:
Wed Jun 06 21:05:34 2007     length 1 : 22735
Wed Jun 06 21:05:34 2007     length 2 : 16342
Wed Jun 06 21:05:34 2007     length 3 : 15825
Wed Jun 06 21:05:34 2007     length 4 : 12688
Wed Jun 06 21:05:34 2007     length 5 : 9623
Wed Jun 06 21:05:34 2007     length 6 : 6425
Wed Jun 06 21:05:34 2007     length 7 : 4104
Wed Jun 06 21:05:34 2007     length 9+: 5545
Wed Jun 06 21:05:34 2007  largest cycle: 20 relations
Wed Jun 06 21:05:34 2007  matrix is 92941 x 93287 with weight 6011165 (avg 64.44/col)
Wed Jun 06 21:05:35 2007  filtering completed in 3 passes
Wed Jun 06 21:05:35 2007  matrix is 91290 x 91354 with weight 5815830 (avg 63.66/col)
Wed Jun 06 21:05:36 2007  saving the first 48 matrix rows for later
Wed Jun 06 21:05:36 2007  matrix is 91242 x 91354 with weight 4375853 (avg 47.90/col)
Wed Jun 06 21:05:36 2007  matrix includes 64 packed rows
Wed Jun 06 21:05:36 2007  using block size 10922 for processor cache size 256 kB
Wed Jun 06 21:05:36 2007  commencing Lanczos iteration
Wed Jun 06 21:07:07 2007  lanczos halted after 1445 iterations
Wed Jun 06 21:07:07 2007  recovered 15 nontrivial dependencies
Wed Jun 06 21:07:08 2007  prp46 factor: 2111007970395248522288822270407200076593257339
Wed Jun 06 21:07:08 2007  prp53 factor: 43610401448779057354383384061999544768111674794916639
Wed Jun 06 21:07:08 2007  elapsed time 08:04:32

4·10¹⁶¹+3 = 4(0)₁₆₀3_<162> = 93187 · 34563163 · 1429384127_<10> · 174991800857_<12> · 5565980346411937268388128381439563107_<37> · C92

C92 = P39 · P54

P39 = 700131433832122433345260550981903682611_<39>

P54 = 127409931013861119158868865095362078118650478133953821_<54>

Wed Jun 06 13:03:32 2007  
Wed Jun 06 13:03:32 2007  
Wed Jun 06 13:03:32 2007  Msieve v. 1.22
Wed Jun 06 13:03:32 2007  random seeds: 42a4d6dc 17b79130
Wed Jun 06 13:03:32 2007  factoring 89203697685186390047288507359292435046300468270991492132748857979599129994346738197714706631 (92 digits)
Wed Jun 06 13:03:33 2007  commencing quadratic sieve (92-digit input)
Wed Jun 06 13:03:33 2007  using multiplier of 31
Wed Jun 06 13:03:33 2007  using 64kb Pentium 4 sieve core
Wed Jun 06 13:03:33 2007  sieve interval: 18 blocks of size 65536
Wed Jun 06 13:03:33 2007  processing polynomials in batches of 6
Wed Jun 06 13:03:33 2007  using a sieve bound of 1854623 (69412 primes)
Wed Jun 06 13:03:33 2007  using large prime bound of 209572399 (27 bits)
Wed Jun 06 13:03:33 2007  using double large prime bound of 951483630575481 (42-50 bits)
Wed Jun 06 13:03:33 2007  using trial factoring cutoff of 50 bits
Wed Jun 06 13:03:33 2007  polynomial 'A' values have 12 factors
Wed Jun 06 17:47:55 2007  69664 relations (17315 full + 52349 combined from 897404 partial), need 69508
Wed Jun 06 17:47:58 2007  begin with 914719 relations
Wed Jun 06 17:47:59 2007  reduce to 178248 relations in 10 passes
Wed Jun 06 17:47:59 2007  attempting to read 178248 relations
Wed Jun 06 17:48:03 2007  recovered 178248 relations
Wed Jun 06 17:48:03 2007  recovered 161681 polynomials
Wed Jun 06 17:48:03 2007  attempting to build 69664 cycles
Wed Jun 06 17:48:03 2007  found 69664 cycles in 6 passes
Wed Jun 06 17:48:03 2007  distribution of cycle lengths:
Wed Jun 06 17:48:03 2007     length 1 : 17315
Wed Jun 06 17:48:03 2007     length 2 : 12552
Wed Jun 06 17:48:03 2007     length 3 : 12009
Wed Jun 06 17:48:03 2007     length 4 : 9448
Wed Jun 06 17:48:03 2007     length 5 : 6958
Wed Jun 06 17:48:03 2007     length 6 : 4647
Wed Jun 06 17:48:03 2007     length 7 : 2820
Wed Jun 06 17:48:03 2007     length 9+: 3915
Wed Jun 06 17:48:03 2007  largest cycle: 19 relations
Wed Jun 06 17:48:04 2007  matrix is 69412 x 69664 with weight 4316925 (avg 61.97/col)
Wed Jun 06 17:48:05 2007  filtering completed in 3 passes
Wed Jun 06 17:48:05 2007  matrix is 68116 x 68180 with weight 4166475 (avg 61.11/col)
Wed Jun 06 17:48:05 2007  saving the first 48 matrix rows for later
Wed Jun 06 17:48:05 2007  matrix is 68068 x 68180 with weight 3190313 (avg 46.79/col)
Wed Jun 06 17:48:05 2007  matrix includes 64 packed rows
Wed Jun 06 17:48:05 2007  using block size 21845 for processor cache size 512 kB
Wed Jun 06 17:48:06 2007  commencing Lanczos iteration
Wed Jun 06 17:49:11 2007  lanczos halted after 1078 iterations
Wed Jun 06 17:49:11 2007  recovered 17 nontrivial dependencies
Wed Jun 06 17:49:13 2007  prp39 factor: 700131433832122433345260550981903682611
Wed Jun 06 17:49:13 2007  prp54 factor: 127409931013861119158868865095362078118650478133953821
Wed Jun 06 17:49:13 2007  elapsed time 04:45:41

Jun 6, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp

(16·10¹⁶⁰-7)/9 = 1(7)₁₆₀_<161> = 19 · 23603 · C155

C155 = P56 · P100

P56 = 16770759996905604146905291574126233673996019246169099349_<56>

P100 = 2363762954520662154675832128367503145931432005400900847902652199986102917164639275903970666869960389_<100>

Number: n
N=39642101199842521752983625582336272547374169157305556113022603678341017706887790307159388253004809330164938394935919782226117058665106749984452863435686761
  ( 155 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=16770759996905604146905291574126233673996019246169099349 (pp56)
 r2=2363762954520662154675832128367503145931432005400900847902652199986102917164639275903970666869960389 (pp100)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 31.87 hours.
Scaled time: 43.51 units (timescale=1.365).
Factorization parameters were as follows:
name: KA_1_7_160
n: 39642101199842521752983625582336272547374169157305556113022603678341017706887790307159388253004809330164938394935919782226117058665106749984452863435686761
skew: 1.70
deg: 5
c5: 1
c0: -14
m: 200000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:250150, AFBsize:250091, largePrimes:7003207 encountered
Relations: rels:6534990, finalFF:569860
Max relations in full relation-set: 28
Initial matrix: 500305 x 569860 with sparse part having weight 31858690.
Pruned matrix : 436112 x 438677 with weight 19800703.
Total sieving time: 28.59 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 2.98 hours.
Total square root time: 0.10 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 31.87 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jun 6, 2007

By suberi / GMP-ECM 6.1.2 B1=5000000

4·10¹⁵⁹+3 = 4(0)₁₅₈3_<160> = 17 · 29 · 409 · 4108499 · 39134819 · 417437569 · C132

C132 = P34 · C98

P34 = 3210493232143522115233150147270451_<34>

C98 = [92061905050509083573242674474131090797477960189592323155314191961704503438069174058130179979963621_<98>]

4·10¹⁷⁰+3 = 4(0)₁₆₉3_<171> = 13 · 2332022449008725190543961_<25> · C146

C146 = P31 · C115

P31 = 9091674957193157331925985427613_<31>

C115 = [1451242577945435488202684730983697729965218073649465682642517742785018455031453318180555507115689620266670700586067_<115>]

4·10¹⁶¹+3 = 4(0)₁₆₀3_<162> = 93187 · 34563163 · 1429384127_<10> · 174991800857_<12> · C129

C129 = P37 · C92

P37 = 5565980346411937268388128381439563107_<37>

C92 = [89203697685186390047288507359292435046300468270991492132748857979599129994346738197714706631_<92>]

Jun 5, 2007 (5th)

By suberi / GMP-ECM 6.1.2 B1=5000000

4·10¹⁶⁵+3 = 4(0)₁₆₄3_<166> = 47 · 2239 · 64301 · 5622060993572083_<16> · C141

C141 = P32 · P109

P32 = 17162193244336712083651773667387_<32>

P109 = 6126634498248786631325750859569676596678356085694049608225501662771812141931771359526911934006293383097455871_<109>

Jun 5, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(46·10¹⁶⁰-1)/9 = 5(1)₁₆₀_<161> = 3 · 16361 · C157

C157 = P56 · P101

P56 = 63188612413904730140907248034497209619568206489435363729_<56>

P101 = 16479552118993128813473617476831373281686860448323688740205309001943172664096989506162049716810356373_<101>

Number: n
N=1041320031601799219915471978304323515496426687674166434633398755396188315936497587985883322354198217531754601615857040342096267773182387203535055133368194917
  ( 157 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=63188612413904730140907248034497209619568206489435363729 (pp56)
 r2=16479552118993128813473617476831373281686860448323688740205309001943172664096989506162049716810356373 (pp101)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 42.51 hours.
Scaled time: 61.64 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_5_1_160
n: 1041320031601799219915471978304323515496426687674166434633398755396188315936497587985883322354198217531754601615857040342096267773182387203535055133368194917
skew: 0.46
deg: 5
c5: 46
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1900001)
Primes: RFBsize:250150, AFBsize:250556, largePrimes:7300603 encountered
Relations: rels:6822189, finalFF:562929
Max relations in full relation-set: 28
Initial matrix: 500772 x 562929 with sparse part having weight 39004994.
Pruned matrix : 449144 x 451711 with weight 26733692.
Total sieving time: 37.13 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 5.08 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 42.51 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jun 5, 2007 (3rd)

By Torbjörn Granlund / GMP-ECM P-1 B1=100000000 / May 25, 2007

10⁹²⁶+1 = 1(0)₉₂₅1_<927> = 101 · 62969 · 118529 · 15103061 · C907

C907 = P29 · C879

P29 = 35034118330919297779082305261_<29>

By Yousuke Koide / GMP-ECM B1=1000000 / May 26, 2007

10¹⁰⁵⁵+1 = 1(0)₁₀₅₄1_<1056> = 11 · 9091 · 14771 · 177196221721_<12> · 8708337574089530396491_<22> · 2708591227536778275869251_<25> · 9376657450882829279982731_<25> · 2764617069785703725933625413_<28> · P183 · C754

C754 = P32 · C722

P32 = 19178509602144721723538217992641_<32>

By Yousuke Koide / GMP-ECM B1=1000000 / May 26, 2007

(10¹¹⁴⁹-1)/9 = (1)₁₁₄₉_<1149> = 3 · 37 · 34471 · 852559 · 145364587 · 1628675880394909638591813700831880313095925587_<46> · 23181229247696012268805890210990826546682789683_<47> · C285 · C752

C752 = P33 · P719

P33 = 347266658845989451344982160757667_<33>

By Yousuke Koide / GMP-ECM B1=5000000 / May 29, 2007

(10⁶¹⁵-1)/9 = (1)₆₁₅_<615> = 3 · 31 · 37 · 41² · 83 · 271 · 1231 · 11071 · 275521 · 538987 · 1364071 · 1811791 · 2906161 · 21158848681_<11> · 626920594693_<12> · 9425856976319889649_<19> · 201763709900322803748657942361_<30> · 234065099292222402013296307835793151_<36> · 5440907236518498609451112390256369995629321_<43> · 8414640003465161203119978906558054839526493_<43> · P143 · C232

C232 = P35 · P198

P35 = 41766848698222033158540558591648271_<35>

By Yousuke Koide / GMP-ECM B1=1250000 / May 30, 2007

(10⁷⁸⁷-1)/9 = (1)₇₈₇_<787> = 26759 · 213141637 · 1074022836653095912870566750079013_<34> · C741

C741 = P40 · C702

P40 = 1629242936815583422402932260494746089387_<40>

By Yousuke Koide / GMP-ECM B1=1250000 / May 31, 2007

(10⁸⁵³-1)/9 = (1)₈₅₃_<853> = 5119 · 13649 · 34505557 · 872209561 · 258392363336333_<15> · C814

C814 = P32 · C782

P32 = 87440115231123175885662305449333_<32>

By Yousuke Koide / GMP-ECM B1=1000000 / Jun 2, 2007

(10¹³¹¹-1)/9 = (1)₁₃₁₁_<1311> = 3 · 37 · 277 · 21319 · 23599 · 81283 · 10749631 · 9021705647077_<13> · 203864078068831_<15> · 1111111111111111111_<19> · 11111111111111111111111_<23> · 2152970896196020817900437_<25> · 3931123022305129377976519_<25> · 1595352086329224644348978893_<28> · C363 · C780

C780 = P33 · C747

P33 = 933052229529582992021083478515963_<33>

By Yousuke Koide / GMP-ECM B1=1000000 / Jun 2, 2007

(10¹⁴⁰⁷-1)/9 = (1)₁₄₀₇_<1407> = 3 · 37 · 43 · 239 · 1609 · 1933 · 4649 · 493121 · 10838689 · 1695022306115797_<16> · 2046166739518832881_<19> · 25877379396467255119_<20> · 79863595778924342083_<20> · 28213380943176667001263153660999177245677_<41> · 184976479633092931103313037835504355363361_<42> · 1479324487468932812154772125499257696540643946328553680234277466780839_<70> · C396 · C758

C758 = P35 · C723

P35 = 39184667823173817016379582631270559_<35>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jun 5, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

9·10¹⁷⁴+1 = 9(0)₁₇₃1_<175> = C175

C175 = P64 · P112

P64 = 6701858154129508946109631584557125937056799890919240999671909373_<64>

P112 = 1342911143897373658594292493986198100072281134132513257099614367422167831910468286290583725850693432647730948437_<112>

Number: 90001_174
N=9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
  ( 175 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=6701858154129508946109631584557125937056799890919240999671909373 (pp64)
 r2=1342911143897373658594292493986198100072281134132513257099614367422167831910468286290583725850693432647730948437 (pp112)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 173.62 hours.
Scaled time: 162.16 units (timescale=0.934).
Factorization parameters were as follows:
n: 9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
m: 100000000000000000000000000000000000
c5: 9
c0: 10
skew: 1.02
type: snfs
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 49/49
Sieved algebraic special-q in [4500000, 7200001)
Primes: RFBsize:602489, AFBsize:602235, largePrimes:10103196 encountered
Relations: rels:10291943, finalFF:1454570
Max relations in full relation-set: 28
Initial matrix: 1204788 x 1454570 with sparse part having weight 67687049.
Pruned matrix : 966267 x 972354 with weight 40422034.
Total sieving time: 167.46 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 5.78 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,49,49,2.6,2.6,100000
total time: 173.62 hours.
 --------- CPU info (if available) ----------

Jun 5, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp

8·10¹⁶⁰-1 = 7(9)₁₆₀_<161> = 939359 · C155

C155 = P40 · P55 · P61

P40 = 7430283334715190763428010216563200237119_<40>

P55 = 8371325514886127521657093908547021699702744768728781303_<55>

P61 = 1369174436449288928232717093121729013383869942151960421280473_<61>

Number: n
N=85164457890966073673643410027476183227072929518959205160114503613634403886054213564781941728348799553738240651337773950108531456024799890137849320653764961
  ( 155 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=7430283334715190763428010216563200237119 (pp40)
 r2=8371325514886127521657093908547021699702744768728781303 (pp55)
 r3=1369174436449288928232717093121729013383869942151960421280473 (pp61)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 37.67 hours.
Scaled time: 51.49 units (timescale=1.367).
Factorization parameters were as follows:
name: KA_7_9_160
n: 85164457890966073673643410027476183227072929518959205160114503613634403886054213564781941728348799553738240651337773950108531456024799890137849320653764961
skew: 0.66
deg: 5
c5: 8
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:250150, AFBsize:249851, largePrimes:7325544 encountered
Relations: rels:6965044, finalFF:662712
Max relations in full relation-set: 28
Initial matrix: 500066 x 662712 with sparse part having weight 42447996.
Pruned matrix : 358049 x 360613 with weight 22237841.
Total sieving time: 34.43 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 2.83 hours.
Total square root time: 0.20 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 37.67 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jun 4, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(14·10¹⁷⁰-41)/9 = 1(5)₁₆₉1_<171> = 89 · C169

C169 = P47 · P122

P47 = 23562871960702446576109209737209512980072163311_<47>

P122 = 74176663773255644917317906830538807621668868770340406914332112105118853831007147436387613726854741316452945435326628021369_<122>

Number: n
N=1747815230961298377028714107365792759051186017478152309612983770287141073657927590511860174781523096129837702871410736579275905118601747815230961298377028714107365792759
  ( 169 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=23562871960702446576109209737209512980072163311 (pp47)
 r2=74176663773255644917317906830538807621668868770340406914332112105118853831007147436387613726854741316452945435326628021369 (pp122)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 101.58 hours.
Scaled time: 134.39 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_1_5_169_1
n: 1747815230961298377028714107365792759051186017478152309612983770287141073657927590511860174781523096129837702871410736579275905118601747815230961298377028714107365792759
skew: 1.24
deg: 5
c5: 14
c0: -41
m: 10000000000000000000000000000000000
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 4000001)
Primes: RFBsize:348513, AFBsize:349737, largePrimes:8140106 encountered
Relations: rels:7766379, finalFF:797968
Max relations in full relation-set: 48
Initial matrix: 698316 x 797968 with sparse part having weight 47933037.
Pruned matrix : 612389 x 615944 with weight 31910090.
Total sieving time: 91.84 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 9.19 hours.
Total square root time: 0.22 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000
total time: 101.58 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Jun 3, 2007 (2nd)

By Robert Backstrom / GMP-ECM 5.0 B1=1175000, GGNFS-0.77.1-20051202-athlon

4·10¹⁵⁹-3 = 3(9)₁₅₈7_<160> = 7 · 80177 · C154

C154 = P37 · P118

P37 = 6869025736566408403013738614059587089_<37>

P118 = 1037569042972137310167842357523279974289448792553913560988035736213951007069294488349444811458102522621741991129070107_<118>

(55·10¹⁵⁹-1)/9 = 6(1)₁₅₉_<160> = 3 · 7 · 2879 · C154

C154 = P46(1033...) · P46(5512...) · P65

P46(1033...) = 1033119730398606727874017412985081979328287301_<46>

P46(5512...) = 5512969028825793796895660458496810276891422129_<46>

P65 = 17746920835907189395385191131490589648783353079850430487298717601_<65>

Number: n
N=101078600557586316530394335187666205380689576590931227957973355680893020246962588053244531188261650227610630528310278223442516599862900661789164741578774229
  ( 156 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=1033119730398606727874017412985081979328287301 (pp46)
 r2=5512969028825793796895660458496810276891422129 (pp46)
 r3=17746920835907189395385191131490589648783353079850430487298717601 (pp65)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 29.00 hours.
Scaled time: 42.05 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_6_1_159
n: 101078600557586316530394335187666205380689576590931227957973355680893020246962588053244531188261650227610630528310278223442516599862900661789164741578774229
skew: 0.71
deg: 5
c5: 11
c0: -2
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:250150, AFBsize:250187, largePrimes:6962438 encountered
Relations: rels:6492622, finalFF:567417
Max relations in full relation-set: 28
Initial matrix: 500404 x 567417 with sparse part having weight 32876452.
Pruned matrix : 437769 x 440335 with weight 20727804.
Total sieving time: 24.93 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.75 hours.
Total square root time: 0.13 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 29.00 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jun 3, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060513-k8

(82·10¹⁶⁴-1)/9 = 9(1)₁₆₄_<165> = 23 · 29 · C163

C163 = P56 · P108

P56 = 11722798638770736454179599031506665643455103982980173427_<56>

P108 = 116523683202366287222326406187442967335215483093587034853875156598506211825703054134781180379470982769675879_<108>

Number: 91111_164
N=1365983674829252040646343494919207063135099117108112610361485923704814259536898217557887722805264034649341995668832250541395968682325503914709312010661335998667333
  ( 163 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=11722798638770736454179599031506665643455103982980173427 (pp56)
 r2=116523683202366287222326406187442967335215483093587034853875156598506211825703054134781180379470982769675879 (pp108)
Version: GGNFS-0.77.1-20060513-k8
Total time: 94.93 hours.
Scaled time: 190.15 units (timescale=2.003).
Factorization parameters were as follows:
name: 91111_164
n: 1365983674829252040646343494919207063135099117108112610361485923704814259536898217557887722805264034649341995668832250541395968682325503914709312010661335998667333
m: 1000000000000000000000000000000000
c5: 41
c0: -5
skew: 1
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 5400001)
Primes: RFBsize:348513, AFBsize:348787, largePrimes:5848756 encountered
Relations: rels:6000231, finalFF:794384
Max relations in full relation-set: 28
Initial matrix: 697365 x 794384 with sparse part having weight 49085999.
Pruned matrix : 622750 x 626300 with weight 35785753.
Total sieving time: 90.29 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 4.20 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 94.93 hours.
 --------- CPU info (if available) ----------

Jun 2, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon

(8·10¹⁵⁷-17)/9 = (8)₁₅₆7_<157> = 7 · C129

8739994595235952825155053837_<28> · C129

C129 = P64 · P66

P64 = 1097338309267008237239239772614316948193823367920986887082646889_<64>

P66 = 132402971590214069443001363228800248580081550757875671603997677837_<66>

Number: n
N=145290852986733231960131889761460491703794538807068334652232282714626655166495302127159129035785015114582751752183571455452299093
  ( 129 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=1097338309267008237239239772614316948193823367920986887082646889 (pp64)
 r2=132402971590214069443001363228800248580081550757875671603997677837 (pp66)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 33.76 hours.
Scaled time: 46.21 units (timescale=1.369).
Factorization parameters were as follows:
name: KA_8_156_7
n: 145290852986733231960131889761460491703794538807068334652232282714626655166495302127159129035785015114582751752183571455452299093
skew: 0.93
deg: 5
c5: 25
c0: -17
m: 20000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:250150, AFBsize:250611, largePrimes:7095641 encountered
Relations: rels:6625206, finalFF:569684
Max relations in full relation-set: 28
Initial matrix: 500825 x 569684 with sparse part having weight 34217548.
Pruned matrix : 439147 x 441715 with weight 21728785.
Total sieving time: 30.25 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.08 hours.
Total square root time: 0.22 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 33.76 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(4·10¹⁵⁸-13)/9 = (4)₁₅₇3_<158> = 131 · 173 · 100467687810755071_<18> · C137

C137 = P53 · P84

P53 = 24842867387305405261100498732839983321474852653757937_<53>

P84 = 785727502087926126786887826591860692223274703506416827388958712572751463133189766243_<84>

Number: n
N=19519724136929079694548208428483677843768554481542628710715214750048789472954415174850519785238780109629364396557689211568718844535920691
  ( 137 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=24842867387305405261100498732839983321474852653757937 (pp53)
 r2=785727502087926126786887826591860692223274703506416827388958712572751463133189766243 (pp84)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 27.07 hours.
Scaled time: 39.06 units (timescale=1.443).
Factorization parameters were as follows:
name: KA_4_157_3
n: 19519724136929079694548208428483677843768554481542628710715214750048789472954415174850519785238780109629364396557689211568718844535920691
skew: 0.64
deg: 5
c5: 125
c0: -13
m: 20000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:250150, AFBsize:249831, largePrimes:7081908 encountered
Relations: rels:6691785, finalFF:636313
Max relations in full relation-set: 28
Initial matrix: 500046 x 636313 with sparse part having weight 35028177.
Pruned matrix : 376037 x 378601 with weight 17367856.
Total sieving time: 24.10 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.72 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 27.07 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Jun 2, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

6·10¹⁵⁹+1 = 6(0)₁₅₈1_<160> = 23 · 47 · 3167 · 36887 · 48599731 · 306920722151401391534780179_<27> · C115

C115 = P42 · P73

P42 = 767698777607940194265527635370316671942213_<42>

P73 = 4149093592080265396266679279339449692918936093049417612900424150237843877_<73>

Number: 60001_159
N=3185254078820957394944482467613194905363252982304778574592502158674083161302549598773054153266870437616423059879801
  ( 115 digits)
Divisors found:
 r1=767698777607940194265527635370316671942213 (pp42)
 r2=4149093592080265396266679279339449692918936093049417612900424150237843877 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 25.89 hours.
Scaled time: 24.21 units (timescale=0.935).
Factorization parameters were as follows:
name: 60001_159
n: 3185254078820957394944482467613194905363252982304778574592502158674083161302549598773054153266870437616423059879801
skew: 86870.00
# norm 7.86e+15
c5: 15660
c4: -1829222984
c3: -350509230841283
c2: 14133342017277827226
c1: 1344214957431756103806100
c0: -9726381717437035313270182575
# alpha -6.19
Y1: 302713102769
Y0: -11525790758021234641354
# Murphy_E 5.34e-10
# M 2665950469727377697888113665250745839518931865279047301705509598646406265442718423335461565637984496738017255771107
type: gnfs
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1800000, 3000001)
Primes: RFBsize:256726, AFBsize:256454, largePrimes:7476860 encountered
Relations: rels:7371207, finalFF:610629
Max relations in full relation-set: 28
Initial matrix: 513260 x 610629 with sparse part having weight 50672315.
Pruned matrix : 433032 x 435662 with weight 31832537.
Polynomial selection time: 1.33 hours.
Total sieving time: 23.09 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.18 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000
total time: 25.89 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

Jun 1, 2007 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-k8

(10¹⁶¹-7)/3 = (3)₁₆₀1_<161> = 563 · C158

C158 = P66 · P93

P66 = 124141466019619851595478970162960620467203748722561182599049555651_<66>

P93 = 476928725276457668401732704761502335824130724124126988122364575060825584612231412476856510987_<93>

Number: 33331_161
N=59206631142687981053878034339846062759029011249259917110716400236826524570751924215512137359384251036116044997039668442865600947306098283007696862048549437537
  ( 158 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=124141466019619851595478970162960620467203748722561182599049555651 (pp66)
 r2=476928725276457668401732704761502335824130724124126988122364575060825584612231412476856510987 (pp93)
Version: GGNFS-0.77.1-20060513-k8
Total time: 66.69 hours.
Scaled time: 133.18 units (timescale=1.997).
Factorization parameters were as follows:
name: 33331_161
n: 59206631142687981053878034339846062759029011249259917110716400236826524570751924215512137359384251036116044997039668442865600947306098283007696862048549437537
m: 100000000000000000000000000000000
c5: 10
c0: -7
skew: 1
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4300001)
Primes: RFBsize:283146, AFBsize:283312, largePrimes:5877861 encountered
Relations: rels:6000830, finalFF:721765
Max relations in full relation-set: 28
Initial matrix: 566524 x 721765 with sparse part having weight 54341674.
Pruned matrix : 457362 x 460258 with weight 38665354.
Total sieving time: 63.28 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.03 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 66.69 hours.
 --------- CPU info (if available) ----------

Jun 1, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=560000, GGNFS-0.77.1-20051202-athlon

4·10¹⁵⁷-3 = 3(9)₁₅₆7_<158> = 37 · 233 · 654148025247903819445200473_<27> · C127

C127 = P32 · P96

P32 = 62340393015907132203772014784207_<32>

P96 = 113777601846523036079732053245822156937012105295007861651633387620863333730618728133717777250487_<96>

(85·10¹⁶⁹+41)/9 = 9(4)₁₆₈9_<170> = 3 · 11 · C169

C169 = P63 · P106

P63 = 337429506941298590268921093583466887034433804138214090669941277_<63>

P106 = 8481631875930594596160003598731475226771065372836124267124902782195037863783694946883546357302023696007989_<106>

Number: n
N=2861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861953
  ( 169 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=337429506941298590268921093583466887034433804138214090669941277 (pp63)
 r2=8481631875930594596160003598731475226771065372836124267124902782195037863783694946883546357302023696007989 (pp106)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 133.60 hours.
Scaled time: 159.65 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_9_4_168_9
n: 2861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861952861953
type: snfs
skew: 1.37
deg: 5
c5: 17
c0: 82
m: 10000000000000000000000000000000000
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4600000)
Primes: RFBsize:348513, AFBsize:348332, largePrimes:8361615 encountered
Relations: rels:7975410, finalFF:799001
Max relations in full relation-set: 28
Initial matrix: 696910 x 799001 with sparse part having weight 48586055.
Pruned matrix : 614721 x 618269 with weight 34462549.
Total sieving time: 122.13 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 10.66 hours.
Total square root time: 0.37 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.6,2.6,100000
total time: 133.60 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

4·10¹⁵⁶-3 = 3(9)₁₅₅7_<157> = 59 · 107 · 1194517 · 1712017 · 268088377 · 131763604859_<12> · C121

C121 = P58 · P64

P58 = 2702234461760532104363775230161432847793282975403282127651_<58>

P64 = 3245841528993986751667674942064439467735740830325023575616058697_<64>

Number: n
N=8771024837061048350610970945063973785556427253671346977621808892523940551674405429952867892855853749371963409409062730747
  ( 121 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=2702234461760532104363775230161432847793282975403282127651 (pp58)
 r2=3245841528993986751667674942064439467735740830325023575616058697 (pp64)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 23.94 hours.
Scaled time: 34.62 units (timescale=1.446).
Factorization parameters were as follows:
name: KA_3_9_155_7
n: 8771024837061048350610970945063973785556427253671346977621808892523940551674405429952867892855853749371963409409062730747
skew: 0.60
deg: 5
c5: 40
c0: -3
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:216816, AFBsize:215821, largePrimes:7084810 encountered
Relations: rels:6713200, finalFF:621804
Max relations in full relation-set: 28
Initial matrix: 432703 x 621804 with sparse part having weight 40249107.
Pruned matrix : 274950 x 277177 with weight 20349576.
Total sieving time: 21.56 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 2.09 hours.
Total square root time: 0.10 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 23.94 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 2007

May 31, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp

4·10¹⁵⁴+3 = 4(0)₁₅₃3_<155> = 1327 · 870755550325850941_<18> · C134

C134 = P35 · P40 · P60

P35 = 22208856755600059957457268067062121_<35>

P40 = 1894425688430070080563866230389466204449_<40>

P60 = 822790066767611381874600814825665810874654564700976063637801_<60>

Number: n
N=34617270133071285415914354745753361151760004396813244310996447931454777677825544431616161322375402810136808065672456644101628679212529
  ( 134 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=22208856755600059957457268067062121 (pp35)
 r2=1894425688430070080563866230389466204449 (pp40)
 r3=822790066767611381874600814825665810874654564700976063637801 (pp60)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 28.57 hours.
Scaled time: 38.97 units (timescale=1.364).
Factorization parameters were as follows:
name: KA_4_0_153_3
n: 34617270133071285415914354745753361151760004396813244310996447931454777677825544431616161322375402810136808065672456644101628679212529
skew: 1.50
deg: 5
c5: 2
c0: 15
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:216816, AFBsize:216721, largePrimes:6921372 encountered
Relations: rels:6417283, finalFF:508343
Max relations in full relation-set: 28
Initial matrix: 433602 x 508343 with sparse part having weight 33814808.
Pruned matrix : 369514 x 371746 with weight 20585563.
Total sieving time: 25.59 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.38 hours.
Total square root time: 0.41 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 28.57 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 31, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

4·10¹⁵⁵+3 = 4(0)₁₅₄3_<156> = 131 · 277 · 1597 · 131311 · 823553 · 667849372139_<12> · C125

C125 = P54 · P72

P54 = 492825456187630481531157139782940959270957733499511907_<54>

P72 = 193927631621634265976915268190761855606404319236001612241209942831445103_<72>

Number: 40003_155
N=95572473521318661498662645987832126295159614647710436217024143597699587551562764245776486857662364971023065753927621965341421
  ( 125 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=492825456187630481531157139782940959270957733499511907 (pp54)
 r2=193927631621634265976915268190761855606404319236001612241209942831445103 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 17.81 hours.
Scaled time: 16.60 units (timescale=0.932).
Factorization parameters were as follows:
n: 95572473521318661498662645987832126295159614647710436217024143597699587551562764245776486857662364971023065753927621965341421
m: 10000000000000000000000000000000
c5: 4
c0: 3
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2500001)
Primes: RFBsize:216816, AFBsize:216936, largePrimes:5532285 encountered
Relations: rels:5477183, finalFF:544684
Max relations in full relation-set: 28
Initial matrix: 433819 x 544684 with sparse part having weight 40709982.
Pruned matrix : 354442 x 356675 with weight 25742292.
Total sieving time: 16.97 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.72 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 17.81 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 31, 2007 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 gnfs

(2·10¹⁸⁸-17)/3 = (6)₁₈₇1_<188> = 1249 · 4441 · 6752297 · 1389323376967_<13> · 16824073891211_<14> · 1216695017169281822145299803_<28> · C122

C122 = P39 · P41 · P43

P39 = 615078923306073798787696079184152415389_<39>

P41 = 85050733879933863941346674478983397401509_<41>

P43 = 1196434264494666367424967458018651028134987_<43>

Number: 66661_188
N=62588962571313430923171131998101606731573624728012758991844454013795770476577693323728766959320614463002807069297413648987
  ( 122 digits)
Divisors found:
 r1=615078923306073798787696079184152415389 (pp39)
 r2=85050733879933863941346674478983397401509 (pp41)
 r3=1196434264494666367424967458018651028134987 (pp43)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 159.90 hours.
Scaled time: 97.54 units (timescale=0.610).
Factorization parameters were as follows:
name: 66661_188
n: 62588962571313430923171131998101606731573624728012758991844454013795770476577693323728766959320614463002807069297413648987
skew: 114576.20
# norm 3.31e+17
c5: 13440
c4: 2462590922
c3: -6373329795304895
c2: 17153346731370743370
c1: 5085559537440422841815590
c0: -17067805229319834584176509187
# alpha -6.44
Y1: 476997068339
Y0: -341680091446117488971230
# Murphy_E 2.10e-10
# M 45437465253762539043198554707571244147803654915231204116125873835555610032596555634445435860298252922599408721648658256309
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 5380001)
Primes: RFBsize:348513, AFBsize:349461, largePrimes:7667930 encountered
Relations: rels:7745473, finalFF:782034
Max relations in full relation-set: 0
Initial matrix: 698054 x 782034 with sparse part having weight 82397365.
Pruned matrix : 631630 x 635184 with weight 58591835.
Total sieving time: 128.25 hours.
Total relation processing time: 1.52 hours.
Matrix solve time: 29.47 hours.
Time per square root: 0.66 hours.
Prototype def-par.txt line would be:
gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 159.90 hours.
 --------- CPU info (if available) ----------

May 31, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GMP-ECM 5.0

(4·10¹⁷⁰+23)/9 = (4)₁₆₉7_<170> = 193 · C168

C168 = P54 · P114

P54 = 549040020458710771002201900655139572384963724205511693_<54>

P114 = 419426794015259711436313029497443646256396503285623169529962875069579148740583046787001583894004049064540008475803_<114>

Number: n
N=230282095567069660333909038572251007484168105929763960852043753598157743235463442717328727691421991940126655152561888313183649971214738054116292458261370178468624064479
  ( 168 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=549040020458710771002201900655139572384963724205511693 (pp54)
 r2=419426794015259711436313029497443646256396503285623169529962875069579148740583046787001583894004049064540008475803 (pp114)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 100.59 hours.
Scaled time: 130.46 units (timescale=1.297).
Factorization parameters were as follows:
name: KA_4_169_7
n: 230282095567069660333909038572251007484168105929763960852043753598157743235463442717328727691421991940126655152561888313183649971214738054116292458261370178468624064479
skew: 1.42
deg: 5
c5: 4
c0: 23
m: 10000000000000000000000000000000000
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 4100001)
Primes: RFBsize:348513, AFBsize:349036, largePrimes:8203799 encountered
Relations: rels:7823329, finalFF:797317
Max relations in full relation-set: 48
Initial matrix: 697613 x 797316 with sparse part having weight 47748724.
Pruned matrix : 612060 x 615612 with weight 32155030.
Total sieving time: 90.86 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 9.30 hours.
Total square root time: 0.11 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000
total time: 100.59 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(89·10¹⁶⁹+1)/9 = 9(8)₁₆₈9_<170> = 3 · 11 · C169

C169 = P31 · P31 · P109

P31 = 1043029760492294778115192930717_<31>

P31 = 2137408286980640850586822612999_<31>

P109 = 1344155050671296329476443457173504996983463628893573178601520913356656425293555294725257688032563620895713451_<109>

4·10¹⁵³-3 = 3(9)₁₅₂7_<154> = 7 · 36598463075809_<14> · C140

C140 = P42 · P98

P42 = 701099996975822570854039960283603801308933_<42>

P98 = 22269944676906901137452796561787706700352178347453639664548712306567745747002959525951900206522943_<98>

Number: n
N=15613458145631164347237085705726909851541504966835942770071043310541639583131603539496937230552694437403073893194338315775770015008095349819
  ( 140 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=701099996975822570854039960283603801308933 (pp42)
 r2=22269944676906901137452796561787706700352178347453639664548712306567745747002959525951900206522943 (pp98)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.25 hours.
Scaled time: 27.83 units (timescale=1.446).
Factorization parameters were as follows:
name: KA_3_9_152_7
n: 15613458145631164347237085705726909851541504966835942770071043310541639583131603539496937230552694437403073893194338315775770015008095349819
skew: 0.47
deg: 5
c5: 125
c0: -3
m: 2000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:216816, AFBsize:216491, largePrimes:6596221 encountered
Relations: rels:6125563, finalFF:526499
Max relations in full relation-set: 28
Initial matrix: 433372 x 526499 with sparse part having weight 29888782.
Pruned matrix : 349897 x 352127 with weight 15831553.
Total sieving time: 16.64 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 2.14 hours.
Total square root time: 0.30 hours, sqrts: 6.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 19.25 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 30, 2007 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-k8

4·10¹⁴⁸+3 = 4(0)₁₄₇3_<149> = 43 · 433 · 100065703 · 12687175129_<11> · 6739023729247306489_<19> · C108

C108 = P45 · P63

P45 = 653001312242351067783538309652220151840959811_<45>

P63 = 384540790042736112351657990250185253692610846424727214146899269_<63>

Number: 40003_148
N=251105640508617088508594586058925115736503829395097331809337690282772505242310817076184722144502554494278159
  ( 108 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=653001312242351067783538309652220151840959811 (pp45)
 r2=384540790042736112351657990250185253692610846424727214146899269 (pp63)
Version: GGNFS-0.77.1-20060513-k8
Total time: 20.03 hours.
Scaled time: 40.12 units (timescale=2.003).
Factorization parameters were as follows:
name: 40003_148
n: 251105640508617088508594586058925115736503829395097331809337690282772505242310817076184722144502554494278159
m: 200000000000000000000000000000
c5: 125
c0: 3
skew: 1
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 3150001)
Primes: RFBsize:114155, AFBsize:113877, largePrimes:2878785 encountered
Relations: rels:2881700, finalFF:275946
Max relations in full relation-set: 28
Initial matrix: 228097 x 275946 with sparse part having weight 29748606.
Pruned matrix : 213753 x 214957 with weight 21355785.
Total sieving time: 19.28 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.52 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 20.03 hours.
 --------- CPU info (if available) ----------

May 30, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon

4·10¹⁴⁶-3 = 3(9)₁₄₅7_<147> = 83 · 42777895789_<11> · 15924396733100297500381_<23> · C112

C112 = P54 · P59

P54 = 396348820700316782956965255363264113551018768822430003_<54>

P59 = 17849330111541476189358027901066221476707550990700167833117_<59>

Number: n
N=7074560940000117910361767328829998654766660683366389419564365970920304578753086742163420558422550942946917809351
  ( 112 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=396348820700316782956965255363264113551018768822430003 (pp54)
 r2=17849330111541476189358027901066221476707550990700167833117 (pp59)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 9.64 hours.
Scaled time: 12.58 units (timescale=1.305).
Factorization parameters were as follows:
name: KA_3_9_145_7
n: 7074560940000117910361767328829998654766660683366389419564365970920304578753086742163420558422550942946917809351
skew: 0.60
deg: 5
c5: 40
c0: -3
m: 100000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1000001)
Primes: RFBsize:183072, AFBsize:182506, largePrimes:6452273 encountered
Relations: rels:5881816, finalFF:435332
Max relations in full relation-set: 28
Initial matrix: 365644 x 435332 with sparse part having weight 25318441.
Pruned matrix : 305134 x 307026 with weight 14058892.
Total sieving time: 7.61 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.77 hours.
Total square root time: 0.09 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 9.64 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10¹⁵²+3 = 4(0)₁₅₁3_<153> = 13 · 31 · 1051 · C147

C147 = P67 · P81

P67 = 2801114324800249062766187692606357600549569364661409619095961178167_<67>

P81 = 337148626424781873328036805457958920928175121942812922349685550558244211164690453_<81>

Number: n
N=944391847065184286264056682398660852360861568682077567624358698911352298295608814009108659364943702441016826701735083921020509829938638139736939651
  ( 147 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=2801114324800249062766187692606357600549569364661409619095961178167 (pp67)
 r2=337148626424781873328036805457958920928175121942812922349685550558244211164690453 (pp81)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 17.49 hours.
Scaled time: 25.34 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_4_0_151_3
n: 944391847065184286264056682398660852360861568682077567624358698911352298295608814009108659364943702441016826701735083921020509829938638139736939651
skew: 0.75
deg: 5
c5: 25
c0: 6
m: 2000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 800001)
Primes: RFBsize:216816, AFBsize:215956, largePrimes:6769972 encountered
Relations: rels:6408744, finalFF:619286
Max relations in full relation-set: 28
Initial matrix: 432836 x 619286 with sparse part having weight 33677825.
Pruned matrix : 266552 x 268780 with weight 14872464.
Total sieving time: 15.76 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.48 hours.
Total square root time: 0.09 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 17.49 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

4·10¹⁵¹+3 = 4(0)₁₅₀3_<152> = 87523 · 4494503443_<10> · C138

C138 = P43 · P95

P43 = 1297415475912073088053509540386798385058609_<43>

P95 = 78374900853242505310466623601273918272208107442148395944232718006339250364736934925355798428203_<95>

Number: n
N=101684809290071168164673608485184602435969068234105883657731058672297789123043221176110896404625443994231824114694450958074636842233549627
  ( 138 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=1297415475912073088053509540386798385058609 (pp43)
 r2=78374900853242505310466623601273918272208107442148395944232718006339250364736934925355798428203 (pp95)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 16.66 hours.
Scaled time: 22.81 units (timescale=1.369).
Factorization parameters were as follows:
name: KA_4_0_150_3
n: 101684809290071168164673608485184602435969068234105883657731058672297789123043221176110896404625443994231824114694450958074636842233549627
skew: 0.60
deg: 5
c5: 40
c0: 3
m: 1000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 700001)
Primes: RFBsize:216816, AFBsize:215821, largePrimes:6287333 encountered
Relations: rels:5832658, finalFF:518542
Max relations in full relation-set: 28
Initial matrix: 432703 x 518542 with sparse part having weight 27684554.
Pruned matrix : 351235 x 353462 with weight 14649647.
Total sieving time: 14.75 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.66 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 16.66 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 30, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

4·10¹⁵³+3 = 4(0)₁₅₂3_<154> = 163 · 647531 · 11061581 · 4124679348155700834063553597_<28> · C111

C111 = P52 · P60

P52 = 3535740861654872658270519573725613482190542128854473_<52>

P60 = 234922167135062332183441254151884253123634863112124506309891_<60>

Number: 40003_153
N=830623905647955297761358148882626558774270445628540572480336272874132992508238565769278537971704421868179492443
  ( 111 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=3535740861654872658270519573725613482190542128854473 (pp52)
 r2=234922167135062332183441254151884253123634863112124506309891 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 17.10 hours.
Scaled time: 15.97 units (timescale=0.934).
Factorization parameters were as follows:
n: 830623905647955297761358148882626558774270445628540572480336272874132992508238565769278537971704421868179492443
m: 2000000000000000000000000000000
c5: 125
c0: 3
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2200001)
Primes: RFBsize:176302, AFBsize:175868, largePrimes:5638026 encountered
Relations: rels:5620624, finalFF:535694
Max relations in full relation-set: 28
Initial matrix: 352235 x 535694 with sparse part having weight 48622419.
Pruned matrix : 279893 x 281718 with weight 25069298.
Total sieving time: 16.52 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.46 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 17.10 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 29, 2007 (8th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs

4·10¹⁵²-3 = 3(9)₁₅₁7_<153> = 21200771 · 25893612998221_<14> · 14503289669621063451952205056921_<32> · C101

C101 = P45 · P57

P45 = 230079279032884613931774793453258451457362123_<45>

P57 = 218359280476393118332391848988420792397153683310217125049_<57>

Number: 39997_152
N=50239945822147965823364715757449975132547131611251114455272136849140078848825124186413611002367119027
  ( 101 digits)
Divisors found:
 r1=230079279032884613931774793453258451457362123 (pp45)
 r2=218359280476393118332391848988420792397153683310217125049 (pp57)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.32 hours.
Scaled time: 4.04 units (timescale=0.935).
Factorization parameters were as follows:
name: 39997_152
n: 50239945822147965823364715757449975132547131611251114455272136849140078848825124186413611002367119027
skew: 2745.59
# norm 4.18e+13
c5: 253440
c4: -2237299026
c3: -1907163396717
c2: 18351442515410243
c1: 16149480465216217123
c0: -4732032708429412165896
# alpha -5.26
Y1: 20037749981
Y0: -11466639011392083421
# Murphy_E 3.20e-09
# M 9786743912553846833483490233928381167753400889953592353099544647107720629570548238023689159496745801
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [750000, 1300001)
Primes: RFBsize:114155, AFBsize:114153, largePrimes:3944606 encountered
Relations: rels:3941658, finalFF:355357
Max relations in full relation-set: 28
Initial matrix: 228389 x 355357 with sparse part having weight 29022648.
Pruned matrix : 163717 x 164922 with weight 11611115.
Polynomial selection time: 0.28 hours.
Total sieving time: 3.83 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,48,48,2.5,2.5,50000
total time: 4.32 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 29, 2007 (7th)

By Max Voznyy / GGNFS-0.77.1-20060513-pentium4

2·10¹⁵⁵-3 = 1(9)₁₅₄7_<156> = 7 · 67 · 71 · 343866401642039_<15> · 141423577541870006652967_<24> · C114

C114 = P46 · P69

P46 = 1176075110392218874344361392155876226533549449_<46>

P69 = 105015204394259862679542119957655122688478278199700532417643933576919_<69>

May 29, 2007 (6th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

4·10¹⁴⁵-3 = 3(9)₁₄₄7_<146> = 29 · 37 · 636458547278605123477_<21> · C122

C122 = P47 · P76

P47 = 22032652827179182252311595341228758697101383067_<47>

P76 = 2658418526818926672086758087119698387445371990728081899202841400303836244571_<76>

Number: 39997_145
N=58572012470742541478080301062763303277153080662009129442516557774603576611369036613001881755526790043397812934327370079257
  ( 122 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=22032652827179182252311595341228758697101383067 (pp47)
 r2=2658418526818926672086758087119698387445371990728081899202841400303836244571 (pp76)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 9.31 hours.
Scaled time: 8.69 units (timescale=0.933).
Factorization parameters were as follows:
n: 58572012470742541478080301062763303277153080662009129442516557774603576611369036613001881755526790043397812934327370079257
m: 100000000000000000000000000000
c5: 4
c0: -3
skew: 1
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 1350001)
Primes: RFBsize:114155, AFBsize:113917, largePrimes:2689998 encountered
Relations: rels:2699548, finalFF:315804
Max relations in full relation-set: 28
Initial matrix: 228139 x 315804 with sparse part having weight 21287815.
Pruned matrix : 191614 x 192818 with weight 10724400.
Total sieving time: 9.13 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000
total time: 9.31 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 29, 2007 (5th)

By suberi / GMP-ECM 6.1.2 B1=3000000

2·10¹⁷³+3 = 2(0)₁₇₂3_<174> = 31 · 3164590541963_<13> · C160

C160 = P43 · C118

P43 = 1377280097548571230432695973091803101076339_<43>

C118 = [1480227622542794165404399819785920618847153787232185974759390499635827513314206276438905310385107334421379192165686509_<118>]

May 29, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon

4·10¹⁴⁴-3 = 3(9)₁₄₃7_<145> = 359 · 9311 · 8600737381_<10> · C129

C129 = P37 · P44 · P49

P37 = 1127069158597835253730690599540227387_<37>

P44 = 25704964961697827080699390888797399431064217_<44>

P49 = 4802484227003858903586540234824184542371863661547_<49>

Number: n
N=139134082728901552207477531234965837137139548962918480744051676763860644141313152952523265954505770179676760121611692870007824513
  ( 129 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=1127069158597835253730690599540227387 (pp37)
 r2=25704964961697827080699390888797399431064217 (pp44)
 r3=4802484227003858903586540234824184542371863661547 (pp49)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 10.39 hours.
Scaled time: 14.13 units (timescale=1.361).
Factorization parameters were as follows:
name: KA_3_9_143_7
n: 139134082728901552207477531234965837137139548962918480744051676763860644141313152952523265954505770179676760121611692870007824513
skew: 1.50
deg: 5
c5: 2
c0: -15
m: 100000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:183072, AFBsize:182991, largePrimes:6720704 encountered
Relations: rels:6184111, finalFF:468239
Max relations in full relation-set: 28
Initial matrix: 366128 x 468238 with sparse part having weight 29402590.
Pruned matrix : 281075 x 282969 with weight 14990558.
Total sieving time: 8.64 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.31 hours.
Total square root time: 0.25 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 10.39 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10¹⁴⁵+3 = 4(0)₁₄₄3_<146> = 15679 · 8391654179_<10> · 1630535804362988309_<19> · C114

C114 = P45 · P69

P45 = 646714525652426822605941812765336474593578059_<45>

P69 = 288304285235034063465342910556093561504177705697017827218911974846793_<69>

Number: n
N=186450569069337016472379512674172687327990157379633781153481333472695354444304795726582573723536382949298211314787
  ( 114 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=646714525652426822605941812765336474593578059 (pp45)
 r2=288304285235034063465342910556093561504177705697017827218911974846793 (pp69)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.95 hours.
Scaled time: 11.52 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_4_0_144_3
n: 186450569069337016472379512674172687327990157379633781153481333472695354444304795726582573723536382949298211314787
skew: 0.94
deg: 5
c5: 4
c0: 3
m: 100000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:183072, AFBsize:182816, largePrimes:6481222 encountered
Relations: rels:5947081, finalFF:465397
Max relations in full relation-set: 28
Initial matrix: 365955 x 465397 with sparse part having weight 26481654.
Pruned matrix : 278114 x 280007 with weight 12854649.
Total sieving time: 6.13 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.30 hours.
Total square root time: 0.37 hours, sqrts: 9.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 7.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 29, 2007 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-k8

4·10¹⁴⁶+3 = 4(0)₁₄₅3_<147> = 13 · 41023 · 2958721 · 248105437 · 1101807494113_<13> · 7014417751034503_<16> · C99

C99 = P41 · P58

P41 = 41503832743290556850451533494303423483207_<41>

P58 = 3185395578251891000053013244421171035550838420033010094357_<58>

Number: 40003_146
N=132206125300983790896326376581325564446111856146621668386739588502853251960027942344108792674962899
  ( 99 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=41503832743290556850451533494303423483207 (pp41)
 r2=3185395578251891000053013244421171035550838420033010094357 (pp58)
Version: GGNFS-0.77.1-20060513-k8
Total time: 14.41 hours.
Scaled time: 28.87 units (timescale=2.003).
Factorization parameters were as follows:
name: 40003_146
n: 132206125300983790896326376581325564446111856146621668386739588502853251960027942344108792674962899
m: 100000000000000000000000000000
c5: 40
c0: 3
skew: 1
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2450001)
Primes: RFBsize:114155, AFBsize:113697, largePrimes:2764799 encountered
Relations: rels:2738945, finalFF:275539
Max relations in full relation-set: 28
Initial matrix: 227918 x 275539 with sparse part having weight 25625759.
Pruned matrix : 211958 x 213161 with weight 17651075.
Total sieving time: 13.81 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.41 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 14.41 hours.
 --------- CPU info (if available) ----------

May 29, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

(5·10¹⁷⁴+1)/3 = 1(6)₁₇₃7_<175> = C175

C175 = P38 · P137

P38 = 38957826032363776525856717580374065723_<38>

P137 = 42781305745400219407473710733596304514150377883882257718360293742320702825809015275337663456972351386349942222557906259254671065933070929_<137>

Number: 16667_174
N=1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667
  ( 175 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=38957826032363776525856717580374065723 (pp38)
 r2=42781305745400219407473710733596304514150377883882257718360293742320702825809015275337663456972351386349942222557906259254671065933070929 (pp137)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 137.22 hours.
Scaled time: 127.48 units (timescale=0.929).
Factorization parameters were as follows:
n: 1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667
m: 100000000000000000000000000000000000
c5: 1
c0: 2
skew: 1.15
type: snfs
Factor base limits: 9000000/9000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 49/49
Sieved algebraic special-q in [4500000, 6600001)
Primes: RFBsize:602489, AFBsize:602700, largePrimes:10034680 encountered
Relations: rels:10282311, finalFF:1497466
Max relations in full relation-set: 28
Initial matrix: 1205253 x 1497466 with sparse part having weight 66712191.
Pruned matrix : 923325 x 929415 with weight 36490841.
Total sieving time: 132.24 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 4.73 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,49,49,2.6,2.6,100000
total time: 137.22 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 29, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon

4·10¹⁴¹-3 = 3(9)₁₄₀7_<142> = 7 · 52313 · C137

C137 = P62 · P75

P62 = 72534046490829353664593295091274835834185520668502881701648559_<62>

P75 = 150594953495731883967116548567354812204313653884473343476632001562146074013_<75>

Number: n
N=10923261358143700964797059458042387715700276631593894989226933485530774923468900109505695115390602172090521066874936849895273231728797267
  ( 137 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=72534046490829353664593295091274835834185520668502881701648559 (pp62)
 r2=150594953495731883967116548567354812204313653884473343476632001562146074013 (pp75)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 7.74 hours.
Scaled time: 10.58 units (timescale=1.366).
Factorization parameters were as follows:
name: KA_3_9_140_7
n: 10923261358143700964797059458042387715700276631593894989226933485530774923468900109505695115390602172090521066874936849895273231728797267
skew: 0.60
deg: 5
c5: 40
c0: -3
m: 10000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 700001)
Primes: RFBsize:183072, AFBsize:182506, largePrimes:5965783 encountered
Relations: rels:5451650, finalFF:451267
Max relations in full relation-set: 28
Initial matrix: 365644 x 451267 with sparse part having weight 21857445.
Pruned matrix : 283591 x 285483 with weight 10333770.
Total sieving time: 6.72 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.83 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 7.74 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10¹⁴²+3 = 4(0)₁₄₁3_<143> = 19 · 397523109523_<12> · 1792722597263327053_<19> · C112

C112 = P51 · P61

P51 = 361944429343387970109181659326070203309043443208301_<51>

P61 = 8161857721768944819535587526816743204330570033059102272751923_<61>

Number: n
N=2954138935487585358037504212441582467115017534237517833386470674579036800877959937028708758566992431307387312823
  ( 112 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=361944429343387970109181659326070203309043443208301 (pp51)
 r2=8161857721768944819535587526816743204330570033059102272751923 (pp61)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.94 hours.
Scaled time: 10.04 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_4_0_141_3
n: 2954138935487585358037504212441582467115017534237517833386470674579036800877959937028708758566992431307387312823
skew: 0.75
deg: 5
c5: 25
c0: 6
m: 20000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 800001)
Primes: RFBsize:183072, AFBsize:182381, largePrimes:6642527 encountered
Relations: rels:6258535, finalFF:588785
Max relations in full relation-set: 28
Initial matrix: 365517 x 588785 with sparse part having weight 31133532.
Pruned matrix : 183587 x 185478 with weight 13613993.
Total sieving time: 5.76 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.93 hours.
Total square root time: 0.10 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 6.94 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 28, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(7·10¹⁶⁰-61)/9 = (7)₁₅₉1_<160> = 1087 · C157

C157 = P60 · P98

P60 = 133767292172935551579599522862258137018645605013343066361981_<60>

P98 = 53490425264281855146460077769801026058944569491640678743898434821351499978338309471009601998689593_<98>

Number: n
N=7155269344781764284984156189307983236226106511295103751405499335582132270264744965756925278544413779004395379740365940917918838802003475416538893999795563733
  ( 157 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=133767292172935551579599522862258137018645605013343066361981 (pp60)
 r2=53490425264281855146460077769801026058944569491640678743898434821351499978338309471009601998689593 (pp98)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 34.44 hours.
Scaled time: 49.48 units (timescale=1.437).
Factorization parameters were as follows:
name: KA_7_159_1
n: 7155269344781764284984156189307983236226106511295103751405499335582132270264744965756925278544413779004395379740365940917918838802003475416538893999795563733
skew: 1.54
deg: 5
c5: 7
c0: -61
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1600001)
Primes: RFBsize:250150, AFBsize:250502, largePrimes:7175624 encountered
Relations: rels:6724740, finalFF:585888
Max relations in full relation-set: 28
Initial matrix: 500717 x 585888 with sparse part having weight 36048352.
Pruned matrix : 426488 x 429055 with weight 21797147.
Total sieving time: 30.15 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 4.01 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 34.44 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 28, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

4·10¹³⁸+3 = 4(0)₁₃₇3_<139> = 7 · 1033 · C135

C135 = P48 · P87

P48 = 930729119481891694801482963283168394796716926087_<48>

P87 = 594344609294641138185135993021839496344619029158623927721993187831394871362972952598299_<87>

Number: 40003_138
N=553173834877610289033328723551376019914258055593970405199834047849536716913290001382934587194025722583321808878440049785645138984926013
  ( 135 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=930729119481891694801482963283168394796716926087 (pp48)
 r2=594344609294641138185135993021839496344619029158623927721993187831394871362972952598299 (pp87)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.68 hours.
Scaled time: 4.37 units (timescale=0.934).
Factorization parameters were as follows:
n: 553173834877610289033328723551376019914258055593970405199834047849536716913290001382934587194025722583321808878440049785645138984926013
m: 2000000000000000000000000000
c5: 125
c0: 3
skew: 1
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [700000, 1550001)
Primes: RFBsize:107126, AFBsize:107023, largePrimes:1652918 encountered
Relations: rels:1714233, finalFF:241604
Max relations in full relation-set: 28
Initial matrix: 214214 x 241604 with sparse part having weight 12448402.
Pruned matrix : 201680 x 202815 with weight 8746891.
Total sieving time: 4.51 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,44,44,2.3,2.3,50000
total time: 4.68 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹³⁸-3 = 3(9)₁₃₇7_<139> = 167 · 61953817 · C129

C129 = P57 · P73

P57 = 234806247524789276541047560136279747605593670548390630143_<57>

P73 = 1646515424474759157709862360552930904493428048558253258347121490936014861_<73>

Number: 39997_138
N=386612108312603782474518587555742467131354168827475971306232718709990983848984480161415704893794803065494070892108722517002555123
  ( 129 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=234806247524789276541047560136279747605593670548390630143 (pp57)
 r2=1646515424474759157709862360552930904493428048558253258347121490936014861 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.94 hours.
Scaled time: 4.61 units (timescale=0.934).
Factorization parameters were as follows:
n: 386612108312603782474518587555742467131354168827475971306232718709990983848984480161415704893794803065494070892108722517002555123
m: 2000000000000000000000000000
c5: 125
c0: -3
skew: 1
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [700000, 1600001)
Primes: RFBsize:107126, AFBsize:107023, largePrimes:1685915 encountered
Relations: rels:1768512, finalFF:259015
Max relations in full relation-set: 28
Initial matrix: 214214 x 259015 with sparse part having weight 14204838.
Pruned matrix : 192969 x 194104 with weight 8814070.
Total sieving time: 4.78 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,44,44,2.3,2.3,50000
total time: 4.94 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹³⁹+3 = 4(0)₁₃₈3_<140> = 730085207 · 4622218820599_<13> · 1090080139886653_<16> · C104

C104 = P40 · P64

P40 = 2443464119454710007355153216679458364521_<40>

P64 = 4450118210277028673112750346091921480847013205495714394729918167_<64>

Number: 40003_139
N=10873704174143929896811554488954462461135888027735618494324499305001323585745628849144582691257986153007
  ( 104 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=2443464119454710007355153216679458364521 (pp40)
 r2=4450118210277028673112750346091921480847013205495714394729918167 (pp64)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.54 hours.
Scaled time: 7.97 units (timescale=0.934).
Factorization parameters were as follows:
n: 10873704174143929896811554488954462461135888027735618494324499305001323585745628849144582691257986153007
m: 10000000000000000000000000000
c5: 2
c0: 15
skew: 1.5
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [700000, 1250001)
Primes: RFBsize:107126, AFBsize:107113, largePrimes:1679573 encountered
Relations: rels:1762335, finalFF:255346
Max relations in full relation-set: 28
Initial matrix: 214304 x 255346 with sparse part having weight 13522951.
Pruned matrix : 192825 x 193960 with weight 8429277.
Total sieving time: 8.39 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,44,44,2.3,2.3,50000
total time: 8.54 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 28, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp

(14·10¹⁵⁹-41)/9 = 1(5)₁₅₈1_<160> = 3² · 11 · 5783 · 6871 · C150

C150 = P34 · P116

P34 = 6031459152120337884517237707176687_<34>

P116 = 65562393470958923411536676667369852579711360794342128936197039393056889008855481635744308817305722437678656721468939_<116>

Number: n
N=395436898135329884560761905239269729221109523772888194939726864412661303745861547763429730960634179030786440951749566920750332476783936500229055425093
  ( 150 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=6031459152120337884517237707176687 (pp34)
 r2=65562393470958923411536676667369852579711360794342128936197039393056889008855481635744308817305722437678656721468939 (pp116)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 38.14 hours.
Scaled time: 52.13 units (timescale=1.367).
Factorization parameters were as follows:
name: KA_1_5_158_1
n: 395436898135329884560761905239269729221109523772888194939726864412661303745861547763429730960634179030786440951749566920750332476783936500229055425093
skew: 1.96
deg: 5
c5: 7
c0: -205
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1600001)
Primes: RFBsize:250150, AFBsize:250442, largePrimes:7155416 encountered
Relations: rels:6677810, finalFF:563496
Max relations in full relation-set: 28
Initial matrix: 500657 x 563496 with sparse part having weight 34543217.
Pruned matrix : 444914 x 447481 with weight 22819760.
Total sieving time: 33.89 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.39 hours.
Total square root time: 0.64 hours, sqrts: 5.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 38.14 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 27, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, Msieve 1.21

4·10¹²⁷-3 = 3(9)₁₂₆7_<128> = 37 · 1663 · 18719 · 5365901 · C112

C112 = P48 · P64

P48 = 705022162775505898789224106446296802990040895033_<48>

P64 = 9179899962009583566770141001685302094407984058465806768333958181_<64>

Number: 39997_127
N=6472032925278781041797362499390546042050955598537907195224264982188752618866909381403194723929818401764832614973
  ( 112 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=705022162775505898789224106446296802990040895033 (pp48)
 r2=9179899962009583566770141001685302094407984058465806768333958181 (pp64)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.86 hours.
Scaled time: 1.74 units (timescale=0.934).
Factorization parameters were as follows:
n: 6472032925278781041797362499390546042050955598537907195224264982188752618866909381403194723929818401764832614973
m: 20000000000000000000000000
c5: 25
c0: -6
skew: 1
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 850001)
Primes: RFBsize:78498, AFBsize:78301, largePrimes:1560655 encountered
Relations: rels:1638252, finalFF:247040
Max relations in full relation-set: 28
Initial matrix: 156863 x 247040 with sparse part having weight 11693537.
Pruned matrix : 113199 x 114047 with weight 4653390.
Total sieving time: 1.80 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 1.86 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹²⁷+3 = 4(0)₁₂₆3_<128> = 17 · 43² · 59 · 11285195303_<11> · C112

C112 = P54 · P58

P54 = 521293731281094645703485420673506602610925860757394203_<54>

P58 = 3666321666068084664903157915264085011548958113765261075461_<58>

Number: 40003_127
N=1911230501381351344749672587619391998018934950167832705841037082931427635475944060798992580228159562795706952583
  ( 112 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=521293731281094645703485420673506602610925860757394203 (pp54)
 r2=3666321666068084664903157915264085011548958113765261075461 (pp58)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.62 hours.
Scaled time: 1.51 units (timescale=0.931).
Factorization parameters were as follows:
n: 1911230501381351344749672587619391998018934950167832705841037082931427635475944060798992580228159562795706952583
m: 20000000000000000000000000
c5: 25
c0: 6
skew: 1
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 800001)
Primes: RFBsize:78498, AFBsize:78301, largePrimes:1453042 encountered
Relations: rels:1464297, finalFF:189090
Max relations in full relation-set: 28
Initial matrix: 156863 x 189090 with sparse part having weight 8244070.
Pruned matrix : 135788 x 136636 with weight 4723501.
Total sieving time: 1.55 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 1.62 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹³¹+3 = 4(0)₁₃₀3_<132> = 29 · 199 · 122709869 · C120

C120 = P47 · P74

P47 = 17745113024976168939376435372018500870859981957_<47>

P74 = 31831027271271917917211409577687106292138046864406391959013403689139371721_<74>

Number: 40003_131
N=564845176629818951808827035744745452246841772623803650887282390890456141189641461532135200682772613833908993808376037997
  ( 120 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=17745113024976168939376435372018500870859981957 (pp47)
 r2=31831027271271917917211409577687106292138046864406391959013403689139371721 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.30 hours.
Scaled time: 2.15 units (timescale=0.935).
Factorization parameters were as follows:
n: 564845176629818951808827035744745452246841772623803650887282390890456141189641461532135200682772613833908993808376037997
m: 200000000000000000000000000
c5: 5
c0: 12
skew: 1.19
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 950001)
Primes: RFBsize:78498, AFBsize:78441, largePrimes:1508956 encountered
Relations: rels:1522496, finalFF:190629
Max relations in full relation-set: 28
Initial matrix: 157005 x 190629 with sparse part having weight 9748353.
Pruned matrix : 142097 x 142946 with weight 5737145.
Total sieving time: 2.22 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 2.30 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹³²+3 = 4(0)₁₃₁3_<133> = 7 · 367699 · 75669648215166599173_<20> · C107

C107 = P49 · P59

P49 = 1112013696695243458462948812197952325199534586937_<49>

P59 = 18468756317073684462309916330756661620043623970152551745171_<59>

Number: 40003_132
N=20537509985512737778662764382555381457009554393279769385933028106871931241847355158296348401924213969431227
  ( 107 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=1112013696695243458462948812197952325199534586937 (pp49)
 r2=18468756317073684462309916330756661620043623970152551745171 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.52 hours.
Scaled time: 2.35 units (timescale=0.934).
Factorization parameters were as follows:
n: 20537509985512737778662764382555381457009554393279769385933028106871931241847355158296348401924213969431227
m: 200000000000000000000000000
c5: 25
c0: 6
skew: 1
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 1000001)
Primes: RFBsize:78498, AFBsize:78301, largePrimes:1515396 encountered
Relations: rels:1524246, finalFF:186816
Max relations in full relation-set: 28
Initial matrix: 156863 x 186816 with sparse part having weight 9456577.
Pruned matrix : 145417 x 146265 with weight 5828837.
Total sieving time: 2.43 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 2.52 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹³³-3 = 3(9)₁₃₂7_<134> = 19 · 37 · 607 · 275521 · 267823455452010358133437_<24> · C100

C100 = P41 · P59

P41 = 19092348197612899949161309484911390214209_<41>

P59 = 66535483009793897303525410667693774065268754524280636711649_<59>

Number: 39997_133
N=1270318609119342242678692386755510163774768851318400499046674123124105513718087324363376691475620641
  ( 100 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=19092348197612899949161309484911390214209 (pp41)
 r2=66535483009793897303525410667693774065268754524280636711649 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.94 hours.
Scaled time: 2.75 units (timescale=0.934).
Factorization parameters were as follows:
n: 1270318609119342242678692386755510163774768851318400499046674123124105513718087324363376691475620641
m: 200000000000000000000000000
c5: 125
c0: -3
skew: 1
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [700000, 1200001)
Primes: RFBsize:107126, AFBsize:107023, largePrimes:1614997 encountered
Relations: rels:1684678, finalFF:247912
Max relations in full relation-set: 28
Initial matrix: 214214 x 247912 with sparse part having weight 10516119.
Pruned matrix : 188686 x 189821 with weight 6629000.
Total sieving time: 2.82 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,44,44,2.3,2.3,50000
total time: 2.94 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹³⁶-3 = 3(9)₁₃₅7_<137> = 23 · 37 · 2293 · C131

C131 = P35 · P97

P35 = 15081196794111057038592942294865571_<35>

P97 = 1359222545014331678259321655350929515123649897436325733988274979310778665003786733637386489826449_<97>

Number: 39997_136
N=20498702688353610820855175128104080113029846623581810066195435656365897743246574282430100705001632209201560156261610593319575287379
  ( 131 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=15081196794111057038592942294865571 (pp35)
 r2=1359222545014331678259321655350929515123649897436325733988274979310778665003786733637386489826449 (pp97)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.84 hours.
Scaled time: 3.58 units (timescale=0.932).
Factorization parameters were as follows:
n: 20498702688353610820855175128104080113029846623581810066195435656365897743246574282430100705001632209201560156261610593319575287379
m: 2000000000000000000000000000
c5: 5
c0: -12
skew: 1.19
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [700000, 1400001)
Primes: RFBsize:107126, AFBsize:106758, largePrimes:1667272 encountered
Relations: rels:1757157, finalFF:266622
Max relations in full relation-set: 28
Initial matrix: 213950 x 266622 with sparse part having weight 12122124.
Pruned matrix : 185668 x 186801 with weight 7034894.
Total sieving time: 3.71 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,44,44,2.3,2.3,50000
total time: 3.84 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹⁵¹-3 = 3(9)₁₅₀7_<152> = 17² · 19 · 37 · 813601 · 94455601 · 97616772977_<11> · 196347596050337_<15> · 5853974215361273_<16> · C92

C92 = P43 · P50

P43 = 1910611134746116246492096414368671609087657_<43>

P50 = 11950731510953569288974090598473301504132412787619_<50>

Sun May 27 21:42:43 2007  
Sun May 27 21:42:43 2007  
Sun May 27 21:42:43 2007  Msieve v. 1.21
Sun May 27 21:42:43 2007  random seeds: 82914263 85d6b2cd
Sun May 27 21:42:43 2007  factoring 22833200693189167378341858058780999507653626440332814574305576940890044459677406916695318683 (92 digits)
Sun May 27 21:42:43 2007  commencing quadratic sieve (92-digit input)
Sun May 27 21:42:43 2007  using multiplier of 3
Sun May 27 21:42:43 2007  using 32kb Intel Core sieve core
Sun May 27 21:42:43 2007  sieve interval: 36 blocks of size 32768
Sun May 27 21:42:43 2007  processing polynomials in batches of 6
Sun May 27 21:42:43 2007  using a sieve bound of 1787717 (67004 primes)
Sun May 27 21:42:43 2007  using large prime bound of 187710285 (27 bits)
Sun May 27 21:42:43 2007  using double large prime bound of 780330238063215 (42-50 bits)
Sun May 27 21:42:43 2007  using trial factoring cutoff of 50 bits
Sun May 27 21:42:43 2007  polynomial 'A' values have 12 factors
Sun May 27 23:02:34 2007  67494 relations (17641 full + 49853 combined from 828022 partial), need 67100
Sun May 27 23:02:35 2007  begin with 845663 relations
Sun May 27 23:02:35 2007  reduce to 168237 relations in 10 passes
Sun May 27 23:02:35 2007  attempting to read 168237 relations
Sun May 27 23:02:36 2007  recovered 168237 relations
Sun May 27 23:02:36 2007  recovered 147912 polynomials
Sun May 27 23:02:36 2007  attempting to build 67494 cycles
Sun May 27 23:02:36 2007  found 67493 cycles in 5 passes
Sun May 27 23:02:37 2007  distribution of cycle lengths:
Sun May 27 23:02:37 2007     length 1 : 17641
Sun May 27 23:02:37 2007     length 2 : 12653
Sun May 27 23:02:37 2007     length 3 : 11612
Sun May 27 23:02:37 2007     length 4 : 9122
Sun May 27 23:02:37 2007     length 5 : 6485
Sun May 27 23:02:37 2007     length 6 : 4245
Sun May 27 23:02:37 2007     length 7 : 2509
Sun May 27 23:02:37 2007     length 9+: 3226
Sun May 27 23:02:37 2007  largest cycle: 19 relations
Sun May 27 23:02:37 2007  matrix is 67004 x 67493 with weight 4127294 (avg 61.15/col)
Sun May 27 23:02:37 2007  filtering completed in 4 passes
Sun May 27 23:02:37 2007  matrix is 65382 x 65446 with weight 3919902 (avg 59.90/col)
Sun May 27 23:02:38 2007  saving the first 48 matrix rows for later
Sun May 27 23:02:38 2007  matrix is 65334 x 65446 with weight 3070899 (avg 46.92/col)
Sun May 27 23:02:38 2007  matrix includes 32 packed rows
Sun May 27 23:02:38 2007  using block size 26178 for processor cache size 4096 kB
Sun May 27 23:02:58 2007  lanczos halted after 1034 iterations
Sun May 27 23:02:58 2007  recovered 18 nontrivial dependencies
Sun May 27 23:02:59 2007  prp43 factor: 1910611134746116246492096414368671609087657
Sun May 27 23:02:59 2007  prp50 factor: 11950731510953569288974090598473301504132412787619
Sun May 27 23:02:59 2007  elapsed time 01:20:16

May 27, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=3000000, Msieve v. 1.21

4·10¹⁴⁸-3 = 3(9)₁₄₇7_<149> = 37 · 157 · 373 · 2389 · 2917 · 201743 · 343164397202925323_<18> · C113

C113 = P32 · P34 · P47

P32 = 64183606304071153348418983401419_<32>

P34 = 6908604692602464799988145292045693_<34>

P47 = 86294287414556460254625701135729827536592888259_<47>

Sat May 19 13:39:49 2007  
Sat May 19 13:39:49 2007  
Sat May 19 13:39:49 2007  Msieve v. 1.21
Sat May 19 13:39:49 2007  random seeds: ab5a05f8 8d5d6b6c
Sat May 19 13:39:49 2007  factoring 13388873082149435308539000672775350680618901926900711188810262897346981830451724894509157440592356995091791 (107 digits)
Sat May 19 13:39:49 2007  commencing quadratic sieve (106-digit input)
Sat May 19 13:39:50 2007  using multiplier of 11
Sat May 19 13:39:50 2007  using 64kb Pentium 4 sieve core
Sat May 19 13:39:50 2007  sieve interval: 21 blocks of size 65536
Sat May 19 13:39:50 2007  processing polynomials in batches of 5
Sat May 19 13:39:50 2007  using a sieve bound of 4662979 (163333 primes)
Sat May 19 13:39:50 2007  using large prime bound of 699446850 (29 bits)
Sat May 19 13:39:50 2007  using double large prime bound of 8328340221930300 (45-53 bits)
Sat May 19 13:39:50 2007  using trial factoring cutoff of 53 bits
Sat May 19 13:39:50 2007  polynomial 'A' values have 14 factors
Sat May 19 13:42:08 2007  18 relations (18 full + 0 combined from 995 partial), need 163429
Sat May 19 13:42:08 2007  c107 factor: 13388873082149435308539000672775350680618901926900711188810262897346981830451724894509157440592356995091791
Sat May 19 13:42:08 2007  elapsed time 00:02:19
Sun May 27 16:46:55 2007  
Sun May 27 16:46:55 2007  
Sun May 27 16:46:55 2007  Msieve v. 1.21
Sun May 27 16:46:55 2007  random seeds: 8d7ccf94 2a377ae6
Sun May 27 16:46:55 2007  factoring 79 (2 digits)
Sun May 27 16:46:55 2007  p2 factor: 79
Sun May 27 16:46:55 2007  elapsed time 00:00:00
Sun May 27 16:47:44 2007  
Sun May 27 16:47:44 2007  
Sun May 27 16:47:44 2007  Msieve v. 1.21
Sun May 27 16:47:44 2007  random seeds: 48e51ae0 131d458c
Sun May 27 16:47:44 2007  factoring 5538678569706254011261695426721774138491854232285156975782913679145001209039521 (79 digits)
Sun May 27 16:47:45 2007  commencing quadratic sieve (79-digit input)
Sun May 27 16:47:45 2007  using multiplier of 1
Sun May 27 16:47:45 2007  using 64kb Pentium 4 sieve core
Sun May 27 16:47:45 2007  sieve interval: 6 blocks of size 65536
Sun May 27 16:47:45 2007  processing polynomials in batches of 17
Sun May 27 16:47:45 2007  using a sieve bound of 1168879 (45267 primes)
Sun May 27 16:47:45 2007  using large prime bound of 116887900 (26 bits)
Sun May 27 16:47:45 2007  using trial factoring cutoff of 27 bits
Sun May 27 16:47:45 2007  polynomial 'A' values have 10 factors
Sun May 27 16:59:38 2007  45549 relations (24447 full + 21102 combined from 238802 partial), need 45363
Sun May 27 16:59:38 2007  begin with 263249 relations
Sun May 27 16:59:39 2007  reduce to 64059 relations in 2 passes
Sun May 27 16:59:39 2007  attempting to read 64059 relations
Sun May 27 16:59:40 2007  recovered 64059 relations
Sun May 27 16:59:40 2007  recovered 47555 polynomials
Sun May 27 16:59:40 2007  attempting to build 45549 cycles
Sun May 27 16:59:40 2007  found 45549 cycles in 1 passes
Sun May 27 16:59:40 2007  distribution of cycle lengths:
Sun May 27 16:59:40 2007     length 1 : 24447
Sun May 27 16:59:40 2007     length 2 : 21102
Sun May 27 16:59:40 2007  largest cycle: 2 relations
Sun May 27 16:59:40 2007  matrix is 45267 x 45549 with weight 1349433 (avg 29.63/col)
Sun May 27 16:59:40 2007  filtering completed in 4 passes
Sun May 27 16:59:40 2007  matrix is 37509 x 37573 with weight 1083366 (avg 28.83/col)
Sun May 27 16:59:41 2007  saving the first 48 matrix rows for later
Sun May 27 16:59:41 2007  matrix is 37461 x 37573 with weight 738243 (avg 19.65/col)
Sun May 27 16:59:41 2007  matrix includes 32 packed rows
Sun May 27 17:00:24 2007  lanczos halted after 593 iterations
Sun May 27 17:00:25 2007  recovered 12 nontrivial dependencies
Sun May 27 17:00:25 2007  prp32 factor: 64183606304071153348418983401419
Sun May 27 17:00:25 2007  prp47 factor: 86294287414556460254625701135729827536592888259
Sun May 27 17:00:25 2007  elapsed time 00:12:41

May 27, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(7·10¹⁶⁰-43)/9 = (7)₁₅₉3_<160> = 3² · 67 · C158

C158 = P49 · P109

P49 = 7569214186545777793665631319644598306342954210369_<49>

P109 = 1704069972394272056243610341411329237778860200857566090684279076415414313907033462129726700942953362876790039_<109>

Number: n
N=12898470609913395983047724341256679565137276580062649714391007923346231803943246729316381057674590012898470609913395983047724341256679565137276580062649714391
  ( 158 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=7569214186545777793665631319644598306342954210369 (pp49)
 r2=1704069972394272056243610341411329237778860200857566090684279076415414313907033462129726700942953362876790039 (pp109)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 41.13 hours.
Scaled time: 59.28 units (timescale=1.441).
Factorization parameters were as follows:
name: KA_7_159_3
n: 12898470609913395983047724341256679565137276580062649714391007923346231803943246729316381057674590012898470609913395983047724341256679565137276580062649714391
skew: 1.44
deg: 5
c5: 7
c0: -43
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1900001)
Primes: RFBsize:250150, AFBsize:250336, largePrimes:7244344 encountered
Relations: rels:6806415, finalFF:586324
Max relations in full relation-set: 28
Initial matrix: 500553 x 586324 with sparse part having weight 39447333.
Pruned matrix : 427427 x 429993 with weight 24457695.
Total sieving time: 36.21 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 4.58 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 41.13 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 26, 2007 (6th)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp

2·10¹⁶⁰+3 = 2(0)₁₅₉3_<161> = 269741 · C155

C155 = P60 · P96

P60 = 300244161062830630302818080353294695395582491459143920704439_<60>

P96 = 246949676822489123478546797860086337445136656832298441810501694114885422418729064737492466489097_<96>

Number: n
N=74145198542305396658275901698295772611505110457809528399464671666524555036127247989738304521744933102494615204955865070567692712639161269514089441353001583
  ( 155 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=300244161062830630302818080353294695395582491459143920704439 (pp60)
 r2=246949676822489123478546797860086337445136656832298441810501694114885422418729064737492466489097 (pp96)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 32.43 hours.
Scaled time: 44.17 units (timescale=1.362).
Factorization parameters were as follows:
name: KA_2_0_159_3
n: 74145198542305396658275901698295772611505110457809528399464671666524555036127247989738304521744933102494615204955865070567692712639161269514089441353001583
skew: 1.08
deg: 5
c5: 2
c0: 3
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:250150, AFBsize:250246, largePrimes:6994412 encountered
Relations: rels:6520555, finalFF:565351
Max relations in full relation-set: 28
Initial matrix: 500461 x 565351 with sparse part having weight 33244971.
Pruned matrix : 440405 x 442971 with weight 21278744.
Total sieving time: 28.78 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.24 hours.
Total square root time: 0.22 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 32.43 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 26, 2007 (5th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

4·10¹²²+3 = 4(0)₁₂₁3_<123> = 13 · 31 · 751 · C118

C118 = P36 · P82

P36 = 140302808583575220937569935644682059_<36>

P82 = 9419950992110895877545261702594558645655155927342812397620420321479963685240471389_<82>

Number: 40003_122
N=1321645580912794520457421535553918183530313593455211083319841534694848555936997155157887085209794715400144720191109951
  ( 118 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=140302808583575220937569935644682059 (pp36)
 r2=9419950992110895877545261702594558645655155927342812397620420321479963685240471389 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.17 hours.
Scaled time: 1.08 units (timescale=0.927).
Factorization parameters were as follows:
n: 1321645580912794520457421535553918183530313593455211083319841534694848555936997155157887085209794715400144720191109951
m: 2000000000000000000000000
c5: 25
c0: 6
skew: 1
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 480001)
Primes: RFBsize:49098, AFBsize:49121, largePrimes:2076587 encountered
Relations: rels:2174816, finalFF:224976
Max relations in full relation-set: 28
Initial matrix: 98283 x 224976 with sparse part having weight 21075220.
Pruned matrix : 75996 x 76551 with weight 4950199.
Total sieving time: 1.11 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 1.17 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹²⁵-3 = 3(9)₁₂₄7_<126> = 13 · 347 · 1919134447_<10> · 3973122502709_<13> · C101

C101 = P44 · P57

P44 = 14176781570225689422590837043552305747546179_<44>

P57 = 820298957620154295413668754748555247326186604713123112531_<57>

Number: 39997_125
N=11629199144464747273873992857836226276685046458776844818521404624591944271991616740778007884136069049
  ( 101 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=14176781570225689422590837043552305747546179 (pp44)
 r2=820298957620154295413668754748555247326186604713123112531 (pp57)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.38 hours.
Scaled time: 1.29 units (timescale=0.935).
Factorization parameters were as follows:
n: 11629199144464747273873992857836226276685046458776844818521404624591944271991616740778007884136069049
m: 10000000000000000000000000
c5: 4
c0: -3
skew: 1
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 750001)
Primes: RFBsize:78498, AFBsize:78486, largePrimes:1470046 encountered
Relations: rels:1503361, finalFF:207858
Max relations in full relation-set: 28
Initial matrix: 157051 x 207858 with sparse part having weight 9056955.
Pruned matrix : 123990 x 124839 with weight 4351782.
Total sieving time: 1.32 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 1.38 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 26, 2007 (4th)

By suberi / GMP-ECM 6.1.2 B1=1000000

4·10¹⁵⁴-3 = 3(9)₁₅₃7_<155> = 37 · 853 · C151

C151 = P32 · P119

P32 = 13650357197160249109048459378477_<32>

P119 = 92846432266895293000127005136899584386269985976279393784014840396257054232599914470996487908411988310488572830000344201_<119>

4·10¹³⁵+3 = 4(0)₁₃₄3_<136> = 11328523 · C129

C129 = P30 · P100

P30 = 167209353214438072108071764699_<30>

P100 = 2111670406352169953615950969505952926778362473341224768552933956228839776053527035084886239827494539_<100>

May 26, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

3·10¹⁷⁰-1 = 2(9)₁₇₀_<171> = 13 · 5783 · C166

C166 = P54 · P113

P54 = 173013747441272949252140271307882198468644836377812061_<54>

P113 = 23064502808650629916626080541133445738284945384523360813873885767965239712427790623664167124028559969692067948321_<113>

Number: n
N=3990476063794410673193311962117080567711728009151491772968515143856662099788504768618896234320754466007794729911278415514970936032668697375596908711209247263198499581
  ( 166 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=173013747441272949252140271307882198468644836377812061 (pp54)
 r2=23064502808650629916626080541133445738284945384523360813873885767965239712427790623664167124028559969692067948321 (pp113)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 83.81 hours.
Scaled time: 110.71 units (timescale=1.321).
Factorization parameters were as follows:
name: KA_2_9_170
n: 3990476063794410673193311962117080567711728009151491772968515143856662099788504768618896234320754466007794729911278415514970936032668697375596908711209247263198499581
skew: 0.80
deg: 5
c5: 3
c0: -1
m: 10000000000000000000000000000000000
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3300001)
Primes: RFBsize:348513, AFBsize:348501, largePrimes:7962339 encountered
Relations: rels:7605195, finalFF:792642
Max relations in full relation-set: 48
Initial matrix: 697079 x 792642 with sparse part having weight 44278165.
Pruned matrix : 611079 x 614628 with weight 28486101.
Total sieving time: 74.99 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 8.38 hours.
Total square root time: 0.10 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000
total time: 83.81 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 26, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

4·10¹¹⁹-3 = 3(9)₁₁₈7_<120> = 13 · 17 · 85819 · 2138429 · C106

C106 = P44 · P63

P44 = 25985319399001881232057951389966634997820353_<44>

P63 = 379543338404314085166151446656730517304702047891649789900943119_<63>

Number: 39997_119
N=9862554874199558511652521413589225413570302672368196255395589043914114001064063424236049653226344033501007
  ( 106 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=25985319399001881232057951389966634997820353 (pp44)
 r2=379543338404314085166151446656730517304702047891649789900943119 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.95 hours.
Scaled time: 0.89 units (timescale=0.934).
Factorization parameters were as follows:
n: 9862554874199558511652521413589225413570302672368196255395589043914114001064063424236049653226344033501007
m: 1000000000000000000000000
c5: 2
c0: -15
skew: 1.5
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 450001)
Primes: RFBsize:49098, AFBsize:49146, largePrimes:1924432 encountered
Relations: rels:1892891, finalFF:125989
Max relations in full relation-set: 28
Initial matrix: 98309 x 125989 with sparse part having weight 10775752.
Pruned matrix : 90888 x 91443 with weight 6048950.
Total sieving time: 0.89 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 0.95 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹²⁰-3 = 3(9)₁₁₉7_<121> = 311 · 2251511 · 9660397 · C105

C105 = P35 · P71

P35 = 14957350687977701210646823592952109_<35>

P71 = 39534466142745973691646463023061454844518637076105956734312901955956709_<71>

Number: 39997_120
N=591330874359032625073270746495953718723219748632694947903328381586309125199738351352363557080262714249281
  ( 105 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=14957350687977701210646823592952109 (pp35)
 r2=39534466142745973691646463023061454844518637076105956734312901955956709 (pp71)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.00 hours.
Scaled time: 0.94 units (timescale=0.934).
Factorization parameters were as follows:
n: 591330874359032625073270746495953718723219748632694947903328381586309125199738351352363557080262714249281
m: 1000000000000000000000000
c5: 4
c0: -3
skew: 1
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 450001)
Primes: RFBsize:49098, AFBsize:49031, largePrimes:2089674 encountered
Relations: rels:2224684, finalFF:262044
Max relations in full relation-set: 28
Initial matrix: 98196 x 262044 with sparse part having weight 24274221.
Pruned matrix : 70560 x 71114 with weight 4834916.
Total sieving time: 0.95 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 1.00 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹²⁰+3 = 4(0)₁₁₉3_<121> = 7 · C120

C120 = P43 · P78

P43 = 5612274364620889506308759859628576707925837_<43>

P78 = 101817647232428482152474928700295254049026878546996061124502636639930949090617_<78>

Number: 40003_120
N=571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429
  ( 120 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=5612274364620889506308759859628576707925837 (pp43)
 r2=101817647232428482152474928700295254049026878546996061124502636639930949090617 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.81 hours.
Scaled time: 0.76 units (timescale=0.927).
Factorization parameters were as follows:
n: 571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429
m: 1000000000000000000000000
c5: 4
c0: 3
skew: 1
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 420001)
Primes: RFBsize:49098, AFBsize:49031, largePrimes:1870291 encountered
Relations: rels:1811935, finalFF:113613
Max relations in full relation-set: 28
Initial matrix: 98196 x 113613 with sparse part having weight 9031756.
Pruned matrix : 93407 x 93961 with weight 6170340.
Total sieving time: 0.75 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 0.81 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹²¹+3 = 4(0)₁₂₀3_<122> = 6961 · 170977595876812450723_<21> · C98

C98 = P41 · P57

P41 = 34585230048100307623332840382749782681057_<41>

P57 = 971758800986673748132478129675100273134597913849135461393_<57>

Number: 40003_121
N=33608501683390235777263910364754662400497207736229051883674130597789461249450276268990816255932401
  ( 98 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=34585230048100307623332840382749782681057 (pp41)
 r2=971758800986673748132478129675100273134597913849135461393 (pp57)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.97 hours.
Scaled time: 0.91 units (timescale=0.929).
Factorization parameters were as follows:
n: 33608501683390235777263910364754662400497207736229051883674130597789461249450276268990816255932401
m: 2000000000000000000000000
c5: 5
c0: 12
skew: 1.19
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 450001)
Primes: RFBsize:49098, AFBsize:49316, largePrimes:1946453 encountered
Relations: rels:1937498, finalFF:144532
Max relations in full relation-set: 28
Initial matrix: 98480 x 144532 with sparse part having weight 12447254.
Pruned matrix : 87105 x 87661 with weight 5405410.
Total sieving time: 0.92 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 0.97 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹²²-3 = 3(9)₁₂₁7_<123> = 31391 · 2684288903_<10> · 58006487029_<11> · C98

C98 = P48 · P51

P48 = 344007467969662880678387556467819763326309749859_<48>

P51 = 237892718439068787805376755582318249071248333701499_<51>

Number: 39997_122
N=81836871718643986185728151933388840266271776853244320350768896586357955470594077763743698263338641
  ( 98 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=344007467969662880678387556467819763326309749859 (pp48)
 r2=237892718439068787805376755582318249071248333701499 (pp51)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.16 hours.
Scaled time: 1.08 units (timescale=0.932).
Factorization parameters were as follows:
n: 81836871718643986185728151933388840266271776853244320350768896586357955470594077763743698263338641
m: 2000000000000000000000000
c5: 25
c0: -6
skew: 1
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 480001)
Primes: RFBsize:49098, AFBsize:49121, largePrimes:2037427 encountered
Relations: rels:2086785, finalFF:182743
Max relations in full relation-set: 28
Initial matrix: 98283 x 182743 with sparse part having weight 16947217.
Pruned matrix : 82061 x 82616 with weight 5173414.
Total sieving time: 1.10 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 1.16 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 26, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

4·10¹¹³+3 = 4(0)₁₁₂3_<114> = 151 · 2521 · 9341 · 9946673530747_<13> · C92

C92 = P39 · P53

P39 = 213150967517384807318120724304052423803_<39>

P53 = 53058095146024700376361296298594029717899946692445353_<53>

Number: 40003_113
N=11309384315004623424899180326922060659645124717317858332549892278146483153678074568773937459
  ( 92 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=213150967517384807318120724304052423803 (pp39)
 r2=53058095146024700376361296298594029717899946692445353 (pp53)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.67 hours.
Scaled time: 0.63 units (timescale=0.935).
Factorization parameters were as follows:
n: 11309384315004623424899180326922060659645124717317858332549892278146483153678074568773937459
m: 20000000000000000000000
c5: 125
c0: 3
skew: 1
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 300001)
Primes: RFBsize:30757, AFBsize:30524, largePrimes:966239 encountered
Relations: rels:870153, finalFF:70742
Max relations in full relation-set: 28
Initial matrix: 61346 x 70742 with sparse part having weight 3221294.
Pruned matrix : 57493 x 57863 with weight 2097058.
Total sieving time: 0.65 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.67 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 25, 2007 (4th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, GMP-ECM 6.1.2

4·10¹¹⁸+3 = 4(0)₁₁₇3_<119> = C119

C119 = P39 · P81

P39 = 211621276763532507670415744223334748617_<39>

P81 = 189016910831212661627315911618686407924531685546937547055501093534558399895914859_<81>

Number: 40003_118
N=40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
  ( 119 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=211621276763532507670415744223334748617 (pp39)
 r2=189016910831212661627315911618686407924531685546937547055501093534558399895914859 (pp81)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.96 hours.
Scaled time: 0.90 units (timescale=0.935).
Factorization parameters were as follows:
n: 40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
m: 200000000000000000000000
c5: 125
c0: 3
skew: 1
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [300000, 420001)
Primes: RFBsize:49098, AFBsize:48756, largePrimes:1908722 encountered
Relations: rels:1884500, finalFF:138422
Max relations in full relation-set: 28
Initial matrix: 97919 x 138422 with sparse part having weight 11276802.
Pruned matrix : 86646 x 87199 with weight 5081607.
Total sieving time: 0.90 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000
total time: 0.96 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹²⁹+3 = 4(0)₁₂₈3_<130> = C130

C130 = P52 · P79

P52 = 2125328766779684187720000305302944444700439100557051_<52>

P79 = 1882061760289836591422460816044047312356413460440607394774696364308476485811353_<79>

Number: 40003_129
N=4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
  ( 130 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=2125328766779684187720000305302944444700439100557051 (pp52)
 r2=1882061760289836591422460816044047312356413460440607394774696364308476485811353 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.58 hours.
Scaled time: 2.37 units (timescale=0.920).
Factorization parameters were as follows:
n: 4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
m: 100000000000000000000000000
c5: 2
c0: 15
skew: 1.5
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 1000001)
Primes: RFBsize:78498, AFBsize:78671, largePrimes:1535768 encountered
Relations: rels:1549847, finalFF:192091
Max relations in full relation-set: 28
Initial matrix: 157234 x 192091 with sparse part having weight 9975542.
Pruned matrix : 143749 x 144599 with weight 5929322.
Total sieving time: 2.49 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 2.58 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹⁷⁴-3 = 3(9)₁₇₃7_<175> = C175

C175 = P32 · C143

P32 = 60245455742914874964935791279271_<32>

C143 = [66395049231085237918736844489235035302968882127983995400674751551693234252075026857441283507447362557455506331177428848643832758876913437458107_<143>]

4·10¹⁰⁹+3 = 4(0)₁₀₈3_<110> = 157 · 659 · 3015622139_<10> · C96

C96 = P46 · P50

P46 = 8789691551616868774948328182836667117193493269_<46>

P50 = 14585602253855018384156891160085996096225659769091_<50>

Number: 40003_109
N=128202944905953414864392618133593516660075229232730226022631615760351226868770194151050202748479
  ( 96 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=8789691551616868774948328182836667117193493269 (pp46)
 r2=14585602253855018384156891160085996096225659769091 (pp50)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.62 hours.
Scaled time: 0.58 units (timescale=0.931).
Factorization parameters were as follows:
n: 128202944905953414864392618133593516660075229232730226022631615760351226868770194151050202748479
m: 10000000000000000000000
c5: 2
c0: 15
skew: 1.5
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 300001)
Primes: RFBsize:30757, AFBsize:30809, largePrimes:1049595 encountered
Relations: rels:976872, finalFF:96164
Max relations in full relation-set: 28
Initial matrix: 61631 x 96164 with sparse part having weight 4380179.
Pruned matrix : 51415 x 51787 with weight 1652064.
Total sieving time: 0.59 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.62 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

4·10¹⁷⁹+3 = 4(0)₁₇₈3_<180> = C180

C180 = P37 · C143

P37 = 9679838127597185553923930374350132743_<37>

C143 = [41323005067574566304410175051619336014247547874804676702862982021554231126531999977945569827460087540832516415965598056089191661607896947926821_<143>]

4·10¹¹³-3 = 3(9)₁₁₂7_<114> = 13 · C113

C113 = P31 · P83

P31 = 1702356884234854309940250225619_<31>

P83 = 18074488994744710410784707596626357056720051107053667811146452741104552488586191851_<83>

Number: 39997_113
N=30769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769
  ( 113 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=1702356884234854309940250225619 (pp31)
 r2=18074488994744710410784707596626357056720051107053667811146452741104552488586191851 (pp83)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.68 hours.
Scaled time: 0.63 units (timescale=0.932).
Factorization parameters were as follows:
n: 30769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769230769
m: 20000000000000000000000
c5: 125
c0: -3
skew: 1
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 300001)
Primes: RFBsize:30757, AFBsize:30524, largePrimes:971787 encountered
Relations: rels:878648, finalFF:73299
Max relations in full relation-set: 28
Initial matrix: 61346 x 73299 with sparse part having weight 3338199.
Pruned matrix : 56856 x 57226 with weight 1991611.
Total sieving time: 0.65 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.68 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 25, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(2·10¹⁷⁰+43)/9 = (2)₁₆₉7_<170> = 3 · 31 · C168

C168 = P72 · P96

P72 = 822727558550038088856535467720496024936606976987042056653456323459910599_<72>

P96 = 290434693188738543956075989104111212671965096094614253375494043532658467524800249969328397926361_<96>

Number: n
N=238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400239
  ( 168 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=822727558550038088856535467720496024936606976987042056653456323459910599 (pp72)
 r2=290434693188738543956075989104111212671965096094614253375494043532658467524800249969328397926361 (pp96)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 101.07 hours.
Scaled time: 120.88 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_2_169_7
n: 238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400238948626045400239
type: snfs
skew: 1.85
deg: 5
c5: 2
c0: 43
m: 10000000000000000000000000000000000
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3500001)
Primes: RFBsize:348513, AFBsize:348531, largePrimes:8123742 encountered
Relations: rels:7797506, finalFF:823183
Max relations in full relation-set: 28
Initial matrix: 697109 x 823183 with sparse part having weight 47249027.
Pruned matrix : 584171 x 587720 with weight 29395354.
Total sieving time: 92.50 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 8.04 hours.
Total square root time: 0.15 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.6,2.6,100000
total time: 101.07 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

May 25, 2007 (2nd)

The factor tables of 399...997 and 400...003 were extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

May 25, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp

2·10¹⁵⁷-3 = 1(9)₁₅₆7_<158> = 43 · 179 · 2733863182530927049217_<22> · C132

C132 = P42 · P91

P42 = 496078180985187011253921599029146472448633_<42>

P91 = 1915938687245105985797755896058272648806048756431283226141003881366035015771171783110925141_<91>

Number: n
N=950455378847699300374424598634237722308057180347692882733859893445386580027802421982455311802165614024833261186121222088656230782253
  ( 132 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=496078180985187011253921599029146472448633 (pp42)
 r2=1915938687245105985797755896058272648806048756431283226141003881366035015771171783110925141 (pp91)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 33.62 hours.
Scaled time: 48.78 units (timescale=1.451).
Factorization parameters were as follows:
name: KA_1_9_156_7
n: 950455378847699300374424598634237722308057180347692882733859893445386580027802421982455311802165614024833261186121222088656230782253
skew: 0.43
deg: 5
c5: 200
c0: -3
m: 10000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1600001)
Primes: RFBsize:183072, AFBsize:183041, largePrimes:7276973 encountered
Relations: rels:6812530, finalFF:487659
Max relations in full relation-set: 28
Initial matrix: 366178 x 487659 with sparse part having weight 43287182.
Pruned matrix : 296199 x 298093 with weight 25524280.
Total sieving time: 30.36 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.00 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 33.62 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(22·10¹⁶⁰-1)/3 = 7(3)₁₆₀_<161> = 13 · 263 · C158

C158 = P62 · P96

P62 = 23426441886445012154981750965676224184494269863736197144797481_<62>

P96 = 915579361128915270723247955082996638837387785389087322699384546746236173167534267878078270621047_<96>

Number: n
N=21448766695914984888368918787169737740079945403139319489129375060933996295213025251048064736277664034318026713463975821390270059471580384127912645022911182607
  ( 158 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=23426441886445012154981750965676224184494269863736197144797481 (pp62)
 r2=915579361128915270723247955082996638837387785389087322699384546746236173167534267878078270621047 (pp96)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 40.17 hours.
Scaled time: 54.87 units (timescale=1.366).
Factorization parameters were as follows:
name: KA_7_3_160
n: 21448766695914984888368918787169737740079945403139319489129375060933996295213025251048064736277664034318026713463975821390270059471580384127912645022911182607
skew: 0.54
deg: 5
c5: 22
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:315948, AFBsize:316347, largePrimes:7309058 encountered
Relations: rels:6944667, finalFF:720963
Max relations in full relation-set: 28
Initial matrix: 632361 x 720963 with sparse part having weight 35299802.
Pruned matrix : 543577 x 546802 with weight 21194774.
Total sieving time: 35.03 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 4.43 hours.
Total square root time: 0.49 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000
total time: 40.17 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 23, 2007 (6th)

By Robert Backstrom / GMP-ECM 5.0 B1=1358500

2·10¹⁵⁶+3 = 2(0)₁₅₅3_<157> = 97 · 125353 · 97436968800347339_<17> · C133

C133 = P38 · P95

P38 = 43135946585687043827750397163601212657_<38>

P95 = 39134557867852232577558454632800142255822036800416522850859882961102818904957125240913476934321_<95>

May 23, 2007 (5th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

2·10¹⁵³-3 = 1(9)₁₅₂7_<154> = 8990693 · 921385311825262730764919_<24> · C123

C123 = P44 · P80

P44 = 18536972846671778888746448349596139528250921_<44>

P80 = 13024370107576147632519746158741250510023486439810098022457117528012765562134071_<80>

Number: 19997_153
N=241432395029142644418795685506626823600720952779925262840558341180193330344056600225360186277355101442030529906274731229391
  ( 123 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=18536972846671778888746448349596139528250921 (pp44)
 r2=13024370107576147632519746158741250510023486439810098022457117528012765562134071 (pp80)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 15.54 hours.
Scaled time: 14.53 units (timescale=0.935).
Factorization parameters were as follows:
n: 241432395029142644418795685506626823600720952779925262840558341180193330344056600225360186277355101442030529906274731229391
m: 2000000000000000000000000000000
c5: 125
c0: -6
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:175758, largePrimes:5489347 encountered
Relations: rels:5372513, finalFF:457707
Max relations in full relation-set: 28
Initial matrix: 352125 x 457707 with sparse part having weight 40251711.
Pruned matrix : 304309 x 306133 with weight 23581787.
Total sieving time: 14.88 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.54 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 15.54 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 23, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp

(35·10¹⁵⁸-53)/9 = 3(8)₁₅₇3_<159> = 27127 · 48923440453_<11> · C144

C144 = P44 · P100

P44 = 42538481348207485813121172033846526577279483_<44>

P100 = 6888502111425675766578155516284879416746833257639594662538596972928631754995038097561460112280873171_<100>

Number: n
N=293026418583968992746656536950228061925053866003057901150847188822375646935590181201198901295151639664429222267982877800737159427578360943450593
  ( 144 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=42538481348207485813121172033846526577279483 (pp44)
 r2=6888502111425675766578155516284879416746833257639594662538596972928631754995038097561460112280873171 (pp100)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 44.00 hours.
Scaled time: 56.27 units (timescale=1.279).
Factorization parameters were as follows:
name: KA_3_8_157_3
n: 293026418583968992746656536950228061925053866003057901150847188822375646935590181201198901295151639664429222267982877800737159427578360943450593
skew: 1.36
deg: 5
c5: 56
c0: -265
m: 50000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:315948, AFBsize:315361, largePrimes:7625944 encountered
Relations: rels:7354460, finalFF:807928
Max relations in full relation-set: 28
Initial matrix: 631375 x 807928 with sparse part having weight 42602060.
Pruned matrix : 465064 x 468284 with weight 20824091.
Total sieving time: 40.25 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 3.27 hours.
Total square root time: 0.24 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000
total time: 44.00 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 23, 2007 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

9·10¹⁸⁴+1 = 9(0)₁₈₃1_<185> = 29 · 53 · 433 · 17907001038501948144357766109_<29> · 56385136584339210524733082811161_<32> · C120

C120 = P59 · P61

P59 = 13545949246627659985095780182634249171497673616306498864681_<59>

P61 = 9887438744319177885322438170306294338262729295517657911743749_<61>

Number: 90001_184
N=133934743409687504113918170515371822798346958185976385775707154210049376559761047550202532079443200522363980365498629069
  ( 120 digits)
Divisors found:
 r1=13545949246627659985095780182634249171497673616306498864681 (pp59)
 r2=9887438744319177885322438170306294338262729295517657911743749 (pp61)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 104.60 hours.
Scaled time: 70.50 units (timescale=0.674).
Factorization parameters were as follows:
name: 90001_184
n: 133934743409687504113918170515371822798346958185976385775707154210049376559761047550202532079443200522363980365498629069
skew: 107220.47
# norm 2.15e+16
c5: 12600
c4: 3067381107
c3: -574230821471740
c2: -9105185955287273434
c1: 2636139457254556317179812
c0: 17112993314701970007764391495
# alpha -6.21
Y1: 12502178138059
Y0: -101228296750123928750236
# Murphy_E 3.30e-10
# M 38349749078379278951104040809096706378944396920633763085781647089002458673724715501130568777671997717738236889041282710
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4170001)
Primes: RFBsize:315948, AFBsize:316633, largePrimes:7605542 encountered
Relations: rels:7609290, finalFF:710379
Max relations in full relation-set: 0
Initial matrix: 632661 x 710379 with sparse part having weight 60425268.
Pruned matrix : 569194 x 572421 with weight 42554618.
Total sieving time: 83.95 hours.
Total relation processing time: 1.24 hours.
Matrix solve time: 18.90 hours.
Time per square root: 0.51 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 104.60 hours.
 --------- CPU info (if available) ----------

May 23, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

2·10¹⁵²+3 = 2(0)₁₅₁3_<153> = 7 · 59 · 9437 · 1077079 · 3473719 · C134

C134 = P39 · P95

P39 = 764892666772199274490037661811796227973_<39>

P95 = 17930947920257063532703516829435538148362253000748922501535367754063948223945638948206096726431_<95>

Number: 20003_152
N=13715250572478845705802125321480208820321833385402835338596419671437335621017472336038044329692466760525852970011068555409269090654363
  ( 134 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=764892666772199274490037661811796227973 (pp39)
 r2=17930947920257063532703516829435538148362253000748922501535367754063948223945638948206096726431 (pp95)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 17.03 hours.
Scaled time: 15.86 units (timescale=0.931).
Factorization parameters were as follows:
n: 13715250572478845705802125321480208820321833385402835338596419671437335621017472336038044329692466760525852970011068555409269090654363
m: 2000000000000000000000000000000
c5: 25
c0: 12
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2200001)
Primes: RFBsize:176302, AFBsize:176368, largePrimes:5425155 encountered
Relations: rels:5251337, finalFF:405163
Max relations in full relation-set: 28
Initial matrix: 352734 x 405163 with sparse part having weight 35624313.
Pruned matrix : 330434 x 332261 with weight 25625210.
Total sieving time: 16.28 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.64 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 17.03 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 23, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

2·10¹⁵¹-3 = 1(9)₁₅₀7_<152> = 109 · 5351699092147_<13> · 41659474526382217853629_<23> · C114

C114 = P51 · P64

P51 = 232357967917576122963811199234684498812206335392391_<51>

P64 = 3541933914244940727356281485918685455317930382157304642870395201_<64>

Number: n
N=822996566812300756270915694973657445507528537129099442009025996149706730952409519399555793857628590326355578315591
  ( 114 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=232357967917576122963811199234684498812206335392391 (pp51)
 r2=3541933914244940727356281485918685455317930382157304642870395201 (pp64)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.36 hours.
Scaled time: 28.14 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_1_9_150_7
n: 822996566812300756270915694973657445507528537129099442009025996149706730952409519399555793857628590326355578315591
skew: 0.68
deg: 5
c5: 20
c0: -3
m: 1000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:183072, AFBsize:182801, largePrimes:6608095 encountered
Relations: rels:6045586, finalFF:420551
Max relations in full relation-set: 28
Initial matrix: 365939 x 420551 with sparse part having weight 29835712.
Pruned matrix : 321725 x 323618 with weight 19335173.
Total sieving time: 16.77 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 2.32 hours.
Total square root time: 0.11 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 19.36 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 22, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

5·10¹⁶⁹-1 = 4(9)₁₆₉_<170> = 7² · 17 · C167

C167 = P38 · P64 · P66

P38 = 51971109847877751141565924226072367623_<38>

P64 = 6247449254103117689987713647000874500741834590985633042232135777_<64>

P66 = 184867374942010724757709190165050993402607186564005758034404013993_<66>

Number: n
N=60024009603841536614645858343337334933973589435774309723889555822328931572629051620648259303721488595438175270108043217286914765906362545018007202881152460984393757503
  ( 167 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=51971109847877751141565924226072367623 (pp38)
 r2=6247449254103117689987713647000874500741834590985633042232135777 (pp64)
 r3=184867374942010724757709190165050993402607186564005758034404013993 (pp66)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 80.00 hours.
Scaled time: 58.00 units (timescale=0.725).
Factorization parameters were as follows:
name: KA_4_9_169
n: 60024009603841536614645858343337334933973589435774309723889555822328931572629051620648259303721488595438175270108043217286914765906362545018007202881152460984393757503
skew: 1.15
deg: 5
c5: 1
c0: -2
m: 10000000000000000000000000000000000
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3100001)
Primes: RFBsize:348513, AFBsize:348176, largePrimes:7957180 encountered
Relations: rels:7622391, finalFF:810632
Max relations in full relation-set: 48
Initial matrix: 696753 x 810632 with sparse part having weight 43718412.
Pruned matrix : 593010 x 596557 with weight 26495728.
Total sieving time: 70.42 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 8.76 hours.
Total square root time: 0.54 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000
total time: 80.00 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 22, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs

(10¹⁷⁸+17)/9 = (1)₁₇₇3_<178> = 3² · 7² · 1046641 · 1290857 · 468836928921920538313_<21> · 297082579660968821734851624509405183_<36> · C107

C107 = P34 · P73

P34 = 6351389277783512750660674500861871_<34>

P73 = 2108022748500441599748310376090833021700915012375759080181462532721767521_<73>

Number: 11113_178
N=13388873082149435308539000672775350680618901926900711188810262897346981830451724894509157440592356995091791
  ( 107 digits)
Divisors found:
 r1=6351389277783512750660674500861871 (pp34)
 r2=2108022748500441599748310376090833021700915012375759080181462532721767521 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.91 hours.
Scaled time: 10.20 units (timescale=0.935).
Factorization parameters were as follows:
name: 11113_178
n: 13388873082149435308539000672775350680618901926900711188810262897346981830451724894509157440592356995091791
skew: 24447.50
# norm 1.03e+15
c5: 11040
c4: 634721972
c3: -57395841951390
c2: -297909801429328773
c1: 7360634883314650193640
c0: 44733769501169737130602075
# alpha -6.20
Y1: 59180280269
Y0: -261068129944292921856
# Murphy_E 1.60e-09
# M 1848511566881534751075889082385374038136846422142820742013036141739596195580891966762660131878038833277554
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1440001)
Primes: RFBsize:135072, AFBsize:135129, largePrimes:4628918 encountered
Relations: rels:4758229, finalFF:429445
Max relations in full relation-set: 28
Initial matrix: 270283 x 429445 with sparse part having weight 42261017.
Pruned matrix : 196380 x 197795 with weight 17946254.
Total sieving time: 10.57 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 10.91 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 22, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

2·10¹⁴⁷-3 = 1(9)₁₄₆7_<148> = 6328193 · 2807442959_<10> · 9315019792951667720337833_<25> · C107

C107 = P38 · P69

P38 = 19847917526656775016866295121378364453_<38>

P69 = 608892479187265731705994468981721335175199066679255978067665568322719_<69>

Number: n
N=12085247709510427120634598202262732105264237067773714462472119550932718546531305768674719902899358701907707
  ( 107 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=19847917526656775016866295121378364453 (pp38)
 r2=608892479187265731705994468981721335175199066679255978067665568322719 (pp69)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 12.22 hours.
Scaled time: 17.76 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_1_9_146_7
n: 12085247709510427120634598202262732105264237067773714462472119550932718546531305768674719902899358701907707
skew: 0.43
deg: 5
c5: 200
c0: -3
m: 100000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:183072, AFBsize:183041, largePrimes:6840115 encountered
Relations: rels:6269711, finalFF:436586
Max relations in full relation-set: 28
Initial matrix: 366178 x 436586 with sparse part having weight 29446300.
Pruned matrix : 310612 x 312506 with weight 17873574.
Total sieving time: 9.61 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 2.38 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 12.22 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 22, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

2·10¹⁴⁷+3 = 2(0)₁₄₆3_<148> = 1689189684351792543788723_<25> · C124

C124 = P32 · P92

P32 = 37217298101001103011342694765763_<32>

P92 = 31813154456124267948681707302764451170058560372489661494512147777300060017072412206709935547_<92>

Number: 20003_147
N=1183999652926768495616698876252051229605874742718666658960661269213398956494208102909274279905772503661905475316163992277361
  ( 124 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=37217298101001103011342694765763 (pp32)
 r2=31813154456124267948681707302764451170058560372489661494512147777300060017072412206709935547 (pp92)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 16.66 hours.
Scaled time: 15.51 units (timescale=0.931).
Factorization parameters were as follows:
n: 1183999652926768495616698876252051229605874742718666658960661269213398956494208102909274279905772503661905475316163992277361
m: 200000000000000000000000000000
c5: 25
c0: 12
skew: 1
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [900000, 1950001)
Primes: RFBsize:135072, AFBsize:135133, largePrimes:2850480 encountered
Relations: rels:2879930, finalFF:356257
Max relations in full relation-set: 28
Initial matrix: 270269 x 356257 with sparse part having weight 24048209.
Pruned matrix : 233955 x 235370 with weight 13959048.
Total sieving time: 16.36 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,45,45,2.3,2.3,75000
total time: 16.66 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 21, 2007 (4th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

2·10¹⁶⁷+3 = 2(0)₁₆₆3_<168> = C168

C168 = P51 · P58 · P60

P51 = 337473788641314954387395638036113417304047480856561_<51>

P58 = 4690700023174550771994364525354487199388452766958125990189_<58>

P60 = 126343321023855007144178242728859599541361819987460022346207_<60>

Number: 20003_167
N=200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
  ( 168 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=337473788641314954387395638036113417304047480856561 (pp51)
 r2=4690700023174550771994364525354487199388452766958125990189 (pp58)
 r3=126343321023855007144178242728859599541361819987460022346207 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 86.06 hours.
Scaled time: 79.78 units (timescale=0.927).
Factorization parameters were as follows:
n: 200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
m: 2000000000000000000000000000000000
c5: 25
c0: 12
skew: 1
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 7200001)
Primes: RFBsize:412849, AFBsize:413001, largePrimes:6107027 encountered
Relations: rels:6383488, finalFF:940116
Max relations in full relation-set: 28
Initial matrix: 825914 x 940116 with sparse part having weight 55379558.
Pruned matrix : 732130 x 736323 with weight 40746913.
Total sieving time: 81.90 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 3.96 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.5,2.5,100000
total time: 86.06 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 21, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp

2·10¹⁴⁶-3 = 1(9)₁₄₅7_<147> = 149 · 1570076584418759_<16> · 2011840031262686851_<19> · C111

C111 = P46 · P65

P46 = 4448748130740857754356733813222510745804262837_<46>

P65 = 95519408968726075748994090904376099816839216393188114257850974641_<65>

Number: n
N=424941792099091652796628671010700958506423837145816971878241180930695799833275848461352158847044391932985716517
  ( 111 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=4448748130740857754356733813222510745804262837 (pp46)
 r2=95519408968726075748994090904376099816839216393188114257850974641 (pp65)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 11.06 hours.
Scaled time: 16.04 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_1_9_145_7
n: 424941792099091652796628671010700958506423837145816971878241180930695799833275848461352158847044391932985716517
skew: 0.68
deg: 5
c5: 20
c0: -3
m: 100000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:183072, AFBsize:182801, largePrimes:6838353 encountered
Relations: rels:6284624, finalFF:453514
Max relations in full relation-set: 28
Initial matrix: 365939 x 453514 with sparse part having weight 30588863.
Pruned matrix : 295556 x 297449 with weight 17145080.
Total sieving time: 8.83 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.91 hours.
Total square root time: 0.16 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 11.06 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

2·10¹⁵⁷+3 = 2(0)₁₅₆3_<158> = 8678368395079_<13> · C145

C145 = P44 · P101

P44 = 59573402681404398007654718102866364909302643_<44>

P101 = 38684724398115424654512004896712075071304442379362845270019006771965113736013768988351468162809875399_<101>

Number: n
N=2304580664188079575933828712914557890427023054102125976725828086702081005763818534064969056410847081186110800103490795263920600961553242811379557
  ( 145 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=59573402681404398007654718102866364909302643 (pp44)
 r2=38684724398115424654512004896712075071304442379362845270019006771965113736013768988351468162809875399 (pp101)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 44.23 hours.
Scaled time: 60.55 units (timescale=1.369).
Factorization parameters were as follows:
name: KA_2_0_156_3
n: 2304580664188079575933828712914557890427023054102125976725828086702081005763818534064969056410847081186110800103490795263920600961553242811379557
skew: 0.43
deg: 5
c5: 200
c0: 3
m: 10000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:315948, AFBsize:316266, largePrimes:7406177 encountered
Relations: rels:7093105, finalFF:765139
Max relations in full relation-set: 28
Initial matrix: 632279 x 765139 with sparse part having weight 36970198.
Pruned matrix : 503294 x 506519 with weight 19243383.
Total sieving time: 39.27 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 4.31 hours.
Total square root time: 0.43 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000
total time: 44.23 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 21, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs

2·10¹⁴³+3 = 2(0)₁₄₂3_<144> = 31 · 79869969541_<11> · 213191226127907995641964733297_<30> · C102

C102 = P30 · P73

P30 = 228969479001528543632608227557_<30>

P73 = 1654770841768982551074895703714451566312262310294250115213002864298336917_<73>

Number: 20003_143
N=352782624717439820453701966298868758723803154243973650848982107895441604203274505013730356962554225349
  ( 102 digits)
Divisors found:
 r1=213191226127907995641964733297 (pp30)
 r2=1654770841768982551074895703714451566312262310294250115213002864298336917 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.26 hours.
Scaled time: 4.92 units (timescale=0.935).
Factorization parameters were as follows:
name: 20003_143
n: 352782624717439820453701966298868758723803154243973650848982107895441604203274505013730356962554225349
skew: 4896.42
# norm 1.65e+14
c5: 414540
c4: -1516615299
c3: -29953559408092
c2: 22157126830643012
c1: 319304041463428098440
c0: -322389009793145912969625
# alpha -6.51
Y1: 29065820179
Y0: -15345772329994469954
# Murphy_E 2.97e-09
# M 71309661546094854819531043168860349419349509853588268376742292160086044115824039856088598435052274054
type: gnfs
rlim: 1700000
alim: 1700000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 1700000/1700000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [850000, 1450001)
Primes: RFBsize:128141, AFBsize:128124, largePrimes:4351260 encountered
Relations: rels:4289278, finalFF:336862
Max relations in full relation-set: 28
Initial matrix: 256353 x 336862 with sparse part having weight 27590776.
Pruned matrix : 202920 x 204265 with weight 14425353.
Polynomial selection time: 0.31 hours.
Total sieving time: 4.63 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1700000,1700000,26,26,49,49,2.6,2.6,50000
total time: 5.26 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 21, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=1035500, GGNFS-0.77.1-20051202-athlon gnfs

2·10¹⁵⁹-3 = 1(9)₁₅₈7_<160> = 52589677955822857981_<20> · C140

C140 = P37 · P49 · P55

P37 = 3896040234710280092225221728653869867_<37>

P49 = 5874207548035032880370430336726048734418437859121_<49>

P55 = 1661715856862486631625209578684315662965911900561608691_<55>

Number: n
N=9761263829071121262365012249257222672340375008383646695682227981460573838578364015976442972225787220611
  ( 103 digits)
Divisors found:
 r1=5874207548035032880370430336726048734418437859121 (pp49)
 r2=1661715856862486631625209578684315662965911900561608691 (pp55)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.26 hours.
Scaled time: 11.92 units (timescale=1.443).
Factorization parameters were as follows:
name: KA_1_9_158_7
n: 9761263829071121262365012249257222672340375008383646695682227981460573838578364015976442972225787220611
skew: 17806.85
# norm 3.92e+14
c5: 24840
c4: 1198081196
c3: -24357592265018
c2: -210683013743336014
c1: 4490637563116177810311
c0: -6227635109584928607029385
# alpha -6.39
Y1: 15093872179
Y0: -52344334656327314746
# Murphy_E 2.17e-09
# M 5247268042512921953463320309399432360648469461756698860444742486375840947181248944205613969233916838496
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [100000, 1000001)
Primes: RFBsize:169511, AFBsize:168934, largePrimes:4068833 encountered
Relations: rels:4045535, finalFF:435835
Max relations in full relation-set: 28
Initial matrix: 338529 x 435835 with sparse part having weight 25375260.
Pruned matrix : 245530 x 247286 with weight 10481944.
Total sieving time: 7.28 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.75 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 8.26 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 20, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(4·10¹⁶⁸-13)/9 = (4)₁₆₇3_<168> = 17 · 419 · C164

C164 = P35 · P52 · P78

P35 = 57223726068551403899392214060994719_<35>

P52 = 2958022467640268007405799325268632922692503207747423_<52>

P78 = 368618337536960736026589540264509215386289010356520617633489625535863749834393_<78>

Number: n
N=62395682218790459700188746938711841140593070959489603319450294039652456050041337139469948679551375044846896594755642909510661862199135819801269752133152385854898841
  ( 164 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=57223726068551403899392214060994719 (pp35)
 r2=2958022467640268007405799325268632922692503207747423 (pp52)
 r3=368618337536960736026589540264509215386289010356520617633489625535863749834393 (pp78)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 82.39 hours.
Scaled time: 98.53 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_4_167_3
n: 62395682218790459700188746938711841140593070959489603319450294039652456050041337139469948679551375044846896594755642909510661862199135819801269752133152385854898841
type: snfs
skew: 0.64
deg: 5
c5: 125
c0: -13
m: 2000000000000000000000000000000000
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2800001)
Primes: RFBsize:348513, AFBsize:348691, largePrimes:7837578 encountered
Relations: rels:7490877, finalFF:784720
Max relations in full relation-set: 28
Initial matrix: 697269 x 784720 with sparse part having weight 41841324.
Pruned matrix : 613981 x 617531 with weight 27192773.
Total sieving time: 73.63 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 7.84 hours.
Total square root time: 0.59 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.6,2.6,100000
total time: 82.39 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

May 20, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

2·10¹³⁷+3 = 2(0)₁₃₆3_<138> = 17 · C137

C137 = P58 · P79

P58 = 1328613771450100770246781828785320550322299965818189662049_<58>

P79 = 8854872751704570530521108482218419399537655969341394293738394189902236177869491_<79>

Number: 20003_137
N=11764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647059
  ( 137 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=1328613771450100770246781828785320550322299965818189662049 (pp58)
 r2=8854872751704570530521108482218419399537655969341394293738394189902236177869491 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.22 hours.
Scaled time: 5.78 units (timescale=0.928).
Factorization parameters were as follows:
n: 11764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647059
m: 2000000000000000000000000000
c5: 25
c0: 12
skew: 1
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [650000, 1850001)
Primes: RFBsize:100021, AFBsize:100128, largePrimes:1640721 encountered
Relations: rels:1668665, finalFF:226443
Max relations in full relation-set: 28
Initial matrix: 200213 x 226443 with sparse part having weight 12812781.
Pruned matrix : 188889 x 189954 with weight 9261748.
Total sieving time: 6.07 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1300000,1300000,25,25,43,43,2.3,2.3,50000
total time: 6.22 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹⁴¹+3 = 2(0)₁₄₀3_<142> = 19 · 167 · 511171 · 31993217 · 416824282517_<12> · 40464415611439_<14> · C100

C100 = P35 · P65

P35 = 40059260051938443901187811141767299_<35>

P65 = 57043556884754993123007599776067037686087494765852279033731828829_<65>

Number: 20003_141
N=2285122679533943884995836369403375958380690166981928865619552380550189111322270262039694582417662871
  ( 100 digits)
Divisors found:
 r1=40059260051938443901187811141767299 (pp35)
 r2=57043556884754993123007599776067037686087494765852279033731828829 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.69 hours.
Scaled time: 3.44 units (timescale=0.933).
Factorization parameters were as follows:
name: 20003_141
n: 2285122679533943884995836369403375958380690166981928865619552380550189111322270262039694582417662871
skew: 31367.47
# norm 6.42e+13
c5: 1440
c4: 75236316
c3: -4337450867666
c2: -75939829829144874
c1: 1832361831257217421219
c0: 16270129288624735982981380
# alpha -6.20
Y1: 10815828199
Y0: -17382273622225387341
# Murphy_E 3.72e-09
# M 1528662353311578042268050061954235525428090049383327581993882190980449819514204253607283249127063063
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [750000, 1200001)
Primes: RFBsize:114155, AFBsize:113995, largePrimes:3892638 encountered
Relations: rels:3880924, finalFF:363769
Max relations in full relation-set: 28
Initial matrix: 228229 x 363769 with sparse part having weight 27334851.
Pruned matrix : 151504 x 152709 with weight 10165771.
Polynomial selection time: 0.25 hours.
Total sieving time: 3.25 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,48,48,2.5,2.5,50000
total time: 3.69 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 20, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

2·10¹³⁵+3 = 2(0)₁₃₄3_<136> = 257 · 1039 · 99257 · C125

C125 = P46 · P80

P46 = 7020006299581572894488170104402102406297674139_<46>

P80 = 10749361742827382298904906120880763303050229911440763032084434365062835850279407_<80>

Number: 20003_135
N=75460587151129379230670063280857121792718817008604043048671091197504696349160888652369718619579296555750824669583497388155573
  ( 125 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=7020006299581572894488170104402102406297674139 (pp46)
 r2=10749361742827382298904906120880763303050229911440763032084434365062835850279407 (pp80)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.55 hours.
Scaled time: 3.32 units (timescale=0.934).
Factorization parameters were as follows:
n: 75460587151129379230670063280857121792718817008604043048671091197504696349160888652369718619579296555750824669583497388155573
m: 1000000000000000000000000000
c5: 2
c0: 3
skew: 1.08
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [650000, 1300001)
Primes: RFBsize:100021, AFBsize:100078, largePrimes:1574128 encountered
Relations: rels:1626678, finalFF:245535
Max relations in full relation-set: 28
Initial matrix: 200164 x 245535 with sparse part having weight 8965702.
Pruned matrix : 173620 x 174684 with weight 5510812.
Total sieving time: 3.45 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1300000,1300000,25,25,43,43,2.3,2.3,50000
total time: 3.55 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 19, 2007 (5th)

By Yousuke Koide / GMP-ECM B1=1250000 / May 15, 2007

(10⁸⁹³-1)/9 = (1)₈₉₃_<893> = 1787 · 37507 · 35121409 · 965588399 · 1111111111111111111_<19> · 21638150846892565213405304766721_<32> · 316362908763458525001406154038726382279_<39> · C780

C780 = P41 · C740

P41 = 10493490498099374383685787869090487099769_<41>

By Yousuke Koide / GMP-ECM B1=1250000 / May 15, 2007

(10⁸⁹⁹-1)/9 = (1)₈₉₉_<899> = 2791 · 3191 · 16763 · 43037 · 62003 · 6943319 · 77843839397_<11> · 480833853881_<12> · 57336415063790604359_<20> · 2257918530532265915349804384025799_<34> · C795

C795 = P36 · C760

P36 = 323713506321948847919927778598102721_<36>

By Yousuke Koide / GMP-ECM B1=1250000 / May 17, 2007

(10⁹²³-1)/9 = (1)₉₂₃_<923> = 53 · 79 · 265371653 · 1632253507_<10> · 104900736929_<12> · 95520614386871982749923_<23> · 241573142393627673576957439049_<30> · 45994811347886846310221728895223034301839_<41> · C797

C797 = P31 · C766

P31 = 7487500179911376323952478489837_<31>

By Yousuke Koide / GMP-ECM B1=1000000 / May 18, 2007

10¹²²¹+1 = 1(0)₁₂₂₀1_<1222> = 7 · 11² · 13 · 23 · 223 · 4093 · 4663 · 7253 · 8779 · 599144041 · 183411838171_<12> · 409038414731_<12> · 422650073734453_<15> · 296557347313446299_<18> · 182160098613913582339_<21> · 21606064498691505246200058094681_<32> · 84713181371149698699040859437321_<32> · 48911689110891303706174193415115219_<35> · 219750014263062386251162088588835607771_<39> · C279 · C700

C700 = P38 · C663

P38 = 19505047835248219128488737914962029531_<38>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

May 19, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp

2·10¹⁵⁴+3 = 2(0)₁₅₃3_<155> = 241 · 141906841 · C144

C144 = P53 · P92

P53 = 32826981394635607932036482961957538515492937504121287_<53>

P92 = 17814706504328977485410892424619338104938573843248529336228689546358190125162267028033028349_<92>

Number: n
N=584803038968501293129681695754773285044568217236351897459123080525426305698095361365508658479597554195571988051288752034745016639946342805365163
  ( 144 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=32826981394635607932036482961957538515492937504121287 (pp53)
 r2=17814706504328977485410892424619338104938573843248529336228689546358190125162267028033028349 (pp92)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 20.71 hours.
Scaled time: 30.05 units (timescale=1.451).
Factorization parameters were as follows:
name: KA_2_0_153_3
n: 584803038968501293129681695754773285044568217236351897459123080525426305698095361365508658479597554195571988051288752034745016639946342805365163
skew: 1.72
deg: 5
c5: 1
c0: 15
m: 10000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1000001)
Primes: RFBsize:183072, AFBsize:182886, largePrimes:6936703 encountered
Relations: rels:6500743, finalFF:530318
Max relations in full relation-set: 28
Initial matrix: 366022 x 530318 with sparse part having weight 39481451.
Pruned matrix : 243009 x 244903 with weight 21177995.
Total sieving time: 18.57 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.83 hours.
Total square root time: 0.15 hours, sqrts: 3. [2 more had ODD EXPONENTS!]
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 20.71 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

2·10¹⁴⁸+3 = 2(0)₁₄₇3_<149> = 151 · 54917 · 79496880961_<11> · 360248308916767_<15> · C116

C116 = P50 · P67

P50 = 22142194087798266515774322687941954125664442651683_<50>

P67 = 3803413556430766247732445539023188610808389140958333384583058412229_<67>

Number: n
N=84215921162653090923161345791936118708491721223162198728702917790987256948208915116143433713706768557404516474631407
  ( 116 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=22142194087798266515774322687941954125664442651683 (pp50)
 r2=3803413556430766247732445539023188610808389140958333384583058412229 (pp67)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 12.42 hours.
Scaled time: 16.92 units (timescale=1.363).
Factorization parameters were as follows:
name: KA_2_0_147_3
n: 84215921162653090923161345791936118708491721223162198728702917790987256948208915116143433713706768557404516474631407
skew: 0.54
deg: 5
c5: 125
c0: 6
m: 200000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:315948, AFBsize:315516, largePrimes:7024094 encountered
Relations: rels:6715776, finalFF:774140
Max relations in full relation-set: 28
Initial matrix: 631529 x 774140 with sparse part having weight 27775308.
Pruned matrix : 477072 x 480293 with weight 12291778.
Total sieving time: 10.14 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.01 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000
total time: 12.42 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

2·10¹³⁴+3 = 2(0)₁₃₃3_<135> = 7 · 157756740409116882389_<21> · C114

C114 = P36 · P78

P36 = 245627325886145161242134796623575019_<36>

P78 = 737339247296593171731659164098751163305183427019906464474193591876106604044019_<78>

Number: n
N=181110667584365268571506917891704517125360677457662669626156617049442655401350747509071891750331736847898624761361
  ( 114 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=245627325886145161242134796623575019 (pp36)
 r2=737339247296593171731659164098751163305183427019906464474193591876106604044019 (pp78)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.54 hours.
Scaled time: 5.12 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_2_0_133_3
n: 181110667584365268571506917891704517125360677457662669626156617049442655401350747509071891750331736847898624761361
skew: 1.72
deg: 5
c5: 1
c0: 15
m: 1000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 500001)
Primes: RFBsize:148933, AFBsize:148925, largePrimes:5017314 encountered
Relations: rels:4491776, finalFF:346937
Max relations in full relation-set: 28
Initial matrix: 297922 x 346937 with sparse part having weight 14433488.
Pruned matrix : 245580 x 247133 with weight 7586313.
Total sieving time: 2.78 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.61 hours.
Total square root time: 0.05 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,75000
total time: 3.54 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 19, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, Msieve v. 1.21

2·10¹²⁶+3 = 2(0)₁₂₅3_<127> = 9496596035573_<13> · 72990180616825855013_<20> · C94

C94 = P34 · P61

P34 = 1363935016086710284190348118562849_<34>

P61 = 2115455595883918282267614450587132366299796154935856176143403_<61>

Number: 20003_126
N=2885343962202653372378528009811363064619245247881531993159016967031147098713516972051692235147
  ( 94 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=1363935016086710284190348118562849 (pp34)
 r2=2115455595883918282267614450587132366299796154935856176143403 (pp61)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.12 hours.
Scaled time: 1.97 units (timescale=0.932).
Factorization parameters were as follows:
n: 2885343962202653372378528009811363064619245247881531993159016967031147098713516972051692235147
m: 10000000000000000000000000
c5: 20
c0: 3
skew: 1
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 900001)
Primes: RFBsize:78498, AFBsize:78241, largePrimes:1570656 encountered
Relations: rels:1629783, finalFF:230731
Max relations in full relation-set: 28
Initial matrix: 156805 x 230731 with sparse part having weight 11797616.
Pruned matrix : 123689 x 124537 with weight 5161895.
Total sieving time: 2.04 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 2.12 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹²⁷+3 = 2(0)₁₂₆3_<128> = 79 · 83 · 32843 · 3835231 · 1195589420583881466001_<22> · C92

C92 = P37 · P55

P37 = 8927757006598681262632931194240133629_<37>

P55 = 2268642375519091333458799446695979155571481664083795247_<55>

Sat May 19 19:31:19 2007  
Sat May 19 19:31:19 2007  
Sat May 19 19:31:19 2007  Msieve v. 1.21
Sat May 19 19:31:19 2007  random seeds: d716045e 858ea74d
Sat May 19 19:31:19 2007  factoring 20253887863507244220879021005238400509953820135797606636390564270556960616638635630755061363 (92 digits)
Sat May 19 19:31:20 2007  commencing quadratic sieve (92-digit input)
Sat May 19 19:31:20 2007  using multiplier of 17
Sat May 19 19:31:20 2007  using 32kb Intel Core sieve core
Sat May 19 19:31:20 2007  sieve interval: 36 blocks of size 32768
Sat May 19 19:31:20 2007  processing polynomials in batches of 6
Sat May 19 19:31:20 2007  using a sieve bound of 1783751 (67059 primes)
Sat May 19 19:31:20 2007  using large prime bound of 187293855 (27 bits)
Sat May 19 19:31:20 2007  using double large prime bound of 777217055970600 (42-50 bits)
Sat May 19 19:31:20 2007  using trial factoring cutoff of 50 bits
Sat May 19 19:31:20 2007  polynomial 'A' values have 12 factors
Sat May 19 21:02:32 2007  67423 relations (17378 full + 50045 combined from 830306 partial), need 67155
Sat May 19 21:02:33 2007  begin with 847684 relations
Sat May 19 21:02:33 2007  reduce to 169734 relations in 10 passes
Sat May 19 21:02:33 2007  attempting to read 169734 relations
Sat May 19 21:02:35 2007  recovered 169734 relations
Sat May 19 21:02:35 2007  recovered 151296 polynomials
Sat May 19 21:02:35 2007  attempting to build 67423 cycles
Sat May 19 21:02:35 2007  found 67422 cycles in 5 passes
Sat May 19 21:02:35 2007  distribution of cycle lengths:
Sat May 19 21:02:35 2007     length 1 : 17378
Sat May 19 21:02:35 2007     length 2 : 12280
Sat May 19 21:02:35 2007     length 3 : 11630
Sat May 19 21:02:35 2007     length 4 : 8996
Sat May 19 21:02:35 2007     length 5 : 6589
Sat May 19 21:02:35 2007     length 6 : 4405
Sat May 19 21:02:35 2007     length 7 : 2691
Sat May 19 21:02:35 2007     length 9+: 3453
Sat May 19 21:02:35 2007  largest cycle: 19 relations
Sat May 19 21:02:35 2007  matrix is 67059 x 67422 with weight 4070500 (avg 60.37/col)
Sat May 19 21:02:35 2007  filtering completed in 3 passes
Sat May 19 21:02:35 2007  matrix is 65530 x 65594 with weight 3893561 (avg 59.36/col)
Sat May 19 21:02:36 2007  saving the first 48 matrix rows for later
Sat May 19 21:02:36 2007  matrix is 65482 x 65594 with weight 2931664 (avg 44.69/col)
Sat May 19 21:02:36 2007  matrix includes 32 packed rows
Sat May 19 21:02:36 2007  using block size 26237 for processor cache size 4096 kB
Sat May 19 21:02:56 2007  lanczos halted after 1037 iterations
Sat May 19 21:02:57 2007  recovered 16 nontrivial dependencies
Sat May 19 21:02:57 2007  prp37 factor: 8927757006598681262632931194240133629
Sat May 19 21:02:57 2007  prp55 factor: 2268642375519091333458799446695979155571481664083795247
Sat May 19 21:02:57 2007  elapsed time 01:31:38

May 19, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=11000000

(10¹⁷⁸+17)/9 = (1)₁₇₇3_<178> = 3² · 7² · 1046641 · 1290857 · 468836928921920538313_<21> · C142

C142 = P36 · C107

P36 = 297082579660968821734851624509405183_<36>

C107 = [13388873082149435308539000672775350680618901926900711188810262897346981830451724894509157440592356995091791_<107>]

May 19, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp

(2·10¹⁶⁸+43)/9 = (2)₁₆₇7_<168> = 47 · C166

C166 = P41 · P55 · P71

P41 = 45965997803609570676069581691927428510183_<41>

P55 = 2946919768053066098412187258879318843529311861174818097_<55>

P71 = 34904757433689170732652558228154689367498858601950291450197647933335691_<71>

Number: n
N=4728132387706855791962174940898345153664302600472813238770685579196217494089834515366430260047281323877068557919621749408983451536643026004728132387706855791962174941
  ( 166 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=45965997803609570676069581691927428510183 (pp41)
 r2=2946919768053066098412187258879318843529311861174818097 (pp55)
 r3=34904757433689170732652558228154689367498858601950291450197647933335691 (pp71)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 101.82 hours.
Scaled time: 134.81 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_2_167_7
n: 4728132387706855791962174940898345153664302600472813238770685579196217494089834515366430260047281323877068557919621749408983451536643026004728132387706855791962174941
skew: 0.93
deg: 5
c5: 125
c0: 86
m: 2000000000000000000000000000000000
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 4000001)
Primes: RFBsize:348513, AFBsize:349516, largePrimes:8195682 encountered
Relations: rels:7828220, finalFF:805085
Max relations in full relation-set: 48
Initial matrix: 698094 x 805085 with sparse part having weight 48480685.
Pruned matrix : 604878 x 608432 with weight 31850567.
Total sieving time: 92.31 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 8.93 hours.
Total square root time: 0.22 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000
total time: 101.82 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

2·10¹⁵⁰+3 = 2(0)₁₄₉3_<151> = 487 · C148

C148 = P64 · P85

P64 = 1824453361909318934020125483109157972584403451163125882265065433_<64>

P85 = 2250962543871412830161298255938234659251521136933600855735504876723568950774217694093_<85>

Number: n
N=4106776180698151950718685831622176591375770020533880903490759753593429158110882956878850102669404517453798767967145790554414784394250513347022587269
  ( 148 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=1824453361909318934020125483109157972584403451163125882265065433 (pp64)
 r2=2250962543871412830161298255938234659251521136933600855735504876723568950774217694093 (pp85)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 16.18 hours.
Scaled time: 22.14 units (timescale=1.368).
Factorization parameters were as follows:
name: KA_2_0_149_3
n: 4106776180698151950718685831622176591375770020533880903490759753593429158110882956878850102669404517453798767967145790554414784394250513347022587269
skew: 1.08
deg: 5
c5: 2
c0: 3
m: 1000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 600001)
Primes: RFBsize:315948, AFBsize:315821, largePrimes:6583994 encountered
Relations: rels:6446442, finalFF:849439
Max relations in full relation-set: 28
Initial matrix: 631834 x 849439 with sparse part having weight 29055982.
Pruned matrix : 406919 x 410142 with weight 10416091.
Total sieving time: 14.39 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.56 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000
total time: 16.18 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 18, 2007 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

2·10¹⁹¹-3 = 1(9)₁₉₀7_<192> = 7 · 53 · 829 · 1031 · 12110972033_<11> · 1278085313563_<13> · 18580007275894843_<17> · 117121349237684572025004166361887_<33> · C113

C113 = P47 · P66

P47 = 49371617551587041843675930397116659530937545163_<47>

P66 = 379266725313477244975216442892897216971059794842475211319820147649_<66>

Number: 19997_191
N=18725011712219814562530479034837840702529034807249997949068275863786847663649064207303543066082563170428265771787
  ( 113 digits)
Divisors found:
 r1=49371617551587041843675930397116659530937545163 (pp47)
 r2=379266725313477244975216442892897216971059794842475211319820147649 (pp66)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 56.52 hours.
Scaled time: 38.15 units (timescale=0.675).
Factorization parameters were as follows:
name: 19997_191
n: 18725011712219814562530479034837840702529034807249997949068275863786847663649064207303543066082563170428265771787
skew: 59546.05
# norm 6.66e+15
c5: 10560
c4: -2374857106
c3: -195238124648465
c2: 1713791335976812382
c1: 286960883326780791878154
c0: -869102931125208602582566965
# alpha -6.63
Y1: 1066141682921
Y0: -4464330115947638126804
# Murphy_E 7.39e-10
# M 15931944624871609380286614016751846664857168747787310376807033596899975510455931096032109076919995223638073753024
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 2750001)
Primes: RFBsize:250150, AFBsize:249696, largePrimes:7656920 encountered
Relations: rels:7706870, finalFF:571600
Max relations in full relation-set: 0
Initial matrix: 499929 x 571600 with sparse part having weight 34433582.
Pruned matrix : 435540 x 438103 with weight 23881885.
Polynomial selection time: 2.15 hours.
Total sieving time: 46.66 hours.
Total relation processing time: 0.59 hours.
Matrix solve time: 6.79 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 56.52 hours.
 --------- CPU info (if available) ----------

May 18, 2007 (2nd)

By Jo Yeong Uk / Msieve v. 1.21, GMP-ECM 6.1.2

2·10¹⁴²+3 = 2(0)₁₄₁3_<143> = 29 · 18121 · 10062555889_<11> · 5499130730309_<13> · 142203315288161311512583_<24> · C91

C91 = P40 · P52

P40 = 1628892178337141932454034590460430447783_<40>

P52 = 2969240859409506695099012352547967144102089819518203_<52>

Thu May 17 23:56:51 2007  
Thu May 17 23:56:51 2007  
Thu May 17 23:56:51 2007  Msieve v. 1.21
Thu May 17 23:56:51 2007  random seeds: ac10f82d 2d0dace6
Thu May 17 23:56:51 2007  factoring 4836573211491198755748211680523749919543813705587359988916604311081614199708621860609493949 (91 digits)
Thu May 17 23:56:52 2007  commencing quadratic sieve (91-digit input)
Thu May 17 23:56:52 2007  using multiplier of 29
Thu May 17 23:56:52 2007  using 32kb Intel Core sieve core
Thu May 17 23:56:52 2007  sieve interval: 36 blocks of size 32768
Thu May 17 23:56:52 2007  processing polynomials in batches of 6
Thu May 17 23:56:52 2007  using a sieve bound of 1719869 (64560 primes)
Thu May 17 23:56:52 2007  using large prime bound of 165107424 (27 bits)
Thu May 17 23:56:52 2007  using double large prime bound of 619412223763104 (42-50 bits)
Thu May 17 23:56:52 2007  using trial factoring cutoff of 50 bits
Thu May 17 23:56:52 2007  polynomial 'A' values have 12 factors
Fri May 18 01:24:55 2007  64901 relations (16394 full + 48507 combined from 770121 partial), need 64656
Fri May 18 01:24:55 2007  begin with 786515 relations
Fri May 18 01:24:55 2007  reduce to 162698 relations in 10 passes
Fri May 18 01:24:56 2007  attempting to read 162698 relations
Fri May 18 01:24:57 2007  recovered 162698 relations
Fri May 18 01:24:57 2007  recovered 145537 polynomials
Fri May 18 01:24:57 2007  attempting to build 64901 cycles
Fri May 18 01:24:57 2007  found 64901 cycles in 5 passes
Fri May 18 01:24:57 2007  distribution of cycle lengths:
Fri May 18 01:24:57 2007     length 1 : 16394
Fri May 18 01:24:57 2007     length 2 : 12017
Fri May 18 01:24:57 2007     length 3 : 11335
Fri May 18 01:24:57 2007     length 4 : 8916
Fri May 18 01:24:57 2007     length 5 : 6442
Fri May 18 01:24:57 2007     length 6 : 4126
Fri May 18 01:24:57 2007     length 7 : 2645
Fri May 18 01:24:57 2007     length 9+: 3026
Fri May 18 01:24:57 2007  largest cycle: 17 relations
Fri May 18 01:24:57 2007  matrix is 64560 x 64901 with weight 3877029 (avg 59.74/col)
Fri May 18 01:24:57 2007  filtering completed in 4 passes
Fri May 18 01:24:57 2007  matrix is 63178 x 63242 with weight 3716626 (avg 58.77/col)
Fri May 18 01:24:58 2007  saving the first 48 matrix rows for later
Fri May 18 01:24:59 2007  matrix is 63130 x 63242 with weight 2795295 (avg 44.20/col)
Fri May 18 01:24:59 2007  matrix includes 32 packed rows
Fri May 18 01:24:59 2007  using block size 25296 for processor cache size 4096 kB
Fri May 18 01:25:17 2007  lanczos halted after 1000 iterations
Fri May 18 01:25:17 2007  recovered 17 nontrivial dependencies
Fri May 18 01:25:17 2007  prp40 factor: 1628892178337141932454034590460430447783
Fri May 18 01:25:17 2007  prp52 factor: 2969240859409506695099012352547967144102089819518203
Fri May 18 01:25:17 2007  elapsed time 01:28:26

2·10¹⁸¹+3 = 2(0)₁₈₀3_<182> = C182

C182 = P34 · C148

P34 = 5511837461824511266624821670808689_<34>

C148 = [3628554023684809875041241575766798527068771437488933383862974033044444603054287454851457985502624509381866036022786923582580265165248809496728968627_<148>]

May 18, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp

3·10¹⁵⁸+1 = 3(0)₁₅₇1_<159> = 7 · 518209 · 1248630547_<10> · C143

C143 = P68 · P76

P68 = 14187037984758391993529228654317591874792986868087928456850474187179_<68>

P76 = 4668663539228271717902874354562882580267735906322278836949839530064145731879_<76>

Number: n
N=66234506969088041957193564483376377591189005460744403342598632681083858520789395982329953995232154901773260034664510126060898123874794593379341
  ( 143 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=14187037984758391993529228654317591874792986868087928456850474187179 (pp68)
 r2=4668663539228271717902874354562882580267735906322278836949839530064145731879 (pp76)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.69 hours.
Scaled time: 51.68 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_3_0_157_1
n: 66234506969088041957193564483376377591189005460744403342598632681083858520789395982329953995232154901773260034664510126060898123874794593379341
skew: 0.20
deg: 5
c5: 3000
c0: 1
m: 10000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:183072, AFBsize:183066, largePrimes:7144631 encountered
Relations: rels:6604207, finalFF:421676
Max relations in full relation-set: 28
Initial matrix: 366205 x 421676 with sparse part having weight 37286804.
Pruned matrix : 331020 x 332915 with weight 26592023.
Total sieving time: 31.64 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 3.56 hours.
Total square root time: 0.27 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 35.69 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(37·10¹⁵⁸-1)/9 = 4(1)₁₅₈_<159> = 3³ · 1113503211871_<13> · C146

C146 = P51 · P95

P51 = 437047077000875706556100910362101256688838117136603_<51>

P95 = 31287852560125735966912304307179361487093589834503079004811219125764118303034275852798460927361_<95>

Number: n
N=13674264507037318634426012072489013175752521746264239263365882696289761263584377804407017898506229087375374061783811632623995055437253177297294683
  ( 146 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=437047077000875706556100910362101256688838117136603 (pp51)
 r2=31287852560125735966912304307179361487093589834503079004811219125764118303034275852798460927361 (pp95)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 49.75 hours.
Scaled time: 67.76 units (timescale=1.362).
Factorization parameters were as follows:
name: KA_4_1_158
n: 13674264507037318634426012072489013175752521746264239263365882696289761263584377804407017898506229087375374061783811632623995055437253177297294683
skew: 0.12
deg: 5
c5: 37000
c0: -1
m: 10000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1800001)
Primes: RFBsize:315948, AFBsize:316896, largePrimes:7462039 encountered
Relations: rels:7093511, finalFF:723313
Max relations in full relation-set: 28
Initial matrix: 632911 x 723313 with sparse part having weight 38195405.
Pruned matrix : 545249 x 548477 with weight 23406323.
Total sieving time: 44.78 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 4.31 hours.
Total square root time: 0.41 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000
total time: 49.75 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

2·10¹⁴⁴+3 = 2(0)₁₄₃3_<145> = 1201 · C142

C142 = P55 · P88

P55 = 1168960033824751568738318599288806794044795142960334049_<55>

P88 = 1424581581949223240674405227318668880791852510435284297667922774714016704281163739428947_<88>

Number: n
N=1665278934221482098251457119067443796835970024979184013322231473771856786011656952539550374687760199833472106577851790174854288093255620316403
  ( 142 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=1168960033824751568738318599288806794044795142960334049 (pp55)
 r2=1424581581949223240674405227318668880791852510435284297667922774714016704281163739428947 (pp88)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 9.47 hours.
Scaled time: 12.92 units (timescale=1.364).
Factorization parameters were as follows:
name: KA_2_0_143_3
n: 1665278934221482098251457119067443796835970024979184013322231473771856786011656952539550374687760199833472106577851790174854288093255620316403
skew: 1.72
deg: 5
c5: 1
c0: 15
m: 100000000000000000000000000000
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 800001)
Primes: RFBsize:283146, AFBsize:282687, largePrimes:6448372 encountered
Relations: rels:6058655, finalFF:650499
Max relations in full relation-set: 28
Initial matrix: 565897 x 650499 with sparse part having weight 22096768.
Pruned matrix : 435350 x 438243 with weight 11275494.
Total sieving time: 7.48 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.61 hours.
Total square root time: 0.22 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000
total time: 9.47 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

2·10¹⁵⁵+3 = 2(0)₁₅₄3_<156> = 23 · C154

C154 = P76 · P79

P76 = 1111621257288759311574554337362336029819886569891919818320899807496833211589_<76>

P79 = 7822495402005635711932598925376137473625943127630073484216479297850123896513649_<79>

Number: n
N=8695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478261
  ( 154 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=1111621257288759311574554337362336029819886569891919818320899807496833211589 (pp76)
 r2=7822495402005635711932598925376137473625943127630073484216479297850123896513649 (pp79)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 18.69 hours.
Scaled time: 27.04 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_2_0_154_3
n: 8695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478261
skew: 1.08
deg: 5
c5: 2
c0: 3
m: 10000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:183072, AFBsize:183201, largePrimes:6621471 encountered
Relations: rels:6096384, finalFF:453480
Max relations in full relation-set: 28
Initial matrix: 366338 x 453480 with sparse part having weight 31199933.
Pruned matrix : 295381 x 297276 with weight 17548748.
Total sieving time: 16.52 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.97 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 18.69 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 17, 2007 (4th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

2·10¹¹⁹+3 = 2(0)₁₁₈3_<120> = C120

C120 = P49 · P71

P49 = 5228659514109126391498531522208323958331928046131_<49>

P71 = 38250721711810786837816564744277352704880578237524903785562032046531313_<71>

Number: 20003_119
N=200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
  ( 120 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=5228659514109126391498531522208323958331928046131 (pp49)
 r2=38250721711810786837816564744277352704880578237524903785562032046531313 (pp71)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.03 hours.
Scaled time: 0.96 units (timescale=0.933).
Factorization parameters were as follows:
n: 200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
m: 1000000000000000000000000
c5: 1
c0: 15
skew: 1.72
type: snfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [350000, 490001)
Primes: RFBsize:56543, AFBsize:56578, largePrimes:2095809 encountered
Relations: rels:2212502, finalFF:259212
Max relations in full relation-set: 28
Initial matrix: 113185 x 259212 with sparse part having weight 21628126.
Pruned matrix : 80815 x 81444 with weight 4666548.
Total sieving time: 0.97 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.4,2.4,35000
total time: 1.03 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹¹⁰+3 = 2(0)₁₀₉3_<111> = 7 · C110

C110 = P35 · P76

P35 = 26184862097599361168293556342151923_<35>

P76 = 1091142984253028074855253881145711454222019861072878061773867745555021996423_<76>

Number: 20003_110
N=28571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429
  ( 110 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=26184862097599361168293556342151923 (pp35)
 r2=1091142984253028074855253881145711454222019861072878061773867745555021996423 (pp76)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.48 hours.
Scaled time: 0.44 units (timescale=0.935).
Factorization parameters were as follows:
n: 28571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429
m: 10000000000000000000000
c5: 2
c0: 3
skew: 1.08
type: snfs
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [250000, 325001)
Primes: RFBsize:41538, AFBsize:41512, largePrimes:1111312 encountered
Relations: rels:1064225, finalFF:121436
Max relations in full relation-set: 28
Initial matrix: 83115 x 121436 with sparse part having weight 4674144.
Pruned matrix : 63518 x 63997 with weight 1815360.
Total sieving time: 0.45 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,25000
total time: 0.48 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹¹⁴+3 = 2(0)₁₁₃3_<115> = 29 · 79 · 269 · 46091 · C104

C104 = P33 · P72

P33 = 141642068744903728734080380860557_<33>

P72 = 497100539534504959831516767690043182490203130774494939527873200330969211_<72>

Number: 20003_114
N=70410348793875085321768849152758164549236425820919737153313863018456745454803368293180589836398051310527
  ( 104 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=141642068744903728734080380860557 (pp33)
 r2=497100539534504959831516767690043182490203130774494939527873200330969211 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.64 hours.
Scaled time: 0.60 units (timescale=0.930).
Factorization parameters were as follows:
n: 70410348793875085321768849152758164549236425820919737153313863018456745454803368293180589836398051310527
m: 100000000000000000000000
c5: 1
c0: 15
skew: 1.72
type: snfs
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [250000, 375001)
Primes: RFBsize:41538, AFBsize:41382, largePrimes:1149521 encountered
Relations: rels:1106102, finalFF:125588
Max relations in full relation-set: 28
Initial matrix: 82983 x 125588 with sparse part having weight 5422596.
Pruned matrix : 65702 x 66180 with weight 2045419.
Total sieving time: 0.61 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,25000
total time: 0.64 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹¹⁸+3 = 2(0)₁₁₇3_<119> = 714997972759321_<15> · C104

C104 = P39 · P65

P39 = 991811671612623385550841555017839892819_<39>

P65 = 28203043059484251487882072762043305121719614244673667495654922297_<65>

Number: 20003_118
N=27972107281389871588317961432884759576381723602570236734004002563659504714454632356237779796988253285243
  ( 104 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=991811671612623385550841555017839892819 (pp39)
 r2=28203043059484251487882072762043305121719614244673667495654922297 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.96 hours.
Scaled time: 0.82 units (timescale=0.853).
Factorization parameters were as follows:
n: 27972107281389871588317961432884759576381723602570236734004002563659504714454632356237779796988253285243
m: 200000000000000000000000
c5: 125
c0: 6
skew: 1
type: snfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [350000, 455001)
Primes: RFBsize:56543, AFBsize:56408, largePrimes:1928404 encountered
Relations: rels:1883991, finalFF:137232
Max relations in full relation-set: 28
Initial matrix: 113016 x 137232 with sparse part having weight 10203633.
Pruned matrix : 104024 x 104653 with weight 5985437.
Total sieving time: 0.89 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.4,2.4,35000
total time: 0.96 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 17, 2007 (3rd)

By suberi / GMP-ECM 6.1.2 B1=11000000

(64·10²³⁵+53)/9 = 7(1)₂₃₄7_<236> = 7 · 11 · 193 · C232

C232 = P32 · C201

P32 = 28107359195838759279509711482249_<32>

C201 = [170243048162211606139168092899412373887432262726392638811930752489088113456154186085588507167609348929816413787030872916649323684810730559987175370389656582406055523330513546443606392638754557740210553_<201>]

May 17, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(35·10¹⁶⁷-53)/9 = 3(8)₁₆₆3_<168> = 11 · 113 · C165

C165 = P46 · P120

P46 = 1481894566930897165561217886297315643190412863_<46>

P120 = 211123754485119892507236798299021028208278038771361562866186890465260883878836081438303807062657374164385131676699256887_<120>

Number: n
N=312863144721551801197818896933941181728792348261374810047376419057834987038526861535711093233217127022436756950031286314472155180119781889693394118172879234826137481
  ( 165 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=1481894566930897165561217886297315643190412863 (pp46)
 r2=211123754485119892507236798299021028208278038771361562866186890465260883878836081438303807062657374164385131676699256887 (pp120)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 94.40 hours.
Scaled time: 112.80 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_3_8_166_3
n: 312863144721551801197818896933941181728792348261374810047376419057834987038526861535711093233217127022436756950031286314472155180119781889693394118172879234826137481
type: snfs
skew: 0.43
deg: 5
c5: 3500
c0: -53
m: 1000000000000000000000000000000000
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3200001)
Primes: RFBsize:348513, AFBsize:348001, largePrimes:7992903 encountered
Relations: rels:7653020, finalFF:801438
Max relations in full relation-set: 28
Initial matrix: 696581 x 801438 with sparse part having weight 45326608.
Pruned matrix : 601811 x 605357 with weight 28677270.
Total sieving time: 85.35 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 8.34 hours.
Total square root time: 0.33 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.6,2.6,100000
total time: 94.40 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

May 17, 2007

The factor table of 200...003 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

May 16, 2007 (5th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

2·10¹³⁷-3 = 1(9)₁₃₆7_<138> = 7² · 283 · 317 · 653 · 17264088293_<11> · C118

C118 = P58 · P60

P58 = 7000751848412477959806057766604418499857831431396426422451_<58>

P60 = 576483264949148720398224057113036271804100390023761971950737_<60>

Number: n
N=4035816282671613171343262279759201422385931092225366246725375548600017972927485571480526777015219311635458678522796387
  ( 118 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=7000751848412477959806057766604418499857831431396426422451 (pp58)
 r2=576483264949148720398224057113036271804100390023761971950737 (pp60)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 5.31 hours.
Scaled time: 7.68 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_1_9_136_7
n: 4035816282671613171343262279759201422385931092225366246725375548600017972927485571480526777015219311635458678522796387
skew: 0.43
deg: 5
c5: 200
c0: -3
m: 1000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 700001)
Primes: RFBsize:114155, AFBsize:114342, largePrimes:6384288 encountered
Relations: rels:5895003, finalFF:424935
Max relations in full relation-set: 28
Initial matrix: 228562 x 424935 with sparse part having weight 33701210.
Pruned matrix : 150857 x 152063 with weight 10360660.
Total sieving time: 4.55 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.44 hours.
Total square root time: 0.17 hours, sqrts: 6.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,75000
total time: 5.31 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 16, 2007 (4th)

By suberi / GMP-ECM 6.1.2 B1=3000000

2·10¹⁷⁷-3 = 1(9)₁₇₆7_<178> = 17 · 66090659226826860491_<20> · C157

C157 = P33 · C124

P33 = 314129679887073807583524645188651_<33>

C124 = [5666723452861111419953301719983874645151689206796263127100108210064996380732130563446722510620008860655369666194925533653301_<124>]

2·10¹⁸⁴-3 = 1(9)₁₈₃7_<185> = 29² · 2713 · 5237 · 66857737 · C167

C167 = P32 · P135

P32 = 89177151216694919128342839012937_<32>

P135 = 280734873559781758253348251445739908956056985830730029555749391702366572037148720479831472201011105110825184173089405824194320945511353_<135>

2·10¹⁸⁵-3 = 1(9)₁₈₄7_<186> = 7 · 10139 · C181

C181 = P34 · C148

P34 = 1629098585915315381840811732409037_<34>

C148 = [1729774401844928654956193898363519632991312797796196776125859358920365912442809486382638218734874672877056576604898068320294799461787530626132748997_<148>]

May 16, 2007 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

(55·10¹⁷⁸-1)/9 = 6(1)₁₇₈_<179> = C179

C179 = P71 · P109

P71 = 10844535479140675215472164272317404597918151109866534169729050994698157_<71>

P109 = 5635198596441272091330699355272671552551459731965648263799402079769287090412428090080019459707087511004675523_<109>

Number: 61111_178
N=61111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
  ( 179 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=10844535479140675215472164272317404597918151109866534169729050994698157 (pp71)
 r2=5635198596441272091330699355272671552551459731965648263799402079769287090412428090080019459707087511004675523 (pp109)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 699.57 hours.
Scaled time: 471.51 units (timescale=0.674).
Factorization parameters were as follows:
name: 61111_178
n: 61111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
m: 500000000000000000000000000000000000
c5: 88
c0: -5
skew: 1
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 8500001)
Primes: RFBsize:501962, AFBsize:502697, largePrimes:6420312 encountered
Relations: rels:6865276, finalFF:1126019
Max relations in full relation-set: 0
Initial matrix: 1004725 x 1126019 with sparse part having weight 61341522.
Pruned matrix : 900119 x 905206 with weight 47244858.
Total sieving time: 650.72 hours.
Total relation processing time: 0.72 hours.
Matrix solve time: 47.78 hours.
Time per square root: 0.35 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 699.57 hours.
 --------- CPU info (if available) ----------

May 16, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp

2·10¹³⁹-3 = 1(9)₁₃₈7_<140> = 53 · 113 · 241 · C134

C134 = P38 · P96

P38 = 41803841074986331004467759752042705661_<38>

P96 = 331468644256359068076837242793801952073119679096103445167011822018914725489819506339762119501373_<96>

Number: n
N=13856662525834015196601792082164466113185376509769986330402418264744008552332110944754179342626073111908485058014381830035563124372553
  ( 134 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=41803841074986331004467759752042705661 (pp38)
 r2=331468644256359068076837242793801952073119679096103445167011822018914725489819506339762119501373 (pp96)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.88 hours.
Scaled time: 7.08 units (timescale=1.451).
Factorization parameters were as follows:
name: KA_1_9_138_7
n: 13856662525834015196601792082164466113185376509769986330402418264744008552332110944754179342626073111908485058014381830035563124372553
skew: 1.72
deg: 5
c5: 1
c0: -15
m: 10000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 600001)
Primes: RFBsize:148933, AFBsize:148925, largePrimes:5871911 encountered
Relations: rels:5357002, finalFF:416257
Max relations in full relation-set: 28
Initial matrix: 297922 x 416257 with sparse part having weight 22774580.
Pruned matrix : 197183 x 198736 with weight 9498448.
Total sieving time: 4.11 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.59 hours.
Total square root time: 0.06 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,75000
total time: 4.88 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(2·10¹⁵⁸+1)/3 = (6)₁₅₇7_<158> = 17 · 277897 · 488347 · C146

C146 = P41 · P106

P41 = 21031561607724268249695576438281644154827_<41>

P106 = 1373965780486348413798444543281701321099663088692889197539420932838074370643421175688293752426150951769707_<106>

Number: n
N=28896645959203594878243179450779359727070264879734381614242857401731103885737949305946301799304495401978678162311838251115093256907566767956425689
  ( 146 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=21031561607724268249695576438281644154827 (pp41)
 r2=1373965780486348413798444543281701321099663088692889197539420932838074370643421175688293752426150951769707 (pp106)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 29.31 hours.
Scaled time: 40.01 units (timescale=1.365).
Factorization parameters were as follows:
name: KA_6_157_7
n: 28896645959203594878243179450779359727070264879734381614242857401731103885737949305946301799304495401978678162311838251115093256907566767956425689
skew: 0.44
deg: 5
c5: 125
c0: 2
m: 20000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:315948, AFBsize:316326, largePrimes:7115036 encountered
Relations: rels:6794108, finalFF:747296
Max relations in full relation-set: 28
Initial matrix: 632339 x 747296 with sparse part having weight 32157852.
Pruned matrix : 514318 x 517543 with weight 16887335.
Total sieving time: 25.80 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.22 hours.
Total square root time: 0.10 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000
total time: 29.31 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

2·10¹³³-3 = 1(9)₁₃₂7_<134> = 557 · 71162352319717499_<17> · C114

C114 = P40 · P74

P40 = 5387015255111323942626049346281287077863_<40>

P74 = 93664776152606764401059753977917406656658975593547100495177002729005709733_<74>

Number: n
N=504573578000679980011194383314501795810950700707844710097611496380308437105732388873064306717211277180237947940579
  ( 114 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=5387015255111323942626049346281287077863 (pp40)
 r2=93664776152606764401059753977917406656658975593547100495177002729005709733 (pp74)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.51 hours.
Scaled time: 5.09 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_1_9_132_7
n: 504573578000679980011194383314501795810950700707844710097611496380308437105732388873064306717211277180237947940579
skew: 0.54
deg: 5
c5: 125
c0: -6
m: 200000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 400001)
Primes: RFBsize:114155, AFBsize:113572, largePrimes:5040741 encountered
Relations: rels:4461042, finalFF:289507
Max relations in full relation-set: 28
Initial matrix: 227792 x 289507 with sparse part having weight 14730733.
Pruned matrix : 176541 x 177743 with weight 6872155.
Total sieving time: 3.03 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.36 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,75000
total time: 3.51 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 16, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

2·10¹²⁴-3 = 1(9)₁₂₃7_<125> = 31536909893_<11> · C114

C114 = P40 · P74

P40 = 9336975976397637344374611852234644275771_<40>

P74 = 67921085334223439767801410472062272050391919676586092874931678368742117499_<74>

Number: 19997_124
N=634177542056498147727386792391213558521105928315688960325495387938387321694086180962789993154640998992817840816729
  ( 114 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=9336975976397637344374611852234644275771 (pp40)
 r2=67921085334223439767801410472062272050391919676586092874931678368742117499 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.37 hours.
Scaled time: 1.28 units (timescale=0.933).
Factorization parameters were as follows:
n: 634177542056498147727386792391213558521105928315688960325495387938387321694086180962789993154640998992817840816729
m: 10000000000000000000000000
c5: 1
c0: -15
skew: 1.72
type: snfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [350000, 560001)
Primes: RFBsize:56543, AFBsize:56578, largePrimes:2126235 encountered
Relations: rels:2218039, finalFF:221963
Max relations in full relation-set: 28
Initial matrix: 113185 x 221963 with sparse part having weight 20278707.
Pruned matrix : 90696 x 91325 with weight 5816729.
Total sieving time: 1.30 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.4,2.4,35000
total time: 1.37 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹²⁵-3 = 1(9)₁₂₄7_<126> = 7 · 233 · 144593 · 10817778017_<11> · C107

C107 = P32 · P76

P32 = 70950032524214449038440162186879_<32>

P76 = 1104938488904480115616998648501886905041655534575552950019302930656654642413_<76>

Number: 19997_125
N=78395421725029230328818426014800087569324238426422046695751860537037254334678996299996708647592753825499027
  ( 107 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=70950032524214449038440162186879 (pp32)
 r2=1104938488904480115616998648501886905041655534575552950019302930656654642413 (pp76)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.41 hours.
Scaled time: 1.31 units (timescale=0.929).
Factorization parameters were as follows:
n: 78395421725029230328818426014800087569324238426422046695751860537037254334678996299996708647592753825499027
m: 10000000000000000000000000
c5: 2
c0: -3
skew: 1.08
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 750001)
Primes: RFBsize:78498, AFBsize:78591, largePrimes:1530358 encountered
Relations: rels:1610360, finalFF:249014
Max relations in full relation-set: 28
Initial matrix: 157154 x 249014 with sparse part having weight 10838770.
Pruned matrix : 105018 x 105867 with weight 4177813.
Total sieving time: 1.36 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 1.41 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹³²-3 = 1(9)₁₃₁7_<133> = 19 · 883 · 312007369 · 2035213286473_<13> · C108

C108 = P48 · P60

P48 = 224921079033736342221790746096952105532091294451_<48>

P60 = 834662212681919642405556463667806222934803506974724243740903_<60>

Number: 19997_132
N=187733125505103299807786248565954705912786141137724869511999365125813198339801086514367050241684111925629253
  ( 108 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=224921079033736342221790746096952105532091294451 (pp48)
 r2=834662212681919642405556463667806222934803506974724243740903 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.24 hours.
Scaled time: 3.02 units (timescale=0.930).
Factorization parameters were as follows:
n: 187733125505103299807786248565954705912786141137724869511999365125813198339801086514367050241684111925629253
m: 200000000000000000000000000
c5: 25
c0: -12
skew: 1
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 1150001)
Primes: RFBsize:78498, AFBsize:78531, largePrimes:1574002 encountered
Relations: rels:1587278, finalFF:187947
Max relations in full relation-set: 28
Initial matrix: 157093 x 187947 with sparse part having weight 12103751.
Pruned matrix : 146454 x 147303 with weight 7639030.
Total sieving time: 3.14 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 3.24 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 15, 2007 (6th)

By Wataru Sakai / GMP-ECM 6.1.2 B1=11000000

9·10¹⁸⁶+1 = 9(0)₁₈₅1_<187> = 61 · 161271954417042232580477_<24> · C162

C162 = P35 · P128

P35 = 71338953778563773721289257398483341_<35>

P128 = 12824105714440400124634673307313813672129762979860127394144076399375268657498186011572935151644208597728853041885465975326330013_<128>

May 15, 2007 (5th)

By suberi / GMP-ECM 6.1.2 B1=3000000

(64·10²¹⁰+53)/9 = 7(1)₂₀₉7_<211> = 13 · 1901 · 215887165601_<12> · C196

C196 = P36 · C161

P36 = 120353750687524054661558403071957407_<36>

C161 = [11074536064618948013173809104218434495785079170068678862536218619877065401976868698025916479343294712320399742216591613798301642308351142097007338459987719559387_<161>]

(64·10²²¹+53)/9 = 7(1)₂₂₀7_<222> = 3² · 11 · 128239 · 503398933 · 1004825417137_<13> · 27740572834433626007911111_<26> · C169

C169 = P38 · C132

P38 = 38068287072532520234581880952761336179_<38>

C132 = [104857737776937132831500531794436978547677820037074899064862334390039119428558654617425288051798995857403608343118733866481109955753_<132>]

May 15, 2007 (4th)

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000, GGNFS-0.77.1-20050930-nocona

2·10¹⁸⁹-3 = 1(9)₁₈₈7_<190> = C190

C190 = P38 · C152

P38 = 26515433818872756128486451063540368813_<38>

C152 = [75427768357931602931753276660580155235389614555331854484100658108640121572138298453489837951680283043601403057326275895068893330216499198205413743316369_<152>]

2·10¹³⁸-3 = 1(9)₁₃₇7_<139> = C139

C139 = P43 · P96

P43 = 2792516776165070836944026656509845283656971_<43>

P96 = 716199815546524866079650590503056034131183398218468977769146136824078266907549975600350599517207_<96>

Number: 19997_138
N=1999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997
  ( 139 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=2792516776165070836944026656509845283656971 (pp43)
 r2=716199815546524866079650590503056034131183398218468977769146136824078266907549975600350599517207 (pp96)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.55 hours.
Scaled time: 7.97 units (timescale=0.932).
Factorization parameters were as follows:
n: 1999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997
m: 10000000000000000000000000000
c5: 1
c0: -150
skew: 1
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [650000, 1200001)
Primes: RFBsize:100021, AFBsize:99568, largePrimes:1619547 encountered
Relations: rels:1694434, finalFF:263039
Max relations in full relation-set: 28
Initial matrix: 199653 x 263039 with sparse part having weight 10868421.
Pruned matrix : 161528 x 162590 with weight 6105713.
Total sieving time: 8.45 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1300000,1300000,25,25,43,43,2.3,2.3,50000
total time: 8.55 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹⁰⁸-3 = 1(9)₁₀₇7_<109> = 97 · 907 · 2334911 · 62038633 · C90

C90 = P40 · P50

P40 = 9795426399848232136433658361416964220351_<40>

P50 = 16021201316639818235833142024355288672757596038111_<50>

Number: 19997_108
N=156934498334296931342888700420223926738874127226828735072542912178143222401314959597796961
  ( 90 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=9795426399848232136433658361416964220351 (pp40)
 r2=16021201316639818235833142024355288672757596038111 (pp50)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.51 hours.
Scaled time: 0.46 units (timescale=0.909).
Factorization parameters were as follows:
n: 156934498334296931342888700420223926738874127226828735072542912178143222401314959597796961
m: 10000000000000000000000
c5: 1
c0: -150
skew: 2.72
type: snfs
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [250000, 325001)
Primes: RFBsize:41538, AFBsize:41357, largePrimes:1146010 encountered
Relations: rels:1115866, finalFF:136839
Max relations in full relation-set: 28
Initial matrix: 82959 x 136839 with sparse part having weight 5203852.
Pruned matrix : 58367 x 58845 with weight 1641515.
Total sieving time: 0.48 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,25000
total time: 0.51 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹¹⁴-3 = 1(9)₁₁₃7_<115> = 19 · 211 · C111

C111 = P50 · P61

P50 = 66720394280058370841709380872145894939733576500903_<50>

P61 = 7477136952660057610131641830487159799848955980602003638351811_<61>

Number: 19997_114
N=498877525567473185333000748316288351209777999501122474432526814666999251683711648790222000498877525567473185333
  ( 111 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=66720394280058370841709380872145894939733576500903 (pp50)
 r2=7477136952660057610131641830487159799848955980602003638351811 (pp61)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.65 hours.
Scaled time: 0.60 units (timescale=0.929).
Factorization parameters were as follows:
n: 498877525567473185333000748316288351209777999501122474432526814666999251683711648790222000498877525567473185333
m: 100000000000000000000000
c5: 1
c0: -15
skew: 1.72
type: snfs
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [250000, 375001)
Primes: RFBsize:41538, AFBsize:41382, largePrimes:1141363 encountered
Relations: rels:1093722, finalFF:121200
Max relations in full relation-set: 28
Initial matrix: 82984 x 121200 with sparse part having weight 5257052.
Pruned matrix : 66846 x 67324 with weight 2100764.
Total sieving time: 0.62 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,25000
total time: 0.65 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹¹⁸-3 = 1(9)₁₁₇7_<119> = 191 · 8248949 · C110

C110 = P32 · P78

P32 = 22950984299621533137884728246439_<32>

P78 = 553091130404568883549143340580413178416536717655739844547962308344784263446097_<78>

Number: 19997_118
N=12693985850175186430016911327810157663880441074803615518059787935833747232907048068371437696826716606008698583
  ( 110 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=22950984299621533137884728246439 (pp32)
 r2=553091130404568883549143340580413178416536717655739844547962308344784263446097 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.06 hours.
Scaled time: 0.98 units (timescale=0.927).
Factorization parameters were as follows:
n: 12693985850175186430016911327810157663880441074803615518059787935833747232907048068371437696826716606008698583
m: 1000000000000000000000000
c5: 1
c0: -150
skew: 2.72
type: snfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [350000, 490001)
Primes: RFBsize:56543, AFBsize:56408, largePrimes:2190525 encountered
Relations: rels:2411404, finalFF:354493
Max relations in full relation-set: 28
Initial matrix: 113015 x 354493 with sparse part having weight 29047533.
Pruned matrix : 69719 x 70348 with weight 4777254.
Total sieving time: 1.00 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.4,2.4,35000
total time: 1.06 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

2·10¹²²-3 = 1(9)₁₂₁7_<123> = 23 · 67 · 6389 · C116

C116 = P48 · P69

P48 = 171991496996710309484092016279706178541733683213_<48>

P69 = 118110223750443992209744996157769492200408400398154132891719193722281_<69>

Number: 19997_122
N=20313954193455270551906774388857227334172367354703680858028922804841099679659099346307111031706121274915953553768853
  ( 116 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=171991496996710309484092016279706178541733683213 (pp48)
 r2=118110223750443992209744996157769492200408400398154132891719193722281 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.36 hours.
Scaled time: 1.27 units (timescale=0.929).
Factorization parameters were as follows:
n: 20313954193455270551906774388857227334172367354703680858028922804841099679659099346307111031706121274915953553768853
m: 2000000000000000000000000
c5: 25
c0: -12
skew: 1
type: snfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [350000, 560001)
Primes: RFBsize:56543, AFBsize:56628, largePrimes:2122377 encountered
Relations: rels:2193156, finalFF:202049
Max relations in full relation-set: 28
Initial matrix: 113235 x 202049 with sparse part having weight 18248550.
Pruned matrix : 93995 x 94625 with weight 5931908.
Total sieving time: 1.29 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.4,2.4,35000
total time: 1.36 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 15, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

2·10¹⁴³-3 = 1(9)₁₄₂7_<144> = 7 · 367 · C140

C140 = P36 · P105

P36 = 300364480242690431385063688008727003_<36>

P105 = 259189448587394079995709224242217573207735348894143323496982198581906017312796640460823662146191460771471_<105>

Number: n
N=77851304009342156481121058777734527053328143246399377189567925262748151031529778123783573374854028804982483456597898014791747761775009731413
  ( 140 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=300364480242690431385063688008727003 (pp36)
 r2=259189448587394079995709224242217573207735348894143323496982198581906017312796640460823662146191460771471 (pp105)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.88 hours.
Scaled time: 9.96 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_1_9_142_7
n: 77851304009342156481121058777734527053328143246399377189567925262748151031529778123783573374854028804982483456597898014791747761775009731413
skew: 0.54
deg: 5
c5: 125
c0: -6
m: 20000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 800001)
Primes: RFBsize:183072, AFBsize:182636, largePrimes:6536042 encountered
Relations: rels:6097591, finalFF:542478
Max relations in full relation-set: 28
Initial matrix: 365773 x 542478 with sparse part having weight 28309689.
Pruned matrix : 211117 x 213009 with weight 11522988.
Total sieving time: 5.77 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.85 hours.
Total square root time: 0.11 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 6.88 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 15, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000

9·10¹⁸⁵+1 = 9(0)₁₈₄1_<186> = C186

C186 = P38 · C149

P38 = 14221071273845475492291671003825582287_<38>

C149 = [63286371516555504143607328750089379622990817116008869593801609303856339184629344856413421757600029944178214967248795969528509796283408631275118450223_<149>]

May 15, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(85·10¹⁵⁶+41)/9 = 9(4)₁₅₅9_<157> = 7 · 43 · 1829647 · 59981311102477643861_<20> · C129

C129 = P45 · P84

P45 = 623026004262418045585258199687571169731749999_<45>

P84 = 458902564109778259210141897723342450686101445324350532928974904781714443488055487153_<84>

Number: n
N=285908230863093280149522567479878460620220761033945807669254236564669687489493297610088438129173451686543805526322851093152262847
  ( 129 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=623026004262418045585258199687571169731749999 (pp45)
 r2=458902564109778259210141897723342450686101445324350532928974904781714443488055487153 (pp84)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 33.23 hours.
Scaled time: 47.88 units (timescale=1.441).
Factorization parameters were as follows:
name: KA_9_4_155_9
n: 285908230863093280149522567479878460620220761033945807669254236564669687489493297610088438129173451686543805526322851093152262847
skew: 0.55
deg: 5
c5: 850
c0: 41
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:216816, AFBsize:216852, largePrimes:7158635 encountered
Relations: rels:6684140, finalFF:532075
Max relations in full relation-set: 28
Initial matrix: 433735 x 532075 with sparse part having weight 38484696.
Pruned matrix : 354237 x 356469 with weight 22829842.
Total sieving time: 29.61 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.29 hours.
Total square root time: 0.13 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 33.23 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

2·10¹⁰⁴-3 = 1(9)₁₀₃7_<105> = 397633 · C99

C99 = P47 · P52

P47 = 81143272388834334896650363044075567399043782163_<47>

P52 = 6198620635061424030493749864953890386771151005333743_<52>

Number: n
N=502976362625838398724451944380873820834789869050103990362972892088936280439500745662457592805426109
  ( 99 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=81143272388834334896650363044075567399043782163 (pp47)
 r2=6198620635061424030493749864953890386771151005333743 (pp52)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.86 hours.
Scaled time: 1.25 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_1_9_103_7
n: 502976362625838398724451944380873820834789869050103990362972892088936280439500745662457592805426109
skew: 1.72
deg: 5
c5: 1
c0: -15
m: 1000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:114155, AFBsize:114187, largePrimes:4382413 encountered
Relations: rels:4136356, finalFF:487915
Max relations in full relation-set: 28
Initial matrix: 228406 x 487915 with sparse part having weight 13647573.
Pruned matrix : 114742 x 115948 with weight 3325133.
Total sieving time: 0.71 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.05 hours.
Total square root time: 0.04 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,105,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,20000
total time: 0.86 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

2·10¹⁰⁶-3 = 1(9)₁₀₅7_<107> = 53299 · 42876259 · C94

C94 = P43 · P52

P43 = 5159197730271147217349752990276548876845323_<43>

P52 = 1696335989904637732334935062814384104990952215712079_<52>

Number: n
N=8751732788893266688487625777268063114486632739211302698544914987497525049574361686915585756517
  ( 94 digits)
SNFS difficulty: 106 digits.
Divisors found:
 r1=5159197730271147217349752990276548876845323 (pp43)
 r2=1696335989904637732334935062814384104990952215712079 (pp52)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.03 hours.
Scaled time: 1.49 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_1_9_105_7
n: 8751732788893266688487625777268063114486632739211302698544914987497525049574361686915585756517
skew: 0.68
deg: 5
c5: 20
c0: -3
m: 1000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:114155, AFBsize:113992, largePrimes:4623427 encountered
Relations: rels:4344731, finalFF:480702
Max relations in full relation-set: 28
Initial matrix: 228213 x 480702 with sparse part having weight 15679088.
Pruned matrix : 114549 x 115754 with weight 4184415.
Total sieving time: 0.87 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.07 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,106,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,50000
total time: 1.03 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 14, 2007 (3rd)

The factor table of 199...997 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

May 14, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(37·10¹⁶⁷-1)/9 = 4(1)₁₆₇_<168> = 3² · 373 · C165

C165 = P81 · P84

P81 = 918223766473056927120072370892676793977105023306840968715720117517723479949296603_<81>

P84 = 133370366287984710553342761808911401909229691328395596089306523023084095806001884041_<84>

Number: n
N=122463840068844537119782874921391454009863303875815046503160891007182338728361963393241319961605931221659550524608612186807003607718531757852580015225234170721212723
  ( 165 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=918223766473056927120072370892676793977105023306840968715720117517723479949296603 (pp81)
 r2=133370366287984710553342761808911401909229691328395596089306523023084095806001884041 (pp84)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 92.87 hours.
Scaled time: 122.86 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_4_1_167
n: 122463840068844537119782874921391454009863303875815046503160891007182338728361963393241319961605931221659550524608612186807003607718531757852580015225234170721212723
skew: 0.19
deg: 5
c5: 3700
c0: -1
m: 1000000000000000000000000000000000
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3600001)
Primes: RFBsize:348513, AFBsize:348256, largePrimes:8066454 encountered
Relations: rels:7685936, finalFF:786082
Max relations in full relation-set: 48
Initial matrix: 696836 x 786082 with sparse part having weight 45848187.
Pruned matrix : 617807 x 621355 with weight 30540514.
Total sieving time: 83.57 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 8.75 hours.
Total square root time: 0.22 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000
total time: 92.87 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

P81 is the second largest factor found by GGNFS so far in our tables. Congratulations!

May 14, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GMP-ECM 5.0 B1=865000

(5·10¹⁵⁹-17)/3 = 1(6)₁₅₈1_<160> = 11 · 10526074387_<11> · C149

C149 = P49 · P100

P49 = 4281777787034366358534397847460791774293780003501_<49>

P100 = 3361750706608769880083150153142444008856468108643668619700589506468289143083298686757456257443067273_<100>

Number: n
N=14394269501104516102021268331661041980010011828843017576094121090800487723317012837974305221059535679220116378939584964492187105376490962770118522773
  ( 149 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=4281777787034366358534397847460791774293780003501 (pp49)
 r2=3361750706608769880083150153142444008856468108643668619700589506468289143083298686757456257443067273 (pp100)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 28.58 hours.
Scaled time: 39.01 units (timescale=1.365).
Factorization parameters were as follows:
name: KA_1_6_158_1
n: 14394269501104516102021268331661041980010011828843017576094121090800487723317012837974305221059535679220116378939584964492187105376490962770118522773
skew: 2.02
deg: 5
c5: 1
c0: -34
m: 100000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:315948, AFBsize:315621, largePrimes:7083979 encountered
Relations: rels:6741752, finalFF:731785
Max relations in full relation-set: 28
Initial matrix: 631633 x 731785 with sparse part having weight 31162081.
Pruned matrix : 526231 x 529453 with weight 17073243.
Total sieving time: 25.13 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.17 hours.
Total square root time: 0.10 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000
total time: 28.58 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(5·10¹⁵⁸-41)/9 = (5)₁₅₇1_<158> = 3 · 139 · 823 · 1460911 · C147

C147 = P33 · P114

P33 = 345932055663238901623643181254069_<33>

P114 = 320314823938951775915028322935805675020923974788887849647682117084206664427032851449437721142740924025642142485979_<114>

May 13, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon

(5·10¹⁵⁹-23)/9 = (5)₁₅₈3_<159> = 7² · 79 · 941 · C153

C153 = P40 · P52 · P62

P40 = 1365275107933766940502292838105456569269_<40>

P52 = 5993070696988687498185746545206764928030823906718791_<52>

P62 = 18639966485678882898966502221797396041802923662890668936753337_<62>

Number: n
N=152515751903114429609847319836116334013035033264753100332578898914969387495825262581032000275504454237785905647228198551960545761146484089450000440770523
  ( 153 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=1365275107933766940502292838105456569269 (pp40)
 r2=5993070696988687498185746545206764928030823906718791 (pp52)
 r3=18639966485678882898966502221797396041802923662890668936753337 (pp62)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 37.16 hours.
Scaled time: 50.72 units (timescale=1.365).
Factorization parameters were as follows:
name: KA_5_158_3
n: 152515751903114429609847319836116334013035033264753100332578898914969387495825262581032000275504454237785905647228198551960545761146484089450000440770523
skew: 2.15
deg: 5
c5: 1
c0: -46
m: 100000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:315948, AFBsize:316251, largePrimes:7486977 encountered
Relations: rels:7195105, finalFF:785470
Max relations in full relation-set: 28
Initial matrix: 632263 x 785470 with sparse part having weight 38165133.
Pruned matrix : 485256 x 488481 with weight 18851472.
Total sieving time: 33.59 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 3.14 hours.
Total square root time: 0.22 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000
total time: 37.16 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(10¹⁶⁶+71)/9 = (1)₁₆₅9_<166> = 3 · 853 · C162

C162 = P52 · P54 · P57

P52 = 2941450565776713211063703481417686180142901689698887_<52>

P54 = 444247718689605355281288325170529968377748965603234359_<54>

P57 = 332277125209997397567433286536766521100002249200099342577_<57>

Number: n
N=434197386131735486952368546741348617081325170422474056706178628804654595979332204420129390821067257175111805826928921887890234900785897268898441231383787069601841
  ( 162 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=2941450565776713211063703481417686180142901689698887 (pp52)
 r2=444247718689605355281288325170529968377748965603234359 (pp54)
 r3=332277125209997397567433286536766521100002249200099342577 (pp57)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 71.23 hours.
Scaled time: 84.90 units (timescale=1.192).
Factorization parameters were as follows:
name: KA_1_165_9
n: 434197386131735486952368546741348617081325170422474056706178628804654595979332204420129390821067257175111805826928921887890234900785897268898441231383787069601841
type: snfs
skew: 1.48
deg: 5
c5: 10
c0: 71
m: 1000000000000000000000000000000000
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2500001)
Primes: RFBsize:348513, AFBsize:347947, largePrimes:7816338 encountered
Relations: rels:7510687, finalFF:820417
Max relations in full relation-set: 28
Initial matrix: 696526 x 820417 with sparse part having weight 42457592.
Pruned matrix : 578274 x 581820 with weight 24476107.
Total sieving time: 63.39 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 7.07 hours.
Total square root time: 0.43 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000
total time: 71.23 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(64·10¹⁵⁶+53)/9 = 7(1)₁₅₅7_<157> = 13 · 113 · 239 · 52860592215645665953858467693317_<32> · C120

C120 = P50 · P70

P50 = 49077828529847726066736868936370114562389265709103_<50>

P70 = 7807291673078649995782734630227484536649932164015296032914517722906237_<70>

Number: n
N=383164922013861954685718096101603237579244787814536099238125074662505933186233933720729459506399443843513551211786375411
  ( 120 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=49077828529847726066736868936370114562389265709103 (pp50)
 r2=7807291673078649995782734630227484536649932164015296032914517722906237 (pp70)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 30.78 hours.
Scaled time: 44.47 units (timescale=1.445).
Factorization parameters were as follows:
name: KA_7_1_155_7
n: 383164922013861954685718096101603237579244787814536099238125074662505933186233933720729459506399443843513551211786375411
skew: 1.22
deg: 5
c5: 20
c0: 53
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:216816, AFBsize:215751, largePrimes:7121172 encountered
Relations: rels:6653609, finalFF:535901
Max relations in full relation-set: 28
Initial matrix: 432633 x 535901 with sparse part having weight 37968592.
Pruned matrix : 347961 x 350188 with weight 22254553.
Total sieving time: 27.34 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.18 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 30.78 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 12, 2007 (4th)

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000

5·10¹⁹⁰-1 = 4(9)₁₉₀_<191> = C191

C191 = P35 · P156

P35 = 99540974625765465275232034702200919_<35>

P156 = 502305710668196126484659145583463988849571937897513433848127456075026044866256022945692253079700553166877184985681787449184093822883155280824677517509895321_<156>

May 12, 2007 (3rd)

By Yousuke Koide / GMP-ECM B1=1000000 / Apr 30, 2007

(10¹¹⁶⁷-1)/9 = (1)₁₁₆₇_<1167> = 3 · 37 · 466801 · 1991681 · 25779031 · 9673567199_<10> · 7657037673276648858853_<22> · 30613946219676519851696681_<26> · 534106762532886493971950663223965323_<36> · 295666607855148525951669299929669849601357_<42> · C270 · C741

C741 = P32 · C710

P32 = 90840806850908670531036620137129_<32>

By Yousuke Koide / GMP-ECM B1=1000000 / May 4, 2007

10⁸⁷⁴+1 = 1(0)₈₇₃1_<875> = 101 · 1289 · 8259301 · 1440247121_<10> · 21631222069_<11> · 18371524594609_<14> · 722817036322379041_<18> · 1369778187490592461_<19> · 4181003300071669867932658901_<28> · C766

C766 = P31 · C735

P31 = 8177669991059740173635806566781_<31>

By Yousuke Koide / GMP-ECM B1=1000000 / May 8, 2007

10⁹¹⁷+1 = 1(0)₉₁₆1_<918> = 11 · 263 · 144887 · 909091 · 288840329 · 1397382241_<10> · 306662501757259_<15> · 525786373041914526306757_<24> · 112506283680098168752627601991569_<33> · 1363608083180796048411168783196497071688492468691_<49> · C767

C767 = P33 · C735

P33 = 223908687382121511269398989390133_<33>

By Yousuke Koide / GMP-ECM B1=1000000 / May 8, 2007

10¹⁰⁷⁷+1 = 1(0)₁₀₇₆1_<1078> = 7 · 11 · 13 · 10771 · 25849 · 91631161 · 19210610797963667218565939_<26> · C329 · C705

C705 = P34 · C671

P34 = 2586114064209667728427534023689533_<34>

By Torbjörn Granlund / GMP-ECM P-1 B1=100000000 / May 9, 2007

(10⁶¹⁵-1)/9 = (1)₆₁₅_<615> = 3 · 31 · 37 · 41² · 83 · 271 · 1231 · 11071 · 275521 · 538987 · 1364071 · 1811791 · 2906161 · 21158848681_<11> · 626920594693_<12> · 9425856976319889649_<19> · 201763709900322803748657942361_<30> · 5440907236518498609451112390256369995629321_<43> · 8414640003465161203119978906558054839526493_<43> · 37654445534598090531061637404570516695225922222356909916889395661871779838862063550827086195341481919418156260385301045484576632937146377914151_<143> · C268

C268 = P36 · C232

P36 = 234065099292222402013296307835793151_<36>

By Torbjörn Granlund / GMP-ECM P-1 B1=10000000 / May 9, 2007

10⁷²²+1 = 1(0)₇₂₁1_<723> = 101 · 1097441 · 722817036322379041_<18> · 1369778187490592461_<19> · C678

C678 = P34 · C645

P34 = 6309203540697794137728747763478561_<34>

By Yousuke Koide / GMP-ECM B1=1000000 / May 7, 2007

10⁷⁵⁸+1 = 1(0)₇₅₇1_<759> = 101 · 4549 · C753

C753 = P32 · C721

P32 = 70488629165410024923533836947449_<32>

By Yousuke Koide / GMP-ECM B1=1000000 / May 12, 2007

10⁷⁷³+1 = 1(0)₇₇₂1_<774> = 11 · 2514771527_<10> · C763

C763 = P35 · C729

P35 = 27542107953980594633792218895027329_<35>

By Yousuke Koide / GMP-ECM B1=1000000 / May 12, 2007

10⁷⁷⁸+1 = 1(0)₇₇₇1_<779> = 101 · 68050337401_<11> · C766

C766 = P37 · C729

P37 = 1763722658625922307781888583674044509_<37>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

May 12, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(4·10¹⁵⁷-13)/9 = (4)₁₅₆3_<157> = 3 · 1607 · 1605739 · 72888289607101616827_<20> · C127

C127 = P38 · P90

P38 = 34994546482661762527459864491196336061_<38>

P90 = 225085369058061657663884263348948816998805899513451328210121428150671196588503313350746851_<90>

Number: n
N=7876760410069416298662868647448204377450768132958815838678289103538428666499430415564938481187821565345250560533702189133493911
  ( 127 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=34994546482661762527459864491196336061 (pp38)
 r2=225085369058061657663884263348948816998805899513451328210121428150671196588503313350746851 (pp90)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 31.88 hours.
Scaled time: 46.19 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_4_156_3
n: 7876760410069416298662868647448204377450768132958815838678289103538428666499430415564938481187821565345250560533702189133493911
skew: 1.01
deg: 5
c5: 25
c0: -26
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:216816, AFBsize:217511, largePrimes:7047079 encountered
Relations: rels:6530657, finalFF:496297
Max relations in full relation-set: 28
Initial matrix: 434391 x 496297 with sparse part having weight 34658844.
Pruned matrix : 383891 x 386126 with weight 22977837.
Total sieving time: 27.71 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.91 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 31.88 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 12, 2007

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000

(23·10¹⁸⁴+1)/3 = 7(6)₁₈₃7_<185> = C185

C185 = P37 · C149

P37 = 5774670075341229996045635806441711249_<37>

C149 = [13276371752222809090293402882959411707829163970866879125339397751880657325581180279608246723848888791937781266906345533410485228874392140408836617083_<149>]

May 11, 2007 (3rd)

By suberi / GMP-ECM 6.1.2 B1=3000000

(64·10¹⁹¹+53)/9 = 7(1)₁₉₀7_<192> = 3 · 11 · 239 · 2437 · 6599 · 244033 · C176

C176 = P34 · C143

P34 = 1215130975899590906278442010355229_<34>

C143 = [18906899481973526282026704495069056756649983846456749409752956664140620093099092451844621769773689315721058796527997944133334364541384120005301_<143>]

(64·10²³⁶+53)/9 = 7(1)₂₃₅7_<237> = 3 · 563 · 2383 · 20431 · 86381 · C222

C222 = P37 · C185

P37 = 6439440434086891745591132827876208899_<37>

C185 = [15546326742142275797343802733855931211964187662623718039519045945410959794410303852402574597376122760199834255719754439546665593662708368862695746542115188846097476249599680897257390819_<185>]

May 11, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp

2·10¹⁶⁰-1 = 1(9)₁₆₀_<161> = 7 · 719 · C157

C157 = P46 · P112

P46 = 3521112583666989208128791647491651766924820281_<46>

P112 = 1128556103542058996746525728749181096617698429611282103116231114503378579024061149030723533547291222035342709663_<112>

Number: n
N=3973773097556129545002980329823167097158752235247367375322869064176435525531492151798132326644148619113848599244983111464335386449433737333598251539837075303
  ( 157 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=3521112583666989208128791647491651766924820281 (pp46)
 r2=1128556103542058996746525728749181096617698429611282103116231114503378579024061149030723533547291222035342709663 (pp112)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 35.80 hours.
Scaled time: 26.88 units (timescale=0.751).
Factorization parameters were as follows:
name: KA_1_9_160
n: 3973773097556129545002980329823167097158752235247367375322869064176435525531492151798132326644148619113848599244983111464335386449433737333598251539837075303
skew: 0.87
deg: 5
c5: 2
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:315948, AFBsize:315591, largePrimes:7290686 encountered
Relations: rels:6987505, finalFF:769990
Max relations in full relation-set: 28
Initial matrix: 631604 x 769990 with sparse part having weight 35494138.
Pruned matrix : 494564 x 497786 with weight 17860283.
Total sieving time: 30.25 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 5.14 hours.
Total square root time: 0.20 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000
total time: 35.80 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 11, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

(5·10¹⁶⁹+13)/9 = (5)₁₆₈7_<169> = 7 · 25841 · 708371 · 14831317 · 13419206138394747668082246000933204319_<38> · C114

C114 = P47 · P68

P47 = 18984589447258019171106580625816675813439927361_<47>

P68 = 11474971458647067240492312991607096103710342389767647453209132372147_<68>

Number: 55557_169
N=217847622061418072255581563015349258221880416028325068401083564087901225152792849614952022038191434366089299614067
  ( 114 digits)
Divisors found:
 r1=18984589447258019171106580625816675813439927361 (pp47)
 r2=11474971458647067240492312991607096103710342389767647453209132372147 (pp68)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 23.52 hours.
Scaled time: 21.99 units (timescale=0.935).
Factorization parameters were as follows:
name: 55557_169
n: 217847622061418072255581563015349258221880416028325068401083564087901225152792849614952022038191434366089299614067
skew: 93167.72
# norm 9.99e+15
c5: 7560
c4: 181240904
c3: -215160469783062
c2: 731926613668539534
c1: -336079217051183466131105
c0: -1719014552327535177050257095
# alpha -6.46
Y1: 515317817773
Y0: -7796973677105581012586
# Murphy_E 6.25e-10
# M 45979753848971241218306109270075070205023824708408177579147395268527404710642628807455036499266215840949482224176
type: gnfs
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1800000, 2925001)
Primes: RFBsize:256726, AFBsize:256868, largePrimes:7423035 encountered
Relations: rels:7314425, finalFF:614838
Max relations in full relation-set: 28
Initial matrix: 513674 x 614838 with sparse part having weight 50290626.
Pruned matrix : 428623 x 431255 with weight 30957143.
Total sieving time: 22.00 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.24 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000
total time: 23.52 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 10, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=3000000

(5·10¹⁶⁰+13)/9 = (5)₁₅₉7_<160> = 443 · 149446961 · 954266828377_<12> · C137

C137 = P34 · P104

P34 = 2950675052531348964676339874534843_<34>

P104 = 29802003977964361400935073001776486894276408425662155711272488748993451457322768666516195405066304062469_<104>

(5·10¹⁶⁵+13)/9 = (5)₁₆₄7_<165> = 113 · 140207 · 7409646089513737_<16> · C142

C142 = P42 · P101

P42 = 120251587054056382828063467457919777275513_<42>

P101 = 39354198578549811165548493668314300005448817734165049827333990543389183856876706209828094658780016667_<101>

May 10, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GMP-ECM 5.0 B1=988000

(16·10¹⁶⁶-61)/9 = 1(7)₁₆₅1_<167> = 13 · 257 · C163

C163 = P41 · P51 · P72

P41 = 15109262159303914200235970117303182989937_<41>

P51 = 583000610683684808553479287729266199706051525409391_<51>

P72 = 604072035468266231595132183421912411669884078283681280966762593973524393_<72>

Number: n
N=5321094815258239382753001430044231600651834114869134324387242675180418371079849679071468954737437227709601250457281585686254946955336060394426153181016994246566231
  ( 163 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=15109262159303914200235970117303182989937 (pp41)
 r2=583000610683684808553479287729266199706051525409391 (pp51)
 r3=604072035468266231595132183421912411669884078283681280966762593973524393 (pp72)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 69.44 hours.
Scaled time: 82.77 units (timescale=1.192).
Factorization parameters were as follows:
name: KA_1_7_165_1
n: 5321094815258239382753001430044231600651834114869134324387242675180418371079849679071468954737437227709601250457281585686254946955336060394426153181016994246566231
type: snfs
skew: 1.65
deg: 5
c5: 5
c0: -61
m: 2000000000000000000000000000000000
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2300001)
Primes: RFBsize:348513, AFBsize:348832, largePrimes:7702629 encountered
Relations: rels:7363647, finalFF:782908
Max relations in full relation-set: 28
Initial matrix: 697410 x 782908 with sparse part having weight 38983048.
Pruned matrix : 613328 x 616879 with weight 24922462.
Total sieving time: 61.20 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 7.66 hours.
Total square root time: 0.28 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.6,2.6,100000
total time: 69.44 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(2·10¹⁵⁶+61)/9 = (2)₁₅₅9_<156> = 7 · 43651 · 6364525991_<10> · 7275092106669707_<16> · C125

C125 = P38 · P87

P38 = 16178975375611820184681864685192671467_<38>

P87 = 970822145125557723186204385444462181385283099465504350555333554320195494843596374000943_<87>

Number: n
N=15706907580085043270694630057489479125382622982598428533807291223433624832987908942174576079356758981977113837332597347193381
  ( 125 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=16178975375611820184681864685192671467 (pp38)
 r2=970822145125557723186204385444462181385283099465504350555333554320195494843596374000943 (pp87)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 24.90 hours.
Scaled time: 35.95 units (timescale=1.444).
Factorization parameters were as follows:
name: KA_2_155_9
n: 15706907580085043270694630057489479125382622982598428533807291223433624832987908942174576079356758981977113837332597347193381
skew: 1.25
deg: 5
c5: 20
c0: 61
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:216816, AFBsize:217357, largePrimes:6745421 encountered
Relations: rels:6220624, finalFF:488017
Max relations in full relation-set: 28
Initial matrix: 434239 x 488017 with sparse part having weight 29966477.
Pruned matrix : 386169 x 388404 with weight 19662895.
Total sieving time: 21.52 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 3.09 hours.
Total square root time: 0.12 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 24.90 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

3·10¹⁵⁶+1 = 3(0)₁₅₅1_<157> = 1297177961174555143_<19> · 2667221954249769199_<19> · C120

C120 = P44 · P77

P44 = 14120876924458604253497663539366736456941609_<44>

P77 = 61404594566872242448503276730228599364013338843483356019440687469832045039377_<77>

(83·10¹⁶⁷+61)/9 = 9(2)₁₆₆9_<168> = 7 · 11 · 17 · C165

C165 = P36(1440...) · P36(2519...) · P46 · P49

P36(1440...) = 144036627455472159894503296079104823_<36>

P36(2519...) = 251944573572582320400006996542619031_<36>

P46 = 7807715710023051816711416095697929674094210463_<46>

P49 = 2486531651431884079209006357389967329362985364599_<49>

Number: n
N=704524233935998641880994822171292759528053645700704524233935998641880994822171292759528053645700704524233935998641880994822171292759528053645700704524233935998641881
  ( 165 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=144036627455472159894503296079104823 (pp36)
 r2=251944573572582320400006996542619031 (pp36)
 r3=7807715710023051816711416095697929674094210463 (pp46)
 r4=2486531651431884079209006357389967329362985364599 (pp49)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 124.98 hours.
Scaled time: 164.85 units (timescale=1.319).
Factorization parameters were as follows:
name: KA_9_2_166_9
n: 704524233935998641880994822171292759528053645700704524233935998641880994822171292759528053645700704524233935998641880994822171292759528053645700704524233935998641881
skew: 0.37
deg: 5
c5: 8300
c0: 61
m: 1000000000000000000000000000000000
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 4900001)
Primes: RFBsize:348513, AFBsize:348547, largePrimes:8346543 encountered
Relations: rels:7970546, finalFF:806767
Max relations in full relation-set: 48
Initial matrix: 697127 x 806767 with sparse part having weight 49889352.
Pruned matrix : 609729 x 613278 with weight 34943447.
Total sieving time: 112.71 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 10.22 hours.
Total square root time: 1.64 hours, sqrts: 13.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000
total time: 124.98 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 9, 2007 (2nd)

By Robert Backstrom / GMP-ECM 5.0 B1=803000, GGNFS-0.77.1-20051202-athlon

(13·10¹⁵⁶-31)/9 = 1(4)₁₅₅1_<157> = 81223 · 33503305313_<11> · 109654833847764713_<18> · C124

C124 = P32 · P93

P32 = 33221106335396792559728583649939_<32>

P93 = 145710983338393792427706737229266963776824439301949657734730802429613705232080064468338379037_<93>

(16·10¹⁵⁵-1)/3 = 5(3)₁₅₅_<156> = 241 · 563 · 9720432861379084146529_<22> · C129

C129 = P56 · P73

P56 = 90029914555725552917405713267859877539437849056631020317_<56>

P73 = 4491597666962551358812885925456249780291015698726653486747753928606021907_<73>

Number: n
N=404378154175334737009800640537312448779192500233832940020546894325311977216650147743526077094343949934288407943962237103864084519
  ( 129 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=90029914555725552917405713267859877539437849056631020317 (pp56)
 r2=4491597666962551358812885925456249780291015698726653486747753928606021907 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 22.14 hours.
Scaled time: 16.09 units (timescale=0.727).
Factorization parameters were as follows:
name: KA_5_3_155
n: 404378154175334737009800640537312448779192500233832940020546894325311977216650147743526077094343949934288407943962237103864084519
skew: 1.15
deg: 5
c5: 1
c0: -2
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1000001)
Primes: RFBsize:216816, AFBsize:216491, largePrimes:6892018 encountered
Relations: rels:6481806, finalFF:584788
Max relations in full relation-set: 28
Initial matrix: 433371 x 584788 with sparse part having weight 34883238.
Pruned matrix : 301211 x 303441 with weight 16933179.
Total sieving time: 18.50 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 3.30 hours.
Total square root time: 0.17 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 22.14 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(5·10¹⁵⁹+31)/9 = (5)₁₅₈9_<159> = 13 · 97 · C156

C156 = P67 · P90

P67 = 1385395064995660441245964715337390478851164754214255342899601827751_<67>

P90 = 318008532012570179000633455554438524970194717548867326486492267515298642222528842549960869_<90>

Number: n
N=440567450876729227244691162216935412811701471495285928275618997268481804564278791082914794255000440567450876729227244691162216935412811701471495285928275619
  ( 156 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=1385395064995660441245964715337390478851164754214255342899601827751 (pp67)
 r2=318008532012570179000633455554438524970194717548867326486492267515298642222528842549960869 (pp90)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 32.40 hours.
Scaled time: 44.32 units (timescale=1.368).
Factorization parameters were as follows:
name: KA_5_158_9
n: 440567450876729227244691162216935412811701471495285928275618997268481804564278791082914794255000440567450876729227244691162216935412811701471495285928275619
skew: 2.28
deg: 5
c5: 1
c0: 62
m: 100000000000000000000000000000000
type: snfs
rlim: 4500000
alim: 4500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:315948, AFBsize:316092, largePrimes:7163062 encountered
Relations: rels:6818762, finalFF:732797
Max relations in full relation-set: 28
Initial matrix: 632104 x 732797 with sparse part having weight 32214102.
Pruned matrix : 527782 x 531006 with weight 17799091.
Total sieving time: 28.25 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 3.53 hours.
Total square root time: 0.41 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000
total time: 32.40 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 9, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona

6·10¹⁶²+1 = 6(0)₁₆₁1_<163> = 7 · 409 · 461 · 1297 · 71355177903228522649_<20> · 105440523536650831469_<21> · C114

C114 = P52 · P63

P52 = 2635929378062082616090181215642985097332592374330359_<52>

P63 = 176734845085883901472849673672121748213269636335439399849960889_<63>

Number: 60001_162
N=465860570289132470526766504662099277577757656808920530081522403634714863130373216991557016779244393574693715329151
  ( 114 digits)
Divisors found:
 r1=2635929378062082616090181215642985097332592374330359 (pp52)
 r2=176734845085883901472849673672121748213269636335439399849960889 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 25.27 hours.
Scaled time: 23.50 units (timescale=0.930).
Factorization parameters were as follows:
name: 60001_162
n: 465860570289132470526766504662099277577757656808920530081522403634714863130373216991557016779244393574693715329151
skew: 52979.34
# norm 6.29e+15
c5: 28800
c4: -4744474328
c3: -240924644592942
c2: 12887096438141057377
c1: 343182609850863365434888
c0: -2211251175528614193036100335
# alpha -6.42
Y1: 962944882867
Y0: -6946638145470387030218
# Murphy_E 6.24e-10
# M 422905541741467303181853397627552337882467775546056669673492939882919014769355778867593327900220590802340709537733
type: gnfs
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1800000, 2925001)
Primes: RFBsize:256726, AFBsize:256259, largePrimes:7444354 encountered
Relations: rels:7318652, finalFF:599647
Max relations in full relation-set: 28
Initial matrix: 513063 x 599647 with sparse part having weight 48328634.
Pruned matrix : 441183 x 443812 with weight 30948811.
Total sieving time: 21.86 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.08 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000
total time: 25.27 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 8, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=3000000

(5·10¹⁶⁹+13)/9 = (5)₁₆₈7_<169> = 7 · 25841 · 708371 · 14831317 · C151

C151 = P38 · C114

P38 = 13419206138394747668082246000933204319_<38>

C114 = [217847622061418072255581563015349258221880416028325068401083564087901225152792849614952022038191434366089299614067_<114>]

May 8, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=618000, B1=522500, GGNFS-0.77.1-20060513-athlon-xp

3·10¹⁵⁷+1 = 3(0)₁₅₆1_<158> = 17 · 772006355756021_<15> · 7401761985090177770309_<22> · C120

C120 = P36 · P85

P36 = 248529780208636811981353203838303673_<36>

P85 = 1242618760787690302557066234608127824342363929964979635799811131131051551936554388849_<85>

(34·10¹⁵⁶-7)/9 = 3(7)₁₅₆_<157> = 3 · 131 · 3931 · 11472824853206904594929_<23> · C129

C129 = P34 · P95

P34 = 6782564829732305170470333318140549_<34>

P95 = 31425087546025715646735982184029372225640172487522725906443903355358448487384609969906116186239_<95>

(10¹⁶⁷+71)/9 = (1)₁₆₆9_<167> = 89 · C165

C165 = P59 · P106

P59 = 91311343163343446323968739512561574329110904059483452421063_<59>

P106 = 1367233694562301051553984933575756012125192786758201704704070474144368666604173622117402417959850492600417_<106>

Number: n
N=124843945068664169787765293383270911360799001248439450686641697877652933832709113607990012484394506866416978776529338327091136079900124843945068664169787765293383271
  ( 165 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=91311343163343446323968739512561574329110904059483452421063 (pp59)
 r2=1367233694562301051553984933575756012125192786758201704704070474144368666604173622117402417959850492600417 (pp106)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 108.25 hours.
Scaled time: 147.65 units (timescale=1.364).
Factorization parameters were as follows:
name: KA_1_166_9
n: 124843945068664169787765293383270911360799001248439450686641697877652933832709113607990012484394506866416978776529338327091136079900124843945068664169787765293383271
skew: 0.93
deg: 5
c5: 100
c0: 71
m: 1000000000000000000000000000000000
type: snfs
rlim: 5000000
alim: 5000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 4500001)
Primes: RFBsize:348513, AFBsize:350387, largePrimes:7881774 encountered
Relations: rels:7565246, finalFF:794688
Max relations in full relation-set: 28
Initial matrix: 698964 x 794688 with sparse part having weight 43936217.
Pruned matrix : 616009 x 619567 with weight 29724900.
Total sieving time: 98.17 hours.
Total relation processing time: 0.59 hours.
Matrix solve time: 8.69 hours.
Total square root time: 0.80 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,48,48,2.5,2.5,100000
total time: 108.25 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(4·10¹⁵⁵-13)/9 = (4)₁₅₄3_<155> = 7 · 3808559 · 6125229081493124399_<19> · C129

C129 = P64 · P66

P64 = 1430852648491397818456316645370885067116465513802945727285403371_<64>

P66 = 190213574326970416645495975919797015608841251458428834035091173959_<66>

Number: n
N=272167596604760973939922895849222045319822735977613961182574173096110354671336539629503110460161984822070057750007276533246015789
  ( 129 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=1430852648491397818456316645370885067116465513802945727285403371 (pp64)
 r2=190213574326970416645495975919797015608841251458428834035091173959 (pp66)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 24.66 hours.
Scaled time: 35.49 units (timescale=1.439).
Factorization parameters were as follows:
name: KA_4_154_3
n: 272167596604760973939922895849222045319822735977613961182574173096110354671336539629503110460161984822070057750007276533246015789
skew: 1.27
deg: 5
c5: 4
c0: -13
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:216816, AFBsize:216856, largePrimes:6824327 encountered
Relations: rels:6301687, finalFF:489949
Max relations in full relation-set: 28
Initial matrix: 433736 x 489949 with sparse part having weight 31276439.
Pruned matrix : 385079 x 387311 with weight 20380733.
Total sieving time: 21.27 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 3.16 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 24.66 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 7, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=184500, B1=595000, GGNFS-0.77.1-20051202-athlon

8·10¹⁶⁷-3 = 7(9)₁₆₆7_<168> = 11 · 71 · C166

C166 = P31 · P35 · P100

P31 = 6263376936571872349805965794179_<31>

P35 = 48366409729269876335151280681703887_<35>

P100 = 3381322183264895436089159421503432927307771620830849708685343102501831818018700928611257460676963669_<100>

6·10¹⁵⁵-1 = 5(9)₁₅₅_<156> = 17 · 855694920236157839951575243_<27> · C155

C155 = P38 · P91

P38 = 23563769814083175297504581851112348513_<38>

P91 = 1750405235111493782019464819415041844908100509751846238928281927522333980653932785261889133_<91>

Number: n
N=41246146041533380581382937109329549557946829659714681794095420363066533915011986623900432662432693705651217155512046742663409229
  ( 128 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=23563769814083175297504581851112348513 (pp38)
 r2=1750405235111493782019464819415041844908100509751846238928281927522333980653932785261889133 (pp91)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.30 hours.
Scaled time: 28.06 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_5_9_155
n: 41246146041533380581382937109329549557946829659714681794095420363066533915011986623900432662432693705651217155512046742663409229
skew: 0.70
deg: 5
c5: 6
c0: -1
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:216816, AFBsize:216821, largePrimes:6743866 encountered
Relations: rels:6305075, finalFF:556166
Max relations in full relation-set: 28
Initial matrix: 433703 x 556166 with sparse part having weight 32299756.
Pruned matrix : 326541 x 328773 with weight 16053392.
Total sieving time: 16.97 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 2.06 hours.
Total square root time: 0.10 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 19.30 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 6, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(86·10¹⁵⁵+31)/9 = 9(5)₁₅₄9_<156> = 11 · 17 · 19 · 107 · 3329 · 234547 · 49916499175544369_<17> · C125

C125 = P51 · P75

P51 = 146893790346276534914663990304041376179590078145821_<51>

P75 = 439021432742427786693807047121586584432982187601506537680594815438795711667_<75>

Number: n
N=64489522298788131872083990903207589990122986848898622434996970678191618339288837124645592388512510110304876458442669496993607
  ( 125 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=146893790346276534914663990304041376179590078145821 (pp51)
 r2=439021432742427786693807047121586584432982187601506537680594815438795711667 (pp75)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 25.08 hours.
Scaled time: 36.31 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_9_5_154_9
n: 64489522298788131872083990903207589990122986848898622434996970678191618339288837124645592388512510110304876458442669496993607
skew: 0.82
deg: 5
c5: 86
c0: 31
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:216816, AFBsize:217122, largePrimes:6799735 encountered
Relations: rels:6278199, finalFF:494460
Max relations in full relation-set: 28
Initial matrix: 434004 x 494460 with sparse part having weight 30387568.
Pruned matrix : 381067 x 383301 with weight 19287909.
Total sieving time: 21.81 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.02 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 25.08 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(43·10¹⁶⁴-7)/9 = 4(7)₁₆₄_<165> = 3² · C164

C164 = P40 · P54 · P71

P40 = 2631129533782044843927495361912765542751_<40>

P54 = 215880931151977979223281199254244241548167819075235827_<54>

P71 = 93460247031749192280709130483295872291224585644076339206811461233287789_<71>

Number: n
N=53086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753
  ( 164 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=2631129533782044843927495361912765542751 (pp40)
 r2=215880931151977979223281199254244241548167819075235827 (pp54)
 r3=93460247031749192280709130483295872291224585644076339206811461233287789 (pp71)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 117.61 hours.
Scaled time: 140.90 units (timescale=1.198).
Factorization parameters were as follows:
name: KA_4_7_164
n: 53086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753
type: snfs
skew: 1.10
deg: 5
c5: 43
c0: -70
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 4500001)
Primes: RFBsize:250150, AFBsize:248761, largePrimes:8106263 encountered
Relations: rels:7638338, finalFF:562340
Max relations in full relation-set: 28
Initial matrix: 498976 x 562340 with sparse part having weight 56255595.
Pruned matrix : 471675 x 474233 with weight 44274525.
Total sieving time: 106.62 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 9.71 hours.
Total square root time: 0.86 hours, sqrts: 5.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 117.61 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

May 5, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(16·10¹⁵⁵-61)/9 = 1(7)₁₅₄1_<156> = 3³ · 11 · 313 · 3413 · 564653293741502455894429_<24> · C123

C123 = P57 · P67

P57 = 147578844538555167154379562564198635879111107545264229249_<57>

P67 = 6724104070964062862708978830908866005677012688304296879046893860907_<67>

Number: n
N=992335509349871354723416775422313367980880327033705308667135048478218116917002201583659164168205143446837552843965167068843
  ( 123 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=147578844538555167154379562564198635879111107545264229249 (pp57)
 r2=6724104070964062862708978830908866005677012688304296879046893860907 (pp67)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.42 hours.
Scaled time: 28.06 units (timescale=1.445).
Factorization parameters were as follows:
name: KA_1_7_154_1
n: 992335509349871354723416775422313367980880327033705308667135048478218116917002201583659164168205143446837552843965167068843
skew: 2.61
deg: 5
c5: 1
c0: -122
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:216816, AFBsize:216857, largePrimes:6849328 encountered
Relations: rels:6484465, finalFF:621032
Max relations in full relation-set: 28
Initial matrix: 433737 x 621032 with sparse part having weight 35182490.
Pruned matrix : 269851 x 272083 with weight 16048658.
Total sieving time: 17.58 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.63 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 19.42 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(31·10¹⁶⁶-13)/9 = 3(4)₁₆₅3_<167> = 3² · C166

C166 = P44 · P55 · P68

P44 = 11249365279272105191944705856137109893341383_<44>

P55 = 4629217185850101516750522211783509052473169342352740507_<55>

P68 = 73492174772991205921386920343213336461480210780035033172068546448767_<68>

Number: n
N=3827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827
  ( 166 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=11249365279272105191944705856137109893341383 (pp44)
 r2=4629217185850101516750522211783509052473169342352740507 (pp55)
 r3=73492174772991205921386920343213336461480210780035033172068546448767 (pp68)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 84.72 hours.
Scaled time: 112.08 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_3_4_165_3
n: 3827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827
skew: 0.53
deg: 5
c5: 310
c0: -13
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3600001)
Primes: RFBsize:216816, AFBsize:216917, largePrimes:7638831 encountered
Relations: rels:7082488, finalFF:488644
Max relations in full relation-set: 48
Initial matrix: 433800 x 488644 with sparse part having weight 62247574.
Pruned matrix : 416718 x 418951 with weight 46486994.
Total sieving time: 74.95 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 8.93 hours.
Total square root time: 0.54 hours, sqrts: 5.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 84.72 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 4, 2007 (3rd)

By Jo Yeong Uk / GMP-ECM 5.0.3 B1=3000000

(8·10¹⁸³-17)/9 = (8)₁₈₂7_<183> = C183

C183 = P31 · C153

P31 = 1259337356542822108306204266629_<31>

C153 = [705838577939987753279711060237017228585936509399199518627682834424778845002336309634782236276759532406698056060483434655977248535150104022612858176741003_<153>]

May 4, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(13·10¹⁵⁵-1)/3 = 4(3)₁₅₅_<156> = 1217 · 1758541 · 451860930139252966767713_<24> · C123

C123 = P42 · P81

P42 = 664604448458801168137249105380355621156169_<42>

P81 = 674234521819545742193894263762175555094507255650621412062733023543616234671763137_<81>

Number: n
N=448099262505762739810790562822297173729543427286178125601790590364287468716846509427825261974678202403285587890997654342153
  ( 123 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=664604448458801168137249105380355621156169 (pp42)
 r2=674234521819545742193894263762175555094507255650621412062733023543616234671763137 (pp81)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 21.55 hours.
Scaled time: 31.23 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_4_3_155
n: 448099262505762739810790562822297173729543427286178125601790590364287468716846509427825261974678202403285587890997654342153
skew: 0.60
deg: 5
c5: 13
c0: -1
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1000001)
Primes: RFBsize:216816, AFBsize:215931, largePrimes:7088794 encountered
Relations: rels:6747346, finalFF:648840
Max relations in full relation-set: 28
Initial matrix: 432812 x 648840 with sparse part having weight 40651871.
Pruned matrix : 253312 x 255540 with weight 20462953.
Total sieving time: 19.43 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.90 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 21.55 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 4, 2007

By suberi / GMP-ECM 6.1.2 B1=3000000

(5·10¹⁹⁰+13)/9 = (5)₁₈₉7_<190> = 811 · 907 · 10837804441_<11> · 2785656325929626661973_<22> · C153

C153 = P30 · C124

P30 = 141420727163771568086127494461_<30>

C124 = [1768957675798608538570697178394242001598658689261756493802670073290117602123758045787374992447868719160331461600669004667317_<124>]

(5·10¹⁷⁹+13)/9 = (5)₁₇₈7_<179> = 3 · 509 · 1067600111_<10> · C167

C167 = P30 · C137

P30 = 501390694625542533719253930763_<30>

C137 = [67967857156207860206815546895977987863005066787709361009704730235070830216414344853956065234054495527685695832614271671186671680546533287_<137>]

May 3, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp

7·10¹⁵⁴+1 = 7(0)₁₅₃1_<155> = 43 · 5623 · 12401 · 79861933 · 1575233648179_<13> · C126

C126 = P51 · P75

P51 = 193370246682439687632641395275617696499919070409857_<51>

P75 = 959688618561589603204660736875782818852796083063317811556994979114317575491_<75>

Number: n
N=185575224909584348798499980746588371732865042833545760086485528245996049062231370685862811259790810958949845914972371908014787
  ( 126 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=193370246682439687632641395275617696499919070409857 (pp51)
 r2=959688618561589603204660736875782818852796083063317811556994979114317575491 (pp75)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 28.11 hours.
Scaled time: 40.70 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_7_0_153_1
n: 185575224909584348798499980746588371732865042833545760086485528245996049062231370685862811259790810958949845914972371908014787
skew: 1.07
deg: 5
c5: 7
c0: 10
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:216816, AFBsize:217031, largePrimes:7072813 encountered
Relations: rels:6598043, finalFF:530393
Max relations in full relation-set: 28
Initial matrix: 433912 x 530393 with sparse part having weight 36370966.
Pruned matrix : 353629 x 355862 with weight 21272652.
Total sieving time: 24.79 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.07 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 28.11 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(4·10¹⁶³-13)/9 = (4)₁₆₂3_<163> = 3 · C163

C163 = P65 · P99

P65 = 11928511488576416652518926449031014706382259688259889449372428463_<65>

P99 = 124196676416856584831190356834443566414147381261107180590809616102721629362131706129660584348140487_<99>

Number: n
N=1481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481
  ( 163 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=11928511488576416652518926449031014706382259688259889449372428463 (pp65)
 r2=124196676416856584831190356834443566414147381261107180590809616102721629362131706129660584348140487 (pp99)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 46.36 hours.
Scaled time: 63.28 units (timescale=1.365).
Factorization parameters were as follows:
name: KA_4_162_3
n: 1481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481481
skew: 0.64
deg: 5
c5: 125
c0: -13
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2000001)
Primes: RFBsize:216816, AFBsize:216271, largePrimes:7206086 encountered
Relations: rels:6681195, finalFF:486083
Max relations in full relation-set: 28
Initial matrix: 433152 x 486083 with sparse part having weight 37948638.
Pruned matrix : 394389 x 396618 with weight 27334391.
Total sieving time: 42.09 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 3.88 hours.
Total square root time: 0.13 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 46.36 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 3, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000

8·10¹⁸⁴-1 = 7(9)₁₈₄_<185> = C185

C185 = P43 · C143

P43 = 1999080062901581503437318550484654902159553_<43>

C143 = [40018407208705453170393588274967598668194718998797708185694406998207268713775631752044327280691107243190075250207288752868081397525726798190783_<143>]

May 3, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 gnfs

(5·10¹⁵⁹+13)/9 = (5)₁₅₈7_<159> = 31 · 88422043643857462597_<20> · 1425603659062897082122821966839_<31> · C108

C108 = P42 · P66

P42 = 963375458771271206396670106466303330684323_<42>

P66 = 147574347817773759929890143833175414071639106091723198758761439283_<66>

Number: 55557_159
N=142169505031818941787456133521823682753734366848698561502053979968080314542932254864568794355447616804460409
  ( 108 digits)
Divisors found:
 r1=963375458771271206396670106466303330684323 (pp42)
 r2=147574347817773759929890143833175414071639106091723198758761439283 (pp66)
Version: GGNFS-0.77.1-20050930-k8
Total time: 11.50 hours.
Scaled time: 10.75 units (timescale=0.935).
Factorization parameters were as follows:
name: 55557_159
n: 142169505031818941787456133521823682753734366848698561502053979968080314542932254864568794355447616804460409
skew: 26374.85
# norm 2.40e+15
c5: 35280
c4: 934399884
c3: -89832636229180
c2: 1523184560386315315
c1: 18999259139000664323700
c0: -99692038060039600471149984
# alpha -8.27
Y1: 264069173159
Y0: -331935532854754032235
# Murphy_E 1.80e-09
# M 123395139583000001562421371741684712074865364389449685364637536523825175006068414011882084180445111450434185
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1380001)
Primes: RFBsize:135072, AFBsize:134617, largePrimes:4669123 encountered
Relations: rels:4865738, finalFF:485020
Max relations in full relation-set: 28
Initial matrix: 269770 x 485020 with sparse part having weight 47009771.
Pruned matrix : 179665 x 181077 with weight 17208918.
Polynomial selection time: 0.61 hours.
Total sieving time: 10.58 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 11.50 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407676)
Calibrating delay using timer specific routine.. 4810.30 BogoMIPS (lpj=2405150)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Calibrating delay using timer specific routine.. 4810.29 BogoMIPS (lpj=2405148)
Total of 4 processors activated (19246.21 BogoMIPS).

May 2, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(8·10¹⁶³-71)/9 = (8)₁₆₂1_<163> = 107 · C161

C161 = P60 · P102

P60 = 331525272836625077861926530888596074621005958963348147811333_<60>

P102 = 250580377244662029958853007009725953486242048898063827611155437846422355414015990463558317384787413751_<102>

Number: n
N=83073727933541017653167185877466251298026998961578400830737279335410176531671858774662512980269989615784008307372793354101765316718587746625129802699896157840083
  ( 161 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=331525272836625077861926530888596074621005958963348147811333 (pp60)
 r2=250580377244662029958853007009725953486242048898063827611155437846422355414015990463558317384787413751 (pp102)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 76.77 hours.
Scaled time: 111.16 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_8_162_1
n: 83073727933541017653167185877466251298026998961578400830737279335410176531671858774662512980269989615784008307372793354101765316718587746625129802699896157840083
skew: 0.78
deg: 5
c5: 250
c0: -71
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3600001)
Primes: RFBsize:216816, AFBsize:215722, largePrimes:7882612 encountered
Relations: rels:7405836, finalFF:485486
Max relations in full relation-set: 28
Initial matrix: 432604 x 485486 with sparse part having weight 50002622.
Pruned matrix : 413633 x 415860 with weight 39761888.
Total sieving time: 68.97 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 7.34 hours.
Total square root time: 0.18 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 76.77 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

May 2, 2007 (2nd)

By Jo Yeong Uk / Msieve v. 1.19

(5·10¹⁷⁸+13)/9 = (5)₁₇₇7_<178> = 1528613 · 9850196670187_<13> · 2526077546800091_<16> · 51897680774988553_<17> · 1936097886341375452565514421758559_<34> · C94

C94 = P44 · P50

P44 = 24797876921485497067144513611132264335092469_<44>

P50 = 58620376640769325233358205994469484508814376477459_<50>

Wed May  2 08:05:47 2007  
Wed May  2 08:05:47 2007  
Wed May  2 08:05:47 2007  Msieve v. 1.19
Wed May  2 08:05:47 2007  random seeds: 0e7d1e7b 64086647
Wed May  2 08:05:47 2007  factoring 1453660885028921178823036658094874193257359268776143901154311382982677794100725313703259156271 (94 digits)
Wed May  2 08:05:47 2007  commencing quadratic sieve (93-digit input)
Wed May  2 08:05:47 2007  using multiplier of 1
Wed May  2 08:05:47 2007  sieve interval: 9 blocks of size 65536
Wed May  2 08:05:47 2007  processing polynomials in batches of 6
Wed May  2 08:05:47 2007  using a sieve bound of 1990607 (74118 primes)
Wed May  2 08:05:47 2007  using large prime bound of 256788303 (27 bits)
Wed May  2 08:05:47 2007  using double large prime bound of 1371624962518986 (42-51 bits)
Wed May  2 08:05:47 2007  using trial factoring cutoff of 53 bits
Wed May  2 08:05:47 2007  polynomial 'A' values have 12 factors
Wed May  2 10:35:55 2007  74609 relations (19982 full + 54627 combined from 1001183 partial), need 74214
Wed May  2 10:35:56 2007  begin with 1021165 relations
Wed May  2 10:35:56 2007  reduce to 185310 relations in 10 passes
Wed May  2 10:35:56 2007  attempting to read 185310 relations
Wed May  2 10:35:57 2007  recovered 185310 relations
Wed May  2 10:35:57 2007  recovered 165356 polynomials
Wed May  2 10:35:58 2007  attempting to build 74609 cycles
Wed May  2 10:35:58 2007  found 74609 cycles in 6 passes
Wed May  2 10:35:58 2007  distribution of cycle lengths:
Wed May  2 10:35:58 2007     length 1 : 19982
Wed May  2 10:35:58 2007     length 2 : 14145
Wed May  2 10:35:58 2007     length 3 : 12995
Wed May  2 10:35:58 2007     length 4 : 9919
Wed May  2 10:35:58 2007     length 5 : 6952
Wed May  2 10:35:58 2007     length 6 : 4552
Wed May  2 10:35:58 2007     length 7 : 2683
Wed May  2 10:35:58 2007     length 9+: 3381
Wed May  2 10:35:58 2007  largest cycle: 21 relations
Wed May  2 10:35:58 2007  matrix is 74118 x 74609 with weight 4562903 (avg 61.16/col)
Wed May  2 10:35:58 2007  filtering completed in 4 passes
Wed May  2 10:35:58 2007  matrix is 72366 x 72430 with weight 4338494 (avg 59.90/col)
Wed May  2 10:35:59 2007  saving the first 48 matrix rows for later
Wed May  2 10:35:59 2007  matrix is 72318 x 72430 with weight 3394140 (avg 46.86/col)
Wed May  2 10:35:59 2007  matrix includes 32 packed rows
Wed May  2 10:35:59 2007  using block size 28972 for processor cache size 4096 kB
Wed May  2 10:36:24 2007  lanczos halted after 1146 iterations
Wed May  2 10:36:24 2007  recovered 17 nontrivial dependencies
Wed May  2 10:36:24 2007  prp44 factor: 24797876921485497067144513611132264335092469
Wed May  2 10:36:24 2007  prp50 factor: 58620376640769325233358205994469484508814376477459
Wed May  2 10:36:24 2007  elapsed time 02:30:37

May 2, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(7·10¹⁶³+11)/9 = (7)₁₆₂9_<163> = 3² · 41 · C161

C161 = P54 · P107

P54 = 514515297087868502474983030087617316989796040442834827_<54>

P107 = 40966689769893610626476927258402725629496499459917386396791475858410644488358780719013787208922173833093833_<107>

Number: n
N=21077988557663354411321890996687744655224330021077988557663354411321890996687744655224330021077988557663354411321890996687744655224330021077988557663354411321891
  ( 161 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=514515297087868502474983030087617316989796040442834827 (pp54)
 r2=40966689769893610626476927258402725629496499459917386396791475858410644488358780719013787208922173833093833 (pp107)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 73.09 hours.
Scaled time: 96.69 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_7_162_9
n: 21077988557663354411321890996687744655224330021077988557663354411321890996687744655224330021077988557663354411321890996687744655224330021077988557663354411321891
skew: 0.27
deg: 5
c5: 7000
c0: 11
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3100001)
Primes: RFBsize:216816, AFBsize:216287, largePrimes:7606035 encountered
Relations: rels:7066578, finalFF:507191
Max relations in full relation-set: 48
Initial matrix: 433170 x 507191 with sparse part having weight 57968673.
Pruned matrix : 408331 x 410560 with weight 39468405.
Total sieving time: 65.31 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 7.28 hours.
Total square root time: 0.20 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 73.09 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

May 1, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon

(34·10¹⁶³-43)/9 = 3(7)₁₆₂3_<164> = 3 · 11 · 127 · C160

C160 = P65 · P95

P65 = 91390426373664897185118886740810108717145752199108537782197799559_<65>

P95 = 98632046262711639984435686270799324642733520958702869493254441867094251159024695060193689043317_<95>

Number: n
N=9014024762056258119250245234497203001140009014024762056258119250245234497203001140009014024762056258119250245234497203001140009014024762056258119250245234497203
  ( 160 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=91390426373664897185118886740810108717145752199108537782197799559 (pp65)
 r2=98632046262711639984435686270799324642733520958702869493254441867094251159024695060193689043317 (pp95)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 79.19 hours.
Scaled time: 108.17 units (timescale=1.366).
Factorization parameters were as follows:
name: KA_3_7_162_3
n: 9014024762056258119250245234497203001140009014024762056258119250245234497203001140009014024762056258119250245234497203001140009014024762056258119250245234497203
skew: 0.53
deg: 5
c5: 2125
c0: -86
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 3500001)
Primes: RFBsize:216816, AFBsize:216441, largePrimes:7805786 encountered
Relations: rels:7321063, finalFF:489799
Max relations in full relation-set: 28
Initial matrix: 433323 x 489799 with sparse part having weight 49107580.
Pruned matrix : 412563 x 414793 with weight 38441893.
Total sieving time: 73.32 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 5.20 hours.
Total square root time: 0.36 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 79.19 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10¹⁶³-3 = 7(9)₁₆₂7_<164> = 7 · 11 · C163

C163 = P47 · P52 · P64

P47 = 89581069649366015235300671433024669118796111357_<47>

P52 = 1328960328047374779277655762328347541585843851574289_<52>

P64 = 8727121078291846984177702899623421473981265858116567223440296757_<64>

Number: n
N=1038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961
  ( 163 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=89581069649366015235300671433024669118796111357 (pp47)
 r2=1328960328047374779277655762328347541585843851574289 (pp52)
 r3=8727121078291846984177702899623421473981265858116567223440296757 (pp64)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 56.88 hours.
Scaled time: 68.02 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_7_9_162_7
n: 1038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961038961
type: snfs
skew: 0.41
deg: 5
c5: 250
c0: -3
m: 200000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2300001)
Primes: RFBsize:216816, AFBsize:216651, largePrimes:7103403 encountered
Relations: rels:6546431, finalFF:496607
Max relations in full relation-set: 28
Initial matrix: 433533 x 496607 with sparse part having weight 35754138.
Pruned matrix : 386820 x 389051 with weight 24746569.
Total sieving time: 51.96 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 4.31 hours.
Total square root time: 0.34 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 56.88 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

May 1, 2007

By suberi / GMP-ECM 6.1.2 B1=3000000

(5·10¹⁹⁵+13)/9 = (5)₁₉₄7_<195> = C195

C195 = P39 · P157

P39 = 293923582732541876305980115142461713161_<39>

P157 = 1890136036008678464132934523184891613446562306896411362973575981503407833876886244603645696907973797637476002009415129925578694940419444733815604163115952637_<157>

(5·10¹⁷⁵+13)/9 = (5)₁₇₄7_<175> = 7 · 43 · 149 · 1499 · 14251 · C163

C163 = P31 · C133

P31 = 3245287931581745301311295513847_<31>

C133 = [1786794155374191302871466689817032767120466283217883352210266480367265472931130656381364399208145044807027729642278741101891201645531_<133>]

(5·10¹⁹⁷+13)/9 = (5)₁₉₆7_<197> = 3 · 151 · 4039753 · 51553300303_<11> · 33119551843253_<14> · C164

C164 = P31 · P133

P31 = 6580404024701852906940026053969_<31>

P133 = 2701972951016802964778536554653481812241749050896874603933106059438368263044746699896453605189606469163356710583422716412312190699563_<133>

(5·10¹⁵⁹+13)/9 = (5)₁₅₈7_<159> = 31 · 88422043643857462597_<20> · C138

C138 = P31 · C108

P31 = 1425603659062897082122821966839_<31>

C108 = [142169505031818941787456133521823682753734366848698561502053979968080314542932254864568794355447616804460409_<108>]

(5·10¹⁷⁸+13)/9 = (5)₁₇₇7_<178> = 1528613 · 9850196670187_<13> · 2526077546800091_<16> · 51897680774988553_<17> · C127

C127 = P34 · C94

P34 = 1936097886341375452565514421758559_<34>

C94 = [1453660885028921178823036658094874193257359268776143901154311382982677794100725313703259156271_<94>]

April 2007

Apr 30, 2007

By suberi / GMP-ECM 6.1.2 B1=3000000

(10¹⁷⁶+17)/9 = (1)₁₇₅3_<176> = 13 · 1879391 · 6718199 · C161

C161 = P35 · C127

P35 = 43731936268508244866927446133249317_<35>

C127 = [1547908998692254006817668407385442013503701471074265130054570365447559543406277463390309132007591482864040879451770914663198017_<127>]

Apr 29, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=3000000

(10¹⁹⁸+17)/9 = (1)₁₉₇3_<198> = 10903 · 14765887 · 30620063 · C179

C179 = P37 · P143

P37 = 1106470306688059445573370198780657763_<37>

P143 = 20370706632593519622375724577942747394309044829544818549592211014459360143604890305766200820243688122193921133924400853893810356993408166701557_<143>

Apr 29, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(5·10¹⁶²+1)/3 = 1(6)₁₆₁7_<163> = 67 · C161

C161 = P77 · P85

P77 = 15021343982458863265099067005237957428313579616162543134808299151295298507741_<77>

P85 = 1656018390870730922037745080017419987395416242647949264972839350025244821735227203661_<85>

Number: n
N=24875621890547263681592039800995024875621890547263681592039800995024875621890547263681592039800995024875621890547263681592039800995024875621890547263681592039801
  ( 161 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=15021343982458863265099067005237957428313579616162543134808299151295298507741 (pp77)
 r2=1656018390870730922037745080017419987395416242647949264972839350025244821735227203661 (pp85)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 40.32 hours.
Scaled time: 58.51 units (timescale=1.451).
Factorization parameters were as follows:
name: KA_1_6_161_7
n: 24875621890547263681592039800995024875621890547263681592039800995024875621890547263681592039800995024875621890547263681592039800995024875621890547263681592039801
skew: 0.29
deg: 5
c5: 500
c0: 1
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2100001)
Primes: RFBsize:216816, AFBsize:216391, largePrimes:7234005 encountered
Relations: rels:6721359, finalFF:495113
Max relations in full relation-set: 28
Initial matrix: 433273 x 495113 with sparse part having weight 39011344.
Pruned matrix : 387351 x 389581 with weight 27248773.
Total sieving time: 35.60 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 4.43 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 40.32 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

P77 is the fourth largest factor found by GGNFS so far in our tables. Congratulations!

See Records.

(83·10¹⁶⁰+61)/9 = 9(2)₁₅₉9_<161> = 3 · C161

C161 = P60 · P101

P60 =763644251892931073537547192111224194051499190901748667513491_<60>

P101 = 40255316090627542913753162624598825771292696705345565195696208829537695183338310830115705652897654973_<101>

Number: n
N=30740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743
  ( 161 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=763644251892931073537547192111224194051499190901748667513491 (pp60)
 r2=40255316090627542913753162624598825771292696705345565195696208829537695183338310830115705652897654973 (pp101)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 61.80 hours.
Scaled time: 73.97 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_9_2_159_9
n: 30740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743
type: snfs
skew: 0.94
deg: 5
c5: 83
c0: 61
m: 100000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2500001)
Primes: RFBsize:216816, AFBsize:216307, largePrimes:7209488 encountered
Relations: rels:6639658, finalFF:486906
Max relations in full relation-set: 28
Initial matrix: 433188 x 486906 with sparse part having weight 36566778.
Pruned matrix : 396137 x 398366 with weight 26704077.
Total sieving time: 56.15 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 5.25 hours.
Total square root time: 0.13 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 61.80 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Apr 28, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon

(82·10¹⁵⁹-1)/9 = 9(1)₁₅₉_<160> = 3 · C160

C160 = P48 · P113

P48 = 241647557727089005892292451432908599283904128733_<48>

P113 = 12568043582161895072963384363446372944023458284330325387157152352247464883030826446963412997874721323844798980689_<113>

Number: n
N=3037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037
  ( 160 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=241647557727089005892292451432908599283904128733 (pp48)
 r2=12568043582161895072963384363446372944023458284330325387157152352247464883030826446963412997874721323844798980689 (pp113)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 45.19 hours.
Scaled time: 61.95 units (timescale=1.371).
Factorization parameters were as follows:
name: KA_9_1_159
n: 3037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037
skew: 0.66
deg: 5
c5: 41
c0: -5
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1900001)
Primes: RFBsize:216816, AFBsize:216857, largePrimes:7255543 encountered
Relations: rels:6763085, finalFF:512657
Max relations in full relation-set: 28
Initial matrix: 433738 x 512657 with sparse part having weight 40151255.
Pruned matrix : 373681 x 375913 with weight 26539749.
Total sieving time: 40.91 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 3.52 hours.
Total square root time: 0.51 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 45.19 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(5·10¹⁶¹+31)/9 = (5)₁₆₀9_<161> = 7 · C160

C160 = P49 · P51 · P62

P49 = 2438969913365590123358917315136313969549616824191_<49>

P51 = 126382113975161545904668128138667915671155888382263_<51>

P62 = 25747638113606124053747971056356175569815887788007147104126489_<62>

Number: n
N=7936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507937
  ( 160 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=2438969913365590123358917315136313969549616824191 (pp49)
 r2=126382113975161545904668128138667915671155888382263 (pp51)
 r3=25747638113606124053747971056356175569815887788007147104126489 (pp62)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 50.81 hours.
Scaled time: 67.32 units (timescale=1.325).
Factorization parameters were as follows:
name: KA_5_160_9
n: 7936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507936507937
skew: 0.91
deg: 5
c5: 50
c0: 31
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2200001)
Primes: RFBsize:216816, AFBsize:217337, largePrimes:7429297 encountered
Relations: rels:6959464, finalFF:557409
Max relations in full relation-set: 48
Initial matrix: 434218 x 557409 with sparse part having weight 52928452.
Pruned matrix : 357779 x 360014 with weight 31099006.
Total sieving time: 45.45 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 4.87 hours.
Total square root time: 0.24 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 50.81 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 28, 2007

By Yousuke Koide / GMP-ECM B1=1e6 / Apr 25, 2007

10¹⁸¹⁰+1 = 1(0)₁₈₀₉1_<1811> = 101 · 3541 · 27961 · 928417781 · 3655211741_<10> · 469968172441_<12> · 2136569912461_<13> · 196636530190361_<15> · 263346017179961_<15> · 15470952779187481_<17> · 3294170239985256241_<19> · 3467369151629862044701_<22> · 3973728652754811772515860861_<28> · 314547891171506427278717744569_<30> · 22780106292572351730658730234738216404394547689_<47> · 2763057708101686443032907255670870301200401399657924257107762182149956480304265507465823191458543338192444247826866701172774820848970862394309509034525824920430145923354279701799097867258088089212682054699054590801_<214> · C651 · C706

C706 = P38 · C668

P38 = 81685556537224955443340015680020142181_<38>

By Yousuke Koide / GMP-ECM B1=125e4 / Apr 28, 2007

(10⁷⁸⁷-1)/9 = (1)₇₈₇_<787> = 26759 · 213141637 · C774

C774 = P34 · C741

P34 = 1074022836653095912870566750079013_<34>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 27, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=548000, B1=580000

(32·10¹⁶¹-23)/9 = 3(5)₁₆₀3_<162> = 11 · C161

C161 = P35 · P36 · P91

P35 = 27259050424085339529239969264230591_<35>

P36 = 803134225042376363531999194958705621_<36>

P91 = 1476440423481398408509200960925473650542806915465777143424498012793825455523287350714672393_<91>

Apr 26, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon

(4·10¹⁵⁹-7)/3 = 1(3)₁₅₈1_<160> = 11 · 23 · C157

C157 = P53 · P105

P53 = 17459658467387443869331205970366143563395038136006397_<53>

P105 = 301843947088533742600289415675999685198956945601568904220026735567745228859461977377699316648532130087291_<105>

Number: n
N=5270092226613965744400527009222661396574440052700922266139657444005270092226613965744400527009222661396574440052700922266139657444005270092226613965744400527
  ( 157 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=17459658467387443869331205970366143563395038136006397 (pp53)
 r2=301843947088533742600289415675999685198956945601568904220026735567745228859461977377699316648532130087291 (pp105)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 27.80 hours.
Scaled time: 37.95 units (timescale=1.365).
Factorization parameters were as follows:
name: KA_1_3_158_1
n: 5270092226613965744400527009222661396574440052700922266139657444005270092226613965744400527009222661396574440052700922266139657444005270092226613965744400527
skew: 1.77
deg: 5
c5: 2
c0: -35
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:216816, AFBsize:216006, largePrimes:6763878 encountered
Relations: rels:6238378, finalFF:487616
Max relations in full relation-set: 28
Initial matrix: 432887 x 487616 with sparse part having weight 29932096.
Pruned matrix : 383769 x 385997 with weight 19502837.
Total sieving time: 24.57 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 2.79 hours.
Total square root time: 0.20 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 27.80 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

2·10¹⁵⁸-9 = 1(9)₁₅₇1_<159> = 449 · 647 · 263423 · C148

C148 = P59 · P90

P59 = 24629981367007296663635744349139127212651564923379917379247_<59>

P90 = 106111291216604957235287331858373630426835509120007905601583219050565604016518888425492737_<90>

Number: n
N=2613519125494065116104920898710776208411387878266129214050977218917923341224771005061211782302690175095868199383407515341058443407151053865673029039
  ( 148 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=24629981367007296663635744349139127212651564923379917379247 (pp59)
 r2=106111291216604957235287331858373630426835509120007905601583219050565604016518888425492737 (pp90)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 37.18 hours.
Scaled time: 44.43 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_1_9_157_1
n: 2613519125494065116104920898710776208411387878266129214050977218917923341224771005061211782302690175095868199383407515341058443407151053865673029039
type: snfs
skew: 0.68
deg: 5
c5: 125
c0: -18
m: 20000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:216816, AFBsize:216826, largePrimes:6772566 encountered
Relations: rels:6340882, finalFF:591658
Max relations in full relation-set: 28
Initial matrix: 433708 x 591658 with sparse part having weight 33045348.
Pruned matrix : 297330 x 299562 with weight 16786027.
Total sieving time: 34.67 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 2.20 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 37.18 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(65·10¹⁵⁸+43)/9 = 7(2)₁₅₇7_<159> = 19 · 7448303743_<10> · C148

C148 = P70 · P79

P70 = 2283906434721397222715225004575163162522053541582590209420748519155831_<70>

P79 = 2234506175283351071706709697979013414681324521591035009309462144344402039107001_<79>

Number: n
N=5103403032154343834741178855604673819491372467573218373515476529946980780374398851423525859559148205166416041259945688339089065263392267437602072831
  ( 148 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=2283906434721397222715225004575163162522053541582590209420748519155831 (pp70)
 r2=2234506175283351071706709697979013414681324521591035009309462144344402039107001 (pp79)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 48.27 hours.
Scaled time: 63.86 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_7_2_157_7
n: 5103403032154343834741178855604673819491372467573218373515476529946980780374398851423525859559148205166416041259945688339089065263392267437602072831
skew: 1.16
deg: 5
c5: 104
c0: 215
m: 50000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2000001)
Primes: RFBsize:216816, AFBsize:216546, largePrimes:7326828 encountered
Relations: rels:6829370, finalFF:530036
Max relations in full relation-set: 48
Initial matrix: 433428 x 530036 with sparse part having weight 48883949.
Pruned matrix : 366007 x 368238 with weight 29896532.
Total sieving time: 42.64 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 4.80 hours.
Total square root time: 0.60 hours, sqrts: 7.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 48.27 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(4·10¹⁵⁹-13)/9 = (4)₁₅₈3_<159> = 19 · C158

C157 = P32 · P60 · P67

P32 = 84189747192092171468535381286471_<32>

P60 = 154525079685364105720550993011600245901181046815079559422881_<60>

P67 = 1798066291303254277894237143922564989013145315594815253125477086847_<67>

Number: n
N=23391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497
  ( 158 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=84189747192092171468535381286471 (pp32)
 r2=154525079685364105720550993011600245901181046815079559422881 (pp60)
 r3=1798066291303254277894237143922564989013145315594815253125477086847 (pp67)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 39.54 hours.
Scaled time: 57.33 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_4_158_3
n: 23391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497076023391812865497
skew: 2.00
deg: 5
c5: 2
c0: -65
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1900001)
Primes: RFBsize:216816, AFBsize:216126, largePrimes:7250354 encountered
Relations: rels:6745505, finalFF:499663
Max relations in full relation-set: 28
Initial matrix: 433007 x 499663 with sparse part having weight 38893311.
Pruned matrix : 382407 x 384636 with weight 26621486.
Total sieving time: 34.75 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 4.30 hours.
Total square root time: 0.29 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 39.54 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Apr 26, 2007

By Wataru Sakai / GMP-ECM 6.1.2 B1=11000000

9·10¹⁸⁷+1 = 9(0)₁₈₆1_<188> = 7 · 13 · 4373 · 5717 · 20183 · C175

C175 = P32 · C143

P32 = 24068660737760877432355395211891_<32>

C143 = [81435881553600072016173523292608504397039692207307496066394773089520233394402320905105063604429647318463867320494190178646753385161893694575807_<143>]

9·10¹⁷⁶+1 = 9(0)₁₇₅1_<177> = 382561419661867013_<18> · C160

C160 = P34 · C126

P34 = 4153302760261926665697975045884449_<34>

C126 = [566431958152526346806249739676161934366904899317226070390042476342664318676795495580542611504898377157441268210176302406249773_<126>]

Apr 25, 2007 (3rd)

By Wataru Sakai / GMP-ECM 6.1.2 B1=11000000

9·10¹⁶⁴+1 = 9(0)₁₆₃1_<165> = 206021 · 987313 · 288154417 · C146

C146 = P33 · P113

P33 = 941596665917777874062834896326197_<33>

P113 = 16307446785923947920819586784374506111817003364273287474816055749579556455124440591984263685499136336546651516313_<113>

Apr 25, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=11000000

(10¹⁹¹+53)/9 = (1)₁₉₀7_<191> = 83 · 257 · 2309 · 4481 · 30274753811_<11> · C169

C169 = P41 · P129

P41 = 14781772991827325758273699724307624723203_<41>

P129 = 112496820824306141289466401848140159736387544454873436102425778272976103436914816351733511282110806424845862379940475925100721451_<129>

Apr 25, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp

(14·10¹⁵⁸-41)/9 = 1(5)₁₅₇1_<159> = 29 · 31 · 32117 · C151

C151 = P74 · P78

P74 = 16890701960639836030505223027599141408171380796039886568589214265562803591_<74>

P78 = 318965097991281408955651198675474281172186567241455132017352484669834254010167_<78>

Number: n
N=5387544406017014319327230238368785164959317286062833999131843397922409716848868223346056288825362813499140553902753137939643009070235018963983138109697
  ( 151 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=16890701960639836030505223027599141408171380796039886568589214265562803591 (pp74)
 r2=318965097991281408955651198675474281172186567241455132017352484669834254010167 (pp78)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 33.67 hours.
Scaled time: 43.06 units (timescale=1.279).
Factorization parameters were as follows:
name: KA_1_5_157_1
n: 5387544406017014319327230238368785164959317286062833999131843397922409716848868223346056288825362813499140553902753137939643009070235018963983138109697
skew: 0.62
deg: 5
c5: 875
c0: -82
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:216816, AFBsize:217337, largePrimes:7010678 encountered
Relations: rels:6493609, finalFF:497084
Max relations in full relation-set: 28
Initial matrix: 434219 x 497084 with sparse part having weight 34384792.
Pruned matrix : 382432 x 384667 with weight 22554464.
Total sieving time: 30.59 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 2.75 hours.
Total square root time: 0.11 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 33.67 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(13·10¹⁵⁸-31)/9 = 1(4)₁₅₇1_<159> = 3² · 59 · 1151 · 1259 · C150

C150 = P40 · P110

P40 = 2666207182373154418160383393318256974037_<40>

P110 = 70406276040739502591454509881526959077496256123980929796389336194469708080034764900330162435965741985863807867_<110>

Number: n
N=187717718863966599371265116913856542848046308152222523692546770394181583257740021639356423657330507580390137290199780576440743769826051452345775349079
  ( 150 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=2666207182373154418160383393318256974037 (pp40)
 r2=70406276040739502591454509881526959077496256123980929796389336194469708080034764900330162435965741985863807867 (pp110)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.69 hours.
Scaled time: 51.68 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_1_4_157_1
n: 187717718863966599371265116913856542848046308152222523692546770394181583257740021639356423657330507580390137290199780576440743769826051452345775349079
skew: 0.30
deg: 5
c5: 13000
c0: -31
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1600001)
Primes: RFBsize:216816, AFBsize:217162, largePrimes:7086581 encountered
Relations: rels:6568699, finalFF:493501
Max relations in full relation-set: 28
Initial matrix: 434045 x 493501 with sparse part having weight 35899314.
Pruned matrix : 385935 x 388169 with weight 24270637.
Total sieving time: 31.12 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 3.85 hours.
Total square root time: 0.50 hours, sqrts: 7.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 35.69 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Apr 24, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(67·10¹⁵⁸+23)/9 = 7(4)₁₅₇7_<159> = 3 · 31 · 1709 · C154

C154 = P44 · P111

P44 = 29260919942103733509905823159085703681886443_<44>

P111 = 160073450317003468362082050116843117920380447672897296042460127280985936066587164006989343231612150440123554917_<111>

Number: n
N=4683896414582157989923330907494443990036583328264937959345177299461072276716211105308672269166049720609074315259784974200119823857531251026786993868290231
  ( 154 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=29260919942103733509905823159085703681886443 (pp44)
 r2=160073450317003468362082050116843117920380447672897296042460127280985936066587164006989343231612150440123554917 (pp111)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 39.41 hours.
Scaled time: 51.55 units (timescale=1.308).
Factorization parameters were as follows:
name: KA_7_4_157_7
n: 4683896414582157989923330907494443990036583328264937959345177299461072276716211105308672269166049720609074315259784974200119823857531251026786993868290231
skew: 0.20
deg: 5
c5: 67000
c0: 23
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1600001)
Primes: RFBsize:216816, AFBsize:217321, largePrimes:7168927 encountered
Relations: rels:6688652, finalFF:543810
Max relations in full relation-set: 48
Initial matrix: 434204 x 543810 with sparse part having weight 44745238.
Pruned matrix : 347629 x 349864 with weight 25223265.
Total sieving time: 35.47 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 3.64 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 39.41 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(5·10¹⁵⁸+13)/9 = (5)₁₅₇7_<158> = 3³ · C157

C157 = P33 · P124

P33 = 382853825496553598188403176353457_<33>

P124 = 5374409322031972772894913517826689979791154924734271046070635240945189138433355533839639709026504877244886570211096873586863_<124>

Number: n
N=2057613168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835391
  ( 157 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=382853825496553598188403176353457 (pp33)
 r2=5374409322031972772894913517826689979791154924734271046070635240945189138433355533839639709026504877244886570211096873586863 (pp124)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 45.40 hours.
Scaled time: 27.15 units (timescale=0.598).
Factorization parameters were as follows:
name: KA_5_157_7
n: 2057613168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835391
type: snfs
skew: 1.52
deg: 5
c5: 8
c0: 65
m: 50000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1800001)
Primes: RFBsize:216816, AFBsize:217216, largePrimes:6949869 encountered
Relations: rels:6482428, finalFF:569218
Max relations in full relation-set: 28
Initial matrix: 434097 x 569218 with sparse part having weight 35384681.
Pruned matrix : 323170 x 325404 with weight 19605330.
Total sieving time: 40.67 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 4.31 hours.
Total square root time: 0.17 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 45.40 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+ (Timesharing)

Apr 23, 2007 (2nd)

By Wataru Sakai / GMP-ECM 6.1.2 B1=11000000

9·10¹⁹⁴+1 = 9(0)₁₉₃1_<195> = 17 · 1249 · 8089 · 1037297 · 106869415441_<12> · C170

C170 = P34 · P136

P34 = 6800424794926771388308831050471833_<34>

P136 = 6950942827174514887338020534901240077527602856760093566826256645756923667399042440819259600295410278353642353978340831657491455631029153_<136>

Apr 23, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=124000, GGNFS-0.77.1-20060513-athlon-xp gnfs, GGNFS-0.77.1-20051202-athlon

(89·10¹⁵⁷+1)/9 = 9(8)₁₅₆9_<158> = 3 · 11 · 83 · 507109 · 7608147321531382277_<19> · C130

C130 = P30 · P45 · P56

P30 = 998766999662301920263579973857_<30>

P45 = 671276082185180309721450498078371896813263139_<45>

P56 = 13957571951968016563167181516143946350859587741613040809_<56>

Number: n
N=9369384216734849844858838821136383764594390595025958560650767203742805702183608663516846355662439451
  ( 100 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=671276082185180309721450498078371896813263139 (pp45)
 r2=13957571951968016563167181516143946350859587741613040809 (pp56)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 30.98 hours.
Scaled time: 42.35 units (timescale=1.367).
Factorization parameters were as follows:
name: KA_9_8_156_9

n: 9369384216734849844858838821136383764594390595025958560650767203742805702183608663516846355662439451

# n: 9357831762831592716696047258075955006494138738306098602738469766935052019174596543063795350498288700538403141385637434411425432507

skew: 0.16
deg: 5
c5: 8900
c0: 1
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:216816, AFBsize:217461, largePrimes:6928854 encountered
Relations: rels:6418255, finalFF:501673
Max relations in full relation-set: 28
Initial matrix: 434344 x 501673 with sparse part having weight 33339151.
Pruned matrix : 377922 x 380157 with weight 21090312.
Total sieving time: 28.11 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 2.53 hours.
Total square root time: 0.11 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 30.98 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(4·10¹⁵⁸-7)/3 = 1(3)₁₅₇1_<159> = 19 · C157

C157 = P57 · P101

P57 = 115570041668777500610211129739853968547382455176953878951_<57>

P101 = 60721132901910066040884017345234420133773553977363086094391872306702156725540345706908544495936768599_<101>

Number: n
N=7017543859649122807017543859649122807017543859649122807017543859649122807017543859649122807017543859649122807017543859649122807017543859649122807017543859649
  ( 157 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=115570041668777500610211129739853968547382455176953878951 (pp57)
 r2=60721132901910066040884017345234420133773553977363086094391872306702156725540345706908544495936768599 (pp101)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.26 hours.
Scaled time: 37.76 units (timescale=1.438).
Factorization parameters were as follows:
name: KA_1_3_157_1
n: 7017543859649122807017543859649122807017543859649122807017543859649122807017543859649122807017543859649122807017543859649122807017543859649122807017543859649
skew: 0.56
deg: 5
c5: 125
c0: -7
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:216816, AFBsize:216506, largePrimes:6919954 encountered
Relations: rels:6439560, finalFF:527050
Max relations in full relation-set: 28
Initial matrix: 433387 x 527050 with sparse part having weight 34175911.
Pruned matrix : 352937 x 355167 with weight 19432489.
Total sieving time: 23.13 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 2.78 hours.
Total square root time: 0.17 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 26.26 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Apr 22, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(13·10¹⁵⁶-1)/3 = 4(3)₁₅₆_<157> = 482233522412249138299599463_<27> · C130

C130 = P51 · P80

P51 = 137685447586916374009095336332502139351312592931137_<51>

P80 = 65264446602257434699232134121438332071155454252336113787950688082621777887383843_<80>

Number: n
N=8985964541944218457144242823891451622905412479065263958964874992630944518378669494178261920751344671254683705993473379975985419491
  ( 130 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=137685447586916374009095336332502139351312592931137 (pp51)
 r2=65264446602257434699232134121438332071155454252336113787950688082621777887383843 (pp80)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.28 hours.
Scaled time: 42.09 units (timescale=1.193).
Factorization parameters were as follows:
name: KA_4_3_156
n: 8985964541944218457144242823891451622905412479065263958964874992630944518378669494178261920751344671254683705993473379975985419491
type: snfs
skew: 0.38
deg: 5
c5: 130
c0: -1
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1400000)
Primes: RFBsize:216816, AFBsize:216816, largePrimes:6426802 encountered
Relations: rels:5897314, finalFF:498059
Max relations in full relation-set: 28
Initial matrix: 433699 x 498059 with sparse part having weight 28485229.
Pruned matrix : 374897 x 377129 with weight 17607571.
Total sieving time: 31.93 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 2.95 hours.
Total square root time: 0.18 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 35.28 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(83·10¹⁵⁶+61)/9 = 9(2)₁₅₅9_<157> = 115603 · 31695397 · 11905360919303_<14> · C132

C132 = P45 · P88

P45 = 185694616568789821030958057358645587169415001_<45>

P88 = 1138487858025295935614061399440799079483198341134630811712967349874304476402618347315973_<88>

Number: n
N=211411066264230152062340716870399973612067889013296080886298760548537066854582641830091382226851007304354037398622074774304913110973
  ( 132 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=185694616568789821030958057358645587169415001 (pp45)
 r2=1138487858025295935614061399440799079483198341134630811712967349874304476402618347315973 (pp88)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 46.26 hours.
Scaled time: 60.70 units (timescale=1.312).
Factorization parameters were as follows:
name: KA_9_2_155_9
n: 211411066264230152062340716870399973612067889013296080886298760548537066854582641830091382226851007304354037398622074774304913110973
skew: 0.59
deg: 5
c5: 830
c0: 61
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 18400001)
Primes: RFBsize:216816, AFBsize:216337, largePrimes:7238483 encountered
Relations: rels:6703027, finalFF:495978
Max relations in full relation-set: 48
Initial matrix: 433220 x 495978 with sparse part having weight 46386571.
Pruned matrix : 387853 x 390083 with weight 30950811.
Total sieving time: 40.61 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 5.13 hours.
Total square root time: 0.28 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 46.26 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 22, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

6·10¹⁷¹+1 = 6(0)₁₇₀1_<172> = C172

C172 = P48 · P125

P48 = 154699561095803788960811837883435548718183965521_<48>

P125 = 38784854704818871237674570715604655076738950339421849949486353744053423298050903282396196418361477719330298221232535393256881_<125>

Number: 60001_171
N=6000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
  ( 172 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=154699561095803788960811837883435548718183965521 (pp48)
 r2=38784854704818871237674570715604655076738950339421849949486353744053423298050903282396196418361477719330298221232535393256881 (pp125)
Version: GGNFS-0.77.1-20050930-k8
Total time: 121.74 hours.
Scaled time: 109.20 units (timescale=0.897).
Factorization parameters were as follows:
n: 6000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
m: 10000000000000000000000000000000000
c5: 60
c0: 1
skew: 1
type: snfs
Factor base limits: 8400000/8400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [4200000, 8300001)
Primes: RFBsize:564877, AFBsize:563981, largePrimes:6631468 encountered
Relations: rels:7286289, finalFF:1293157
Max relations in full relation-set: 28
Initial matrix: 1128925 x 1293157 with sparse part having weight 57494928.
Pruned matrix : 980575 x 986283 with weight 39531468.
Total sieving time: 115.09 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 6.39 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,8400000,8400000,27,27,49,49,2.6,2.6,100000
total time: 121.74 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.60 BogoMIPS (lpj=2335802)
Calibrating delay using timer specific routine.. 4668.49 BogoMIPS (lpj=2334246)
Total of 2 processors activated (9340.09 BogoMIPS).

Apr 22, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon

(5·10¹⁵⁵-23)/9 = (5)₁₅₄3_<155> = 455809 · 22178359105380078019_<20> · C130

C130 = P41(7816...) · P41(9862...) · P48

P41(7816...) = 78168599768506389915769096471731999506381_<41>

P41(9862...) = 98627970534811576733762760709847556429329_<41>

P48 = 712824730143064724192573094052187772119187236807_<48>

Number: n
N=5495600920608415791807485198227477664347272781973051325964290441482871529967054684754824258422291187953818426925644487404889381643
  ( 130 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=78168599768506389915769096471731999506381 (pp41)
 r2=98627970534811576733762760709847556429329 (pp41)
 r3=712824730143064724192573094052187772119187236807 (pp48)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 25.32 hours.
Scaled time: 34.53 units (timescale=1.364).
Factorization parameters were as follows:
name: KA_5_154_3
n: 5495600920608415791807485198227477664347272781973051325964290441482871529967054684754824258422291187953818426925644487404889381643
skew: 1.36
deg: 5
c5: 5
c0: -23
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:216816, AFBsize:217341, largePrimes:6728171 encountered
Relations: rels:6204172, finalFF:487768
Max relations in full relation-set: 28
Initial matrix: 434222 x 487768 with sparse part having weight 30334453.
Pruned matrix : 385580 x 387815 with weight 19867980.
Total sieving time: 22.41 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 2.52 hours.
Total square root time: 0.21 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 25.32 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(55·10¹⁵⁷-1)/9 = 6(1)₁₅₇_<158> = 12659 · 5115353 · 2427133077049363_<16> · C132

C132 = P61 · P72

P61 = 1756885727384775588518191961618990892705830617844120872919597_<61>

P72 = 221313582188953735910104077220440356480321006702394425598594316859809763_<72>

Number: n
N=388822673824170299517613128480124207165358916317761241208979819858125521756603961615264259628492731976257986840051227899003814625511
  ( 132 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=1756885727384775588518191961618990892705830617844120872919597 (pp61)
 r2=221313582188953735910104077220440356480321006702394425598594316859809763 (pp72)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 37.76 hours.
Scaled time: 54.64 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_6_1_157
n: 388822673824170299517613128480124207165358916317761241208979819858125521756603961615264259628492731976257986840051227899003814625511
skew: 0.89
deg: 5
c5: 44
c0: -25
m: 50000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1800001)
Primes: RFBsize:216816, AFBsize:217237, largePrimes:7155233 encountered
Relations: rels:6639789, finalFF:492384
Max relations in full relation-set: 28
Initial matrix: 434120 x 492384 with sparse part having weight 37041926.
Pruned matrix : 389521 x 391755 with weight 25693721.
Total sieving time: 33.10 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 4.39 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 37.76 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Apr 21, 2007 (2nd)

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000

4·10¹⁹⁴+1 = 4(0)₁₉₃1_<195> = 721324202162977116296517293557_<30> · C165

C165 = P36 · C130

P36 = 230366834312643340988031253121778481_<36>

C130 = [2407185357318598997321950360974409607977596627073563023341105908056951583447549498371976960901544198606857339244488454067274390253_<130>]

Apr 21, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon

(5·10¹⁵⁶-17)/3 = 1(6)₁₅₅1_<157> = 23 · 45530803605118052249663_<23> · C133

C133 = P43 · P90

P43 = 6980802854042367720418771014299511108668407_<43>

P90 = 227987074000655558378765635891409896833438917225088630429302578069324695128035262416578827_<90>

Number: n
N=1591532816868544812411804196768146464448799537512375973859933367030542841491293027937220386483931368319354400599625525690188520018589
  ( 133 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=6980802854042367720418771014299511108668407 (pp43)
 r2=227987074000655558378765635891409896833438917225088630429302578069324695128035262416578827 (pp90)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 25.80 hours.
Scaled time: 35.30 units (timescale=1.368).
Factorization parameters were as follows:
name: KA_1_6_155_1
n: 1591532816868544812411804196768146464448799537512375973859933367030542841491293027937220386483931368319354400599625525690188520018589
skew: 0.81
deg: 5
c5: 50
c0: -17
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:216816, AFBsize:217226, largePrimes:6873287 encountered
Relations: rels:6405229, finalFF:536584
Max relations in full relation-set: 28
Initial matrix: 434107 x 536584 with sparse part having weight 33216707.
Pruned matrix : 344478 x 346712 with weight 17968311.
Total sieving time: 23.46 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.06 hours.
Total square root time: 0.09 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 25.80 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(34·10¹⁵⁵-7)/9 = 3(7)₁₅₅_<156> = 1963259 · 15914463295100393_<17> · C134

C134 = P63 · P71

P63 = 614145112547407319622447176567788678504259865720750939348025889_<63>

P71 = 19687737655841001340058422437548321514709788974293541871489336377296939_<71>

Number: n
N=12091127858450300921796173885173780987451322407445921454256127552779197749846655382931701572574680369104650104260662112804527612453771
  ( 134 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=614145112547407319622447176567788678504259865720750939348025889 (pp63)
 r2=19687737655841001340058422437548321514709788974293541871489336377296939 (pp71)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 36.10 hours.
Scaled time: 43.17 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_3_7_155
n: 12091127858450300921796173885173780987451322407445921454256127552779197749846655382931701572574680369104650104260662112804527612453771
type: snfs
skew: 0.73
deg: 5
c5: 34
c0: -7
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:216816, AFBsize:216741, largePrimes:6612115 encountered
Relations: rels:6128536, finalFF:545288
Max relations in full relation-set: 28
Initial matrix: 433623 x 545288 with sparse part having weight 31990210.
Pruned matrix : 334870 x 337102 with weight 17003441.
Total sieving time: 33.37 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 2.42 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 36.10 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Apr 20, 2007 (3rd)

By Bos

10³⁰⁷+1 = 1(0)₃₀₆1_<308> = 11 · 3311436805543_<13> · 1490473286202873492575327109823_<31> · C264

C264 = P52 · C212

P52 = 5523722596446330977448218249241349336929189661174997_<52>

By Yousuke Koide / GMP-ECM / Apr 19, 2007

10⁷⁹⁹+1 = 1(0)₇₉₈1_<800> = 11 · 103 · 4013 · 6299 · 21993833369_<11> · 4855067598095567_<16> · 149419107039492234761_<21> · 297262705009139006771611927_<27> · C716

C716 = P31 · C686

P31 = 4588162642029183238011363957761_<31>

By Yousuke Koide / GMP-ECM / Apr 20, 2007

10⁸⁸⁹+1 = 1(0)₈₈₈1_<890> = 11 · 3557 · 909091 · 857772733 · 1094479651_<10> · 1125629957_<10> · 616896149073719728613_<21> · 4514666454616035926293_<22> · 10860110813777339731289_<23> · 52034716615139419063969613_<26> · 36099531273603138218699301565567581705151216702113889_<53> · C709

C709 = P31 · C679

P31 = 1515780514077670348158815644201_<31>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 20, 2007 (2nd)

By suberi / GGNFS-0.77.1-20060513-pentium4 gnfs

(16·10²³⁵-61)/9 = 1(7)₂₃₄1_<236> = 11 · 29 · 37037719357719760261079_<23> · 386429589610739568586536276533_<30> · 713567298076051856522358950335091_<33> · 151909019354249419571440528481694434053_<39> · C110

C110 = P39 · P72

P39 = 125605990791686900936504691140588363699_<39>

P72 = 285985047765230062977841876142162519940065363490818809053547121928669731_<72>

Number: 17771_235
N=35921435276159625817527432090229298251807652677226377310650377800268125022879271309502187214950639477080494969
  ( 110 digits)
Divisors found:
 r1=125605990791686900936504691140588363699 (pp39)
 r2=285985047765230062977841876142162519940065363490818809053547121928669731 (pp72)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 41.18 hours.
Scaled time: 24.75 units (timescale=0.601).
Factorization parameters were as follows:
name: 17771_235
n: 35921435276159625817527432090229298251807652677226377310650377800268125022879271309502187214950639477080494969
skew: 72976.38
# norm 1.70e+015
c5: 1260
c4: -836799224
c3: -25758351942273
c2: 3873905822348724057
c1: 36021861400424370105497
c0: -2749686868191143529867179949
# alpha -6.14
Y1: 46032740939
Y0: -1954330392375004368760
# Murphy_E 1.02e-009
# M 29519177398588835710920117477561627763408019706375126725127183876838642123095149601369374918428495280763074661
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2300001)
Primes: RFBsize:230209, AFBsize:230179, largePrimes:7349364 encountered
Relations: rels:7139629, finalFF:551314
Max relations in full relation-set: 28
Initial matrix: 460468 x 551314 with sparse part having weight 43597310.
Pruned matrix : 383114 x 385480 with weight 25752079.
Total sieving time: 31.84 hours.
Total relation processing time: 0.46 hours.
Matrix solve time: 8.38 hours.
Time per square root: 0.50 hours.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 41.18 hours.
 --------- CPU info (if available) ----------

Apr 20, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(25·10¹⁵⁵-7)/9 = 2(7)₁₅₅_<156> = 17 · 402851 · 119336766838382837_<18> · C132

C132 = P31 · P101

P31 = 5881365932046077344716432736879_<31>

P101 = 57789862723272576198135690999645341036774247444723327437699375463079889097341640177561574510207039697_<101>

Number: n
N=339883329838274876627404891772536715222229406033570353904935102531895001966367483580976478361229259406097110234232438139054308885663
  ( 132 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=5881365932046077344716432736879 (pp31)
 r2=57789862723272576198135690999645341036774247444723327437699375463079889097341640177561574510207039697 (pp101)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 22.44 hours.
Scaled time: 29.59 units (timescale=1.319).
Factorization parameters were as follows:
name: KA_2_7_155
n: 339883329838274876627404891772536715222229406033570353904935102531895001966367483580976478361229259406097110234232438139054308885663
skew: 0.78
deg: 5
c5: 25
c0: -7
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1000001)
Primes: RFBsize:216816, AFBsize:216906, largePrimes:6631137 encountered
Relations: rels:6138516, finalFF:516545
Max relations in full relation-set: 48
Initial matrix: 433786 x 516545 with sparse part having weight 31142732.
Pruned matrix : 360553 x 362785 with weight 16512544.
Total sieving time: 19.62 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 2.53 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 22.44 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(61·10¹⁵⁵-7)/9 = 6(7)₁₅₅_<156> = 103651 · 971857 · 19870534292309_<14> · C132

C132 = P43 · P89

P43 = 9817212608718080906317171875037375502190241_<43>

P89 = 34491630159507572267087764175508621104295293798871859880831023317096973793390053303999519_<89>

Number: n
N=338611666497158570577221038924531523369668099643294585815227989598756413572175554597195188944774585124940329355800182760989710494079
  ( 132 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=9817212608718080906317171875037375502190241 (pp43)
 r2=34491630159507572267087764175508621104295293798871859880831023317096973793390053303999519 (pp89)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 25.00 hours.
Scaled time: 36.23 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_6_7_155
n: 338611666497158570577221038924531523369668099643294585815227989598756413572175554597195188944774585124940329355800182760989710494079
skew: 0.65
deg: 5
c5: 61
c0: -7
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:216816, AFBsize:217077, largePrimes:6791757 encountered
Relations: rels:6281039, finalFF:499165
Max relations in full relation-set: 28
Initial matrix: 433958 x 499165 with sparse part having weight 31139720.
Pruned matrix : 377515 x 379748 with weight 19352078.
Total sieving time: 21.80 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 2.97 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 25.00 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Apr 19, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GMP-ECM 5.0, GGNFS-0.77.1-20060513-athlon-xp

(5·10¹⁵⁷-17)/3 = 1(6)₁₅₆1_<158> = 11 · 29 · 2757874996319_<13> · C143

C143 = P70 · P74

P70 = 1656783190595643799692672752239702194832989548613617120528492532923753_<70>

P74 = 11434516605064564778112562546194861690949907853799120239681553336330622717_<74>

Number: n
N=18944514903857738707332591646436452068207141455181594958816450014272137613307196266921465281243223714647216073470199710589087367939471170696901
  ( 143 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=1656783190595643799692672752239702194832989548613617120528492532923753 (pp70)
 r2=11434516605064564778112562546194861690949907853799120239681553336330622717 (pp74)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.71 hours.
Scaled time: 34.64 units (timescale=1.297).
Factorization parameters were as follows:
name: KA_1_6_156_1
n: 18944514903857738707332591646436452068207141455181594958816450014272137613307196266921465281243223714647216073470199710589087367939471170696901

# skew: 0.51
# deg: 5
# c5: 500
# c0: -17
# m: 10000000000000000000000000000000

skew: 2.54
deg: 5
c5: 4
c0: -425
m: 50000000000000000000000000000000

type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:216816, AFBsize:215811, largePrimes:6744488 encountered
Relations: rels:6227113, finalFF:502366
Max relations in full relation-set: 48
Initial matrix: 432691 x 502366 with sparse part having weight 33307367.
Pruned matrix : 372729 x 374956 with weight 19077430.
Total sieving time: 23.44 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.03 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 26.71 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(17·10¹⁵⁷-71)/9 = 1(8)₁₅₆1_<158> = 11 · 67 · 233 · 257 · 100133357531_<12> · C139

C139 = P34 · P50 · P56

P34 = 1974898746446825564654925588408067_<34>

P50 = 26084785568241325536093167306732883156016781297647_<50>

P56 = 82973420930499973861919069602007448123945832667668347767_<56>

Number: n
N=2164343892835518454505300706637153514507175780157952502388586254372879429209130030340885911229358734804249
  ( 106 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=26084785568241325536093167306732883156016781297647 (pp50)
 r2=82973420930499973861919069602007448123945832667668347767 (pp56)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 31.74 hours.
Scaled time: 45.71 units (timescale=1.440).
Factorization parameters were as follows:
name: KA_1_8_156_1

n: 2164343892835518454505300706637153514507175780157952502388586254372879429209130030340885911229358734804249

# n: 4274360040840707962086046706090075912461905742295530890501180085682533476011747446857603996863402993422314665552906852413675572058777476683

skew: 0.53
deg: 5
c5: 1700
c0: -71
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:216816, AFBsize:216847, largePrimes:6984289 encountered
Relations: rels:6460078, finalFF:494384
Max relations in full relation-set: 28
Initial matrix: 433730 x 494384 with sparse part having weight 33551013.
Pruned matrix : 384136 x 386368 with weight 22030613.
Total sieving time: 27.98 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 3.49 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 31.74 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(10¹⁵⁵+11)/3 = (3)₁₅₄7_<155> = 37 · 56896144739519611259_<20> · C134

C134 = P66 · P68

P66 = 208670671770760497643092645164757469100993644951788309366799053839_<66>

P68 = 75880951367873792594180307042805485428254654408601835762623060247601_<68>

Number: n
N=15834129096538631981876151311557857936639270420692829139295670131179001593315499680760105008976521203731578626121888596331739869590239
  ( 134 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=208670671770760497643092645164757469100993644951788309366799053839 (pp66)
 r2=75880951367873792594180307042805485428254654408601835762623060247601 (pp68)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 20.74 hours.
Scaled time: 28.29 units (timescale=1.364).
Factorization parameters were as follows:
name: KA_3_154_7
n: 15834129096538631981876151311557857936639270420692829139295670131179001593315499680760105008976521203731578626121888596331739869590239
skew: 1.62
deg: 5
c5: 1
c0: 11
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 800001)
Primes: RFBsize:216816, AFBsize:216602, largePrimes:6531775 encountered
Relations: rels:6070085, finalFF:530729
Max relations in full relation-set: 28
Initial matrix: 433482 x 530729 with sparse part having weight 30061199.
Pruned matrix : 345492 x 347723 with weight 15473918.
Total sieving time: 18.60 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.83 hours.
Total square root time: 0.16 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 20.74 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 19, 2007

By Robert Backstrom / GMP-ECM 5.0 B1=297500

(8·10¹⁵⁶-17)/9 = (8)₁₅₅7_<156> = 191413 · 294293 · 2247379721_<10> · C136

C136 = P31 · P106

P31 = 5289913621585527848874348853313_<31>

P106 = 1327306059679471772390175491604367168135356343238374722780556040926974678339394316436973392646103133527191_<106>

6·10¹⁵⁷+1 = 6(0)₁₅₆1_<158> = 83 · 151 · 72179234791_<11> · C143

C143 = P62 · P81

P62 = 72357737078330308558694680661590216271249223389638162975859539_<62>

P81 = 916640329258611436341178406620060063987449880780814068401233780150914565592579353_<81>

Number: n
N=66326019939888731124137750913895090055834491742411539232321131200926135913206081132490874613518312074140366269836829752912617349628935239498267
  ( 143 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=72357737078330308558694680661590216271249223389638162975859539 (pp62)
 r2=916640329258611436341178406620060063987449880780814068401233780150914565592579353 (pp81)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 34.58 hours.
Scaled time: 41.32 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_6_0_156_1
n: 66326019939888731124137750913895090055834491742411539232321131200926135913206081132490874613518312074140366269836829752912617349628935239498267
type: snfs
skew: 0.28
deg: 5
c5: 600
c0: 1
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:216816, AFBsize:216936, largePrimes:6418969 encountered
Relations: rels:5891747, finalFF:502734
Max relations in full relation-set: 28
Initial matrix: 433818 x 502734 with sparse part having weight 28026248.
Pruned matrix : 370197 x 372430 with weight 16844017.
Total sieving time: 31.66 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 2.62 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 34.58 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Apr 18, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(4·10¹⁵⁷-7)/3 = 1(3)₁₅₆1_<158> = 11² · 829048691 · C147

C147 = P43 · P51 · P54

P43 = 1298908648477793769569563217697406042467797_<43>

P51 = 227836378491183675155418024092575662345597837669647_<51>

P54 = 449129571882613139545490492415647300223051508767591019_<54>

Number: n
N=132914795791607779393998246218504139069715027270851061093644960498598981368472560242293430048107688956563142563482955158125504335329938049244764521
  ( 147 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=1298908648477793769569563217697406042467797 (pp43)
 r2=227836378491183675155418024092575662345597837669647 (pp51)
 r3=449129571882613139545490492415647300223051508767591019 (pp54)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.19 hours.
Scaled time: 34.65 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_1_3_156_1
n: 132914795791607779393998246218504139069715027270851061093644960498598981368472560242293430048107688956563142563482955158125504335329938049244764521
skew: 0.89
deg: 5
c5: 25
c0: -14
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:216816, AFBsize:216976, largePrimes:6729179 encountered
Relations: rels:6208493, finalFF:500339
Max relations in full relation-set: 48
Initial matrix: 433856 x 500339 with sparse part having weight 32743641.
Pruned matrix : 376565 x 378798 with weight 19065606.
Total sieving time: 22.56 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.26 hours.
Total square root time: 0.19 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 26.19 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

2·10¹⁵⁷-1 = 1(9)₁₅₇_<158> = 29 · 121465463101_<12> · C145

C145 = P36 · P46 · P63

P36 = 904379301033768345717044160825785309_<36>

P46 = 6457091006561228200494377454089107772956770149_<46>

P63 = 972280702625490682212362702573778085813248187465970804365743191_<63>

Number: n
N=5677788194330897959207179477750316482872150625851073181155520400292142060208311316770349874503902856555645676417079579230816761535189098741201831
  ( 145 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=904379301033768345717044160825785309 (pp36)
 r2=6457091006561228200494377454089107772956770149 (pp46)
 r3=972280702625490682212362702573778085813248187465970804365743191 (pp63)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 25.26 hours.
Scaled time: 36.63 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_1_9_157
n: 5677788194330897959207179477750316482872150625851073181155520400292142060208311316770349874503902856555645676417079579230816761535189098741201831
skew: 0.35
deg: 5
c5: 200
c0: -1
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:216816, AFBsize:216391, largePrimes:6772954 encountered
Relations: rels:6243826, finalFF:486214
Max relations in full relation-set: 28
Initial matrix: 433272 x 486214 with sparse part having weight 30147915.
Pruned matrix : 387238 x 389468 with weight 19941665.
Total sieving time: 21.50 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.35 hours.
Total square root time: 0.23 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 25.26 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(34·10¹⁵⁷-43)/9 = 3(7)₁₅₆3_<158> = 3² · 11 · 19 · 199194337 · C147

C147 = P42 · P43 · P62

P42 = 173250819925329757405611840037528690186427_<42>

P43 = 9035055010084847015301845327796377263688437_<43>

P62 = 64411664896149439159157921804791266771402346028235778213017491_<62>

Number: n
N=100825555763678864123952879910449161112867780638776593433396049472041667630761409311563611469958002535998500901578741834425443631381346614299281109
  ( 147 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=173250819925329757405611840037528690186427 (pp42)
 r2=9035055010084847015301845327796377263688437 (pp43)
 r3=64411664896149439159157921804791266771402346028235778213017491 (pp62)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 36.63 hours.
Scaled time: 50.00 units (timescale=1.365).
Factorization parameters were as follows:
name: KA_3_7_156_3
n: 100825555763678864123952879910449161112867780638776593433396049472041667630761409311563611469958002535998500901578741834425443631381346614299281109
skew: 0.42
deg: 5
c5: 3400
c0: -43
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:216816, AFBsize:216666, largePrimes:7082322 encountered
Relations: rels:6565724, finalFF:496808
Max relations in full relation-set: 28
Initial matrix: 433549 x 496808 with sparse part having weight 35449720.
Pruned matrix : 382013 x 384244 with weight 23549409.
Total sieving time: 32.88 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.07 hours.
Total square root time: 0.46 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 36.63 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 17, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(67·10¹⁵⁷+23)/9 = 7(4)₁₅₆7_<158> = 7 · 11 · 127 · 6967 · C151

C151 = P63 · P88

P63 = 196947610222755818047239895555064844541747218059447880546494957_<63>

P88 = 5548062197786922108597350799550470655831242112272889027561109789284452833290497739281647_<88>

Number: n
N=1092677591221344731989402195062399694133774596337703177710456117434346634094828337879663080921205556013746255934117947275589207350751367595680888154179
  ( 151 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=196947610222755818047239895555064844541747218059447880546494957 (pp63)
 r2=5548062197786922108597350799550470655831242112272889027561109789284452833290497739281647 (pp88)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 45.06 hours.
Scaled time: 53.85 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_7_4_156_7
n: 1092677591221344731989402195062399694133774596337703177710456117434346634094828337879663080921205556013746255934117947275589207350751367595680888154179
type: snfs
skew: 0.32
deg: 5
c5: 6700
c0: 23
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1800001)
Primes: RFBsize:216816, AFBsize:217156, largePrimes:6920532 encountered
Relations: rels:6425312, finalFF:546121
Max relations in full relation-set: 28
Initial matrix: 434039 x 546121 with sparse part having weight 33794146.
Pruned matrix : 340986 x 343220 with weight 19013316.
Total sieving time: 41.78 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 2.93 hours.
Total square root time: 0.10 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 45.06 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Apr 17, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=5000000

(16·10²³⁵-61)/9 = 1(7)₂₃₄1_<236> = 11 · 29 · 37037719357719760261079_<23> · 386429589610739568586536276533_<30> · 713567298076051856522358950335091_<33> · C148

C148 = P39 · C110

P39 = 151909019354249419571440528481694434053_<39>

C110 = [35921435276159625817527432090229298251807652677226377310650377800268125022879271309502187214950639477080494969_<110>]

Apr 17, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GMP-ECM 5.0

4·10¹⁵⁷+1 = 4(0)₁₅₆1_<158> = 1321757 · C152

C152 = P65 · P87

P65 = 46712194341161070054665870112933244096080435997557581817007450649_<65>

P87 = 647855429982898406721265781990638069224565341233236221727068040304877394852504476748157_<87>

Number: n
N=30262748750337618790745954059634259549977794708104439772212290156208743362055203793132928367317139232097881834558091994216788713810481049088448179203893
  ( 152 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=46712194341161070054665870112933244096080435997557581817007450649 (pp65)
 r2=647855429982898406721265781990638069224565341233236221727068040304877394852504476748157 (pp87)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 28.48 hours.
Scaled time: 37.71 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_4_0_156_1
n: 30262748750337618790745954059634259549977794708104439772212290156208743362055203793132928367317139232097881834558091994216788713810481049088448179203893
skew: 0.60
deg: 5
c5: 25
c0: 2
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:216816, AFBsize:216361, largePrimes:6961579 encountered
Relations: rels:6487180, finalFF:542616
Max relations in full relation-set: 48
Initial matrix: 433241 x 542616 with sparse part having weight 39514323.
Pruned matrix : 341666 x 343896 with weight 20499298.
Total sieving time: 25.18 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.92 hours.
Total square root time: 0.19 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 28.48 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(25·10¹⁵⁷-7)/9 = 2(7)₁₅₇_<158> = 3 · 10521845651_<11> · C147

C147 = P31 · P39 · P79

P31 = 4362956850742075039517980258627_<31>

P39 = 100040644971784701090248442620273077603_<39>

P79 = 2016168926089972285768717434483905209452257464658912852672219715284978714326289_<79>

(22·10¹⁵⁷-1)/3 = 7(3)₁₅₇_<158> = 19 · 673 · 10321 · C150

C150 = P42 · P109

P42 = 115927686658862052161466450041710948154663_<42>

P109 = 4793180825233510269061418780918265393286504290775973495713741172906980788176434671437734774907012714375415233_<109>

Number: n
N=555662364806936210043869518444127395285863041941640292215664555985699685541322525073954809005319888749019410627569595884012866604527954705515730181479
  ( 150 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=115927686658862052161466450041710948154663 (pp42)
 r2=4793180825233510269061418780918265393286504290775973495713741172906980788176434671437734774907012714375415233 (pp109)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.30 hours.
Scaled time: 38.12 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_7_3_157
n: 555662364806936210043869518444127395285863041941640292215664555985699685541322525073954809005319888749019410627569595884012866604527954705515730181479
skew: 0.43
deg: 5
c5: 275
c0: -4
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:216816, AFBsize:216402, largePrimes:6807486 encountered
Relations: rels:6293241, finalFF:497347
Max relations in full relation-set: 28
Initial matrix: 433285 x 497347 with sparse part having weight 31188309.
Pruned matrix : 378686 x 380916 with weight 19580498.
Total sieving time: 22.84 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.22 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 26.30 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Apr 16, 2007 (4th)

By Wataru Sakai / GMP-ECM 6.1.2 B1=11000000

9·10¹⁸²+1 = 9(0)₁₈₁1_<183> = 96497 · C178

C178 = P37 · C142

P37 = 6693857016013088704017026959632722629_<37>

C142 = [1393324476133628308508018984618709804986257885467422408615899381022222419474636732587515795416876689048777120508243524120001407382238214675677_<142>]

Apr 16, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp

9·10¹⁵⁷+1 = 9(0)₁₅₆1_<158> = 7 · 13 · C156

C156 = P46 · P111

P46 = 2130403278394440947268336034474352786160213379_<46>

P111 = 464236512889873201316103265893901452919829671364175589843047024998926643175420109046920841497010559322144023409_<111>

Number: n
N=989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989011
  ( 156 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=2130403278394440947268336034474352786160213379 (pp46)
 r2=464236512889873201316103265893901452919829671364175589843047024998926643175420109046920841497010559322144023409 (pp111)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 28.69 hours.
Scaled time: 39.18 units (timescale=1.366).
Factorization parameters were as follows:
name: KA_9_0_156_1
n: 989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989011
skew: 0.26
deg: 5
c5: 900
c0: 1
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:216816, AFBsize:215581, largePrimes:6978011 encountered
Relations: rels:6516913, finalFF:544066
Max relations in full relation-set: 28
Initial matrix: 432461 x 544066 with sparse part having weight 35226913.
Pruned matrix : 337254 x 339480 with weight 19166632.
Total sieving time: 25.92 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 2.07 hours.
Total square root time: 0.45 hours, sqrts: 5.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 28.69 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 16, 2007 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

(71·10¹⁷⁶-17)/9 = 7(8)₁₇₅7_<177> = C177

C177 = P38 · P40 · P101

P38 = 12444683223615891402820327212798136433_<38>

P40 = 3674375738140870081368352967131977691087_<40>

P101 = 17252356679429901956285793702431420438333359105122269293068907650150673519737446668316923181906393897_<101>

Number: 78887_176
N=788888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887
  ( 177 digits)
SNFS difficulty: 177 digits.
Divisors found:
 r1=12444683223615891402820327212798136433 (pp38)
 r2=3674375738140870081368352967131977691087 (pp40)
 r3=17252356679429901956285793702431420438333359105122269293068907650150673519737446668316923181906393897 (pp101)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 853.40 hours.
Scaled time: 520.57 units (timescale=0.610).
Factorization parameters were as follows:
name: 78887_176
n: 788888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887
m: 100000000000000000000000000000000000
c5: 710
c0: -17
skew: 4
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 21600001
)
Primes: RFBsize:501962, AFBsize:500612, largePrimes:7104377 encountered
Relations: rels:7627236, finalFF:1123512
Max relations in full relation-set: 0
Initial matrix: 1002641 x 1123512 with sparse part having weight 126171183.
Pruned matrix : 914469 x 919546 with weight 104654058.
Total sieving time: 754.46 hours.
Total relation processing time: 2.84 hours.
Matrix solve time: 95.54 hours.
Time per square root: 0.56 hours.
Prototype def-par.txt line would be:
snfs,177,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 853.40 hours.
 --------- CPU info (if available) ----------

Apr 16, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GMP-ECM 5.0

5·10¹⁵⁷-1 = 4(9)₁₅₇_<158> = 7 · 1784911 · 8397428359_<10> · C141

C141 = P54 · P88

P54 = 154950203473026832889059234829083441818646269399640511_<54>

P88 = 3075508559189988737150043030934655780723081191090507472552844326729132490697996382741663_<88>

Number: n
N=476550677029524343665946953895574025260049383895835025193583187834239548403156077893198662913632520004443527829226385778591426880376782309793
  ( 141 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=154950203473026832889059234829083441818646269399640511 (pp54)
 r2=3075508559189988737150043030934655780723081191090507472552844326729132490697996382741663 (pp88)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 36.22 hours.
Scaled time: 43.28 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_4_9_157
n: 476550677029524343665946953895574025260049383895835025193583187834239548403156077893198662913632520004443527829226385778591426880376782309793
type: snfs
skew: 1.44
deg: 5
c5: 4
c0: -25
m: 50000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:216816, AFBsize:216391, largePrimes:6478765 encountered
Relations: rels:5936078, finalFF:494034
Max relations in full relation-set: 28
Initial matrix: 433271 x 494034 with sparse part having weight 27845713.
Pruned matrix : 377954 x 380184 with weight 17470532.
Total sieving time: 33.06 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 2.86 hours.
Total square root time: 0.09 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 36.22 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

8·10¹⁵⁷-3 = 7(9)₁₅₆7_<158> = 7 · 11 · 17 · C155

C155 = P33 · P45 · P78

P33 = 483761069946232439153779120078097_<33>

P45 = 436213016886190495057964600551787363398983829_<45>

P78 = 289614834453526840832030464582741641059169146938996316648050252271982757768141_<78>

Number: n
N=126333760671967568596793372125212909881306461592993045537085173685497608635758283948439567406499845534841917918495390391889
  ( 123 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=436213016886190495057964600551787363398983829 (pp45)
 r2=289614834453526840832030464582741641059169146938996316648050252271982757768141 (pp78)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 21.82 hours.
Scaled time: 31.43 units (timescale=1.440).
Factorization parameters were as follows:
name: KA_7_9_156_7

# n: 61115355233002291825821237585943468296409472880061115355233002291825821237585943468296409472880061115355233002291825821237585943468296409472880061115355233

n: 126333760671967568596793372125212909881306461592993045537085173685497608635758283948439567406499845534841917918495390391889
skew: 0.65
deg: 5
c5: 25
c0: -3
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1000001)
Primes: RFBsize:216816, AFBsize:216986, largePrimes:6644013 encountered
Relations: rels:6128099, finalFF:494219
Max relations in full relation-set: 28
Initial matrix: 433866 x 494219 with sparse part having weight 28895318.
Pruned matrix : 378977 x 381210 with weight 17891718.
Total sieving time: 18.85 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 2.72 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 21.82 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Apr 15, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(4·10¹⁵⁷+41)/9 = (4)₁₅₆9_<157> = 3 · 17 · 1777 · 2051898841117_<13> · C140

C140 = P69 · P71

P69 = 260221357440021455388738938889122776721896955085397138037228688252251_<69>

P71 = 91846157923309577470616859933689268561584874926674871536459883391952261_<71>

Number: n
N=23900331890454200261779183585229763492153402399157688484259917920736681255730620727738466525300767323925829369751318965287932481166917789511
  ( 140 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=260221357440021455388738938889122776721896955085397138037228688252251 (pp69)
 r2=91846157923309577470616859933689268561584874926674871536459883391952261 (pp71)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 30.44 hours.
Scaled time: 44.13 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_4_156_9
n: 23900331890454200261779183585229763492153402399157688484259917920736681255730620727738466525300767323925829369751318965287932481166917789511
skew: 1.27
deg: 5
c5: 25
c0: 82
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:216816, AFBsize:217007, largePrimes:6992395 encountered
Relations: rels:6471718, finalFF:493995
Max relations in full relation-set: 28
Initial matrix: 433887 x 493995 with sparse part having weight 33421745.
Pruned matrix : 384649 x 386882 with weight 22052690.
Total sieving time: 26.58 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.55 hours.
Total square root time: 0.13 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 30.44 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(14·10¹⁵⁷-41)/9 = 1(5)₁₅₆1_<158> = 11 · 71 · 41893 · 4009117163_<10> · C141

C141 = P46 · P95

P46 = 1367055426296824724730956100096423270901258669_<46>

P95 = 86747738019244962078804322447103067350502553941506493682108511037049165854640129475050452781201_<95>

Number: n
N=118588965978184191291589169425730928531988106038187106414487352675590392264054198803378536910232046817358432344625794912915634728702561481469
  ( 141 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=1367055426296824724730956100096423270901258669 (pp46)
 r2=86747738019244962078804322447103067350502553941506493682108511037049165854640129475050452781201 (pp95)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 30.51 hours.
Scaled time: 41.55 units (timescale=1.362).
Factorization parameters were as follows:
name: KA_1_5_156_1
n: 118588965978184191291589169425730928531988106038187106414487352675590392264054198803378536910232046817358432344625794912915634728702561481469
skew: 0.49
deg: 5
c5: 1400
c0: -41
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:216816, AFBsize:216347, largePrimes:6833902 encountered
Relations: rels:6305635, finalFF:490090
Max relations in full relation-set: 28
Initial matrix: 433230 x 490090 with sparse part having weight 31304275.
Pruned matrix : 384277 x 386507 with weight 20392536.
Total sieving time: 27.27 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 2.93 hours.
Total square root time: 0.10 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 30.51 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(16·10¹⁵⁷-1)/3 = 5(3)₁₅₇_<158> = 41 · 53 · C155

C155 = P39 · P117

P39 = 129797383107911921189114592848736731761_<39>

P117 = 189091960678640538527657346264288860676014584874491438046542017422669365733841635944493393437125375006515513942447561_<117>

Number: n
N=24543641662831722656849210001533977603926982666053075625095873600245436416628317226568492100015339776039269826660530756250958736002454364166283172265684921
  ( 155 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=129797383107911921189114592848736731761 (pp39)
 r2=189091960678640538527657346264288860676014584874491438046542017422669365733841635944493393437125375006515513942447561 (pp117)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 25.92 hours.
Scaled time: 33.95 units (timescale=1.310).
Factorization parameters were as follows:
name: KA_5_3_157
n: 24543641662831722656849210001533977603926982666053075625095873600245436416628317226568492100015339776039269826660530756250958736002454364166283172265684921
skew: 0.46
deg: 5
c5: 50
c0: -1
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:216816, AFBsize:216926, largePrimes:6830845 encountered
Relations: rels:6343658, finalFF:527782
Max relations in full relation-set: 48
Initial matrix: 433807 x 527782 with sparse part having weight 36099796.
Pruned matrix : 353105 x 355338 with weight 19042809.
Total sieving time: 22.85 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.82 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 25.92 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 14, 2007 (6th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(4·10¹⁵⁶+41)/9 = (4)₁₅₅9_<156> = 35407 · 66888310787_<11> · C141

C141 = P43 · P98

P43 = 2320556509695116444764087997770288474407797_<43>

P98 = 80869726412245288072803531579541476425890112919981517500054469876923320277924027316762711210159313_<98>

Number: n
N=187662770063198897254648711120578344957882722203045389305266787504281116290486371530577287601901816312256753988043095526936254851027699363461
  ( 141 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=2320556509695116444764087997770288474407797 (pp43)
 r2=80869726412245288072803531579541476425890112919981517500054469876923320277924027316762711210159313 (pp98)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 38.23 hours.
Scaled time: 50.65 units (timescale=1.325).
Factorization parameters were as follows:
name: KA_4_155_9
n: 187662770063198897254648711120578344957882722203045389305266787504281116290486371530577287601901816312256753988043095526936254851027699363461
skew: 1.00
deg: 5
c5: 40
c0: 41
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1600001)
Primes: RFBsize:216816, AFBsize:215452, largePrimes:7235441 encountered
Relations: rels:6753303, finalFF:539005
Max relations in full relation-set: 48
Initial matrix: 432334 x 539005 with sparse part having weight 48979549.
Pruned matrix : 350527 x 352752 with weight 27546472.
Total sieving time: 33.84 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 4.08 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 38.23 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 14, 2007 (5th)

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000

4·10¹⁹¹+1 = 4(0)₁₉₀1_<192> = 7 · 19 · 41 · 647 · 46903543 · 4164599914798824246547757_<25> · C153

C153 = P36 · P117

P36 = 765226605021062082766257793518013247_<36>

P117 = 758492370060731172732749892408126693839219951872236949815340112500285954615089467270693873387494136665940937734088263_<117>

Apr 14, 2007 (4th)

By Robert Backstrom / GMP-ECM 5.0 B1=624500, GGNFS-0.77.1-20051202-athlon

(5·10¹⁵⁷+1)/3 = 1(6)₁₅₆7_<158> = 398873142122850667_<18> · C140

C140 = P37 · P104

P37 = 2404393197926639638979396362008033281_<37>

P104 = 17378346996287391689755245493306607889153873952262426287646796171801225403604837211739059462503566941121_<104>

3·10¹⁵⁶-1 = 2(9)₁₅₆_<157> = 23² · 757 · 37958325803_<11> · C140

C141 = P68 · P73

P68 = 34508927160252119290871470429799344288040408510935452205656946628557_<68>

P73 = 5719146168209700929932117892283471025039070385347664045593119483067546173_<73>

Number: n
N=197361598537583584072731037228204834039638876801120022701727429667743993129175140505213658215476850235031414454539015439269856571655277862361
  ( 141 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=34508927160252119290871470429799344288040408510935452205656946628557 (pp68)
 r2=5719146168209700929932117892283471025039070385347664045593119483067546173 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 29.42 hours.
Scaled time: 34.63 units (timescale=1.177).
Factorization parameters were as follows:
name: KA_2_9_156
n: 197361598537583584072731037228204834039638876801120022701727429667743993129175140505213658215476850235031414454539015439269856571655277862361
type: snfs
skew: 0.51
deg: 5
c5: 30
c0: -1
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:216816, AFBsize:215581, largePrimes:6375624 encountered
Relations: rels:5906725, finalFF:544951
Max relations in full relation-set: 28
Initial matrix: 432464 x 544951 with sparse part having weight 28722573.
Pruned matrix : 329414 x 331640 with weight 14402843.
Total sieving time: 27.08 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 1.98 hours.
Total square root time: 0.15 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 29.42 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Apr 14, 2007 (3rd)

By Alfred Reich / GMP-ECM B1=1000000, B1=250000

10¹⁴⁴³+1 = 1(0)₁₄₄₂1_<1444> = 7 · 11 · 13² · 157 · 223 · 859 · 2887 · 4663 · 6397 · 7253 · 158731 · 216451 · 1058313049_<10> · 1961853739_<10> · 78426117823_<11> · 388847808493_<12> · 126294442654927_<15> · 422650073734453_<15> · 1690016281413487_<16> · 296557347313446299_<18> · 5406655992229067083561_<22> · 21606064498691505246200058094681_<32> · 48911689110891303706174193415115219_<35> · C406 · C801

C801 = P32 · C779

P32 = 37344700192938647404842813656089_<32>

10¹⁷⁰⁹+1 = 1(0)₁₇₀₈1_<1710> = 11 · 6157019338133_<13> · C1696

C1696 = P34 · C1662

P34 = 5903378160150749077165810087494863_<34>

10¹⁸⁹²+1 = 1(0)₁₈₉₁1_<1893> = 73 · 137 · 617 · 1207097 · 7265281 · 1110411017_<10> · 277641151780258438310079109077611969_<36> · 2645778409917434965592366282025495569_<37> · 16205834846012967584927082656402106953_<38> · 38993135849791157061060738352944105076217_<41> · 34908493290773859017057784025792153817150916131843303273_<56> · C1659

C1659 = P25 · C1634

P25 = 2565225443270547964001657_<25>

Apr 14, 2007 (2nd)

By Yousuke Koide / GMP-ECM B1=1000000 / Apr 10, 2007

10⁷⁴³+1 = 1(0)₇₄₂1_<744> = 11 · 1487 · 8172691019111011124393086241_<28> · C711

C711 = P37 · C675

P37 = 2750793293893633690646483974559334689_<37>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 14, 2007

By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp

(4·10¹⁵⁶+23)/9 = (4)₁₅₅7_<156> = 3 · 29 · 31 · 233 · 1162061 · C144

C144 = P60 · P84

P60 = 658237800790060433128895853813992111237171477712259462648973_<60>

P84 = 924631893046383441534389809744737352040680519541286830846552261752181915098853210999_<84>

Number: n
N=608627663819201808417041980929346102662496861775520416798486790021398126579659692253604025739413646460016835809359875088363094393568287439654027
  ( 144 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=658237800790060433128895853813992111237171477712259462648973 (pp60)
 r2=924631893046383441534389809744737352040680519541286830846552261752181915098853210999 (pp84)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 33.77 hours.
Scaled time: 46.16 units (timescale=1.367).
Factorization parameters were as follows:
name: KA_4_155_7
n: 608627663819201808417041980929346102662496861775520416798486790021398126579659692253604025739413646460016835809359875088363094393568287439654027
skew: 0.90
deg: 5
c5: 40
c0: 23
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2900001)
Primes: RFBsize:216816, AFBsize:216736, largePrimes:7433946 encountered
Relations: rels:6919180, finalFF:495297
Max relations in full relation-set: 28
Initial matrix: 433618 x 495297 with sparse part having weight 39970576.
Pruned matrix : 400661 x 402893 with weight 28886141.
Total sieving time: 29.38 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.80 hours.
Total square root time: 0.42 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 33.77 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 13, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(5·10¹⁵⁶-41)/9 = (5)₁₅₅1_<156> = 31 · 97 · 2749 · 24137 · C145

C145 = P46 · P47 · P54

P46 = 1600207301265369924631020682960816113990739459_<46>

P47 = 16568556547968489324062487443384412430491937807_<47>

P54 = 105020749778702090985515156596077622754794211159073697_<54>

Number: n
N=2784428283225929846214187821651575527617305853520025468536849587506685784217150177340144999173317301288623436378801171185958744655260831867158861
  ( 145 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=1600207301265369924631020682960816113990739459 (pp46)
 r2=16568556547968489324062487443384412430491937807 (pp47)
 r3=105020749778702090985515156596077622754794211159073697 (pp54)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 34.15 hours.
Scaled time: 40.63 units (timescale=1.190).
Factorization parameters were as follows:
name: KA_5_155_1
n: 2784428283225929846214187821651575527617305853520025468536849587506685784217150177340144999173317301288623436378801171185958744655260831867158861
type: snfs
skew: 0.96
deg: 5
c5: 50
c0: -41
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1500000)
Primes: RFBsize:216816, AFBsize:217342, largePrimes:6380461 encountered
Relations: rels:5851563, finalFF:499097
Max relations in full relation-set: 28
Initial matrix: 434223 x 499097 with sparse part having weight 26951928.
Pruned matrix : 373558 x 375793 with weight 16358185.
Total sieving time: 30.79 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 2.65 hours.
Total square root time: 0.49 hours, sqrts: 6.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 34.15 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(52·10¹⁵⁶-7)/9 = 5(7)₁₅₆_<157> = 219147336769_<12> · C146

C146 = P47 · P99

P47 = 43392867949703635301629857402687959159726060863_<47>

P99 = 607583935024911523260847922586741220802757668680390878600315487487290409913946585708438696721115791_<99>

Number: n
N=26364809460897299259653125087975172032777393582242597341147785718166934780842624212004109229722134427960631940677808720415122325641908370536387633
  ( 146 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=43392867949703635301629857402687959159726060863 (pp47)
 r2=607583935024911523260847922586741220802757668680390878600315487487290409913946585708438696721115791 (pp99)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 36.15 hours.
Scaled time: 47.79 units (timescale=1.322).
Factorization parameters were as follows:
name: KA_5_7_156
n: 26364809460897299259653125087975172032777393582242597341147785718166934780842624212004109229722134427960631940677808720415122325641908370536387633
skew: 0.84
deg: 5
c5: 65
c0: -28
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:216816, AFBsize:217161, largePrimes:7027687 encountered
Relations: rels:6501938, finalFF:500738
Max relations in full relation-set: 48
Initial matrix: 434044 x 500738 with sparse part having weight 41292245.
Pruned matrix : 382040 x 384274 with weight 25445788.
Total sieving time: 31.64 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 4.23 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 36.15 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(2·10¹⁵⁶-17)/3 = (6)₁₅₅1_<156> = 582040501417_<12> · C145

C145 = P57 · P88

P57 = 262422346638094064709676275686532663519430097478059007977_<57>

P88 = 4364703230483737983340490207355193123826831844937412896837700663993603235377768373454229_<88>

Number: n
N=1145395664122412462028343745791750881390136369783276989631757880007432044155235692531185871687582370102016007875929567627122973983826576555384733
  ( 145 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=262422346638094064709676275686532663519430097478059007977 (pp57)
 r2=4364703230483737983340490207355193123826831844937412896837700663993603235377768373454229 (pp88)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 28.89 hours.
Scaled time: 41.65 units (timescale=1.442).
Factorization parameters were as follows:
name: KA_6_155_1
n: 1145395664122412462028343745791750881390136369783276989631757880007432044155235692531185871687582370102016007875929567627122973983826576555384733
skew: 0.97
deg: 5
c5: 20
c0: -17
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:216816, AFBsize:216481, largePrimes:7006733 encountered
Relations: rels:6508602, finalFF:508486
Max relations in full relation-set: 28
Initial matrix: 433363 x 508486 with sparse part having weight 34854295.
Pruned matrix : 370976 x 373206 with weight 21764226.
Total sieving time: 25.33 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.31 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 28.89 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Apr 12, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp

(43·10¹⁵⁶-7)/9 = 4(7)₁₅₆_<157> = 86036339801_<11> · C146

C146 = P38 · P109

P38 = 19163362490036635820158997010258849551_<38>

P109 = 2897826003981773784334186754550525299012182064741398699239307009312692916090017208342332671221035127546930327_<109>

Number: n
N=55532090147357078614709045295335410496884507949289740354906265287483458384991574448553960954638656267233942947332864511635639261192072916572233177
  ( 146 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=19163362490036635820158997010258849551 (pp38)
 r2=2897826003981773784334186754550525299012182064741398699239307009312692916090017208342332671221035127546930327 (pp109)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 29.34 hours.
Scaled time: 42.51 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_4_7_156
n: 55532090147357078614709045295335410496884507949289740354906265287483458384991574448553960954638656267233942947332864511635639261192072916572233177
skew: 0.44
deg: 5
c5: 430
c0: -7
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:216816, AFBsize:216651, largePrimes:6922881 encountered
Relations: rels:6392211, finalFF:486337
Max relations in full relation-set: 28
Initial matrix: 433534 x 486337 with sparse part having weight 33091584.
Pruned matrix : 388899 x 391130 with weight 22447641.
Total sieving time: 25.47 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 3.53 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 29.34 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(31·10¹⁵⁶-13)/9 = 3(4)₁₅₅3_<157> = 4253 · 3873379 · C147

C147 = P47 · P101

P47 = 11446246509035109137458172315152085129446188827_<47>

P101 = 18267146564210168096334403162624796291792049909993727669100813582789777576039312403346776495047622407_<101>

Number: n
N=209090262590623324674662272817826497803277807296152930210058551570312356683432041453306992533523096953980424674313366594580396798468355453918246589
  ( 147 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=11446246509035109137458172315152085129446188827 (pp47)
 r2=18267146564210168096334403162624796291792049909993727669100813582789777576039312403346776495047622407 (pp101)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 38.38 hours.
Scaled time: 52.43 units (timescale=1.366).
Factorization parameters were as follows:
name: KA_3_4_155_3
n: 209090262590623324674662272817826497803277807296152930210058551570312356683432041453306992533523096953980424674313366594580396798468355453918246589
skew: 0.53
deg: 5
c5: 310
c0: -13
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 1300001)
Primes: RFBsize:216816, AFBsize:216917, largePrimes:7085921 encountered
Relations: rels:6631140, finalFF:560970
Max relations in full relation-set: 48
Initial matrix: 433800 x 560970 with sparse part having weight 45010433.
Pruned matrix : 328753 x 330986 with weight 22946855.
Total sieving time: 35.71 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 2.22 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 38.38 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 11, 2007 (4th)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

(4·10¹⁵⁸+41)/9 = (4)₁₅₇9_<158> = 7 · C157

C157 = P33 · P124

P33 = 707520375170029031923901699222657_<33>

P124 = 8973884812406325767083604587285833707833311930101241764893886063877897082565108219201301770248476197905635918804130248304151_<124>

Number: 44449_158
N=6349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349207
  ( 157 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=707520375170029031923901699222657 (pp33)
 r2=8973884812406325767083604587285833707833311930101241764893886063877897082565108219201301770248476197905635918804130248304151 (pp124)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 71.54 hours.
Scaled time: 48.29 units (timescale=0.675).
Factorization parameters were as follows:
name: 44449_158
n: 6349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349207
m: 20000000000000000000000000000000
c5: 125
c0: 41
skew: 1
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:283743, largePrimes:5731791 encountered
Relations: rels:5827031, finalFF:640293
Max relations in full relation-set: 0
Initial matrix: 566954 x 640293 with sparse part having weight 33663472.
Pruned matrix : 507252 x 510150 with weight 25148829.
Total sieving time: 61.49 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 9.35 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 71.54 hours.
 --------- CPU info (if available) ----------

Apr 11, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(4·10¹⁵⁶-13)/9 = (4)₁₅₅3_<156> = 467 · 907 · 4013 · C147

C147 = P71 · P76

P71 = 64377798252552010796638898829797497824812459415960828753897946965206549_<71>

P76 = 4061514751851283812525668056120841387861479610200189702623134793785876634331_<76>

Number: n
N=261471377294445792783700915361605809384343473963181914540349510658242476460029162453106898744077559972780706732100864581694126371426615288359433719
  ( 147 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=64377798252552010796638898829797497824812459415960828753897946965206549 (pp71)
 r2=4061514751851283812525668056120841387861479610200189702623134793785876634331 (pp76)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 28.69 hours.
Scaled time: 37.95 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_4_155_3
n: 261471377294445792783700915361605809384343473963181914540349510658242476460029162453106898744077559972780706732100864581694126371426615288359433719
skew: 0.80
deg: 5
c5: 40
c0: -13
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:216816, AFBsize:216811, largePrimes:7010544 encountered
Relations: rels:6558496, finalFF:561592
Max relations in full relation-set: 48
Initial matrix: 433693 x 561592 with sparse part having weight 41536616.
Pruned matrix : 326842 x 329074 with weight 20810724.
Total sieving time: 25.66 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 2.76 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 28.69 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(89·10¹⁵⁶+1)/9 = 9(8)₁₅₅9_<157> = 23 · 173 · 3395911 · C147

C147 = P59 · P89

P59 = 35190907398243504644236934773128038169516636457174728867557_<59>

P89 = 20796334442362108455107590366458381110422317923673323714312825264926001029408728804836633_<89>

Number: n
N=731841879584066931047543751234400010997014602921761226349534798267800406145405129532579566785063134021457398220721966959322822974289311948478815581
  ( 147 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=35190907398243504644236934773128038169516636457174728867557 (pp59)
 r2=20796334442362108455107590366458381110422317923673323714312825264926001029408728804836633 (pp89)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.30 hours.
Scaled time: 42.22 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_9_8_155_9
n: 731841879584066931047543751234400010997014602921761226349534798267800406145405129532579566785063134021457398220721966959322822974289311948478815581
type: snfs
skew: 0.26
deg: 5
c5: 890
c0: 1
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:216816, AFBsize:217061, largePrimes:6420765 encountered
Relations: rels:5891265, finalFF:498686
Max relations in full relation-set: 28
Initial matrix: 433944 x 498686 with sparse part having weight 28275743.
Pruned matrix : 373550 x 375783 with weight 17348083.
Total sieving time: 32.31 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 2.69 hours.
Total square root time: 0.09 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 35.30 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Apr 11, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 gnfs

3·10¹⁶²+1 = 3(0)₁₆₁1_<163> = 7130941393003213_<16> · 103809697153908617469853075665675511_<36> · C112

C112 = P43 · P70

P43 = 3853176322382181446159610642291595255342267_<43>

P70 = 1051762253929606176068974362696177686302006839768383025664246236931321_<70>

Number: 30001_162
N=4052625413616873991636843572634283505999285953539026570840954837694883840351540445126100833603885531257627444707
  ( 112 digits)
Divisors found:
 r1=3853176322382181446159610642291595255342267 (pp43)
 r2=1051762253929606176068974362696177686302006839768383025664246236931321 (pp70)
Version: GGNFS-0.77.1-20050930-k8
Total time: 22.19 hours.
Scaled time: 20.06 units (timescale=0.904).
Factorization parameters were as follows:
name: 30001_162
n: 4052625413616873991636843572634283505999285953539026570840954837694883840351540445126100833603885531257627444707
skew: 24998.54
# norm 8.26e+14
c5: 30720
c4: 13614228
c3: -60084665928514
c2: -116456741736186697
c1: 23483511012036749253564
c0: 202273762000039556636441520
# alpha -4.74
Y1: 33561962467
Y0: -2654990979919421104393
# Murphy_E 7.76e-10
# M 2153405058310236367653909476962872255556716105115408821461399974313824697223037807778680206665493728900569170632
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1400000, 2310001)
Primes: RFBsize:203362, AFBsize:203526, largePrimes:7619804 encountered
Relations: rels:7521013, finalFF:564629
Max relations in full relation-set: 28
Initial matrix: 406962 x 564629 with sparse part having weight 52440036.
Pruned matrix : 295985 x 298083 with weight 30474900.
Total sieving time: 21.10 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.81 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000
total time: 22.19 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335815)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239)
Total of 2 processors activated (9340.10 BogoMIPS).

Apr 11, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

10¹⁵⁶-3 = (9)₁₅₅7_<156> = 47 · 193 · 123229 · C147

C147 = P39 · P45 · P65

P39 = 216167489536594248535065060052412135027_<39>

P45 = 272299045624505473727969700938204637516311713_<45>

P65 = 15198313925884879986745118948436722105397649149262271143998265333_<65>

Number: n
N=894606210623443562437370687971114782906997814554858187251616555435460536420072344317247852347721206591645711492794592431809126919097277671344041583
  ( 147 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=216167489536594248535065060052412135027 (pp39)
 r2=272299045624505473727969700938204637516311713 (pp45)
 r3=15198313925884879986745118948436722105397649149262271143998265333 (pp65)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 25.97 hours.
Scaled time: 37.69 units (timescale=1.451).
Factorization parameters were as follows:
name: KA_9_155_7
n: 894606210623443562437370687971114782906997814554858187251616555435460536420072344317247852347721206591645711492794592431809126919097277671344041583
skew: 0.78
deg: 5
c5: 10
c0: -3
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:216816, AFBsize:216741, largePrimes:6968935 encountered
Relations: rels:6496067, finalFF:534842
Max relations in full relation-set: 28
Initial matrix: 433623 x 534842 with sparse part having weight 36166595.
Pruned matrix : 346951 x 349183 with weight 20208618.
Total sieving time: 22.49 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 2.90 hours.
Total square root time: 0.41 hours, sqrts: 7.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 25.97 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Apr 10, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(28·10¹⁵⁶+17)/9 = 3(1)₁₅₅3_<157> = 569 · 49207 · C150

C150 = P51 · P99

P51 = 258041949489809142594628345727012558270007587714629_<51>

P99 = 430611925331515945278355234075202645116773258228763345695469212454697948997089854505386842086459659_<99>

Number: n
N=111115940686104503581856079641429811828289504979952561192074352342782581339735770340843425627146405295941295416701187016275354222042833472837412651511
  ( 150 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=258041949489809142594628345727012558270007587714629 (pp51)
 r2=430611925331515945278355234075202645116773258228763345695469212454697948997089854505386842086459659 (pp99)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 44.65 hours.
Scaled time: 18.48 units (timescale=0.414).
Factorization parameters were as follows:
name: KA_3_1_155_3
n: 111115940686104503581856079641429811828289504979952561192074352342782581339735770340843425627146405295941295416701187016275354222042833472837412651511
skew: 1.14
deg: 5
c5: 35
c0: 68
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:216816, AFBsize:216351, largePrimes:6885946 encountered
Relations: rels:6345666, finalFF:487688
Max relations in full relation-set: 48
Initial matrix: 433234 x 487688 with sparse part having weight 35977625.
Pruned matrix : 388722 x 390952 with weight 23183672.
Total sieving time: 37.04 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 6.68 hours.
Total square root time: 0.55 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 44.65 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 2100+ stepping 02
Memory: 904260k/917504k available (1815k kernel code, 12496k reserved, 846k data, 272k init, 0k highmem)
Calibrating delay loop... 3440.64 BogoMIPS

Apr 10, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

7·10¹⁴⁹+1 = 7(0)₁₄₈1_<150> = 353 · 4957 · 2883242209_<10> · C135

C135 = P41 · P94

P41 = 27592287833712963754580710491390334851359_<41>

P94 = 5028466680407615659824747536024164572850397380074196151582478698822339725661178413486182331051_<94>

Number: 70001_149
N=138746900008042067535370063618473556687052409299714471241482567692765626546602017744157274419812068105656310602659059177232164215248309
  ( 135 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=27592287833712963754580710491390334851359 (pp41)
 r2=5028466680407615659824747536024164572850397380074196151582478698822339725661178413486182331051 (pp94)
Version: GGNFS-0.77.1-20050930-k8
Total time: 18.01 hours.
Scaled time: 16.32 units (timescale=0.906).
Factorization parameters were as follows:
n: 138746900008042067535370063618473556687052409299714471241482567692765626546602017744157274419812068105656310602659059177232164215248309
m: 1000000000000000000000000000000
c5: 7
c0: 10
skew: 1.07
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176463, largePrimes:5488427 encountered
Relations: rels:5366494, finalFF:447917
Max relations in full relation-set: 28
Initial matrix: 352830 x 447917 with sparse part having weight 39079032.
Pruned matrix : 310526 x 312354 with weight 23800589.
Total sieving time: 17.11 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.77 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 18.01 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.64 BogoMIPS (lpj=2335820)
Calibrating delay using timer specific routine.. 4668.46 BogoMIPS (lpj=2334232)
Total of 2 processors activated (9340.10 BogoMIPS).

Apr 10, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

7·10¹⁵⁰+1 = 7(0)₁₄₉1_<151> = 12583 · 7011677 · 48703953167_<11> · C130

C130 = P57 · P73

P57 = 565102429506584132764175102442628047540137331998418471757_<57>

P73 = 2882707341673302681845839339823884543514446084956768454184275090583469569_<73>

Number: n
N=1629024922336050068657788659269692317382596619897579011120619204318148940361751514344610856083178940847911436720610767527695462733
  ( 130 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=565102429506584132764175102442628047540137331998418471757 (pp57)
 r2=2882707341673302681845839339823884543514446084956768454184275090583469569 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 15.03 hours.
Scaled time: 21.67 units (timescale=1.442).
Factorization parameters were as follows:
name: KA_7_0_149_1
n: 1629024922336050068657788659269692317382596619897579011120619204318148940361751514344610856083178940847911436720610767527695462733
skew: 0.68
deg: 5
c5: 7
c0: 1
m: 1000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 700001)
Primes: RFBsize:216816, AFBsize:216696, largePrimes:6671835 encountered
Relations: rels:6397715, finalFF:678424
Max relations in full relation-set: 28
Initial matrix: 433579 x 678424 with sparse part having weight 37818009.
Pruned matrix : 218215 x 220446 with weight 16835240.
Total sieving time: 13.48 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.35 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 15.03 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

7·10¹⁴⁸+1 = 7(0)₁₄₇1_<149> = 3684925389750999011_<19> · C131

C131 = P47 · P84

P47 = 22029725720760974922384230516355618304117854041_<47>

P84 = 862303702875318574684178933529694530368164638218030948135135277879348224342523674051_<84>

Number: n
N=18996314062339835051280977654167871538038033379285440954628687044055360698019796646292113856477734419790670423046806412629077190091
  ( 131 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=22029725720760974922384230516355618304117854041 (pp47)
 r2=862303702875318574684178933529694530368164638218030948135135277879348224342523674051 (pp84)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 23.53 hours.
Scaled time: 27.62 units (timescale=1.174).
Factorization parameters were as follows:
name: KA_7_0_147_1
n: 18996314062339835051280977654167871538038033379285440954628687044055360698019796646292113856477734419790670423046806412629077190091
type: snfs
skew: 1.7
deg: 5
c5: 7
c0: 100
m: 1000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1000000)
Primes: RFBsize:216816, AFBsize:216861, largePrimes:6027370 encountered
Relations: rels:5537118, finalFF:521472
Max relations in full relation-set: 28
Initial matrix: 433744 x 521472 with sparse part having weight 22021191.
Pruned matrix : 345863 x 348095 with weight 11418721.
Total sieving time: 21.50 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.71 hours.
Total square root time: 0.13 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 23.53 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(71·10¹⁵⁶-17)/9 = 7(8)₁₅₅7_<157> = 3 · 599 · 12277 · C150

C150 = P29 · P53 · P69

P29 = 31099767261536178071546920819_<29>

P53 = 36223816354507886781000373247374248840998059419011231_<53>

P69 = 317412601069020689414883025797217762217539557105881695471292639044507_<69>

Number: n
N=357581882436031711187298212073967816854980617777699009036351023750130322227963174162910004582537732531280192848039016675810941946173440982402131437823
  ( 150 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=31099767261536178071546920819 (pp29)
 r2=36223816354507886781000373247374248840998059419011231 (pp53)
 r3=317412601069020689414883025797217762217539557105881695471292639044507 (pp69)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 41.42 hours.
Scaled time: 54.67 units (timescale=1.320).
Factorization parameters were as follows:
name: KA_7_8_155_7
n: 357581882436031711187298212073967816854980617777699009036351023750130322227963174162910004582537732531280192848039016675810941946173440982402131437823
skew: 0.47
deg: 5
c5: 710
c0: -17
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:216816, AFBsize:216537, largePrimes:7225880 encountered
Relations: rels:6720908, finalFF:521001
Max relations in full relation-set: 48
Initial matrix: 433420 x 521001 with sparse part having weight 48206832.
Pruned matrix : 366512 x 368743 with weight 28578075.
Total sieving time: 36.36 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 4.66 hours.
Total square root time: 0.17 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 41.42 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 9, 2007 (2nd)

By Alfred Reich / GMP-ECM B1=250000

10¹⁸³⁷+1 = 1(0)₁₈₃₆1_<1838> = 11² · 23 · 4093 · 8779 · 18371 · 84503 · 15849637 · 63716179 · 76272241 · 79402489 · 1657278943_<10> · 116011189311149998139_<21> · 272828068791212993437_<21> · 301525294918950432087520298129941558711551656822567015411_<57> · 14950128044255312629457887411604300692966728690551568705030373_<62> · C1619

C1619 = P27 · C1592

P27 = 562460722085835631233826201_<27>

10¹⁶⁶⁹+1 = 1(0)₁₆₆₈1_<1670> = 11 · 114715401881453_<15> · 534378091190893_<15> · C1640

C1640 = P28 · C1612

P28 = 1988409572496065915208771397_<28>

10¹⁷⁸⁶+1 = 1(0)₁₇₈₅1_<1787> = 101 · 45121 · 117640249 · 722817036322379041_<18> · 1369778187490592461_<19> · 2144906157509411684424913774078958939881_<40> · 1023037643093214557651333120422980213172396059301_<49> · C1648

C1648 = P28 · C1621

P28 = 2660633905954597855218572789_<28>

Apr 9, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(16·10¹⁵⁶-7)/9 = 1(7)₁₅₆_<157> = 1528717 · C151

C151 = P69 · P82

P69 = 692135084257927329335410999683545165787859841786762908730251918987703_<69>

P82 = 1680194326615894932898979882414438056196314851519751157531292592032120525164197427_<82>

Number: n
N=1162921441821983910545756852169353632999291417428979842428505588528012560714493119248217804719760281188590025346599650411278070288861691063668277240181
  ( 151 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=692135084257927329335410999683545165787859841786762908730251918987703 (pp69)
 r2=1680194326615894932898979882414438056196314851519751157531292592032120525164197427 (pp82)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 32.60 hours.
Scaled time: 38.99 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_1_7_156
n: 1162921441821983910545756852169353632999291417428979842428505588528012560714493119248217804719760281188590025346599650411278070288861691063668277240181
type: snfs
skew: 1.07
deg: 5
c5: 5
c0: -7
m: 20000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:216816, AFBsize:216351, largePrimes:6344958 encountered
Relations: rels:5824312, finalFF:504391
Max relations in full relation-set: 28
Initial matrix: 433232 x 504391 with sparse part having weight 26881004.
Pruned matrix : 366674 x 368904 with weight 15845665.
Total sieving time: 29.40 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 2.84 hours.
Total square root time: 0.16 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 32.60 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(8·10¹⁵⁶-53)/9 = (8)₁₅₅3_<156> = 17 · 67 · 1723 · C150

C150 = P39 · P111

P39 = 512558391416894469920990361025843583071_<39>

P111 = 883680207797077854491786259675284953644239544020825359606312622673009480184253210227866307594638649702739828909_<111>

Number: n
N=452937705835417271409275473485507946707123062551886137348943151958392236466546898613801136454674268999590261227858635650851384174798172373710068799539
  ( 150 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=512558391416894469920990361025843583071 (pp39)
 r2=883680207797077854491786259675284953644239544020825359606312622673009480184253210227866307594638649702739828909 (pp111)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 28.95 hours.
Scaled time: 41.97 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_8_155_3
n: 452937705835417271409275473485507946707123062551886137348943151958392236466546898613801136454674268999590261227858635650851384174798172373710068799539
skew: 1.84
deg: 5
c5: 5
c0: -106
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:216816, AFBsize:216631, largePrimes:6978351 encountered
Relations: rels:6449777, finalFF:487734
Max relations in full relation-set: 28
Initial matrix: 433512 x 487734 with sparse part having weight 33253798.
Pruned matrix : 388763 x 390994 with weight 22572948.
Total sieving time: 24.84 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.85 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 28.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Apr 8, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

9·10¹⁵⁶+1 = 9(0)₁₅₅1_<157> = 29 · C156

C156 = P39 · P40 · P77

P39 = 706993936910368903640116661982625450877_<39>

P40 = 8380009192709174113059633311180980138633_<40>

P77 = 52382271492126465895543889093087824425922340013871527868319133952371915809809_<77>

Number: n
N=310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862069
  ( 156 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=706993936910368903640116661982625450877 (pp39)
 r2=8380009192709174113059633311180980138633 (pp40)
 r3=52382271492126465895543889093087824425922340013871527868319133952371915809809 (pp77)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 33.66 hours.
Scaled time: 44.53 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_9_0_155_1
n: 310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862069
skew: 1.22
deg: 5
c5: 10
c0: 27
m: 30000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:216816, AFBsize:216791, largePrimes:7067476 encountered
Relations: rels:6585869, finalFF:536410
Max relations in full relation-set: 48
Initial matrix: 433674 x 536410 with sparse part having weight 43854241.
Pruned matrix : 350813 x 353045 with weight 23765257.
Total sieving time: 29.76 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 3.46 hours.
Total square root time: 0.21 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 33.66 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(68·10¹⁵⁶+13)/9 = 7(5)₁₅₅7_<157> = 3 · 10891 · C153

C153 = P59 · P94

P59 = 31355131076919367852714514174234199910740419431555686047929_<59>

P94 = 7375114545207978805546688095481618474842984019533230866001850209009963716005668089754841511021_<94>

Number: n
N=231247683272290746351897761318383850750024655083878295704574283217199386513499083511019972318292031816960657287532689240521395511754523782804014187725509
  ( 153 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=31355131076919367852714514174234199910740419431555686047929 (pp59)
 r2=7375114545207978805546688095481618474842984019533230866001850209009963716005668089754841511021 (pp94)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 47.14 hours.
Scaled time: 38.93 units (timescale=0.826).
Factorization parameters were as follows:
name: KA_7_5_155_7
n: 231247683272290746351897761318383850750024655083878295704574283217199386513499083511019972318292031816960657287532689240521395511754523782804014187725509
skew: 0.91
deg: 5
c5: 85
c0: 52
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [1500000, 1500000)
Primes: RFBsize:216816, AFBsize:216711, largePrimes:7114301 encountered
Relations: rels:6617701, finalFF:528432
Max relations in full relation-set: 28
Initial matrix: 433594 x 528432 with sparse part having weight 42665152.
Pruned matrix : 357775 x 360006 with weight 24579218.
Total sieving time: 42.61 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 3.98 hours.
Total square root time: 0.14 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 47.14 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 2100+ stepping 02
Memory: 904260k/917504k available (1815k kernel code, 12496k reserved, 846k data, 272k init, 0k highmem)
Calibrating delay loop... 3440.64 BogoMIPS

Apr 8, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(7·10¹⁵⁴+11)/9 = (7)₁₅₃9_<154> = 3³ · 7337683 · C146

C146 = P61 · P85

P61 = 4690896086141897500802584645763269881758309040800801140340477_<61>

P85 = 8369066300074838263082780406544591031236656625018906009192714626063310059189782184047_<85>

Number: trial
N=39258420351683109907409806377308183471730678056647106489618840664198654664521826615849423260912085866169540206093100999511586553239286882257770419
  ( 146 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=4690896086141897500802584645763269881758309040800801140340477 (pp61)
 r2=8369066300074838263082780406544591031236656625018906009192714626063310059189782184047 (pp85)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 84.95 hours.
Scaled time: 45.45 units (timescale=0.535).
Factorization parameters were as follows:
n: 39258420351683109907409806377308183471730678056647106489618840664198654664521826615849423260912085866169540206093100999511586553239286882257770419
m: 10000000000000000000000000000000
c5: 7
c0: 110
skew: 1.73
type: snfsFactor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 1
)
Primes: RFBsize:216816, AFBsize:217222, largePrimes:5753913 encountered
Relations: rels:5757438, finalFF:546532
Max relations in full relation-set: 0
Initial matrix: 434103 x 546532 with sparse part having weight 42400010.
Pruned matrix : 403492 x 405726 with weight 24843896.
Total sieving time: 77.64 hours.
Total relation processing time: 0.62 hours.
Matrix solve time: 6.39 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 84.95 hours.
 --------- CPU info (if available) ----------

Apr 7, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(5·10¹⁵⁵+13)/9 = (5)₁₅₄7_<155> = 3 · 107 · 197 · 3333804296728811_<16> · C135

C135 = P35 · P100

P35 = 41216820093313356609207852589825031_<35>

P100 = 6393543903130201756244045739931302422886188966077224891742387211909421803577183769409636962325124421_<100>

Number: n
N=263521548814018004580209891831459686451851910557430681666590679838019891784536826927571192291545123292460712443696823152316035695182051
  ( 135 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=41216820093313356609207852589825031 (pp35)
 r2=6393543903130201756244045739931302422886188966077224891742387211909421803577183769409636962325124421 (pp100)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 25.43 hours.
Scaled time: 32.98 units (timescale=1.297).
Factorization parameters were as follows:
name: KA_5_154_7
n: 263521548814018004580209891831459686451851910557430681666590679838019891784536826927571192291545123292460712443696823152316035695182051
skew: 1.21
deg: 5
c5: 5
c0: 13
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:216816, AFBsize:217321, largePrimes:6770644 encountered
Relations: rels:6260192, finalFF:509405
Max relations in full relation-set: 48
Initial matrix: 434202 x 509405 with sparse part having weight 33986023.
Pruned matrix : 369089 x 371324 with weight 19110819.
Total sieving time: 22.15 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 2.97 hours.
Total square root time: 0.13 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 25.43 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(68·10¹⁵⁵+13)/9 = 7(5)₁₅₄7_<156> = 11 · 29 · 421 · 2475023 · 80018997103_<11> · C134

C134 = P48 · P86

P48 = 557831249566315798418346398963812640291677422857_<48>

P86 = 50923523018443023950549144339844652596348663112551716875431260247044827931812945961671_<86>

Number: n
N=28406732477697117682136345726381636050128121431425594294290731080826521212711193096225911030485159627911792905855674723329202781314047
  ( 134 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=557831249566315798418346398963812640291677422857 (pp48)
 r2=50923523018443023950549144339844652596348663112551716875431260247044827931812945961671 (pp86)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 25.88 hours.
Scaled time: 37.40 units (timescale=1.445).
Factorization parameters were as follows:
name: KA_7_5_154_7
n: 28406732477697117682136345726381636050128121431425594294290731080826521212711193096225911030485159627911792905855674723329202781314047
skew: 0.72
deg: 5
c5: 68
c0: 13
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:216816, AFBsize:217331, largePrimes:6856703 encountered
Relations: rels:6351061, finalFF:504197
Max relations in full relation-set: 28
Initial matrix: 434213 x 504197 with sparse part having weight 32033747.
Pruned matrix : 373953 x 376188 with weight 19778157.
Total sieving time: 22.57 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.07 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 25.88 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

9·10¹⁵⁰+1 = 9(0)₁₄₉1_<151> = 4253 · C148

C148 = P61 · P87

P61 = 3566992060520775519655367333427319075823880194840139594754009_<61>

P87 = 593259886101759296204495700498020412031125484426971874909743168024374007473423673233213_<87>

Number: n
N=2116153303550434987067952033858452856806959793087232541735245708911356689395720667763931342581707030331530684222901481307312485304490947566423700917
  ( 148 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=3566992060520775519655367333427319075823880194840139594754009 (pp61)
 r2=593259886101759296204495700498020412031125484426971874909743168024374007473423673233213 (pp87)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 20.35 hours.
Scaled time: 24.33 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_9_0_149_1
n: 2116153303550434987067952033858452856806959793087232541735245708911356689395720667763931342581707030331530684222901481307312485304490947566423700917
type: snfs
skew: .64
deg: 5
c5: 9
c0: 1
m: 1000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 800001)
Primes: RFBsize:216816, AFBsize:216846, largePrimes:6003304 encountered
Relations: rels:5565342, finalFF:557446
Max relations in full relation-set: 28
Initial matrix: 433726 x 557446 with sparse part having weight 22454058.
Pruned matrix : 311345 x 313577 with weight 9852861.
Total sieving time: 18.68 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.33 hours.
Total square root time: 0.16 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 20.35 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

2·10¹⁵⁶-1 = 1(9)₁₅₆_<157> = 31543 · C152

C152 = P32 · P120

P32 = 99879751314103257507070930078903_<32>

P120 = 634818460244410667590194554947948312452377489168571246831381943469948522781850559392697592627523228359592226813837713231_<120>

Number: n
N=63405509938813682909044795992771771866975240148368893256824018007164822623085946168722061947183210220968202136765684938021114034809624956408711917065593
  ( 152 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=99879751314103257507070930078903 (pp32)
 r2=634818460244410667590194554947948312452377489168571246831381943469948522781850559392697592627523228359592226813837713231 (pp120)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 21.97 hours.
Scaled time: 31.77 units (timescale=1.446).
Factorization parameters were as follows:
name: KA_1_9_156
n: 63405509938813682909044795992771771866975240148368893256824018007164822623085946168722061947183210220968202136765684938021114034809624956408711917065593
skew: 0.55
deg: 5
c5: 20
c0: -1
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1000001)
Primes: RFBsize:216816, AFBsize:216361, largePrimes:6725175 encountered
Relations: rels:6222839, finalFF:505496
Max relations in full relation-set: 28
Initial matrix: 433243 x 505496 with sparse part having weight 30126514.
Pruned matrix : 369600 x 371830 with weight 17843621.
Total sieving time: 19.07 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 2.68 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 21.97 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Apr 6, 2007 (7th)

By suberi / GMP-ECM 6.1.2 B1=3000000

(16·10¹⁵⁶-61)/9 = 1(7)₁₅₅1_<157> = 353 · 9320453 · 52622551337_<11> · 118052925097_<12> · C125

C125 = P40 · P86

P40 = 2966774020885178915193117624664369288559_<40>

P86 = 29317884310296032844640928591941378129027096529790688817039501129820426892441986873169_<86>

Apr 6, 2007 (6th)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

(2·10¹⁵⁷+61)/9 = (2)₁₅₆9_<157> = 3 · C156

C156 = P70 · P87

P70 = 2124001047704260764969871594481033371460532700579941038302624662161929_<70>

P87 = 348747822672392181906445498167694063047435422994624510314413787974685333027581184663567_<87>

Number: 22229_157
N=740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743
  ( 156 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=2124001047704260764969871594481033371460532700579941038302624662161929 (pp70)
 r2=348747822672392181906445498167694063047435422994624510314413787974685333027581184663567 (pp87)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 62.82 hours.
Scaled time: 42.34 units (timescale=0.674).
Factorization parameters were as follows:
name: 22229_157
n: 740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743
m: 10000000000000000000000000000000
c5: 200
c0: 61
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3000001)
Primes: RFBsize:216816, AFBsize:216677, largePrimes:5625784 encountered
Relations: rels:5541384, finalFF:486522
Max relations in full relation-set: 0
Initial matrix: 433558 x 486522 with sparse part having weight 37329396.
Pruned matrix : 410517 x 412748 with weight 28627425.
Total sieving time: 54.70 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 7.44 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 62.82 hours.
 --------- CPU info (if available) ----------

Apr 6, 2007 (5th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(85·10¹⁵⁵+41)/9 = 9(4)₁₅₄9_<156> = 11 · 541 · 12918769 · C146

C146 = P42 · P48 · P57

P42 = 211700555063119929890875235473012007515787_<42>

P48 = 168922285910824157078507837032846030320795260327_<48>

P57 = 343523448472478512600512197801355359657515353958015774379_<57>

Number: n
N=12284722009921359929131917984001874509741121627632771385728056425443589682952011109511750289812874167807618558883312054960486639823425788913136271
  ( 146 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=211700555063119929890875235473012007515787 (pp42)
 r2=168922285910824157078507837032846030320795260327 (pp48)
 r3=343523448472478512600512197801355359657515353958015774379 (pp57)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 32.63 hours.
Scaled time: 39.03 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_9_4_154_9
n: 12284722009921359929131917984001874509741121627632771385728056425443589682952011109511750289812874167807618558883312054960486639823425788913136271
type: snfs
skew: 1
deg: 5
c5: 85
c0: 41
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:216816, AFBsize:216987, largePrimes:6273146 encountered
Relations: rels:5738314, finalFF:489456
Max relations in full relation-set: 28
Initial matrix: 433869 x 489456 with sparse part having weight 25703479.
Pruned matrix : 380465 x 382698 with weight 16215397.
Total sieving time: 29.29 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 2.69 hours.
Total square root time: 0.41 hours, sqrts: 5.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 32.63 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

9·10¹⁴¹+1 = 9(0)₁₄₀1_<142> = 66031908616111316843093170997_<29> · C114

C114 = P35 · P80

P35 = 10183815601095370522960916473439173_<35>

P80 = 13383759748561580248834032773181350478449614572726727955728581327175944905132921_<80>

Number: n
N=136297741328713674413693066891690669437698508191359111723956358226887622689098652320651044431037249295329573314333
  ( 114 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=10183815601095370522960916473439173 (pp35)
 r2=13383759748561580248834032773181350478449614572726727955728581327175944905132921 (pp80)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 11.33 hours.
Scaled time: 9.37 units (timescale=0.827).
Factorization parameters were as follows:
name: KA_9_0_140_1
n: 136297741328713674413693066891690669437698508191359111723956358226887622689098652320651044431037249295329573314333
skew: 1.22
deg: 5
c5: 10
c0: 27
m: 30000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:183072, AFBsize:183066, largePrimes:6647249 encountered
Relations: rels:6179370, finalFF:529120
Max relations in full relation-set: 48
Initial matrix: 366205 x 529120 with sparse part having weight 32879271.
Pruned matrix : 228116 x 230011 with weight 13740621.
Total sieving time: 9.36 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 1.59 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 11.33 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 2100+ stepping 02
Memory: 904260k/917504k available (1815k kernel code, 12496k reserved, 846k data, 272k init, 0k highmem)
Calibrating delay loop... 3440.64 BogoMIPS

Apr 6, 2007 (4th)

By Jo Yeong Uk / GMP-ECM 5.0.3 B1=3000000, GGNFS-0.77.1-20050930-k8

9·10¹⁶⁰+1 = 9(0)₁₅₉1_<161> = C161

C161 = P42 · C120

P42 = 196668336511615844317373683402996797341833_<42>

C120 = [457623233085536978487969224809644797039838287759370817200669676684400841774026444495529209155367065867115087869248173497_<120>]

9·10¹⁴²+1 = 9(0)₁₄₁1_<143> = 229133 · C138

C138 = P39 · P100

P39 = 310418237090102149002920451352517921093_<39>

P100 = 1265341173550541325953165241360932050982648906067589633583866154278345401523423025383948873896217729_<100>

Number: 90001_142
N=392784976411080027756804999716321961480886646620085277982656361152692977441049521456970405834166182959242012281076929119768867862769657797
  ( 138 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=310418237090102149002920451352517921093 (pp39)
 r2=1265341173550541325953165241360932050982648906067589633583866154278345401523423025383948873896217729 (pp100)
Version: GGNFS-0.77.1-20050930-k8
Total time: 9.89 hours.
Scaled time: 8.98 units (timescale=0.908).
Factorization parameters were as follows:
n: 392784976411080027756804999716321961480886646620085277982656361152692977441049521456970405834166182959242012281076929119768867862769657797
m: 10000000000000000000000000000
c5: 900
c0: 1
skew: 1
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 1300001)
Primes: RFBsize:114155, AFBsize:113802, largePrimes:2682733 encountered
Relations: rels:2690141, finalFF:314070
Max relations in full relation-set: 28
Initial matrix: 228021 x 314070 with sparse part having weight 20532393.
Pruned matrix : 190077 x 191281 with weight 10216464.
Total sieving time: 9.68 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000
total time: 9.89 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239)
Total of 2 processors activated (9340.09 BogoMIPS).

7·10¹⁶⁸+1 = 7(0)₁₆₇1_<169> = C169

C169 = P32 · P138

P32 = 39874420514155621405930029196213_<32>

P138 = 175551140549239192504522004124894766597610705708295751211644739831183679452961360088433039867758405935282447575807483052676447787480773277_<138>

Apr 6, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

9·10¹³⁹+1 = 9(0)₁₃₈1_<140> = 7 · 13² · 59 · 4424608127_<10> · C126

C126 = P38 · P41 · P47

P38 = 78922087410589632675170017604509175183_<38>

P41 = 80446991336116621276555908785459354423609_<41>

P47 = 45901044757666544367296133139543971866289750757_<47>

Number: 90001_139
N=291427774943488532047152968430812186544474227918461927420354897872451236915447049045959903935550375259390389351446759644503379
  ( 126 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=78922087410589632675170017604509175183 (pp38)
 r2=80446991336116621276555908785459354423609 (pp41)
 r3=45901044757666544367296133139543971866289750757 (pp47)
Version: GGNFS-0.77.1-20050930-k8
Total time: 7.37 hours.
Scaled time: 6.69 units (timescale=0.908).
Factorization parameters were as follows:
n: 291427774943488532047152968430812186544474227918461927420354897872451236915447049045959903935550375259390389351446759644503379
m: 10000000000000000000000000000
c5: 9
c0: 10
skew: 1.02
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:114347, largePrimes:2606524 encountered
Relations: rels:2587319, finalFF:291732
Max relations in full relation-set: 28
Initial matrix: 228566 x 291732 with sparse part having weight 17521246.
Pruned matrix : 192093 x 193299 with weight 9457557.
Total sieving time: 7.17 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000
total time: 7.37 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239)
Total of 2 processors activated (9340.09 BogoMIPS).

Apr 6, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(7·10¹⁵⁵-1)/3 = 2(3)₁₅₅_<156> = 23 · 179 · 2130837571_<10> · C143

C143 = P68 · P75

P68 = 77461896204587304692802549568692094784149038435678059800315429975651_<68>

P75 = 343366126043325324679343651655973979954780461786276458351742207522660246169_<75>

Number: n
N=26597791215739308044490594222247537267372861584429149293061049124427324190079794935545891769979405882539329762729960567612604616679833336031019
  ( 143 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=77461896204587304692802549568692094784149038435678059800315429975651 (pp68)
 r2=343366126043325324679343651655973979954780461786276458351742207522660246169 (pp75)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 28.30 hours.
Scaled time: 23.40 units (timescale=0.827).
Factorization parameters were as follows:
name: KA_2_3_155
n: 26597791215739308044490594222247537267372861584429149293061049124427324190079794935545891769979405882539329762729960567612604616679833336031019
skew: 1
deg: 5
c5: 7
c0: -1
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:216816, AFBsize:216696, largePrimes:6565054 encountered
Relations: rels:6066011, finalFF:508144
Max relations in full relation-set: 48
Initial matrix: 433579 x 508144 with sparse part having weight 30474705.
Pruned matrix : 365661 x 367892 with weight 17059396.
Total sieving time: 24.44 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 3.44 hours.
Total square root time: 0.10 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 28.30 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 2100+ stepping 02
Memory: 904260k/917504k available (1815k kernel code, 12496k reserved, 846k data, 272k init, 0k highmem)
Calibrating delay loop... 3440.64 BogoMIPS

Apr 6, 2007

By Philippe Strohl / GGNFS-0.77.1-20060722-pentium-m

(7·10¹⁷⁵+11)/9 = (7)₁₇₄9_<175> = 3 · 506195919767_<12> · 18822712509076627_<17> · 12007442890556404705517171537299_<32> · C116

C116 = P36 · P80

P36 = 498624942550109485805814460298361641_<36>

P80 = 45447384816690114799306728579382713054661212062218116456521891841090634833086503_<80>

Apr 5, 2007 (8th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(5·10¹⁵⁵-17)/3 = 1(6)₁₅₄1_<156> = 11 · 61 · 10061 · 10351541267_<11> · C139

C139 = P64 · P76

P64 = 1850217218604904705518625678066942001084019396417929806014990607_<64>

P76 = 1289013139523539875414561025232330466630448746167402715567364053956199454099_<76>

Number: n
N=2384954305754419907374721739212565653128503425209626432308736488438207987809067828309162718996422968888385930009018811111685156024012648093
  ( 139 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=1850217218604904705518625678066942001084019396417929806014990607 (pp64)
 r2=1289013139523539875414561025232330466630448746167402715567364053956199454099 (pp76)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.79 hours.
Scaled time: 25.77 units (timescale=1.302).
Factorization parameters were as follows:
name: KA_1_6_154_1
n: 2384954305754419907374721739212565653128503425209626432308736488438207987809067828309162718996422968888385930009018811111685156024012648093
skew: 1.28
deg: 5
c5: 5
c0: -17
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 800001)
Primes: RFBsize:216816, AFBsize:216751, largePrimes:6454719 encountered
Relations: rels:5971797, finalFF:513567
Max relations in full relation-set: 48
Initial matrix: 433632 x 513567 with sparse part having weight 28449479.
Pruned matrix : 359396 x 361628 with weight 15123330.
Total sieving time: 17.30 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 2.27 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 19.79 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

9·10¹⁵¹+1 = 9(0)₁₅₀1_<152> = 7 · 13 · 157 · C148

C148 = P37 · P55 · P57

P37 = 1740270742464737399801648274260382251_<37>

P55 = 6819290242424764524862346427986183895917940998262231863_<55>

P57 = 530817791290284114816038893859259470090732398434626858971_<57>

Number: n
N=6299433051025407713305802477777000069993700566948974592286694197522222999930006299433051025407713305802477777000069993700566948974592286694197522223
  ( 148 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=1740270742464737399801648274260382251 (pp37)
 r2=6819290242424764524862346427986183895917940998262231863 (pp55)
 r3=530817791290284114816038893859259470090732398434626858971 (pp57)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 18.56 hours.
Scaled time: 26.73 units (timescale=1.440).
Factorization parameters were as follows:
name: KA_9_0_150_1
n: 6299433051025407713305802477777000069993700566948974592286694197522222999930006299433051025407713305802477777000069993700566948974592286694197522223
skew: 1.22
deg: 5
c5: 10
c0: 27
m: 3000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 850001)
Primes: RFBsize:183072, AFBsize:183066, largePrimes:6485918 encountered
Relations: rels:5920454, finalFF:416460
Max relations in full relation-set: 28
Initial matrix: 366205 x 416460 with sparse part having weight 28593043.
Pruned matrix : 325166 x 327061 with weight 18726059.
Total sieving time: 16.07 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 2.24 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 18.56 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Apr 5, 2007 (7th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

9·10¹³⁷+1 = 9(0)₁₃₆1_<138> = 12487 · C134

C134 = P30 · P38 · P67

P30 = 499844315469822755436751497077_<30>

P38 = 22694932497912076567821810183311352533_<38>

P67 = 6353612804509099688291593709903803564908420180194675150217717604303_<67>

Number: 90001_137
N=72074957956274525506526787859373748698646592456154400576599663650196204052214302874989989589172739649235204612797309201569632417714423
  ( 134 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=499844315469822755436751497077 (pp30)
 r2=22694932497912076567821810183311352533 (pp38)
 r3=6353612804509099688291593709903803564908420180194675150217717604303 (pp67)
Version: GGNFS-0.77.1-20050930-k8
Total time: 6.82 hours.
Scaled time: 6.18 units (timescale=0.905).
Factorization parameters were as follows:
n: 72074957956274525506526787859373748698646592456154400576599663650196204052214302874989989589172739649235204612797309201569632417714423
m: 1000000000000000000000000000
c5: 900
c0: 1
skew: 1
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [650000, 1700001)
Primes: RFBsize:100021, AFBsize:99793, largePrimes:1621648 encountered
Relations: rels:1655072, finalFF:231349
Max relations in full relation-set: 28
Initial matrix: 199878 x 231349 with sparse part having weight 11731570.
Pruned matrix : 185095 x 186158 with weight 8027989.
Total sieving time: 6.66 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1300000,1300000,25,25,43,43,2.3,2.3,50000
total time: 6.82 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239)
Total of 2 processors activated (9340.09 BogoMIPS).

Apr 5, 2007 (6th)

By Alfred Reich / GMP-ECM B1=150000

10¹⁸²³+1 = 1(0)₁₈₂₂1_<1824> = 11 · 1187345615675521_<16> · C1807

C1807 = P26 · C1782

P26 = 31955183441582314302903853_<26>

10¹⁹⁴³+1 = 1(0)₁₉₄₂1_<1944> = 11 · 59 · 8685211 · 182142902141813_<15> · 154083204930662557781201849_<27> · 909090909090909090909090909090909090909090909090909090909090909091_<66> · C1827

C1827 = P27 · C1801

P27 = 549079354489571267845038917_<27>

Apr 5, 2007 (5th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

7·10¹⁴⁷+1 = 7(0)₁₄₆1_<148> = 283183 · 1902961 · 4224729381223999559_<19> · C118

C118 = P43 · P76

P43 = 1257698080821893649965656268769551561386291_<43>

P76 = 2444700608743657571446769617615111125524512245960929287873490693266909697683_<76>

Number: 70001_147
N=3074695263801013246179651465377774841536765090589909013606376195809919254938620808513180930889035167934758547190663753
  ( 118 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=1257698080821893649965656268769551561386291 (pp43)
 r2=2444700608743657571446769617615111125524512245960929287873490693266909697683 (pp76)
Version: GGNFS-0.77.1-20050930-k8
Total time: 15.32 hours.
Scaled time: 13.88 units (timescale=0.906).
Factorization parameters were as follows:
n: 3074695263801013246179651465377774841536765090589909013606376195809919254938620808513180930889035167934758547190663753
m: 100000000000000000000000000000
c5: 700
c0: 1
skew: 1
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [900000, 1725001)
Primes: RFBsize:135072, AFBsize:134603, largePrimes:2749251 encountered
Relations: rels:2756068, finalFF:334962
Max relations in full relation-set: 28
Initial matrix: 269742 x 334962 with sparse part having weight 19110574.
Pruned matrix : 236626 x 238038 with weight 11511077.
Total sieving time: 15.00 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.24 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,45,45,2.3,2.3,75000
total time: 15.32 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239)
Total of 2 processors activated (9340.09 BogoMIPS).

9·10¹¹⁸+1 = 9(0)₁₁₇1_<119> = 196073 · C114

C114 = P33 · P40 · P43

P33 = 186381179361616798004946995918881_<33>

P40 = 1741085366837536144261031347273683656221_<40>

P43 = 1414498837021419722168181729011819304044237_<43>

Number: 90001_118
N=459012714652195865825483365889235131813151224288912802884639904525355352343259908299459895039092582864545347906137
  ( 114 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=186381179361616798004946995918881 (pp33)
 r2=1741085366837536144261031347273683656221 (pp40)
 r3=1414498837021419722168181729011819304044237 (pp43)
Version: GGNFS-0.77.1-20050930-k8
Total time: 1.71 hours.
Scaled time: 1.55 units (timescale=0.903).
Factorization parameters were as follows:
n: 459012714652195865825483365889235131813151224288912802884639904525355352343259908299459895039092582864545347906137
m: 100000000000000000000000000000
c4: 900
c0: 1
skew: 1
type: snfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [350000, 625001)
Primes: RFBsize:56543, AFBsize:56367, largePrimes:1979349 encountered
Relations: rels:1930833, finalFF:130207
Max relations in full relation-set: 28
Initial matrix: 112979 x 130207 with sparse part having weight 10923724.
Pruned matrix : 108529 x 109157 with weight 7699852.
Total sieving time: 1.63 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,118,4,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.4,2.4,25000
total time: 1.71 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239)
Total of 2 processors activated (9340.09 BogoMIPS).

9·10¹³⁰+1 = 9(0)₁₂₉1_<131> = 17 · 24593 · C126

C126 = P33 · P93

P33 = 216594009296418960195645951195437_<33>

P93 = 993883859583954448735204608842181266122491024424875540660278630042828155798346154067493353733_<93>

Number: 90001_130
N=215269289922287786338054109131962466603361549556186480610216680499711778339604048019402938664995539141936610369760883656516321
  ( 126 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=216594009296418960195645951195437 (pp33)
 r2=993883859583954448735204608842181266122491024424875540660278630042828155798346154067493353733 (pp93)
Version: GGNFS-0.77.1-20050930-k8
Total time: 2.48 hours.
Scaled time: 2.26 units (timescale=0.909).
Factorization parameters were as follows:
n: 215269289922287786338054109131962466603361549556186480610216680499711778339604048019402938664995539141936610369760883656516321
m: 100000000000000000000000000
c5: 9
c0: 1
skew: 1
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 900001)
Primes: RFBsize:78498, AFBsize:78476, largePrimes:1520791 encountered
Relations: rels:1555753, finalFF:208863
Max relations in full relation-set: 28
Initial matrix: 157038 x 208863 with sparse part having weight 10306656.
Pruned matrix : 132322 x 133171 with weight 5117766.
Total sieving time: 2.41 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 2.48 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239)
Total of 2 processors activated (9340.09 BogoMIPS).

Apr 5, 2007 (4th)

By Shaopu Lin / GGNFS-0.77.1-20060722-pentium4

9·10¹¹⁵+1 = 9(0)₁₁₄1_<116> = 7 · 13 · 103 · 3391343 · 4528368424529_<13> · C93

C93 = P35 · P59

P35 = 40963716780981360581121590745000013_<35>

P59 = 15263392336091573406619034605037192244798168990720053726167_<59>

Number: 9.115.+1
N=625245280772656676746155571910659372750816392845660093458760975741039193818228550885113440171
  ( 93 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=40963716780981360581121590745000013 (pp35)
 r2=15263392336091573406619034605037192244798168990720053726167 (pp59)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 1.71 hours.
Scaled time: 2.14 units (timescale=1.248).
Factorization parameters were as follows:
n: 625245280772656676746155571910659372750816392845660093458760975741039193818228550885113440171
m: 100000000000000000000000
c5: 9
c0: 1
skew: 0.6443940149772542505082929811
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:64013, largePrimes:2156403 encountered
Relations: rels:2356568, finalFF:351185
Max relations in full relation-set: 32
Initial matrix: 113175 x 351185 with sparse part having weight 28702487.
Pruned matrix : 67902 x 68531 with weight 4049822.
Total sieving time: 1.55 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.71 hours.
 --------- CPU info (if available) ----------

9·10¹⁰⁶+1 = 9(0)₁₀₅1_<107> = 53 · 109 · 601 · C101

C101 = P36 · P65

P36 = 273608402981042587412878642296398297_<36>

P65 = 94740623536944631063360702956769539501899999853290343142238204929_<65>

Number: 9.106.+1
N=25921830703371594915519313636006229303938361342831476130170217141415395320879141768508259127292605913
  ( 101 digits)
SNFS difficulty: 106 digits.
Divisors found:
 r1=273608402981042587412878642296398297 (pp36)
 r2=94740623536944631063360702956769539501899999853290343142238204929 (pp65)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 1.31 hours.
Scaled time: 1.64 units (timescale=1.253).
Factorization parameters were as follows:
n: 25921830703371594915519313636006229303938361342831476130170217141415395320879141768508259127292605913
m: 1000000000000000000000
c5: 90
c0: 1 
skew: 0.4065851364889782182814046414
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:64158, largePrimes:1914669 encountered
Relations: rels:1900606, finalFF:178309
Max relations in full relation-set: 32
Initial matrix: 113323 x 178309 with sparse part having weight 12518519.
Pruned matrix : 87858 x 88488 with weight 3836011.
Total sieving time: 1.14 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,106,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.31 hours.
 --------- CPU info (if available) ----------

9·10¹²⁰+1 = 9(0)₁₁₉1_<121> = 261066330188528555113_<21> · C101

C101 = P36 · P66

P36 = 177543491136813067537023060576498121_<36>

P66 = 194172127768048952704457311156481550648638322505777201579412750737_<66>

Number: 9.120.+1
N=34473997445402733752180794441478216709139205993978969681670845367942169957821117137970678303321865177
  ( 101 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=177543491136813067537023060576498121 (pp36)
 r2=194172127768048952704457311156481550648638322505777201579412750737 (pp66)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 2.19 hours.
Scaled time: 2.78 units (timescale=1.270).
Factorization parameters were as follows:
n: 34473997445402733752180794441478216709139205993978969681670845367942169957821117137970678303321865177
m: 1000000000000000000000000
c5: 9
c0: 1
skew: 0.6443940149772542505082929811
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64013, largePrimes:2116235 encountered
Relations: rels:2216077, finalFF:252753
Max relations in full relation-set: 32
Initial matrix: 113175 x 252753 with sparse part having weight 22900072.
Pruned matrix : 83496 x 84125 with weight 4936282.
Total sieving time: 1.99 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.19 hours.
 --------- CPU info (if available) ----------

9·10¹¹³+1 = 9(0)₁₁₂1_<114> = 22699 · 1184459 · C104

C104 = P45 · P60

P45 = 184673635431641860805463910676143935673766213_<45>

P60 = 181263705428764681773841097459967268253297158583781910475797_<60>

Number: 9.113.+1
N=33474627453340210450558941161791675296296994782280919086160013356355525225661891419848286880377772846761
  ( 104 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=184673635431641860805463910676143935673766213 (pp45)
 r2=181263705428764681773841097459967268253297158583781910475797 (pp60)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 2.33 hours.
Scaled time: 2.97 units (timescale=1.277).
Factorization parameters were as follows:
n: 33474627453340210450558941161791675296296994782280919086160013356355525225661891419848286880377772846761
m: 100000000000000000000000
c5: 9
c0: 100
skew: 1.618644582767346099223495031
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63918, largePrimes:2311851 encountered
Relations: rels:2665234, finalFF:483823
Max relations in full relation-set: 32
Initial matrix: 113080 x 483823 with sparse part having weight 41507232.
Pruned matrix : 65593 x 66222 with weight 6026429.
Total sieving time: 2.12 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.33 hours.
 --------- CPU info (if available) ----------

Apr 5, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

9·10¹¹¹+1 = 9(0)₁₁₀1_<112> = 89 · C111

C111 = P38 · P73

P38 = 76439746214259187150670786361768507023_<38>

P73 = 1322919037723783381478589398425519069856963653988055358561452629090981383_<73>

Number: n
N=101123595505617977528089887640449438202247191011235955056179775280898876404494382022471910112359550561797752809
  ( 111 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=76439746214259187150670786361768507023 (pp38)
 r2=1322919037723783381478589398425519069856963653988055358561452629090981383 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.17 hours.
Scaled time: 1.55 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_9_0_110_1
n: 101123595505617977528089887640449438202247191011235955056179775280898876404494382022471910112359550561797752809
skew: 1.22
deg: 5
c5: 10
c0: 27
m: 30000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:114155, AFBsize:114062, largePrimes:4028981 encountered
Relations: rels:3581766, finalFF:312084
Max relations in full relation-set: 48
Initial matrix: 228284 x 312084 with sparse part having weight 9536524.
Pruned matrix : 136996 x 138201 with weight 2950017.
Total sieving time: 0.98 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.11 hours.
Total square root time: 0.01 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,50000
total time: 1.17 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

9·10¹¹⁶+1 = 9(0)₁₁₅1_<117> = 3917 · 719189 · C108

C108 = P34 · P75

P34 = 1814814873154884385579882421783353_<34>

P75 = 176040896601909387016192468843434263374254628094985647651842242628087932409_<75>

Number: n
N=319481637436666301862417530975811618189214620608706212631721564718698248156838639004348142600655848305387377
  ( 108 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=1814814873154884385579882421783353 (pp34)
 r2=176040896601909387016192468843434263374254628094985647651842242628087932409 (pp75)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.15 hours.
Scaled time: 3.12 units (timescale=1.451).
Factorization parameters were as follows:
name: KA_9_0_115_1
n: 319481637436666301862417530975811618189214620608706212631721564718698248156838639004348142600655848305387377
skew: 1.22
deg: 5
c5: 10
c0: 27
m: 300000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [500000, 600001)
Primes: RFBsize:148933, AFBsize:148730, largePrimes:6414980 encountered
Relations: rels:5825796, finalFF:426956
Max relations in full relation-set: 28
Initial matrix: 297730 x 426956 with sparse part having weight 22437789.
Pruned matrix : 181983 x 183535 with weight 7617386.
Total sieving time: 1.61 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.41 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,50000
total time: 2.15 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Apr 5, 2007 (2nd)

By Thomas Womack / ggnfs

(52·10¹⁸⁰-7)/9 = 5(7)₁₈₀_<181> = 1907145664709063958354268537876114943171_<40> · C142

C142 = P49 · P94

P49 = 2282249079063136761889376337454791894323802478621_<49>

P94 = 1327437030532454031084789475205826920108788207304808616927065055833914814194080582426819377847_<94>

57777_180 factors as

1907145664709063958354268537876114943171 *
2282249079063136761889376337454791894323802478621 *
1327437030532454031084789475205826920108788207304808616927065055833914814194080582426819377847

The calculation took about 300 CPU-hours on a Core2 system, using 
ggnfs with a factor base bound of 7400000 on each side and a large-
prime bound of 2^27; 7883395 relations were collected and converted 
into 1146658 full relations, which were pruned to a 951774*956854 
matrix of sparse-weight 53453875 which took 6.7 hours to solve.  The 
factors were found using the first three dependencies, each sqrt took 
about nine minutes.

Apr 5, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

9·10¹¹⁷+1 = 9(0)₁₁₆1_<118> = 12527 · C114

C114 = P38 · P77

P38 = 12134790579207611427656536951386453899_<38>

P77 = 59205649022301612078526981553969233951090001376598142943906491679184248013837_<77>

Number: 90001_117
N=718448151991697932465873712780394348207870998642931268460126127564460764748144008940688113674463159575317314600463
  ( 114 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=12134790579207611427656536951386453899 (pp38)
 r2=59205649022301612078526981553969233951090001376598142943906491679184248013837 (pp77)
Version: GGNFS-0.77.1-20050930-k8
Total time: 1.19 hours.
Scaled time: 1.08 units (timescale=0.903).
Factorization parameters were as follows:
n: 718448151991697932465873712780394348207870998642931268460126127564460764748144008940688113674463159575317314600463
m: 100000000000000000000000000000
c4: 90
c0: 1
skew: 1
type: snfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [350000, 525001)
Primes: RFBsize:56543, AFBsize:56607, largePrimes:1944145 encountered
Relations: rels:1962930, finalFF:194575
Max relations in full relation-set: 28
Initial matrix: 113217 x 194575 with sparse part having weight 14642351.
Pruned matrix : 89791 x 90421 with weight 4553687.
Total sieving time: 1.13 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,117,4,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.4,2.4,25000
total time: 1.19 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239)
Total of 2 processors activated (9340.09 BogoMIPS).

Apr 4, 2007 (8th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(19·10¹⁵⁵-1)/9 = 2(1)₁₅₅_<156> = 47 · 1013 · 9323 · C147

C147 = P50 · P97

P50 = 77169526100999077209508970939525278156116721502063_<50>

P97 = 6163143371863327704942361909436417682834706242621502254644653631482204422647185993572154300515649_<97>

Number: n
N=475606853299206529041167619811211929776266623611930728781991072004773154333717744575067588796563610919593618264888389363516617868790235646717283887
  ( 147 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=77169526100999077209508970939525278156116721502063 (pp50)
 r2=6163143371863327704942361909436417682834706242621502254644653631482204422647185993572154300515649 (pp97)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 30.43 hours.
Scaled time: 25.17 units (timescale=0.827).
Factorization parameters were as follows:
name: KA_2_1_155
n: 475606853299206529041167619811211929776266623611930728781991072004773154333717744575067588796563610919593618264888389363516617868790235646717283887
skew: 1
deg: 5
c5: 19
c0: -1
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1000001)
Primes: RFBsize:216816, AFBsize:216156, largePrimes:6663371 encountered
Relations: rels:6163538, finalFF:514891
Max relations in full relation-set: 48
Initial matrix: 433037 x 514891 with sparse part having weight 31257635.
Pruned matrix : 360736 x 362965 with weight 16947413.
Total sieving time: 26.40 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 3.49 hours.
Total square root time: 0.22 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 30.43 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 2100+ stepping 02
Memory: 904260k/917504k available (1815k kernel code, 12496k reserved, 846k data, 272k init, 0k highmem)
Calibrating delay loop... 3440.64 BogoMIPS

9·10¹⁵⁵-1 = 8(9)₁₅₅_<156> = 20201 · 1225603 · C146

C146 = P69 · P77

P69 = 884030473598129112046273401306743817009226878392237244963203638811597_<69>

P77 = 41119951100362876196136581974904931337399314543041289673940222500296800769089_<77>

Number: n
N=36351289845585703754357293351820365559093981716913508546008889472133037852153863056158211461589371839905909794802634372142747091837105359572325133
  ( 146 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=884030473598129112046273401306743817009226878392237244963203638811597 (pp69)
 r2=41119951100362876196136581974904931337399314543041289673940222500296800769089 (pp77)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 28.22 hours.
Scaled time: 29.07 units (timescale=1.030).
Factorization parameters were as follows:
name: KA_8_9_155
n: 36351289845585703754357293351820365559093981716913508546008889472133037852153863056158211461589371839905909794802634372142747091837105359572325133
type: snfs
skew: .68
deg: 5
c5: 9
c0: -1
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:216816, AFBsize:216846, largePrimes:6333419 encountered
Relations: rels:5866544, finalFF:544993
Max relations in full relation-set: 48
Initial matrix: 433726 x 544993 with sparse part having weight 28008672.
Pruned matrix : 331320 x 333552 with weight 13763173.
Total sieving time: 26.29 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 1.64 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 28.22 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 3000+ stepping 00
Memory: 2076900k/2097088k available (1540k kernel code, 19412k reserved, 599k data, 144k init, 0k highmem)
Calibrating delay loop... 4292.60 BogoMIPS
x86info v1.12b.  Dave Jones 2001-2003
Feedback to <davej@redhat.com>.

Found 1 CPU
--------------------------------------------------------------------------
Family: 6 Model: 10 Stepping: 0
CPU Model : Athlon XP (Barton)
2.2Ghz processor (estimate).

(28·10¹⁵⁵-1)/9 = 3(1)₁₅₅_<156> = 281 · 503771 · C148

C148 = P37 · P39 · P73

P37 = 1832323937877638424687563602099971871_<37>

P39 = 528132257091941690986148848873348959257_<39>

P73 = 2271072974612884347124933126129315615770172419175193664363341850801604363_<73>

Number: n
N=2197738613463458673765104938773203892054743135182716091261846294825289666128882382672101325759210236475583788427898222997958020616419230301091312461
  ( 148 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=1832323937877638424687563602099971871 (pp37)
 r2=528132257091941690986148848873348959257 (pp39)
 r3=2271072974612884347124933126129315615770172419175193664363341850801604363 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 32.07 hours.
Scaled time: 38.39 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_3_1_155
n: 2197738613463458673765104938773203892054743135182716091261846294825289666128882382672101325759210236475583788427898222997958020616419230301091312461
type: snfs
skew: 1
deg: 5
c5: 28
c0: -1
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1300001)
Primes: RFBsize:216816, AFBsize:216531, largePrimes:6407029 encountered
Relations: rels:5912080, finalFF:529027
Max relations in full relation-set: 28
Initial matrix: 433413 x 529027 with sparse part having weight 28005595.
Pruned matrix : 346817 x 349048 with weight 14991508.
Total sieving time: 29.48 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 2.24 hours.
Total square root time: 0.15 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 32.07 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Apr 4, 2007 (7th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

9·10¹¹⁴+1 = 9(0)₁₁₃1_<115> = 17 · C114

C114 = P37 · P78

P37 = 4029232093952705808639019244540988181_<37>

P78 = 131392720091863853149542807291473246596308272142652439543027874153558812956013_<78>

Number: 90001_114
N=529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882353
  ( 114 digits)
SNFS difficulty: 114 digits.
Divisors found:
 r1=4029232093952705808639019244540988181 (pp37)
 r2=131392720091863853149542807291473246596308272142652439543027874153558812956013 (pp78)
Version: GGNFS-0.77.1-20050930-k8
Total time: 1.42 hours.
Scaled time: 1.20 units (timescale=0.845).
Factorization parameters were as follows:
n: 529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882353
m: 10000000000000000000000000000
c4: 900
c0: 1
skew: 1
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [250000, 550001)
Primes: RFBsize:37706, AFBsize:41295, largePrimes:1090214 encountered
Relations: rels:1015192, finalFF:91472
Max relations in full relation-set: 28
Initial matrix: 79070 x 91472 with sparse part having weight 5609598.
Pruned matrix : 76378 x 76837 with weight 3831971.
Total sieving time: 1.38 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,114,4,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,25000
total time: 1.42 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239)
Total of 2 processors activated (9340.09 BogoMIPS).

Apr 4, 2007 (6th)

By suberi / GMP-ECM 6.1.2, Msieve 1.16

(16·10²³²-61)/9 = 1(7)₂₃₁1_<233> = 13² · 107 · 5424611 · 2251879303_<10> · 3383480632586611_<16> · 659860332420269216293_<21> · C176

C176 = P33 · C143

P33 = 401303020798046802054496312007947_<33>

C143 = [89826636072279131116714353972287582321596844330753481523328414047161154003015891965880718193219424721650631512860323732891810346797182170707969_<143>]

(16·10²¹³-61)/9 = 1(7)₂₁₂1_<214> = 7 · 11 · 36739 · 701735753995253_<15> · 9242562959716967_<16> · C176 = P38 · C139

P38 = 15343317696192422017522869439279665157_<38>

C139 = [6315011082326212861759378001460381655744123914330053236853058428366793582916494518062439711742158493507181037630191574610156925315769334851_<139>]

(4·10¹⁹⁹-1)/3 = 1(3)₁₉₉_<200> = 13 · 55845151 · 75263849 · 2539115591_<10> · 420639307341993281_<18> · 1360635813347265266561_<22> · C135

C135 = P37 · P44 · P56

P37 = 1123948400800834624403052798992224711_<37>

P44 = 12880349982971406781750299797656170118282799_<44>

P56 = 11598857935350921114383370001898924491763276297022728801_<56>

Tue Mar 27 13:24:17 2007  
Tue Mar 27 13:24:17 2007  
Tue Mar 27 13:24:17 2007  Msieve v. 1.16
Tue Mar 27 13:24:17 2007  random seeds: ff62f22c 6ed97300
Tue Mar 27 13:24:17 2007  factoring 149397349610085003198289424892102693516048525125417141999554174989126877688006523176555899200193999 (99 digits)
Tue Mar 27 13:24:18 2007  using multiplier of 1
Tue Mar 27 13:24:18 2007  sieve interval: 9 blocks of size 65536
Tue Mar 27 13:24:18 2007  processing polynomials in batches of 6
Tue Mar 27 13:24:18 2007  using a sieve bound of 2577427 (93822 primes)
Tue Mar 27 13:24:18 2007  using large prime bound of 386614050 (28 bits)
Tue Mar 27 13:24:18 2007  using double large prime bound of 2864835627027300 (43-52 bits)
Tue Mar 27 13:24:18 2007  using trial factoring cutoff of 56 bits
Tue Mar 27 13:24:18 2007  polynomial 'A' values have 13 factors
Tue Mar 27 22:30:35 2007  
Tue Mar 27 22:30:35 2007  
Tue Mar 27 22:30:35 2007  Msieve v. 1.16
Tue Mar 27 22:30:35 2007  random seeds: 9434b414 a2be0c24
Tue Mar 27 22:30:35 2007  factoring 149397349610085003198289424892102693516048525125417141999554174989126877688006523176555899200193999 (99 digits)
Tue Mar 27 22:30:35 2007  using multiplier of 1
Tue Mar 27 22:30:35 2007  sieve interval: 9 blocks of size 65536
Tue Mar 27 22:30:35 2007  processing polynomials in batches of 6
Tue Mar 27 22:30:35 2007  using a sieve bound of 2577427 (93822 primes)
Tue Mar 27 22:30:35 2007  using large prime bound of 386614050 (28 bits)
Tue Mar 27 22:30:35 2007  using double large prime bound of 2864835627027300 (43-52 bits)
Tue Mar 27 22:30:35 2007  using trial factoring cutoff of 56 bits
Tue Mar 27 22:30:35 2007  polynomial 'A' values have 13 factors
Tue Mar 27 22:30:48 2007  restarting with 23343 full and 1384965 partial relations
Tue Mar 27 22:31:53 2007  94284 relations (23387 full + 70897 combined from 1387390 partial), need 93918
Tue Mar 27 22:31:56 2007  begin with 1410777 relations
Tue Mar 27 22:31:58 2007  reduce to 244426 relations in 10 passes
Tue Mar 27 22:31:58 2007  attempting to read 244426 relations
Tue Mar 27 22:32:03 2007  recovered 244426 relations
Tue Mar 27 22:32:03 2007  recovered 231965 polynomials
Tue Mar 27 22:32:04 2007  attempting to build 94284 cycles
Tue Mar 27 22:32:04 2007  found 94284 cycles in 6 passes
Tue Mar 27 22:32:04 2007  distribution of cycle lengths:
Tue Mar 27 22:32:04 2007     length 1 : 23387
Tue Mar 27 22:32:04 2007     length 2 : 16540
Tue Mar 27 22:32:04 2007     length 3 : 15894
Tue Mar 27 22:32:04 2007     length 4 : 12715
Tue Mar 27 22:32:04 2007     length 5 : 9498
Tue Mar 27 22:32:04 2007     length 6 : 6539
Tue Mar 27 22:32:04 2007     length 7 : 4103
Tue Mar 27 22:32:04 2007     length 9+: 5608
Tue Mar 27 22:32:04 2007  largest cycle: 19 relations
Tue Mar 27 22:32:04 2007  matrix is 93822 x 94284 with weight 6322109 (avg 67.05/col)
Tue Mar 27 22:32:05 2007  filtering completed in 4 passes
Tue Mar 27 22:32:05 2007  matrix is 92216 x 92280 with weight 6091770 (avg 66.01/col)
Tue Mar 27 22:32:06 2007  saving the first 48 matrix rows for later
Tue Mar 27 22:32:06 2007  matrix is 92168 x 92280 with weight 4799651 (avg 52.01/col)
Tue Mar 27 22:32:06 2007  matrix includes 32 packed rows
Tue Mar 27 22:38:17 2007  lanczos halted after 1459 iterations
Tue Mar 27 22:38:18 2007  recovered 16 nontrivial dependencies
Tue Mar 27 22:38:21 2007  prp44 factor: 12880349982971406781750299797656170118282799
Tue Mar 27 22:38:21 2007  prp56 factor: 11598857935350921114383370001898924491763276297022728801
Tue Mar 27 22:38:21 2007  elapsed time 00:07:46

Apr 4, 2007 (5th)

By Jo Yeong Uk / Msieve 1.17

9·10¹⁷⁷+1 = 9(0)₁₇₆1_<178> = 3167 · 387077 · 2076611 · 308752979 · 54988062023_<11> · 212417999009_<12> · 60289087720622533_<17> · 479166086119340027893509641_<27> · C89

C89 = P32 · P57

P32 = 54841284613190781418275599643521_<32>

P57 = 618783381714794412883445208544663378606596249013437821041_<57>

Wed Apr  4 18:38:40 2007  
Wed Apr  4 18:38:40 2007  
Wed Apr  4 18:38:40 2007  Msieve v. 1.17
Wed Apr  4 18:38:40 2007  random seeds: 4ee254d4 6fb50e17
Wed Apr  4 18:38:40 2007  factoring 33934875550533712760892172906874721223936456836224646032179227094613311427555598593125361 (89 digits)
Wed Apr  4 18:38:40 2007  commencing quadratic sieve (89-digit input)
Wed Apr  4 18:38:40 2007  using multiplier of 1
Wed Apr  4 18:38:40 2007  sieve interval: 8 blocks of size 65536
Wed Apr  4 18:38:40 2007  processing polynomials in batches of 7
Wed Apr  4 18:38:40 2007  using a sieve bound of 1556179 (58760 primes)
Wed Apr  4 18:38:40 2007  using large prime bound of 124494320 (26 bits)
Wed Apr  4 18:38:40 2007  using double large prime bound of 372622455260160 (42-49 bits)
Wed Apr  4 18:38:40 2007  using trial factoring cutoff of 49 bits
Wed Apr  4 18:38:40 2007  polynomial 'A' values have 11 factors
Wed Apr  4 19:42:36 2007  59084 relations (16766 full + 42318 combined from 610550 partial), need 58856
Wed Apr  4 19:42:36 2007  begin with 627316 relations
Wed Apr  4 19:42:36 2007  reduce to 139149 relations in 10 passes
Wed Apr  4 19:42:36 2007  attempting to read 139149 relations
Wed Apr  4 19:42:37 2007  recovered 139149 relations
Wed Apr  4 19:42:37 2007  recovered 117719 polynomials
Wed Apr  4 19:42:38 2007  attempting to build 59084 cycles
Wed Apr  4 19:42:38 2007  found 59084 cycles in 5 passes
Wed Apr  4 19:42:38 2007  distribution of cycle lengths:
Wed Apr  4 19:42:38 2007     length 1 : 16766
Wed Apr  4 19:42:38 2007     length 2 : 12234
Wed Apr  4 19:42:38 2007     length 3 : 10460
Wed Apr  4 19:42:38 2007     length 4 : 7570
Wed Apr  4 19:42:38 2007     length 5 : 5279
Wed Apr  4 19:42:38 2007     length 6 : 3087
Wed Apr  4 19:42:38 2007     length 7 : 1738
Wed Apr  4 19:42:38 2007     length 9+: 1950
Wed Apr  4 19:42:38 2007  largest cycle: 18 relations
Wed Apr  4 19:42:38 2007  matrix is 58760 x 59084 with weight 3361174 (avg 56.89/col)
Wed Apr  4 19:42:38 2007  filtering completed in 3 passes
Wed Apr  4 19:42:38 2007  matrix is 56982 x 57046 with weight 3171521 (avg 55.60/col)
Wed Apr  4 19:42:39 2007  saving the first 48 matrix rows for later
Wed Apr  4 19:42:39 2007  matrix is 56934 x 57046 with weight 2578905 (avg 45.21/col)
Wed Apr  4 19:42:39 2007  matrix includes 32 packed rows
Wed Apr  4 19:43:20 2007  lanczos halted after 902 iterations
Wed Apr  4 19:43:20 2007  recovered 14 nontrivial dependencies
Wed Apr  4 19:43:20 2007  prp32 factor: 54841284613190781418275599643521
Wed Apr  4 19:43:20 2007  prp57 factor: 618783381714794412883445208544663378606596249013437821041
Wed Apr  4 19:43:20 2007  elapsed time 01:04:40

Apr 4, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(73·10¹⁵⁵-1)/9 = 8(1)₁₅₅_<156> = 7 · 2381242217_<10> · C146

C146 = P56 · P91

P56 = 15791022294533422641288302975988124695328339669549748081_<56>

P91 = 3081544831696971298063038747475176795596646326721934407174520528715845529258633313218743849_<91>

Number: n
N=48660743138931117403363681365899398975704039381650133500834457897155563917113693551241063443598865051121287514059312460533229751601122345218303769
  ( 146 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=15791022294533422641288302975988124695328339669549748081 (pp56)
 r2=3081544831696971298063038747475176795596646326721934407174520528715845529258633313218743849 (pp91)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.00 hours.
Scaled time: 34.22 units (timescale=1.316).
Factorization parameters were as follows:
name: KA_8_1_155
n: 48660743138931117403363681365899398975704039381650133500834457897155563917113693551241063443598865051121287514059312460533229751601122345218303769
skew: 1.0
deg: 5
c5: 73
c0: -1
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:216816, AFBsize:217091, largePrimes:6703712 encountered
Relations: rels:6172652, finalFF:490474
Max relations in full relation-set: 48
Initial matrix: 433972 x 490474 with sparse part having weight 32278992.
Pruned matrix : 383630 x 385863 with weight 19757440.
Total sieving time: 22.53 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.22 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 26.00 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 4, 2007 (3rd)

By Robert Backstrom / GMP-ECM 6.0.1 B1=477500

7·10¹⁵³+1 = 7(0)₁₅₂1_<154> = 53 · 167 · 569 · 173483 · 58181687021_<11> · 240810772871_<12> · 438563879448152243_<18> · C103

C103 = P38 · P65

P38 = 20339748706129911647205888791801144203_<38>

P65 = 64105581640209598722446044764182036063686833229677824048410717867_<65>

Apr 4, 2007 (2nd)

The factor table of 900...001 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Apr 4, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

(29·10¹⁵⁶+7)/9 = 3(2)₁₅₅3_<157> = 47 · C155

C155 = P45 · P111

P45 = 132991322100848707636379191275380420166513791_<45>

P111 = 515506715316065682586052266156769034918158527259325062152327432762009776789896785062695830891823340065597055199_<111>

Number: 32223_156
N=68557919621749408983451536643026004728132387706855791962174940898345153664302600472813238770685579196217494089834515366430260047281323877068557919621749409
  ( 155 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=132991322100848707636379191275380420166513791 (pp45)
 r2=515506715316065682586052266156769034918158527259325062152327432762009776789896785062695830891823340065597055199 (pp111)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 55.91 hours.
Scaled time: 34.22 units (timescale=0.612).
Factorization parameters were as follows:
name: 32223_156
n: 68557919621749408983451536643026004728132387706855791962174940898345153664302600472813238770685579196217494089834515366430260047281323877068557919621749409
m: 10000000000000000000000000000000
c5: 290
c0: 7
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:216531, largePrimes:5599595 encountered
Relations: rels:5525117, finalFF:486163
Max relations in full relation-set: 0
Initial matrix: 433414 x 486163 with sparse part having weight 34136603.
Pruned matrix : 403149 x 405380 with weight 26162517.
Total sieving time: 48.51 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 6.75 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 55.91 hours.
 --------- CPU info (if available) ----------

Apr 3, 2007 (9th)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(5·10¹⁸⁸+1)/3 = 1(6)₁₈₇7_<189> = 27749 · C184

C184

C184 = P39 · C145

P39 = 755690361809164985290505633810819050583_<39>

C145 = [7947993980067834235465756271687538769230388089784361354522292128822489146923171127507833276229709407451844578838435579896131515961401437185117001_<145>]

Apr 3, 2007 (8th)

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000

4·10¹⁶²+1 = 4(0)₁₆₁1_<163> = 2497329853_<10> · 75396687085921_<14> · 376268494658838666197_<21> · C119

C119 = P34 · P85

P34 = 7033585355523255976857977544415093_<34>

P85 = 8027072786280128866004929270459039253458495879153981797095597384581952824282996219837_<85>

Apr 3, 2007 (7th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(2·10¹⁵⁵+1)/3 = (6)₁₅₄7_<155> = 1329067 · C149

C149 = P72 · P78

P72 = 288925333565467115077893873169172388791121847831390307889083748917752483_<72>

P78 = 173610601895909678116740701583211225083394536165258694847576929928468819956747_<78>

Number: n
N=50160501063277221288818898269738596072783890252836513634501997767356097673530880434670838013935088800389044846246778128316079374980092551140511852801
  ( 149 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=288925333565467115077893873169172388791121847831390307889083748917752483 (pp72)
 r2=173610601895909678116740701583211225083394536165258694847576929928468819956747 (pp78)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 27.24 hours.
Scaled time: 22.53 units (timescale=0.827).
Factorization parameters were as follows:
name: KA_6_154_7
n: 50160501063277221288818898269738596072783890252836513634501997767356097673530880434670838013935088800389044846246778128316079374980092551140511852801
skew: 1
deg: 5
c5: 2
c0: 1
m: 10000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:183072, AFBsize:182816, largePrimes:6581937 encountered
Relations: rels:6044442, finalFF:453719
Max relations in full relation-set: 48
Initial matrix: 365953 x 453719 with sparse part having weight 34516891.
Pruned matrix : 295057 x 296950 with weight 18465767.
Total sieving time: 23.76 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 2.98 hours.
Total square root time: 0.20 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 27.24 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 2100+ stepping 02
Memory: 904260k/917504k available (1815k kernel code, 12496k reserved, 846k data, 272k init, 0k highmem)
Calibrating delay loop... 3440.64 BogoMIPS

(82·10¹⁵⁵-1)/9 = 9(1)₁₅₅_<156> = 32527021 · C149

C149 = P47 · P103

P47 = 20585795344968187217304961622088033967729763899_<47>

P103 = 1360690654509266104508496867081510258619887149538180594731855032123036171966583286697625777439752406809_<103>

Number: n
N=28010899341538566077450225494400827887408167846391807940576885633366520441915388166383607988912083621525349988586754105490051213454534035290569988291
  ( 149 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=20585795344968187217304961622088033967729763899 (pp47)
 r2=1360690654509266104508496867081510258619887149538180594731855032123036171966583286697625777439752406809 (pp103)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 28.64 hours.
Scaled time: 37.75 units (timescale=1.318).
Factorization parameters were as follows:
name: KA_9_1_155
n: 28010899341538566077450225494400827887408167846391807940576885633366520441915388166383607988912083621525349988586754105490051213454534035290569988291
skew: 1.0
deg: 5
c5: 82
c0: -1
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:216816, AFBsize:216752, largePrimes:7136773 encountered
Relations: rels:6741053, finalFF:610738
Max relations in full relation-set: 48
Initial matrix: 433636 x 610738 with sparse part having weight 47311105.
Pruned matrix : 290143 x 292375 with weight 22847109.
Total sieving time: 25.77 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 2.60 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 28.64 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10¹⁴⁰+1 = 7(0)₁₃₉1_<141> = 53 · 19597 · 61541309707039_<14> · 52143054355223185883_<20> · C102

C102 = P32 · P71

P32 = 10854524950314912484667997912049_<32>

P71 = 19349001352421860990031887892254003455517463005159744816652778091636397_<71>

Number: n
N=210024217943540075133468448585998713651423975051285334416970611675803218930172853494308591985693247453
  ( 102 digits)
Divisors found:
 r1=10854524950314912484667997912049 (pp32)
 r2=19349001352421860990031887892254003455517463005159744816652778091636397 (pp71)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.73 hours.
Scaled time: 7.94 units (timescale=1.027).
Factorization parameters were as follows:
name: n
n: 210024217943540075133468448585998713651423975051285334416970611675803218930172853494308591985693247453
skew: 4857.17
# norm 1.15e+13
c5: 17700
c4: 289407331
c3: -1642729399766
c2: -6867015070714932
c1: 17195621348974928392
c0: 769880280619743055872
# alpha -4.40
Y1: 10035206137
Y0: -25993135675887091241
# Murphy_E 3.01e-09
# M 78178482628374967068165789630605424947992957095981539722006975876156390065512434849895881884496153165
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [100000, 800001)
Primes: RFBsize:169511, AFBsize:169675, largePrimes:3831878 encountered
Relations: rels:3726342, finalFF:397041
Max relations in full relation-set: 48
Initial matrix: 339264 x 397041 with sparse part having weight 19046546.
Pruned matrix : 268634 x 270394 with weight 8777420.
Total sieving time: 6.72 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.73 hours.
Total square root time: 0.11 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 7.73 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 3000+ stepping 00
Memory: 2076900k/2097088k available (1540k kernel code, 19412k reserved, 599k data, 144k init, 0k highmem)
Calibrating delay loop... 4292.60 BogoMIPS
x86info v1.12b.  Dave Jones 2001-2003
Feedback to <davej@redhat.com>.

Found 1 CPU
--------------------------------------------------------------------------
Family: 6 Model: 10 Stepping: 0
CPU Model : Athlon XP (Barton)
2.2Ghz processor (estimate).

Apr 3, 2007 (6th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

3·10¹⁶³+1 = 3(0)₁₆₂1_<164> = C164

C164 = P43 · P122

P43 = 2693727049321118094591486398079193352608837_<43>

P122 = 11136985838101413491867306813366781640721780664180020279181015243224647866545476655493916704578164265918304339860447237773_<122>

Number: 30001_163
N=30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
  ( 164 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=2693727049321118094591486398079193352608837 (pp43)
 r2=11136985838101413491867306813366781640721780664180020279181015243224647866545476655493916704578164265918304339860447237773 (pp122)
Version: GGNFS-0.77.1-20050930-k8
Total time: 69.52 hours.
Scaled time: 62.78 units (timescale=0.903).
Factorization parameters were as follows:
n: 30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
m: 500000000000000000000000000000000
c5: 24
c0: 25
skew: 1.01
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 5400001)
Primes: RFBsize:348513, AFBsize:348511, largePrimes:5904444 encountered
Relations: rels:6083619, finalFF:819600
Max relations in full relation-set: 28
Initial matrix: 697090 x 819600 with sparse part having weight 50328626.
Pruned matrix : 598977 x 602526 with weight 35613761.
Total sieving time: 66.39 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 2.94 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.3,2.3,100000
total time: 69.52 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239)
Total of 2 processors activated (9340.09 BogoMIPS).

7·10¹³³+1 = 7(0)₁₃₂1_<134> = 43 · 31938787737893_<14> · C119

C119 = P34 · P86

P34 = 2453625078680201566748816367059723_<34>

P86 = 20773178568202312946561506523760891062078565941949791090519972188145838947872363815413_<86>

Number: 70001_133
N=50969591898843277031731533454957690483593397704702865881216299727962991255065213977531205848685177328201602448718910599
  ( 119 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=2453625078680201566748816367059723 (pp34)
 r2=20773178568202312946561506523760891062078565941949791090519972188145838947872363815413 (pp86)
Version: GGNFS-0.77.1-20050930-k8
Total time: 5.53 hours.
Scaled time: 5.00 units (timescale=0.904).
Factorization parameters were as follows:
n: 50969591898843277031731533454957690483593397704702865881216299727962991255065213977531205848685177328201602448718910599
m: 500000000000000000000000000
c5: 56
c0: 25
skew: 1
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [650000, 1450001)
Primes: RFBsize:100021, AFBsize:100763, largePrimes:1591563 encountered
Relations: rels:1628120, finalFF:233486
Max relations in full relation-set: 28
Initial matrix: 200851 x 233486 with sparse part having weight 10220243.
Pruned matrix : 184070 x 185138 with weight 6892410.
Total sieving time: 5.38 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1300000,1300000,25,25,43,43,2.3,2.3,50000
total time: 5.53 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239)
Total of 2 processors activated (9340.09 BogoMIPS).

Apr 3, 2007 (5th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

4·10¹⁵⁵+1 = 4(0)₁₅₄1_<156> = 7 · 19 · 90173 · C149

C149 = P68 · P81

P68 = 63329687397592132145980877526417873030946686466430656344663544587463_<68>

P81 = 526652909060236900579923203193911048657743442112564846958614597680814721066334503_<81>

Number: n
N=33352764097817320073719614485405622558942463897092047542030527951742552682150075931736564193356312831917327836575458252386869717182735375250698135889
  ( 149 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=63329687397592132145980877526417873030946686466430656344663544587463 (pp68)
 r2=526652909060236900579923203193911048657743442112564846958614597680814721066334503 (pp81)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 25.81 hours.
Scaled time: 30.85 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_4_0_154_1
n: 33352764097817320073719614485405622558942463897092047542030527951742552682150075931736564193356312831917327836575458252386869717182735375250698135889
type: snfs
skew: 1
deg: 5
c5: 4
c0: 1
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:216816, AFBsize:216491, largePrimes:6134762 encountered
Relations: rels:5639317, finalFF:512645
Max relations in full relation-set: 28
Initial matrix: 433371 x 512645 with sparse part having weight 23754018.
Pruned matrix : 355721 x 357951 with weight 13043634.
Total sieving time: 23.48 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 2.02 hours.
Total square root time: 0.13 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 25.81 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Apr 3, 2007 (4th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

7·10¹⁴⁴+1 = 7(0)₁₄₃1_<145> = 23 · C144

C144 = P66 · P78

P66 = 809940785427965343526229739355042505157936405047381591533420897433_<66>

P78 = 375765527014597615163944861799356289186159071363960150031523628164542872741439_<78>

Number: 70001_144
N=304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826087
  ( 144 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=809940785427965343526229739355042505157936405047381591533420897433 (pp66)
 r2=375765527014597615163944861799356289186159071363960150031523628164542872741439 (pp78)
Version: GGNFS-0.77.1-20050930-k8
Total time: 14.94 hours.
Scaled time: 13.49 units (timescale=0.903).
Factorization parameters were as follows:
n: 304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826087
m: 100000000000000000000000000000
c5: 7
c0: 10
skew: 1.07
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 1600001)
Primes: RFBsize:114155, AFBsize:114342, largePrimes:2746135 encountered
Relations: rels:2738222, finalFF:297904
Max relations in full relation-set: 28
Initial matrix: 228562 x 297904 with sparse part having weight 23793466.
Pruned matrix : 205655 x 206861 with weight 13817480.
Total sieving time: 14.65 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000
total time: 14.94 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239)
Total of 2 processors activated (9340.09 BogoMIPS).

Apr 3, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

7·10¹⁵⁵+1 = 7(0)₁₅₄1_<156> = 1129 · 1193 · C150

C150 = P62 · P88

P62 = 55130793260966415361235729756577932205405829083406166227977587_<62>

P88 = 9426911131444313172543736731542159160773688947699429609478209619825750212976152411926859_<88>

Number: n
N=519713088677159426444635335886856975700443315264641616990757273941511489000272478147920739299293115954672109300117232423860176390622297027909335309233
  ( 150 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=55130793260966415361235729756577932205405829083406166227977587 (pp62)
 r2=9426911131444313172543736731542159160773688947699429609478209619825750212976152411926859 (pp88)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 27.19 hours.
Scaled time: 27.90 units (timescale=1.026).
Factorization parameters were as follows:
name: KA_7_0_154_1
n: 519713088677159426444635335886856975700443315264641616990757273941511489000272478147920739299293115954672109300117232423860176390622297027909335309233
type: snfs
skew: .68
deg: 5
c5: 7
c0: 1
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:216816, AFBsize:216696, largePrimes:6092352 encountered
Relations: rels:5565111, finalFF:487372
Max relations in full relation-set: 48
Initial matrix: 433579 x 487372 with sparse part having weight 24045932.
Pruned matrix : 379538 x 381769 with weight 14885224.
Total sieving time: 24.79 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 2.03 hours.
Total square root time: 0.15 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 27.19 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 3000+ stepping 00
Memory: 2076900k/2097088k available (1540k kernel code, 19412k reserved, 599k data, 144k init, 0k highmem)
Calibrating delay loop... 4292.60 BogoMIPS
x86info v1.12b.  Dave Jones 2001-2003
Feedback to <davej@redhat.com>.

Found 1 CPU
--------------------------------------------------------------------------
Family: 6 Model: 10 Stepping: 0
CPU Model : Athlon XP (Barton)
2.2Ghz processor (estimate).

Apr 3, 2007 (2nd)

By Alfred Reich / GMP-ECM B1=250000

10¹⁷⁹²+1 = 1(0)₁₇₉₁1_<1793> = 10753 · 32257 · 8253953 · 9524994049_<10> · 73171503617_<11> · 45723922339769773677559297_<26> · 161659663356434944948942201164163009493717089102370771373121362150985544514761379133487997023996012149425048654486737380370333511296921220558813648612791137845552210697266256120930676972710885926127946416909582894897995807233_<225> · C1506

C1506 = P30 · C1476

P30 = 949383321082513089661541033473_<30>

Apr 3, 2007

By Bruce Dodson / GMP-ECM B1=43000000 / Mar 30, 2007

10³⁶¹+1 = 1(0)₃₆₀1_<362> = 11 · 43321 · 909090909090909091_<18> · C338

C338 = P55 · C283

P55 = 5140192330491733331414521378576126342075768810496980939_<55>

By Yousuke Koide / GMP-ECM B1=1250000 / Apr 2, 2007

(10⁸⁹⁵-1)/9 = (1)₈₉₅_<895> = 41 · 271 · 359 · 36558961 · 252812074841_<12> · 4201521652717_<13> · 352543640588653_<15> · 571544047837540227171107263031017853607119654486278118381637405539602949994236278780111557713711574640626700398384915989416568503505447054089_<141> · C701

C701 = P42 · C660

P42 = 160448729579634932307271265568632037109271_<42>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 2, 2007 (6th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

7·10¹³⁸+1 = 7(0)₁₃₇1_<139> = 683 · 323565643 · C128

C128 = P34 · P94

P34 = 5455759339741710826253913205440113_<34>

P94 = 5805768712228287085116276448327387554343755401317995474938232335903884659779580329249392645433_<94>

Number: 70001_138
N=31674876876119682273182173592100422640303476152979377067510779551529709019971793502322392463306558652053674526010259588124453929
  ( 128 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=5455759339741710826253913205440113 (pp34)
 r2=5805768712228287085116276448327387554343755401317995474938232335903884659779580329249392645433 (pp94)
Version: GGNFS-0.77.1-20050930-k8
Total time: 10.45 hours.
Scaled time: 9.26 units (timescale=0.886).
Factorization parameters were as follows:
n: 31674876876119682273182173592100422640303476152979377067510779551529709019971793502322392463306558652053674526010259588124453929
m: 5000000000000000000000000000
c5: 56
c0: 25
skew: 1
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [650000, 1250001)
Primes: RFBsize:100021, AFBsize:100763, largePrimes:1595353 encountered
Relations: rels:1636224, finalFF:234205
Max relations in full relation-set: 28
Initial matrix: 200851 x 234205 with sparse part having weight 10228624.
Pruned matrix : 183788 x 184856 with weight 6854937.
Total sieving time: 10.30 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1300000,1300000,25,25,43,43,2.3,2.3,50000
total time: 10.45 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239)
Total of 2 processors activated (9340.09 BogoMIPS).

Apr 2, 2007 (5th)

By suberi / GMP-ECM 6.1.2 B1=3000000

(16·10¹⁸⁷-61)/9 = 1(7)₁₈₆1_<188> = 11 · C187

C187 = P36 · P151

P36 = 224187443841669121284171214256607419_<36>

P151 = 7208974724307126960936798016662298358054035706538253992990330169438604402959170146020867892824891898686186801010965926966443527148977721432936345060819_<151>

Apr 2, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(2·10¹⁵⁵+43)/9 = (2)₁₅₄7_<155> = 3² · 31 · C152

C152 = P42 · P50 · P61

P42 = 661935245772807400405303706022642863715601_<42>

P50 = 39969992495755205306998842332734817740510356056777_<50>

P61 = 3010465883270152612607869483290283204139039754469978537289069_<61>

Number: n
N=79649542015133412982875348466746316208681800079649542015133412982875348466746316208681800079649542015133412982875348466746316208681800079649542015133413
  ( 152 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=661935245772807400405303706022642863715601 (pp42)
 r2=39969992495755205306998842332734817740510356056777 (pp50)
 r3=3010465883270152612607869483290283204139039754469978537289069 (pp61)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 30.67 hours.
Scaled time: 25.36 units (timescale=0.827).
Factorization parameters were as follows:
name: KA_2_154_7
n: 79649542015133412982875348466746316208681800079649542015133412982875348466746316208681800079649542015133412982875348466746316208681800079649542015133413
skew: 1
deg: 5
c5: 2
c0: 43
m: 10000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1000001)
Primes: RFBsize:183072, AFBsize:183126, largePrimes:6529615 encountered
Relations: rels:5939827, finalFF:413909
Max relations in full relation-set: 48
Initial matrix: 366263 x 413909 with sparse part having weight 31561080.
Pruned matrix : 329480 x 331375 with weight 20050356.
Total sieving time: 26.37 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 3.66 hours.
Total square root time: 0.33 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 30.67 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 2100+ stepping 02
Memory: 904260k/917504k available (1815k kernel code, 12496k reserved, 846k data, 272k init, 0k highmem)
Calibrating delay loop... 3440.64 BogoMIPS

7·10¹³²+1 = 7(0)₁₃₁1_<133> = 3917 · 8731 · C126

C126 = P47 · P80

P47 = 14638283495713663736241157708855869290229636409_<47>

P80 = 13982677029538623333501754987296211103374639783010627959614701454655065820539607_<80>

Number: n
N=204682390387389786939374567224670824662719240059899424336625103763006798350154668248296231092500738391723322508656383793751263
  ( 126 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=14638283495713663736241157708855869290229636409 (pp47)
 r2=13982677029538623333501754987296211103374639783010627959614701454655065820539607 (pp80)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 5.29 hours.
Scaled time: 6.32 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_7_0_131_1
n: 204682390387389786939374567224670824662719240059899424336625103763006798350154668248296231092500738391723322508656383793751263
type: snfs
skew: .27
deg: 5
c5: 700
c0: 1
m: 100000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 600001)
Primes: RFBsize:148933, AFBsize:148445, largePrimes:5256226 encountered
Relations: rels:4734818, finalFF:475275
Max relations in full relation-set: 28
Initial matrix: 297445 x 475275 with sparse part having weight 14694290.
Pruned matrix : 149989 x 151540 with weight 4433861.
Total sieving time: 4.88 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.24 hours.
Total square root time: 0.03 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.2,2.2,50000
total time: 5.29 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(32·10¹⁵⁵-23)/9 = 3(5)₁₅₄3_<156> = 11 · 6121 · C151

C151 = P44 · P107

P44 = 61328780631367967021026430277387968633477083_<44>

P107 = 86104941161045057261632331707436338464311272986903568019467121044209094189256912159281648305922546899162961_<107>

Number: n
N=5280711047742578538200168652709087278602063767886345896474960353411586870172068669046287082555666120443117665793699121586721652070451286265695675922763
  ( 151 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=61328780631367967021026430277387968633477083 (pp44)
 r2=86104941161045057261632331707436338464311272986903568019467121044209094189256912159281648305922546899162961 (pp107)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 20.77 hours.
Scaled time: 27.49 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_3_5_154_3
n: 5280711047742578538200168652709087278602063767886345896474960353411586870172068669046287082555666120443117665793699121586721652070451286265695675922763
skew: 1.0
deg: 5
c5: 1
c0: -23
m: 20000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:183072, AFBsize:183106, largePrimes:6476865 encountered
Relations: rels:5900796, finalFF:422371
Max relations in full relation-set: 48
Initial matrix: 366242 x 422371 with sparse part having weight 31319894.
Pruned matrix : 321698 x 323593 with weight 18573106.
Total sieving time: 18.14 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 2.41 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 20.77 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 2, 2007 (3rd)

By suberi / GMP-ECM 6.1.2 B1=1500000

(16·10²⁴³-61)/9 = 1(7)₂₄₂1_<244> = 7 · 11 · 30296731 · 60143609 · 1911168697_<10> · C217

C217 = P32 · P185

P32 = 73816070285390658060425630041457_<32>

P185 = 89815552858504538029397848590765921832955963914835824465961063265706776182932599671826275231815308372814936304804714931802441141565531885161718561173705190056377611445342403457383082453_<185>

Apr 2, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

7·10¹⁴⁵+1 = 7(0)₁₄₄1_<146> = 67 · 599 · 412457 · 466747 · 1141698744217337_<16> · 2434518084465653_<16> · C100

C100 = P34 · P67

P34 = 1795008466954729168800209414936453_<34>

P67 = 1815955371841082430332694563327821684185611841419005671789292422271_<67>

Number: 70001_145
N=3259655268066666531787153780348226028624564585225737486803402609014796394727034639592215715906944763
  ( 100 digits)
Divisors found:
 r1=1795008466954729168800209414936453 (pp34)
 r2=1815955371841082430332694563327821684185611841419005671789292422271 (pp67)
Version: GGNFS-0.77.1-20050930-k8
Total time: 4.36 hours.
Scaled time: 3.94 units (timescale=0.904).
Factorization parameters were as follows:
name: 70001_145
n: 3259655268066666531787153780348226028624564585225737486803402609014796394727034639592215715906944763
skew: 5434.66
# norm 8.87e+13
c5: 138600
c4: -628977735
c3: -4844662654778
c2: 56975616878785198
c1: 12597830851657240872
c0: -315955197528020586762632
# alpha -6.43
Y1: 27202766879
Y0: -7486573984825469671
# Murphy_E 3.49e-09
# M 2021588631885662640472603336663148478076687078668088154026142239430095812078564709322760587979382906
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [750000, 1200001)
Primes: RFBsize:114155, AFBsize:114915, largePrimes:3762566 encountered
Relations: rels:3629001, finalFF:277528
Max relations in full relation-set: 28
Initial matrix: 229154 x 277528 with sparse part having weight 19757876.
Pruned matrix : 193470 x 194679 with weight 11201879.
Polynomial selection time: 0.25 hours.
Total sieving time: 3.82 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,48,48,2.5,2.5,50000
total time: 4.36 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239)
Total of 2 processors activated (9340.09 BogoMIPS).

Apr 2, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(4·10¹⁵⁵+23)/9 = (4)₁₅₄7_<155> = 13 · 61 · C152

C152 = P54 · P99

P54 = 148385991234646868255677763169400682719601527549176821_<54>

P99 = 377703833218830785744902903453732714767953802089122910383042080301772785279239335742045411173229499_<99>

Number: n
N=56045957685301947597029564242678996777357433095138013170800056045957685301947597029564242678996777357433095138013170800056045957685301947597029564242679
  ( 152 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=148385991234646868255677763169400682719601527549176821 (pp54)
 r2=377703833218830785744902903453732714767953802089122910383042080301772785279239335742045411173229499 (pp99)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 30.59 hours.
Scaled time: 36.56 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_4_154_7
n: 56045957685301947597029564242678996777357433095138013170800056045957685301947597029564242678996777357433095138013170800056045957685301947597029564242679
type: snfs
skew: 1
deg: 5
c5: 4
c0: 23
m: 10000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [1600000, 1600000)
Primes: RFBsize:230209, AFBsize:230627, largePrimes:6238983 encountered
Relations: rels:5736835, finalFF:526134
Max relations in full relation-set: 28
Initial matrix: 460900 x 526134 with sparse part having weight 23788925.
Pruned matrix : 395232 x 397600 with weight 14177810.
Total sieving time: 27.64 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.50 hours.
Total square root time: 0.26 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 30.59 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

7·10¹³¹+1 = 7(0)₁₃₀1_<132> = 16573 · 827182080526619_<15> · C113

C113 = P32 · P81

P32 = 60570823643539584765292420545299_<32>

P81 = 843009197215127294834358695906019746493107625259983272341093175391722476971875477_<81>

Number: n
N=51061761414399357027026281791696991073532907727375622679324186881116608610691045434679404986513298702271065732623
  ( 113 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=60570823643539584765292420545299 (pp32)
 r2=843009197215127294834358695906019746493107625259983272341093175391722476971875477 (pp81)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.67 hours.
Scaled time: 6.85 units (timescale=1.027).
Factorization parameters were as follows:
name: KA_7_0_130_1
n: 51061761414399357027026281791696991073532907727375622679324186881116608610691045434679404986513298702271065732623
type: snfs
skew: 2.34
deg: 5
c5: 70
c0: 1
m: 100000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 700001)
Primes: RFBsize:148933, AFBsize:149260, largePrimes:4789248 encountered
Relations: rels:4160441, finalFF:353209
Max relations in full relation-set: 48
Initial matrix: 298260 x 353209 with sparse part having weight 10465394.
Pruned matrix : 209368 x 210923 with weight 4935962.
Total sieving time: 6.13 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.34 hours.
Total square root time: 0.07 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.2,2.2,50000
total time: 6.67 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 3000+ stepping 00
Memory: 2076900k/2097088k available (1540k kernel code, 19412k reserved, 599k data, 144k init, 0k highmem)
Calibrating delay loop... 4292.60 BogoMIPS
x86info v1.12b.  Dave Jones 2001-2003
Feedback to <davej@redhat.com>.

Found 1 CPU
--------------------------------------------------------------------------
Family: 6 Model: 10 Stepping: 0
CPU Model : Athlon XP (Barton)
2.2Ghz processor (estimate).

Apr 1, 2007 (7th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs

7·10¹⁵⁷+1 = 7(0)₁₅₆1_<158> = 107 · 131 · 257 · 44701 · 36067159 · 412688953 · 11433124763162139881_<20> · 50150999103831809543_<20> · C92

C92 = P44 · P48

P44 = 58723657563182981121109730736410322969118927_<44>

P48 = 867361611497461809778725449710059255808380370747_<48>

Number: n
N=50934646257027501761195466390338358257517450725863747999950593705003914525713753040194828469
  ( 92 digits)
Divisors found:
 r1=58723657563182981121109730736410322969118927 (pp44)
 r2=867361611497461809778725449710059255808380370747 (pp48)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.26 hours.
Scaled time: 4.37 units (timescale=1.027).
Factorization parameters were as follows:
name: KA_7_0_156_1
n:  50934646257027501761195466390338358257517450725863747999950593705003914525713753040194828469
m:  1232264682236136063145
deg: 4
c4: 22090080
c3: -246466740744
c2: -33306940536444256
c1: 1000581673960989041
c0: 43321014325197429213924
skew: 1635.250
type: gnfs
# adj. I(F,S) = 53.214
# E(F1,F2) = 1.198140e-04
# GGNFS version 0.77.1-20051202-athlon polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=58.00000000, seed=1175417502.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 700000
alim: 700000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.4
alambda: 2.4
qintsize: 40000

type: gnfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [175000, 655001)
Primes: RFBsize:56543, AFBsize:57008, largePrimes:1529129 encountered
Relations: rels:1493247, finalFF:136569
Max relations in full relation-set: 48
Initial matrix: 113627 x 136569 with sparse part having weight 12059376.
Pruned matrix : 106514 x 107146 with weight 7026392.
Polynomial selection time: 0.17 hours.
Total sieving time: 3.73 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.17 hours.
Total square root time: 0.10 hours, sqrts: 3.
Prototype def-par.txt line would be:
gnfs,91,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,25,25,44,44,2.4,2.4,40000
total time: 4.26 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 3000+ stepping 00
Memory: 2076900k/2097088k available (1540k kernel code, 19412k reserved, 599k data, 144k init, 0k highmem)
Calibrating delay loop... 4292.60 BogoMIPS
x86info v1.12b.  Dave Jones 2001-2003
Feedback to <davej@redhat.com>.

Found 1 CPU
--------------------------------------------------------------------------
Family: 6 Model: 10 Stepping: 0
CPU Model : Athlon XP (Barton)
2.2Ghz processor (estimate).

Apr 1, 2007 (6th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

7·10¹¹⁸+1 = 7(0)₁₁₇1_<119> = 233 · 2053 · 3761 · 68777 · C105

C105 = P45 · P60

P45 = 573478493821804383126117265442725302450908591_<45>

P60 = 986482696674090871440722049772557294942194567424256350401987_<60>

Number: 70001_118
N=565726611069929549103721920736813842762633274721108994347074829384094876815420884707818446157636241770317
  ( 105 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=573478493821804383126117265442725302450908591 (pp45)
 r2=986482696674090871440722049772557294942194567424256350401987 (pp60)
Version: GGNFS-0.77.1-20050930-k8
Total time: 1.23 hours.
Scaled time: 1.11 units (timescale=0.908).
Factorization parameters were as follows:
n: 565726611069929549103721920736813842762633274721108994347074829384094876815420884707818446157636241770317
m: 500000000000000000000000
c5: 56
c0: 25
skew: 1
type: snfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [350000, 500001)
Primes: RFBsize:56543, AFBsize:56853, largePrimes:2008292 encountered
Relations: rels:2032184, finalFF:180139
Max relations in full relation-set: 28
Initial matrix: 113463 x 180139 with sparse part having weight 15070540.
Pruned matrix : 95115 x 95746 with weight 5531881.
Total sieving time: 1.15 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.4,2.4,25000
total time: 1.23 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239)
Total of 2 processors activated (9340.09 BogoMIPS).

7·10¹²⁹+1 = 7(0)₁₂₈1_<130> = C130

C130 = P47 · P84

P47 = 20339094283792370330464042356579607994600801891_<47>

P84 = 344164784445593301152541755553359867327580661913692995263470054136783938426510011211_<84>

Number: 70001_129
N=7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
  ( 130 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=20339094283792370330464042356579607994600801891 (pp47)
 r2=344164784445593301152541755553359867327580661913692995263470054136783938426510011211 (pp84)
Version: GGNFS-0.77.1-20050930-k8
Total time: 3.36 hours.
Scaled time: 3.05 units (timescale=0.906).
Factorization parameters were as follows:
n: 7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
m: 100000000000000000000000000
c5: 7
c0: 10
skew: 1.07
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 1050001)
Primes: RFBsize:78498, AFBsize:78531, largePrimes:1534031 encountered
Relations: rels:1534832, finalFF:179547
Max relations in full relation-set: 28
Initial matrix: 157094 x 179547 with sparse part having weight 10290326.
Pruned matrix : 149259 x 150108 with weight 7019841.
Total sieving time: 3.25 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 3.36 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.61 BogoMIPS (lpj=2335806)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239)
Total of 2 processors activated (9340.09 BogoMIPS).

Apr 1, 2007 (5th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(67·10¹⁵⁵+23)/9 = 7(4)₁₅₄7_<156> = 3² · 11 · 59 · 757 · 1277 · 769297 · 1235879 · 433604364641179_<15> · C120

C120 = P50 · P71

P50 = 22928700027420573259550411439689826644603502508189_<50>

P71 = 13948106057056804745088320535643843511280832362656801314221379280509351_<71>

Number: n
N=319811939732903422928211520638581135594400328539761352160261824264315953518741377685581991531923423122342513529968575339
  ( 120 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=22928700027420573259550411439689826644603502508189 (pp50)
 r2=13948106057056804745088320535643843511280832362656801314221379280509351 (pp71)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 28.49 hours.
Scaled time: 29.26 units (timescale=1.027).
Factorization parameters were as follows:
name: KA_7_4_154_7
n: 319811939732903422928211520638581135594400328539761352160261824264315953518741377685581991531923423122342513529968575339
type: snfs
skew: 1
deg: 5
c5: 67
c0: 23
m: 10000000000000000000000000000000
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [700000, 1700001)
Primes: RFBsize:203362, AFBsize:203097, largePrimes:6631404 encountered
Relations: rels:6131336, finalFF:499186
Max relations in full relation-set: 48
Initial matrix: 406524 x 499186 with sparse part having weight 36598443.
Pruned matrix : 333552 x 335648 with weight 20323473.
Total sieving time: 25.34 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 2.56 hours.
Total square root time: 0.41 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.3,2.3,100000
total time: 28.49 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 3000+ stepping 00
Memory: 2076900k/2097088k available (1540k kernel code, 19412k reserved, 599k data, 144k init, 0k highmem)
Calibrating delay loop... 4292.60 BogoMIPS
x86info v1.12b.  Dave Jones 2001-2003
Feedback to <davej@redhat.com>.

Found 1 CPU
--------------------------------------------------------------------------
Family: 6 Model: 10 Stepping: 0
CPU Model : Athlon XP (Barton)
2.2Ghz processor (estimate).

Apr 1, 2007 (4th)

The factor table of 700...001 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Apr 1, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

3·10¹⁵⁵+1 = 3(0)₁₅₄1_<156> = 13 · 29² · C152

C152 = P42 · P51 · P60

P42 = 847002118930358570602520920381717175156063_<42>

P51 = 213090300524279549137442960054809434214996463074123_<51>

P60 = 152031551632891694465641580404499699339343734544590141354153_<60>

Number: n
N=27439860971371078386536174883380590871672916857221256745632488795390103356809658831061922619592060733558949967986828866733741882374462636055977316381597
  ( 152 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=847002118930358570602520920381717175156063 (pp42)
 r2=213090300524279549137442960054809434214996463074123 (pp51)
 r3=152031551632891694465641580404499699339343734544590141354153 (pp60)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.48 hours.
Scaled time: 25.79 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_3_0_154_1
n: 27439860971371078386536174883380590871672916857221256745632488795390103356809658831061922619592060733558949967986828866733741882374462636055977316381597
skew: 1.0
deg: 5
c5: 3
c0: 1
m: 10000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:183072, AFBsize:183166, largePrimes:6441974 encountered
Relations: rels:5875787, finalFF:426749
Max relations in full relation-set: 48
Initial matrix: 366303 x 426749 with sparse part having weight 31449065.
Pruned matrix : 316723 x 318618 with weight 18266116.
Total sieving time: 16.85 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 2.29 hours.
Total square root time: 0.18 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 19.48 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Apr 1, 2007 (2nd)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

3·10¹⁷⁸+1 = 3(0)₁₇₇1_<179> = 2050459 · 12264541 · 340688242377207018081711127_<27> · C139

C139 = P31 · P108

P31 = 5069346827014420672241942756293_<31>

P108 = 690732220068543526727568186205626712603241853899400661384995347253624067067728995244495344555464573552973589_<108>

3·10¹⁶²+1 = 3(0)₁₆₁1_<163> = 7130941393003213_<16> · C147

C147 = P36 · C112

P36 = 103809697153908617469853075665675511_<36>

C112 = [4052625413616873991636843572634283505999285953539026570840954837694883840351540445126100833603885531257627444707_<112>]

Apr 1, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(2·10¹⁷²+43)/9 = (2)₁₇₁7_<172> = C172

C172 = P43 · P130

P43 = 1754614804757565785712489120426881346518977_<43>

P130 = 1266501465846952949874835380376498574495553770154845880082310728334619055651692455210844385139552416214859403953453928983218567251_<130>

Number: n
N=2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227
  ( 172 digits)
SNFS difficulty: 172 digits.
Divisors found:
 r1=1754614804757565785712489120426881346518977 (pp43)
 r2=1266501465846952949874835380376498574495553770154845880082310728334619055651692455210844385139552416214859403953453928983218567251 (pp130)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 271.55 hours.
Scaled time: 224.57 units (timescale=0.827).
Factorization parameters were as follows:
name: KA_C172_2_171_7
n: 2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227
skew: 1
deg: 5
c5: 200
c0: 43
m: 10000000000000000000000000000000000
type: snfs
rlim: 4800000
alim: 4800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 200000
Factor base limits: 4800000/4800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [2400000, 10000001)
Primes: RFBsize:335439, AFBsize:335372, largePrimes:8991273 encountered
Relations: rels:8540919, finalFF:760748
Max relations in full relation-set: 48
Initial matrix: 670876 x 760748 with sparse part having weight 107554650.
Pruned matrix : 626583 x 630001 with weight 85954256.
Total sieving time: 236.73 hours.
Total relation processing time: 0.72 hours.
Matrix solve time: 33.80 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,172,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,48,48,2.5,2.5,100000
total time: 271.55 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 2100+ stepping 02
Memory: 904260k/917504k available (1815k kernel code, 12496k reserved, 846k data, 272k init, 0k highmem)
Calibrating delay loop... 3440.64 BogoMIPS

March 2007

Mar 31, 2007 (4th)

By suberi / GGNFS-0.77.1-20060513-pentium4, GMP-ECM 6.1.2 B1=1500000

6·10¹³⁴+1 = 6(0)₁₃₃1_<135> = 13183 · 56512788861073_<14> · C117

C117 = P37 · P38 · P43

P37 = 4433404553816215317147736447963746529_<37>

P38 = 95562856740921441632025329178966092257_<38>

P43 = 1900919699476513791402495760985135475898063_<43>

Number: 60001_134
N=805360376054171448926513211091415837287242409322705512939398427708441937403689882581959931662204102681244824764929039
  ( 117 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=4433404553816215317147736447963746529 (pp37)
 r2=95562856740921441632025329178966092257 (pp38)
 r3=1900919699476513791402495760985135475898063 (pp43)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 8.00 hours.
Scaled time: 4.86 units (timescale=0.607).
Factorization parameters were as follows:
n: 805360376054171448926513211091415837287242409322705512939398427708441937403689882581959931662204102681244824764929039
m: 1000000000000000000000000000
c5: 3
c0: 5
skew: 1.11
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:63968, largePrimes:1495955 encountered
Relations: rels:1492100, finalFF:171961
Max relations in full relation-set: 28
Initial matrix: 142531 x 171961 with sparse part having weight 12288325.
Pruned matrix : 132417 x 133193 with weight 7795674.
Total sieving time: 7.41 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.43 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.00 hours.
 --------- CPU info (if available) ----------

The factor table of 600...001 was completed up to n=150.

(16·10²³⁸-61)/9 = 1(7)₂₃₇1_<239> = 13 · 127 · 5657 · 46430180224264648553519_<23> · 254357642020012614687158935739_<30> · C180

C180 = P37 · P143

P37 = 2995094195117222887884298164866532149_<37>

P143 = 53813170009834495019293890293026883737954771285601624407366337052839069598577066902859258931966909830488746548353116927917982040532206068831417_<143>

(16·10²¹⁶-61)/9 = 1(7)₂₁₅1_<217> = 83 · 45734749 · 13663537919328949_<17> · C191

C191 = P38 · C154

P38 = 16993254544088994418802208329222111041_<38>

C154 = [2017034616574578333352594311052563596623521835744304536991343545930368699537861663516241055764361488063643138782918033528620871827176764508692767386386057_<154>]

(16·10²⁰³-61)/9 = 1(7)₂₀₂1_<204> = 3 · 11 · C202

C202 = P29 · C173

P29 = 91665371598605909009152456397_<29>

C173 = [58770343623276365051701043350027004518200626964137470076070836828570454371967585994649096276964859765755465444625233759214408845503984098397332260968196397777431561428879671_<173>]

Mar 31, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(25·10¹⁵⁵-1)/3 = 8(3)₁₅₅_<156> = 2203249 · 37543801 · 49716496603_<11> · 1653308001329_<13> · C120

C120 = P50 · P70

P50 = 65913944802091178855770112634329104658420382602159_<50>

P70 = 1859453593432094313519823692595586227335273265860674689594622234181449_<70>

Number: n
N=122563921519533157167610503791526745333137558744384949027973528499465329568652035634459486477105324578747237805985148391
  ( 120 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=65913944802091178855770112634329104658420382602159 (pp50)
 r2=1859453593432094313519823692595586227335273265860674689594622234181449 (pp70)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 24.11 hours.
Scaled time: 31.49 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_8_3_155
n: 122563921519533157167610503791526745333137558744384949027973528499465329568652035634459486477105324578747237805985148391
skew: 1.0
deg: 5
c5: 25
c0: -1
m: 10000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:183072, AFBsize:182826, largePrimes:6955717 encountered
Relations: rels:6516252, finalFF:543037
Max relations in full relation-set: 48
Initial matrix: 365962 x 543037 with sparse part having weight 47109883.
Pruned matrix : 241555 x 243448 with weight 23127030.
Total sieving time: 21.71 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.11 hours.
Total square root time: 0.11 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 24.11 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Mar 31, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

6·10¹⁵⁴+1 = 6(0)₁₅₃1_<155> = 53 · 110164333547_<12> · C143

C143 = P39 · P104

P39 = 238374791151267475667638647382887847013_<39>

P104 = 43109605018575408648854020726186133527988347085935528901089943775031879035223884740987728777643420089547_<104>

Number: 60001_154
N=10276243092916545282599038127331836714616312273924222818750214626679157163539329590634914587427396014343641520606720047587449248821562496473111
  ( 143 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=238374791151267475667638647382887847013 (pp39)
 r2=43109605018575408648854020726186133527988347085935528901089943775031879035223884740987728777643420089547 (pp104)
Version: GGNFS-0.77.1-20050930-k8
Total time: 21.24 hours.
Scaled time: 19.28 units (timescale=0.908).
Factorization parameters were as follows:
n: 10276243092916545282599038127331836714616312273924222818750214626679157163539329590634914587427396014343641520606720047587449248821562496473111
m: 10000000000000000000000000000000
c5: 3
c0: 5
skew: 1.11
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2500001)
Primes: RFBsize:216816, AFBsize:216596, largePrimes:5572811 encountered
Relations: rels:5543695, finalFF:566815
Max relations in full relation-set: 28
Initial matrix: 433477 x 566815 with sparse part having weight 42556585.
Pruned matrix : 338451 x 340682 with weight 26438100.
Total sieving time: 20.17 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.93 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 21.24 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335810)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238)
Total of 2 processors activated (9340.09 BogoMIPS).

Mar 31, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

6·10¹⁵³+1 = 6(0)₁₅₂1_<154> = 21617 · 1541654209_<10> · C141

C141 = P36 · P105

P36 = 984429390961917259297755699215421271_<36>

P105 = 182887609531191459362098716133019089012168238316933698590744176357181073877813369466618012759402594754327_<105>

Number: n
N=180039938065271742432802419890207882745250058570293387508818336338413580893400078723650876563405461280952457200558289033306093322248055089617
  ( 141 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=984429390961917259297755699215421271 (pp36)
 r2=182887609531191459362098716133019089012168238316933698590744176357181073877813369466618012759402594754327 (pp105)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 27.14 hours.
Scaled time: 27.95 units (timescale=1.030).
Factorization parameters were as follows:
name: KA_6_0_152_1
n: 180039938065271742432802419890207882745250058570293387508818336338413580893400078723650876563405461280952457200558289033306093322248055089617
type: snfs
skew: 1
deg: 5
c5: 375
c0: 2
m: 2000000000000000000000000000000
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [700000, 1700001)
Primes: RFBsize:203362, AFBsize:203002, largePrimes:6512346 encountered
Relations: rels:5970054, finalFF:457938
Max relations in full relation-set: 48
Initial matrix: 406430 x 457938 with sparse part having weight 33384429.
Pruned matrix : 366052 x 368148 with weight 21666820.
Total sieving time: 23.81 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.02 hours.
Total square root time: 0.11 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.3,2.3,100000
total time: 27.14 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 3000+ stepping 00
Memory: 2076900k/2097088k available (1540k kernel code, 19412k reserved, 599k data, 144k init, 0k highmem)
Calibrating delay loop... 4292.60 BogoMIPS
x86info v1.12b.  Dave Jones 2001-2003
Feedback to <davej@redhat.com>.

Found 1 CPU
--------------------------------------------------------------------------
Family: 6 Model: 10 Stepping: 0
CPU Model : Athlon XP (Barton)
2.2Ghz processor (estimate).

Mar 30, 2007 (6th)

By Alfred Reich / GMP-ECM B1=250000

10¹⁵⁰²+1 = 1(0)₁₅₀₁1_<1503> = 101 · C1500

C1500 = P29 · C1472

P29 = 15038232004133372033157105509_<29>

Mar 30, 2007 (5th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

6·10¹⁵¹+1 = 6(0)₁₅₀1_<152> = 139 · 498255827 · C141

C141 = P35 · P52 · P55

P35 = 85355460087173921743066987368891301_<35>

P52 = 4059984657865523211612358150944087268984576395068423_<52>

P55 = 2499932966831125928910143611140847400709468157774550779_<55>

Number: n
N=866331416248530507913950966103277323181094369907219304082316894962353482612304182861456519612999020205316992825763695151993423853564736053617
  ( 141 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=85355460087173921743066987368891301 (pp35)
 r2=4059984657865523211612358150944087268984576395068423 (pp52)
 r3=2499932966831125928910143611140847400709468157774550779 (pp55)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 17.90 hours.
Scaled time: 23.70 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_6_0_150_1
n: 866331416248530507913950966103277323181094369907219304082316894962353482612304182861456519612999020205316992825763695151993423853564736053617
skew: 1.0
deg: 5
c5: 60
c0: 1
m: 1000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [625000, 1225001)
Primes: RFBsize:183072, AFBsize:182401, largePrimes:6997715 encountered
Relations: rels:6415375, finalFF:435403
Max relations in full relation-set: 48
Initial matrix: 365540 x 435403 with sparse part having weight 40361151.
Pruned matrix : 313619 x 315510 with weight 23532552.
Total sieving time: 14.43 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 3.06 hours.
Total square root time: 0.27 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 17.90 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Mar 30, 2007 (4th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

6·10¹⁴⁹+1 = 6(0)₁₄₈1_<150> = 19 · 109 · 113 · 10579907627_<11> · 5679856078924981_<16> · C119

C119 = P38 · P82

P38 = 22501049938160881627846852996382188283_<38>

P82 = 1896141385290142214720833871694818954129695297495385547007001852440390777837062947_<82>

Number: 60001_149
N=42665172000227042905248666636269907370987871316211270116976905960540274050479954940900986182398874236738120753476850001
  ( 119 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=22501049938160881627846852996382188283 (pp38)
 r2=1896141385290142214720833871694818954129695297495385547007001852440390777837062947 (pp82)
Version: GGNFS-0.77.1-20050930-k8
Total time: 16.31 hours.
Scaled time: 14.81 units (timescale=0.908).
Factorization parameters were as follows:
n: 42665172000227042905248666636269907370987871316211270116976905960540274050479954940900986182398874236738120753476850001
m: 1000000000000000000000000000000
c5: 3
c0: 5
skew: 1.11
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [900000, 1800001)
Primes: RFBsize:135072, AFBsize:135068, largePrimes:2722233 encountered
Relations: rels:2706884, finalFF:317643
Max relations in full relation-set: 28
Initial matrix: 270205 x 317643 with sparse part having weight 18554762.
Pruned matrix : 249291 x 250706 with weight 12273618.
Total sieving time: 15.95 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,45,45,2.3,2.3,75000
total time: 16.31 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335810)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238)
Total of 2 processors activated (9340.09 BogoMIPS).

Mar 30, 2007 (3rd)

By suberi / GMP-ECM 6.1.2 B1=1500000

10¹⁹³-3 = (9)₁₉₂7_<193> = 7 · 877 · 8231 · 1678751 · C180

C180 = P40 · C140

P40 = 2788197000323965150474047104253804184927_<40>

C140 = [42280491275836758755087153978652869290832724846826455289157915903635208116355748143771841425689564560801169376081032947336654089972281806529_<140>]

Mar 30, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM 6.1.1 B1=1000000

6·10¹⁵⁵+1 = 6(0)₁₅₄1_<156> = 15679 · C152

C152 = P28 · P124

P28 = 5838172087029064235976796069_<28>

P124 = 6554747975404540742365128375128746950110811434716985062195497790142313250580415385937683038666601418715210100773572817781651_<124>

Mar 30, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

6·10¹⁴⁷+1 = 6(0)₁₄₆1_<148> = 17 · 2543 · C144

C144 = P57 · P88

P57 = 115760644183242053581470522727778242831221097437922034717_<57>

P88 = 1198933330911430747361811027483210008562962708283177147904000051570352016647574586611563_<88>

Number: n
N=138789294719067335939487867502486641530383289768915824292752885660752700608359741851911822534755152552566445374846753487081029816566815479632671
  ( 144 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=115760644183242053581470522727778242831221097437922034717 (pp57)
 r2=1198933330911430747361811027483210008562962708283177147904000051570352016647574586611563 (pp88)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 13.08 hours.
Scaled time: 13.45 units (timescale=1.028).
Factorization parameters were as follows:
name: KA_6_0_146_1
n: 138789294719067335939487867502486641530383289768915824292752885660752700608359741851911822534755152552566445374846753487081029816566815479632671
type: snfs
skew: 1
deg: 5
c5: 75
c0: 4
m: 200000000000000000000000000000
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [700000, 1900001)
Primes: RFBsize:203362, AFBsize:203327, largePrimes:6772732 encountered
Relations: rels:6313076, finalFF:556374
Max relations in full relation-set: 48
Initial matrix: 406755 x 556374 with sparse part having weight 34465165.
Pruned matrix : 285284 x 287381 with weight 17097564.
Total sieving time: 10.71 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 1.79 hours.
Total square root time: 0.38 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.3,2.3,100000
total time: 13.08 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 3000+ stepping 00
Memory: 2076900k/2097088k available (1540k kernel code, 19412k reserved, 599k data, 144k init, 0k highmem)
Calibrating delay loop... 4292.60 BogoMIPS
x86info v1.12b.  Dave Jones 2001-2003
Feedback to <davej@redhat.com>.

Found 1 CPU
--------------------------------------------------------------------------
Family: 6 Model: 10 Stepping: 0
CPU Model : Athlon XP (Barton)
2.2Ghz processor (estimate).

Mar 29, 2007 (12th)

By Yousuke Koide / GMP-ECM B1=1000000

10¹²⁸¹+1 = 1(0)₁₂₈₀1_<1282> = 7² · 11 · 13 · 127 · 367 · 2689 · 81131 · 169093 · 459691 · 909091 · 51745081 · 55405813 · 2483310733_<10> · 231360835259_<12> · 40498340376691_<14> · 169894323769969_<15> · 1332637657781062159783634743_<28> · 42936744040512685057308971520417028077990465463_<47> · 33277993916065498965234812212436587255656671587921_<50> · 11205222530116836855321528257890437575145023592596037161_<56> · [85811889790895883206807096720145730209605387250726861790562462772043327254561512798528835064828732240331260028758501757852432823556792336743465054983401115181231428794965186955289754661244071239184706008290121155783429407286412102316839112807634956146135131037171420203944224539158836762412373845312102917244800561831603104330815842760273933_<341>] · C664

C664 = P33 · C632

P33 = 182686188880054439969850506100637_<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 29, 2007 (11th)

By Alfred Reich / GMP-ECM B1=3000000

10⁶⁰⁸+1 = 1(0)₆₀₇1_<609> = 1217 · 19841 · 665153 · 976193 · 1601473 · 6187457 · 65384321 · 834427406578561_<15> · 911712031611457_<15> · 18542613285686578370456001857_<29> · C510

C510 = P35 · C475

P35 = 89360919064107809136921297069895873_<35>

Mar 29, 2007 (10th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

6·10¹⁴⁴+1 = 6(0)₁₄₃1_<145> = 7 · 29 · 9419 · C139

C139 = P52 · P87

P52 = 8690737773132673400046895125462569162199460287601619_<52>

P87 = 361071965016480062594290480035242393015221651315524279120702561149015142886111978824947_<87>

Number: n
N=3137981765187962492749954630013644990708958990239307719382842666301266123342557256399783060860633338859667886469911723342975653968474789193
  ( 139 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=8690737773132673400046895125462569162199460287601619 (pp52)
 r2=361071965016480062594290480035242393015221651315524279120702561149015142886111978824947 (pp87)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.84 hours.
Scaled time: 11.70 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_6_0_143_1
n: 3137981765187962492749954630013644990708958990239307719382842666301266123342557256399783060860633338859667886469911723342975653968474789193
skew: 1.0
deg: 5
c5: 3
c0: 5
m: 100000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [625000, 1425001)
Primes: RFBsize:183072, AFBsize:183061, largePrimes:6812550 encountered
Relations: rels:6210007, finalFF:436143
Max relations in full relation-set: 48
Initial matrix: 366198 x 436143 with sparse part having weight 31494582.
Pruned matrix : 309296 x 311190 with weight 17011799.
Total sieving time: 6.46 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 2.19 hours.
Total square root time: 0.06 hours, sqrts: 1
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 8.84 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Mar 29, 2007 (9th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

6·10¹⁴²+1 = 6(0)₁₄₁1_<143> = 179 · 193 · 1949 · 20250697 · C128

C128 = P36 · P93

P36 = 168722167314338241440719151552099503_<36>

P93 = 260805622756239731875686742670995926907630708041156681530524921153215720747176911819093845937_<93>

Number: 60001_142
N=44003689919198461148612843709883711482295308168094192381135593052331773504067100100819483505234335724777643856075977739176269311
  ( 128 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=168722167314338241440719151552099503 (pp36)
 r2=260805622756239731875686742670995926907630708041156681530524921153215720747176911819093845937 (pp93)
Version: GGNFS-0.77.1-20050930-k8
Total time: 9.01 hours.
Scaled time: 7.81 units (timescale=0.867).
Factorization parameters were as follows:
n: 44003689919198461148612843709883711482295308168094192381135593052331773504067100100819483505234335724777643856075977739176269311
m: 20000000000000000000000000000
c5: 75
c0: 4
skew: 1
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 1250001)
Primes: RFBsize:114155, AFBsize:113902, largePrimes:2662818 encountered
Relations: rels:2669079, finalFF:313554
Max relations in full relation-set: 28
Initial matrix: 228123 x 313554 with sparse part having weight 20150084.
Pruned matrix : 187065 x 188269 with weight 9927048.
Total sieving time: 8.80 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000
total time: 9.01 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335810)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238)
Total of 2 processors activated (9340.09 BogoMIPS).

Mar 29, 2007 (8th)

By suberi / GGNFS-0.77.1-20060513-pentium4

6·10¹³²+1 = 6(0)₁₃₁1_<133> = 7² · 347 · C129

C129 = P62 · P67

P62 = 36596493239037447170949018613664094139517120346108317971376267_<62>

P67 = 9642423972646013466783289114801468750815943389674239701142494172201_<67>

Number: 60001_132
N=352878903722872434276304181615009116038346174204552137858025054402164323942833617596894665647238722578368523201787919778862553667
  ( 129 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=36596493239037447170949018613664094139517120346108317971376267 (pp62)
 r2=9642423972646013466783289114801468750815943389674239701142494172201 (pp67)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 6.36 hours.
Scaled time: 3.95 units (timescale=0.620).
Factorization parameters were as follows:
n: 352878903722872434276304181615009116038346174204552137858025054402164323942833617596894665647238722578368523201787919778862553667
m: 100000000000000000000000000
c5: 600
c0: 1
skew: 1
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1000001)
Primes: RFBsize:63951, AFBsize:63758, largePrimes:1465168 encountered
Relations: rels:1451436, finalFF:159411
Max relations in full relation-set: 28
Initial matrix: 127775 x 159411 with sparse part having weight 11544070.
Pruned matrix : 118379 x 119081 with weight 6897026.
Total sieving time: 5.94 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 6.36 hours.
 --------- CPU info (if available) ----------

Mar 29, 2007 (7th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

6·10¹³⁵+1 = 6(0)₁₃₄1_<136> = C136

C136 = P46 · P90

P46 = 6880668114947944749317742283818949380447951589_<46>

P90 = 872008342760387973294859623740096978369380316479863520578687666785407351034250325563331309_<90>

Number: n
N=6000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
  ( 136 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=6880668114947944749317742283818949380447951589 (pp46)
 r2=872008342760387973294859623740096978369380316479863520578687666785407351034250325563331309 (pp90)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.93 hours.
Scaled time: 6.43 units (timescale=1.303).
Factorization parameters were as follows:
name: KA_6_0_134_1
n: 6000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
skew: 1.0
deg: 5
c5: 6
c0: 1
m: 1000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [625000, 1025001)
Primes: RFBsize:183072, AFBsize:183151, largePrimes:6757053 encountered
Relations: rels:6176901, finalFF:469461
Max relations in full relation-set: 48
Initial matrix: 366289 x 469461 with sparse part having weight 27534006.
Pruned matrix : 275137 x 277032 with weight 11713717.
Total sieving time: 3.49 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 1.27 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,75000
total time: 4.93 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

6·10¹³⁹+1 = 6(0)₁₃₈1_<140> = 2277647 · 1508867401072225998121996787_<28> · C107

C107 = P36 · P71

P36 = 323196751600306705639682362661998583_<36>

P71 = 54019028760861303562927364638531753025925788771571944925497170577303123_<71>

Number: n
N=17458774620113914470450750350485650721062967459553658304917158020724895264651040876779047803300485387474709
  ( 107 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=323196751600306705639682362661998583 (pp36)
 r2=54019028760861303562927364638531753025925788771571944925497170577303123 (pp71)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.00 hours.
Scaled time: 7.19 units (timescale=1.027).
Factorization parameters were as follows:
name: KA_6_0_138_1
n: 17458774620113914470450750350485650721062967459553658304917158020724895264651040876779047803300485387474709
type: snfs
skew: 1
deg: 5
c5: 3
c0: 5
m: 10000000000000000000000000000
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [700000, 1300001)
Primes: RFBsize:203362, AFBsize:203187, largePrimes:6332246 encountered
Relations: rels:5935476, finalFF:580430
Max relations in full relation-set: 48
Initial matrix: 406614 x 580430 with sparse part having weight 28996765.
Pruned matrix : 249589 x 251686 with weight 11668387.
Total sieving time: 5.78 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.00 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.3,2.3,75000
total time: 7.00 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 3000+ stepping 00
Memory: 2076900k/2097088k available (1540k kernel code, 19412k reserved, 599k data, 144k init, 0k highmem)
Calibrating delay loop... 4292.60 BogoMIPS
x86info v1.12b.  Dave Jones 2001-2003
Feedback to <davej@redhat.com>.

Found 1 CPU
--------------------------------------------------------------------------
Family: 6 Model: 10 Stepping: 0
CPU Model : Athlon XP (Barton)
2.2Ghz processor (estimate).

Mar 29, 2007 (6th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

6·10¹³⁷+1 = 6(0)₁₃₆1_<138> = 23 · 48323971 · 4272684397523_<13> · C117

C117 = P35 · P82

P35 = 14655169765563672253443781435081771_<35>

P82 = 8621228002824546712512779722593849212894060284244445369802723033429410273152233309_<82>

Number: 60001_137
N=126345559969025178596852180111068916025623690265881256100032965758421964815162261474428762273655471555768749684910239
  ( 117 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=14655169765563672253443781435081771 (pp35)
 r2=8621228002824546712512779722593849212894060284244445369802723033429410273152233309 (pp82)
Version: GGNFS-0.77.1-20050930-k8
Total time: 6.19 hours.
Scaled time: 5.61 units (timescale=0.906).
Factorization parameters were as follows:
n: 126345559969025178596852180111068916025623690265881256100032965758421964815162261474428762273655471555768749684910239
m: 2000000000000000000000000000
c5: 75
c0: 4
skew: 1
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [650000, 1600001)
Primes: RFBsize:100021, AFBsize:99653, largePrimes:1606035 encountered
Relations: rels:1640566, finalFF:232314
Max relations in full relation-set: 28
Initial matrix: 199740 x 232314 with sparse part having weight 11569395.
Pruned matrix : 183772 x 184834 with weight 7837658.
Total sieving time: 6.03 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1300000,1300000,25,25,43,43,2.3,2.3,50000
total time: 6.19 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335810)
Calibrating delay using timer specific routine.. 4668.46 BogoMIPS (lpj=2334234)
Total of 2 processors activated (9340.08 BogoMIPS).

Mar 29, 2007 (5th)

By Jo Yeong Uk / GMP-ECM 6.1.1 B1=1000000

6·10¹⁵²+1 = 6(0)₁₅₁1_<153> = 97 · 107 · 4413797 · 146950709 · 312531144238105714806234223_<27> · C108

C108 = P36 · P72

P36 = 298164910200576610275597713265821141_<36>

P72 = 956449101954012566944100844383139842704712531307907202661451759300471921_<72>

Mar 29, 2007 (4th)

By Shaopu Lin / GGNFS-0.77.1-20060722-pentium4

6·10¹¹⁶+1 = 6(0)₁₁₅1_<117> = 29 · 83 · 131 · 685813586041_<12> · C100

C100 = P49 · P52

P49 = 1844456395138388719546644007583570020351357048013_<49>

P52 = 1504282446191996744686075825671917165322581155319641_<52>

Number: 6.116.+1
N=2774583377973247515120418666588758007725716130878216258584319823955305330744998010385552113198923333
  ( 100 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=1844456395138388719546644007583570020351357048013 (pp49)
 r2=1504282446191996744686075825671917165322581155319641 (pp52)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 1.68 hours.
Scaled time: 2.14 units (timescale=1.277).
Factorization parameters were as follows:
n: 2774583377973247515120418666588758007725716130878216258584319823955305330744998010385552113198923333
m: 100000000000000000000000
c5: 60
c0: 1
skew: 0.4409301031108602482135000634
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:63828, largePrimes:2028041 encountered
Relations: rels:2073919, finalFF:216782
Max relations in full relation-set: 32
Initial matrix: 112993 x 216782 with sparse part having weight 17583425.
Pruned matrix : 84139 x 84767 with weight 4244399.
Total sieving time: 1.49 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.68 hours.
 --------- CPU info (if available) ----------

6·10¹³³+1 = 6(0)₁₃₂1_<134> = 4390696903639_<13> · 206718352549405901933_<21> · C101

C101 = P48 · P54

P48 = 366262675924266703046624692745658752739944862649_<48>

P54 = 180487069279920119803199143358086060304773059562666427_<54>

Number: 6.133.+1
N=66105676964192055331339699187649664746820562965637914107453371282434427610071830386331809334718585123
  ( 101 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=366262675924266703046624692745658752739944862649 (pp48)
 r2=180487069279920119803199143358086060304773059562666427 (pp54)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 7.67 hours.
Scaled time: 8.97 units (timescale=1.170).
Factorization parameters were as follows:
n: 66105676964192055331339699187649664746820562965637914107453371282434427610071830386331809334718585123
m: 1000000000000000000000000000
c5: 3
c0: 50
skew: 1.755374357613263695354790869
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1150001)
Primes: RFBsize:78498, AFBsize:64108, largePrimes:1522627 encountered
Relations: rels:1528331, finalFF:182412
Max relations in full relation-set: 32
Initial matrix: 142671 x 182412 with sparse part having weight 13819576.
Pruned matrix : 129373 x 130150 with weight 7940935.
Total sieving time: 7.28 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 7.67 hours.
 --------- CPU info (if available) ----------

6·10¹¹⁷+1 = 6(0)₁₁₆1_<118> = 19249 · 104513 · C109

C109 = P38 · P71

P38 = 84949547191298834829861938440359659209_<38>

P71 = 35108453167910401652183651057262560059278692771200689617890345494466697_<71>

Number: 6.117.+1
N=2982447199200909740641087772219643336028900593358218233194233006680820410004800661338976420353409286119862673
  ( 109 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=84949547191298834829861938440359659209 (pp38)
 r2=35108453167910401652183651057262560059278692771200689617890345494466697 (pp71)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 2.30 hours.
Scaled time: 2.94 units (timescale=1.282).
Factorization parameters were as follows:
n: 2982447199200909740641087772219643336028900593358218233194233006680820410004800661338976420353409286119862673
m: 100000000000000000000000
c5: 600
c0: 1
skew: 0.2782080869602061787542021946
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63758, largePrimes:2260345 encountered
Relations: rels:2575810, finalFF:449631
Max relations in full relation-set: 32
Initial matrix: 112922 x 449631 with sparse part having weight 38977979.
Pruned matrix : 65873 x 66501 with weight 5825304.
Total sieving time: 2.11 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.30 hours.
 --------- CPU info (if available) ----------

Mar 29, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

6·10¹³⁶+1 = 6(0)₁₃₅1_<137> = 287271635614354961093_<21> · C117

C117 = P32 · P85

P32 = 41930632229393576833881200665999_<32>

P85 = 4981121010552314579673023411353830652553041863694028008692298895946066995164432699043_<85>

Number: 60001_136
N=208861553183574384641496570438992202326763001190184099906600714715092191323809412019926563630101556877732704729938957
  ( 117 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=41930632229393576833881200665999 (pp32)
 r2=4981121010552314579673023411353830652553041863694028008692298895946066995164432699043 (pp85)
Version: GGNFS-0.77.1-20050930-k8
Total time: 5.30 hours.
Scaled time: 4.80 units (timescale=0.906).
Factorization parameters were as follows:
n: 208861553183574384641496570438992202326763001190184099906600714715092191323809412019926563630101556877732704729938957
m: 1000000000000000000000000000
c5: 60
c0: 1
skew: 1
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [650000, 1450001)
Primes: RFBsize:100021, AFBsize:99983, largePrimes:1573606 encountered
Relations: rels:1601867, finalFF:226059
Max relations in full relation-set: 28
Initial matrix: 200071 x 226059 with sparse part having weight 9991724.
Pruned matrix : 187226 x 188290 with weight 7125975.
Total sieving time: 5.14 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,25,25,43,43,2.3,2.3,50000
total time: 5.30 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335810)
Calibrating delay using timer specific routine.. 4668.46 BogoMIPS (lpj=2334234)
Total of 2 processors activated (9340.08 BogoMIPS).

Mar 29, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs

4·10¹⁵³+1 = 4(0)₁₅₂1_<154> = 59 · 397 · 13063 · 167318969 · 606641514185778295831468249_<27> · C111

C111 = P40 · P71

P40 = 3183635597702264953513076409369407360357_<40>

P71 = 40455156645999949292666657280615001667447267467607551015375410772491397_<71>

Number: n
N=128794476808826804929695919713988641507228964089871710247262117670748049694912958575750188571024002234261348729
  ( 111 digits)
Divisors found:
 r1=3183635597702264953513076409369407360357 (pp40)
 r2=40455156645999949292666657280615001667447267467607551015375410772491397 (pp71)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.67 hours.
Scaled time: 27.47 units (timescale=1.030).
Factorization parameters were as follows:
name: KA_4_0_152_1
n: 128794476808826804929695919713988641507228964089871710247262117670748049694912958575750188571024002234261348729
skew: 14591.00
# norm 2.53e+15
c5: 36480
c4: -8024516008
c3: -131143870906614
c2: 1592694215541131949
c1: 3060500624120386397906
c0: -21438494886951988228976328
# alpha -5.87
Y1: 296695470809
Y0: -1286983226642882909381
# Murphy_E 9.13e-10
# M 81130056266918107766482766309667539814896027352219876292127076829404897674136589364351342555408655652570877199
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [800000, 1600001)
Primes: RFBsize:230209, AFBsize:230219, largePrimes:7117685 encountered
Relations: rels:6769651, finalFF:521875
Max relations in full relation-set: 48
Initial matrix: 460509 x 521875 with sparse part having weight 43506096.
Pruned matrix : 404830 x 407196 with weight 25473744.
Total sieving time: 22.50 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 3.57 hours.
Time per square root: 0.35 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 26.67 hours.
 --------- CPU info (if available) ----------
CPU: AMD Athlon(tm) XP 3000+ stepping 00
Memory: 2076900k/2097088k available (1540k kernel code, 19412k reserved, 599k data, 144k init, 0k highmem)
Calibrating delay loop... 4292.60 BogoMIPS
x86info v1.12b.  Dave Jones 2001-2003
Feedback to <davej@redhat.com>.

Found 1 CPU
--------------------------------------------------------------------------
Family: 6 Model: 10 Stepping: 0
CPU Model : Athlon XP (Barton)
2.2Ghz processor (estimate).

Mar 29, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

6·10¹³⁰+1 = 6(0)₁₂₉1_<131> = 31 · 325910589480211013_<18> · C112

C112 = P32 · P80

P32 = 80533406104775313809314886144551_<32>

P80 = 73742017814548265755028178719963181032292046951828193081508776580982918009049717_<80>

Number: 60001_130
N=5938695867644591250096964108036195170468256919566410685964230328223435047888048980160458151235501463313407642067
  ( 112 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=80533406104775313809314886144551 (pp32)
 r2=73742017814548265755028178719963181032292046951828193081508776580982918009049717 (pp80)
Version: GGNFS-0.77.1-20050930-k8
Total time: 2.49 hours.
Scaled time: 2.26 units (timescale=0.907).
Factorization parameters were as follows:
n: 5938695867644591250096964108036195170468256919566410685964230328223435047888048980160458151235501463313407642067
m: 100000000000000000000000000
c5: 6
c0: 1
skew: 1
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 900001)
Primes: RFBsize:78498, AFBsize:78381, largePrimes:1552605 encountered
Relations: rels:1607977, finalFF:227611
Max relations in full relation-set: 28
Initial matrix: 156945 x 227611 with sparse part having weight 11540004.
Pruned matrix : 124379 x 125227 with weight 5154950.
Total sieving time: 2.41 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 2.49 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335810)
Calibrating delay using timer specific routine.. 4668.46 BogoMIPS (lpj=2334234)
Total of 2 processors activated (9340.08 BogoMIPS).

Mar 28, 2007 (7th)

By suberi / GMP-ECM 6.1.2 B1=3000000

10¹⁸⁸-3 = (9)₁₈₇7_<188> = 330546084791304846847511_<24> · 3562247528919238271756225579280817_<34> · C131

C131 = P37 · P95

P37 = 4509864049590597579503737782555387503_<37>

P95 = 18831305910794443918566298283063276453852879246305489811969783216115588049782475570558077809077_<95>

Mar 28, 2007 (6th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

6·10¹²³+1 = 6(0)₁₂₂1_<124> = 677 · 85482211 · C114

C114 = P50 · P64

P50 = 46731777018239824577493857223667185843576140952323_<50>

P64 = 2218577168058000218769466780291988857687020303171346242507278821_<64>

Number: 60001_123
N=103678053515444447646496968098004446630653870257492258219735430328279463228768508005623250938029042426190228651183
  ( 114 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=46731777018239824577493857223667185843576140952323 (pp50)
 r2=2218577168058000218769466780291988857687020303171346242507278821 (pp64)
Version: GGNFS-0.77.1-20050930-k8
Total time: 1.95 hours.
Scaled time: 1.77 units (timescale=0.907).
Factorization parameters were as follows:
n: 103678053515444447646496968098004446630653870257492258219735430328279463228768508005623250938029042426190228651183
m: 10000000000000000000000000
c5: 3
c0: 50
skew: 1
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 800001)
Primes: RFBsize:78498, AFBsize:78466, largePrimes:1533564 encountered
Relations: rels:1603464, finalFF:239699
Max relations in full relation-set: 28
Initial matrix: 157029 x 239699 with sparse part having weight 10890124.
Pruned matrix : 112192 x 113041 with weight 4386011.
Total sieving time: 1.88 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 1.95 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335810)
Calibrating delay using timer specific routine.. 4668.46 BogoMIPS (lpj=2334234)
Total of 2 processors activated (9340.08 BogoMIPS).

Mar 28, 2007 (5th)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(55·10¹⁵⁴-1)/9 = 6(1)₁₅₄_<155> = 19 · 128377 · 226199 · C144

C144 = P50 · P94

P50 = 16248596023798486378875874181609325104910632542109_<50>

P94 = 6816678862166327195133898481525866304745806685872685135817314924536862399999758640164030283967_<94>

Number: trial
N=110761461055306974447980312674705813315103228543298256296113664338475244695680369736492417399835256980582636072338158897343349693799730355066403
  ( 144 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=16248596023798486378875874181609325104910632542109 (pp50)
 r2=6816678862166327195133898481525866304745806685872685135817314924536862399999758640164030283967
(pp94)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 54.70 hours.
Scaled time: 28.44 units (timescale=0.520).
Factorization parameters were as follows:
n:
110761461055306974447980312674705813315103228543298256296113664338475244695680369736492417399835256980582636072338158897343349693799730355066403
m: 10000000000000000000000000000000
c5: 11
c0: -2
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2500001)
Primes: RFBsize:216816, AFBsize:216807, largePrimes:5696111 encountered
Relations: rels:5771677, finalFF:510455
Max relations in full relation-set: 0
Initial matrix: 433690 x 510455 with sparse part having weight 27237870.
Pruned matrix : 372255 x 374487 with weight 19501034.
Total sieving time: 44.73 hours.
Total relation processing time: 0.45 hours.
Matrix solve time: 9.25 hours.
Time per square root: 0.26 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 54.70 hours.
 --------- CPU info (if available) ----------

Mar 28, 2007 (4th)

By Yousuke Koide / GMP-ECM / Mar 25, 2007

(10⁷⁷³-1)/9 = (1)₇₇₃_<773> = 375567158615806379291689_<24> · C749

C749 = P34 · C715

P34 = 6567859785032228933216616467308837_<34>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 28, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

3·10¹⁵⁴+1 = 3(0)₁₅₃1_<155> = 709 · C152

C152 = P55 · P97

P55 = 8035475151373083659527183835942623308307448782043954239_<55>

P97 = 5265789050328925623147256769024288482438775097245447059422020562309429069222311849609536376272051_<97>

Number: 30001_154
N=42313117066290550070521861777150916784203102961918194640338504936530324400564174894217207334273624823695345557122708039492242595204513399153737658674189
  ( 152 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=8035475151373083659527183835942623308307448782043954239 (pp55)
 r2=5265789050328925623147256769024288482438775097245447059422020562309429069222311849609536376272051 (pp97)
Version: GGNFS-0.77.1-20050930-k8
Total time: 25.09 hours.
Scaled time: 22.81 units (timescale=0.909).
Factorization parameters were as follows:
n: 42313117066290550070521861777150916784203102961918194640338504936530324400564174894217207334273624823695345557122708039492242595204513399153737658674189
m: 10000000000000000000000000000000
c5: 3
c0: 10
skew: 1.27
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2700001)
Primes: RFBsize:216816, AFBsize:216741, largePrimes:5696550 encountered
Relations: rels:5707769, finalFF:592403
Max relations in full relation-set: 28
Initial matrix: 433622 x 592403 with sparse part having weight 47733820.
Pruned matrix : 340633 x 342865 with weight 29522903.
Total sieving time: 23.87 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 25.09 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335810)
Calibrating delay using timer specific routine.. 4668.46 BogoMIPS (lpj=2334234)
Total of 2 processors activated (9340.08 BogoMIPS).

Mar 28, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs

4·10¹⁶¹+1 = 4(0)₁₆₀1_<162> = 7 · 41 · 24481 · 1793611 · 6778769 · 51739157 · 24543891373_<11> · 7075521653495357_<16> · C108

C108 = P33 · P76

P33 = 365498852272237776807460331845037_<33>

P76 = 1425813087563283653143535013962362288561660254770001654328238688640363615813_<76>

Number: n
N=521133047059115837675537348646844584746004512762351827978879158236088378419334683421375333805308762918770081
  ( 108 digits)
Divisors found:
 r1=365498852272237776807460331845037 (pp33)
 r2=1425813087563283653143535013962362288561660254770001654328238688640363615813 (pp76)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 20.75 hours.
Scaled time: 12.43 units (timescale=0.599).
Factorization parameters were as follows:
name: n
n: 521133047059115837675537348646844584746004512762351827978879158236088378419334683421375333805308762918770081
skew: 40447.48
# norm 6.43e+14
c5: 9420
c4: -213953527
c3: -44488420510166
c2: 182961566955378338
c1: 36117031924044341100564
c0: 205146067720706725943643840
# alpha -5.48
Y1: 186574095169
Y0: -560505913690756339519
# Murphy_E 1.20e-09
# M 494134786016776996625202565666137705191913286564593986533208980979121777485925174812435415313414375388025445
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [100000, 1750001)
Primes: RFBsize:183072, AFBsize:182852, largePrimes:4389613 encountered
Relations: rels:4471974, finalFF:474620
Max relations in full relation-set: 28
Initial matrix: 366004 x 474620 with sparse part having weight 34411549.
Pruned matrix : 274273 x 276167 with weight 17131889.
Total sieving time: 16.62 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 3.50 hours.
Total square root time: 0.40 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 20.75 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Mar 28, 2007

The factor table of 600...001 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Mar 27, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

4·10¹⁴⁷+1 = 4(0)₁₄₆1_<148> = 47 · 251 · 733 · 863 · C138

C138 = P55 · P83

P55 = 6442862514461602713781483216855754068454488467466706327_<55>

P83 = 83194530963377483428159654973172315536690121265505564170886744203220844329565112601_<83>

Number: n
N=536010924952159916075418732709442497083178964476160436594019920977080518174084042417641026577862786883052013317047243497600983876354126527
  ( 138 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=6442862514461602713781483216855754068454488467466706327 (pp55)
 r2=83194530963377483428159654973172315536690121265505564170886744203220844329565112601 (pp83)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 12.48 hours.
Scaled time: 14.92 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_4_0_146_1
n: 536010924952159916075418732709442497083178964476160436594019920977080518174084042417641026577862786883052013317047243497600983876354126527
type: snfs
skew: 1
deg: 5
c5: 25
c0: 2
m: 200000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1200001)
Primes: RFBsize:230209, AFBsize:229762, largePrimes:6131938 encountered
Relations: rels:5626042, finalFF:530810
Max relations in full relation-set: 28
Initial matrix: 460035 x 530810 with sparse part having weight 20240880.
Pruned matrix : 379958 x 382322 with weight 10978773.
Total sieving time: 10.35 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 1.87 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 12.48 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

The factor table of 400...001 was completed up to n=150.

Mar 27, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

(82·10¹⁵⁴-1)/9 = 9(1)₁₅₄_<155> = 607 · 40241 · C148

C148 = P60 · P89

P60 = 232620404026051435877540073297669760912942073309419855799819_<60>

P89 = 16034893568762225974436715045034787578075921818623102241641956001895225911887448184842587_<89>

Number: 91111_154
N=3730043420480202787722551164289157460203063654787611031963683678616856958698270887880385222326713475163503610315849932947693241756764387117498091753
  ( 148 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=232620404026051435877540073297669760912942073309419855799819 (pp60)
 r2=16034893568762225974436715045034787578075921818623102241641956001895225911887448184842587 (pp89)
Version: GGNFS-0.77.1-20050930-k8
Total time: 27.18 hours.
Scaled time: 24.63 units (timescale=0.906).
Factorization parameters were as follows:
n: 3730043420480202787722551164289157460203063654787611031963683678616856958698270887880385222326713475163503610315849932947693241756764387117498091753
m: 10000000000000000000000000000000
c5: 41
c0: -5
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:216857, largePrimes:5742989 encountered
Relations: rels:5785422, finalFF:617603
Max relations in full relation-set: 28
Initial matrix: 433738 x 617603 with sparse part having weight 50496076.
Pruned matrix : 331821 x 334053 with weight 31384416.
Total sieving time: 25.97 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.06 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 27.18 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335810)
Calibrating delay using timer specific routine.. 4668.46 BogoMIPS (lpj=2334234)
Total of 2 processors activated (9340.08 BogoMIPS).

Mar 27, 2007

By suberi / GMP-ECM 6.1.2 B1=3000000

(4·10¹⁸⁹-1)/3 = 1(3)₁₈₉_<190> = 1379239 · 1407246178887083_<16> · 13561187776115168413489_<23> · C146

C146 = P45 · P101

P45 = 609907445068425332836810159001893712243111053_<45>

P101 = 83055321804349639576102906880439026197926622771540000562342810500715775296766525603462725052646736477_<101>

Mar 26, 2007 (4th)

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000

4·10¹⁷⁸+1 = 4(0)₁₇₇1_<179> = 13 · C178

C178 = P36 · C142

P36 = 566167021042476149422414249581680453_<36>

C142 = [5434656139556799894979519578367289662179199394390968777423929565472413299191034750588773051949376501146939751768504380636817182877903411483009_<142>]

4·10¹⁹⁴+1 = 4(0)₁₉₃1_<195> = C195

C195 = P30 · C165

P30 = 721324202162977116296517293557_<30>

C165 = [554535670369234852818186783094108976406476630773560262269780712723019734760680133249031167487487578182210303192224034007942925509576722640178918674833524064211545693_<165>]

4·10¹⁷⁹+1 = 4(0)₁₇₈1_<180> = 7 · 18457340200388066441_<20> · C160

C160 = P34 · P126

P34 = 6004231495142581556980974994915411_<34>

P126 = 515626709759236369230555350134883854087864590105169849025864162520888571350730707352467835084057429485986388639654825004337893_<126>

Mar 26, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs

4·10¹⁷¹+1 = 4(0)₁₇₀1_<172> = 23 · 41 · 641 · 55305917 · 571780967537331426467595011_<27> · 983788565105385106532942023_<27> · C105

C105 = P43 · P62

P43 = 3392183977152881040429986688657533088590419_<43>

P62 = 62705813661270651499429351472678860702534232323580249870005333_<62>

Number: n
N=212709656376096539510259200807618971840532704002253441256324493571381200520965039506099236731956982704527
  ( 105 digits)
Divisors found:
 r1=3392183977152881040429986688657533088590419 (pp43)
 r2=62705813661270651499429351472678860702534232323580249870005333 (pp62)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 10.75 hours.
Scaled time: 10.64 units (timescale=0.990).
Factorization parameters were as follows:
name: KA_4_0_170_1
n: 212709656376096539510259200807618971840532704002253441256324493571381200520965039506099236731956982704527
skew: 14380.93
# norm 3.19e+14
c5: 48600
c4: -227361600
c3: -38191978082154
c2: 33010484434394054
c1: 3025096088669510617169
c0: -3257925683541972899940235
# alpha -6.19
Y1: 130154725151
Y0: -84767780379198762372
# Murphy_E 1.99e-09
# M 125472220538461468590658822163936950389663905049084161686308835154986406703146680462682841295132032235112
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [100000, 1150001)
Primes: RFBsize:183072, AFBsize:182819, largePrimes:4056153 encountered
Relations: rels:4064115, finalFF:467875
Max relations in full relation-set: 28
Initial matrix: 365969 x 467875 with sparse part having weight 24168525.
Pruned matrix : 265860 x 267753 with weight 9755268.
Total sieving time: 9.31 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.10 hours.
Total square root time: 0.14 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 10.75 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Mar 26, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

4·10¹⁴⁶+1 = 4(0)₁₄₅1_<147> = 41 · 2729 · C142

C142 = P34 · P45 · P64

P34 = 2184156109565083400994331504190413_<34>

P45 = 185296227258331476479382730913150879294782961_<45>

P64 = 8833287103024449941246276528945173645345205610821578498935895813_<64>

Number: 40001_146
N=3574971623662737177023657374719588163268954052677206874670432303443591416493131585768037966198643298268819991241319522026293916292039431937009
  ( 142 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=2184156109565083400994331504190413 (pp34)
 r2=185296227258331476479382730913150879294782961 (pp45)
 r3=8833287103024449941246276528945173645345205610821578498935895813 (pp64)
Version: GGNFS-0.77.1-20050930-k8
Total time: 11.10 hours.
Scaled time: 10.07 units (timescale=0.907).
Factorization parameters were as follows:
n: 3574971623662737177023657374719588163268954052677206874670432303443591416493131585768037966198643298268819991241319522026293916292039431937009
m: 200000000000000000000000000000
c5: 5
c0: 4
skew: 1
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [900000, 1500001)
Primes: RFBsize:135072, AFBsize:135393, largePrimes:2641367 encountered
Relations: rels:2616307, finalFF:305586
Max relations in full relation-set: 28
Initial matrix: 270531 x 305586 with sparse part having weight 16440611.
Pruned matrix : 246464 x 247880 with weight 11245106.
Total sieving time: 10.77 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.26 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,45,45,2.3,2.3,75000
total time: 11.10 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335813)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334235)
Total of 2 processors activated (9340.09 BogoMIPS).

Mar 26, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

4·10¹³⁷+1 = 4(0)₁₃₆1_<138> = 7 · 19 · 53 · 1009 · 3823 · 218117 · 1603681 · C116

C116 = P44 · P73

P44 = 23055346723785830899288317321960983887657807_<44>

P73 = 1824138707895749513832021600956777695371243638120294559951871173502726613_<73>

Number: n
N=42056150382815187340608288415963360727540025238675488454995900690060512257700402921594947707089725919687392816117691
  ( 116 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=23055346723785830899288317321960983887657807 (pp44)
 r2=1824138707895749513832021600956777695371243638120294559951871173502726613 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.70 hours.
Scaled time: 9.21 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_4_0_136_1
n: 42056150382815187340608288415963360727540025238675488454995900690060512257700402921594947707089725919687392816117691
type: snfs
skew: 1
deg: 5
c5: 25
c0: 2
m: 2000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 600001)
Primes: RFBsize:230209, AFBsize:229762, largePrimes:5695614 encountered
Relations: rels:5305013, finalFF:609531
Max relations in full relation-set: 28
Initial matrix: 460035 x 609531 with sparse part having weight 16764403.
Pruned matrix : 274172 x 276536 with weight 5369499.
Total sieving time: 6.73 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.71 hours.
Total square root time: 0.11 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,75000
total time: 7.70 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Mar 25, 2007 (4th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

3·10¹⁴⁹+1 = 3(0)₁₄₈1_<150> = 13 · 43 · 280811 · C142

C142 = P38 · P105

P38 = 18451977947946169372964490164450899739_<38>

P105 = 103574394682250651492366474771488310679253472549528420564006228321981430254572052540584974107852577311191_<105>

Number: n
N=1911152446648762013735210554754743749526551797018741060305721068612736293216245262117711459414680641106790682028450574753297771585417343679149
  ( 142 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=18451977947946169372964490164450899739 (pp38)
 r2=103574394682250651492366474771488310679253472549528420564006228321981430254572052540584974107852577311191 (pp105)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 22.38 hours.
Scaled time: 26.75 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_3_0_148_1
n: 1911152446648762013735210554754743749526551797018741060305721068612736293216245262117711459414680641106790682028450574753297771585417343679149
type: snfs
skew: 1
deg: 5
c5: 3
c0: 10
m: 1000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1000001)
Primes: RFBsize:230209, AFBsize:230152, largePrimes:6038524 encountered
Relations: rels:5584733, finalFF:558762
Max relations in full relation-set: 28
Initial matrix: 460426 x 558762 with sparse part having weight 21884723.
Pruned matrix : 358008 x 360374 with weight 10725995.
Total sieving time: 20.29 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.86 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 22.38 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

The factor table of 300...001 was completed up to n=150.

Mar 25, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

4·10¹⁴¹+1 = 4(0)₁₄₀1_<142> = 41 · 3167 · C137

C137 = P40 · P41 · P57

P40 = 1385099246529648770253437136267455844731_<40>

P41 = 41102459480233672086378912659093765960173_<41>

P57 = 541102285545511773447658741193840771596059733459284964441_<57>

Number: 40001_141
N=30805486457138016280699592597441604349734687747887898834782474758754534182537910001771315471285435936140226574352892250109744545503554183
  ( 137 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=1385099246529648770253437136267455844731 (pp40)
 r2=41102459480233672086378912659093765960173 (pp41)
 r3=541102285545511773447658741193840771596059733459284964441 (pp57)
Version: GGNFS-0.77.1-20050930-k8
Total time: 7.40 hours.
Scaled time: 6.62 units (timescale=0.895).
Factorization parameters were as follows:
n: 30805486457138016280699592597441604349734687747887898834782474758754534182537910001771315471285435936140226574352892250109744545503554183
m: 20000000000000000000000000000
c5: 5
c0: 4
skew: 1
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:114197, largePrimes:2653362 encountered
Relations: rels:2673267, finalFF:324511
Max relations in full relation-set: 28
Initial matrix: 228418 x 324511 with sparse part having weight 19927266.
Pruned matrix : 177819 x 179025 with weight 9374541.
Total sieving time: 7.21 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000
total time: 7.40 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335813)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334235)
Total of 2 processors activated (9340.09 BogoMIPS).

Mar 25, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=1500000

(10¹⁹⁰+53)/9 = (1)₁₈₉7_<190> = 317 · 827 · 44875162230601_<14> · C170

C170 = P33 · P138

P33 = 497811278826090990386154752018161_<33>

P138 = 189723861350920471225486081015749698379077197353000850772531811636527991762209575613746494032092565495097753015031636182159064743140805883_<138>

Mar 25, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(61·10¹⁵⁴-7)/9 = 6(7)₁₅₄_<155> = 47 · 1901127231469_<13> · C141

C141 = P65 · P77

P65 = 15449228959889505678903871315182748873746361954118799891643517789_<65>

P77 = 49098867557942295120670149975881643072020141070454812365305226919065044586551_<77>

Number: trial
N=758539646573941437749720403994032529006687526133316212579427198765475459899081071283698953488066677740729619955184599536546418305464718655739
  ( 141 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=15449228959889505678903871315182748873746361954118799891643517789 (pp65)
 r2=49098867557942295120670149975881643072020141070454812365305226919065044586551 (pp77)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 86.37 hours.
Scaled time: 45.95 units (timescale=0.532).
Factorization parameters were as follows:
n: 758539646573941437749720403994032529006687526133316212579427198765475459899081071283698953488066677740729619955184599536546418305464718655739
m: 10000000000000000000000000000000
c5: 61
c0: -70
skew: 1.03
type: snfsFactor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3100001)
Primes: RFBsize:216816, AFBsize:215937, largePrimes:5630489 encountered
Relations: rels:5528421, finalFF:498175
Max relations in full relation-set: 0
Initial matrix: 432818 x 498175 with sparse part having weight 45488559.
Pruned matrix : 406257 x 408485 with weight 32614309.
Total sieving time: 68.87 hours.
Total relation processing time: 0.60 hours.
Matrix solve time: 16.55 hours.
Time per square root: 0.35 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 86.37 hours.
 --------- CPU info (if available) ----------

Mar 24, 2007 (6th)

By suberi / GMP-ECM 6.1.2 B1=1500000

(10¹⁸¹+53)/9 = (1)₁₈₀7_<181> = 7 · 191 · 1447 · 12373 · C170

C170 = P35 · P135

P35 = 59944560930672769912224103774471799_<35>

P135 = 774341892801138722769038296323949007707741157304392299689179236900059833331313025992038840594454667820419468024609247807834263463108289_<135>

(10¹⁹⁸+53)/9 = (1)₁₉₇7_<198> = 3 · 11618966467_<11> · 272033009875993867_<18> · C170

C170 = P32 · C138

P32 = 30874217309083734095351287845727_<32>

C138 = [379534425199519751802558862062259553534112280564965144585212678040651849592463853984445240166695146589693057988042923980473715294957117713_<138>]

Mar 24, 2007 (5th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(10¹⁵⁴+11)/3 = (3)₁₅₃7_<154> = 379 · 22973 · 120588737 · C139

C139 = P43 · P47 · P49

P43 = 7544120729352931097852968698233932678745227_<43>

P47 = 48431736813392301590373185023279934003162249891_<47>

P49 = 8689132158836105024407698702203742306290102326679_<49>

Number: n
N=3174790529927899534422665391360944333364806413078654198479087131608603674228467671965504741912997056441681538202948620630712819782034036503
  ( 139 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=7544120729352931097852968698233932678745227 (pp43)
 r2=48431736813392301590373185023279934003162249891 (pp47)
 r3=8689132158836105024407698702203742306290102326679 (pp49)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.18 hours.
Scaled time: 42.19 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_3_153_7
n: 3174790529927899534422665391360944333364806413078654198479087131608603674228467671965504741912997056441681538202948620630712819782034036503
type: snfs
skew: 1
deg: 5
c5: 1
c0: 110
m: 10000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [1600000, 2800001)
Primes: RFBsize:230209, AFBsize:230648, largePrimes:7397308 encountered
Relations: rels:6898240, finalFF:534130
Max relations in full relation-set: 28
Initial matrix: 460921 x 534130 with sparse part having weight 38277702.
Pruned matrix : 408055 x 410423 with weight 26420103.
Total sieving time: 29.30 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 5.21 hours.
Total square root time: 0.49 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 35.18 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Mar 24, 2007 (4th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

4·10¹³⁹+1 = 4(0)₁₃₈1_<140> = 641 · 27851 · C133

C133 = P61 · P72

P61 = 7102095496029555951338486428062736055043334947960741098720689_<61>

P72 = 315482054875753501037036269251586513863489506091455405288439226913423699_<72>

Number: 30001_139
N=2240583681011238151583440092477850850057843468454906376930815985287431317007805801442498976753440178180176648737702766521489914208611
  ( 133 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=7102095496029555951338486428062736055043334947960741098720689 (pp61)
 r2=315482054875753501037036269251586513863489506091455405288439226913423699 (pp72)
Version: GGNFS-0.77.1-20050930-k8
Total time: 8.58 hours.
Scaled time: 7.77 units (timescale=0.905).
Factorization parameters were as follows:
n: 2240583681011238151583440092477850850057843468454906376930815985287431317007805801442498976753440178180176648737702766521489914208611
m: 10000000000000000000000000000
c5: 2
c0: 5
skew: 1.2
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [650000, 1150001)
Primes: RFBsize:100021, AFBsize:99363, largePrimes:1578992 encountered
Relations: rels:1629798, finalFF:241123
Max relations in full relation-set: 28
Initial matrix: 199449 x 241123 with sparse part having weight 10143150.
Pruned matrix : 172207 x 173268 with weight 6295764.
Total sieving time: 8.46 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1300000,1300000,25,25,43,43,2.3,2.3,50000
total time: 8.58 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335813)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334235)
Total of 2 processors activated (9340.09 BogoMIPS).

Mar 24, 2007 (3rd)

By Alfred Reich / GMP-ECM B1=500000

10⁹⁰⁸+1 = 1(0)₉₀₇1_<909> = 73 · 137 · 285113 · 9419593 · 227165039897_<12> · C881

C881 = P37 · C844

P37 = 3807960958399006163762044938087483809_<37>

C844 = [4304011589843391014650658235505329949871751140563599604819840057463188843469403445050796836064297177141743491344058167353249785331012310283113532723970464380415218789297453601728394059603084153179243926781291576513844045576686305866338578844027945196495337813932986508166348651300882380217196839427590038172195743290681854096987188298138279008174571726499244450616512700403834454792857104888796722367969930545996327346289992694880432920507844931852753107934643879174985688347282698671170664733023120429358285265783370040535302435624377564200840845165362706841047727730263552281976488781141247675441240545610662922217686249874781389229039939830542986976575550678328214886238059683964908857311171270037200840332507004282564390954411475394337980444799820049557055125339576122509817486779514751262773644681965508670248363470452661827609186970683193_<844>]

Mar 24, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

3·10¹⁷⁷+1 = 3(0)₁₇₆1_<178> = 67 · 971 · 1181 · 1487 · 230479 · 825733 · 3109400284219346651_<19> · 126785306124523882133503879_<27> · C111

C111 = P36 · P75

P36 = 559219839704943337643116206350631409_<36>

P75 = 625845632053760575390249120386323002760427242323498242975273828154385498197_<75>

Number: 30001_177
N=349985294037142937023626087334501084652991562744579542870530549887165774441375073483589661777470537343981069573
  ( 111 digits)
Divisors found:
 r1=559219839704943337643116206350631409 (pp36)
 r2=625845632053760575390249120386323002760427242323498242975273828154385498197 (pp75)
Version: GGNFS-0.77.1-20050930-k8
Total time: 21.23 hours.
Scaled time: 19.24 units (timescale=0.906).
Factorization parameters were as follows:
name: 30001_177
n: 349985294037142937023626087334501084652991562744579542870530549887165774441375073483589661777470537343981069573
skew: 15601.15
# norm 9.84e+14
c5: 29640
c4: 5032753936
c3: -30601470931224
c2: -1120220487668463327
c1: 7586541853076428459816
c0: 4867968944726300546755167
# alpha -5.28
Y1: 215853844679
Y0: -1638446920404058499690
# Murphy_E 8.64e-10
# M 310554946319189235575576633090641599125096887599022052198451856874598952273869120055693059034498175184100593502
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176298, largePrimes:7590968 encountered
Relations: rels:7376238, finalFF:430717
Max relations in full relation-set: 28
Initial matrix: 352681 x 430717 with sparse part having weight 43746566.
Pruned matrix : 303195 x 305022 with weight 28868426.
Total sieving time: 20.15 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.81 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000
total time: 21.23 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335813)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334235)
Total of 2 processors activated (9340.09 BogoMIPS).

Mar 24, 2007

By Shaopu Lin / Msieve v. 1.17

4·10¹³⁴+1 = 4(0)₁₃₃1_<135> = 2521769 · 6482122769_<10> · 498771505631914848917_<21> · C98

C98 = P45 · P54

P45 = 339732985011027186094197732510445277293910533_<45>

P54 = 144410272621457596142773322790127495868916847945915681_<54>

Fri Mar 23 14:54:47 2007  
Fri Mar 23 14:54:47 2007  
Fri Mar 23 14:54:47 2007  Msieve v. 1.17
Fri Mar 23 14:54:47 2007  random seeds: 43e71c9a 60c79983
Fri Mar 23 14:54:47 2007  factoring 49060932983944003138619507865794328431537398530751722286000745421350817401943951719152669975767973 (98 digits)
Fri Mar 23 14:54:48 2007  commencing quadratic sieve (98-digit input)
Fri Mar 23 14:54:48 2007  using multiplier of 13
Fri Mar 23 14:54:48 2007  sieve interval: 9 blocks of size 65536
Fri Mar 23 14:54:48 2007  processing polynomials in batches of 6
Fri Mar 23 14:54:48 2007  using a sieve bound of 2500601 (91765 primes)
Fri Mar 23 14:54:48 2007  using large prime bound of 375090150 (28 bits)
Fri Mar 23 14:54:48 2007  using double large prime bound of 2712964789985100 (43-52 bits)
Fri Mar 23 14:54:48 2007  using trial factoring cutoff of 57 bits
Fri Mar 23 14:54:48 2007  polynomial 'A' values have 13 factors
Sat Mar 24 01:26:18 2007  92124 relations (23135 full + 68989 combined from 1351734 partial), need 91861
Sat Mar 24 01:26:19 2007  begin with 1374869 relations
Sat Mar 24 01:26:22 2007  reduce to 237829 relations in 11 passes
Sat Mar 24 01:26:22 2007  attempting to read 237829 relations
Sat Mar 24 01:26:26 2007  recovered 237829 relations
Sat Mar 24 01:26:26 2007  recovered 225415 polynomials
Sat Mar 24 01:26:27 2007  attempting to build 92124 cycles
Sat Mar 24 01:26:27 2007  found 92124 cycles in 5 passes
Sat Mar 24 01:26:27 2007  distribution of cycle lengths:
Sat Mar 24 01:26:27 2007     length 1 : 23135
Sat Mar 24 01:26:27 2007     length 2 : 16209
Sat Mar 24 01:26:27 2007     length 3 : 15558
Sat Mar 24 01:26:27 2007     length 4 : 12658
Sat Mar 24 01:26:27 2007     length 5 : 9124
Sat Mar 24 01:26:27 2007     length 6 : 6091
Sat Mar 24 01:26:27 2007     length 7 : 4022
Sat Mar 24 01:26:27 2007     length 9+: 5327
Sat Mar 24 01:26:27 2007  largest cycle: 19 relations
Sat Mar 24 01:26:28 2007  matrix is 91765 x 92124 with weight 5948053 (avg 64.57/col)
Sat Mar 24 01:26:29 2007  filtering completed in 3 passes
Sat Mar 24 01:26:29 2007  matrix is 90084 x 90148 with weight 5741377 (avg 63.69/col)
Sat Mar 24 01:26:30 2007  saving the first 48 matrix rows for later
Sat Mar 24 01:26:30 2007  matrix is 90036 x 90148 with weight 4391751 (avg 48.72/col)
Sat Mar 24 01:26:30 2007  matrix includes 32 packed rows
Sat Mar 24 01:31:47 2007  lanczos halted after 1425 iterations
Sat Mar 24 01:31:48 2007  recovered 14 nontrivial dependencies
Sat Mar 24 01:31:50 2007  prp45 factor: 339732985011027186094197732510445277293910533
Sat Mar 24 01:31:50 2007  prp54 factor: 144410272621457596142773322790127495868916847945915681
Sat Mar 24 01:31:50 2007  elapsed time 10:37:03

Mar 23, 2007 (6th)

The factor table of 400...001 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Mar 23, 2007 (5th)

By Alfred Reich / GMP-ECM B1=1000000

10¹³²⁹+1 = 1(0)₁₃₂₈1_<1330> = 7 · 11 · 13 · 887 · 2659 · 37265161 · 68209597 · 3646836465960880692292201915543408162476049_<43> · [1056936920749964722929828576624217604146887673567661698146974403860730882430792714566017124364090647084708761042672412110583342292077804307482388499001109008194875836195841990475402074719478633242189283412047635153545645032028344137331511134704077687538175641102136020445005471151998617932091877877913277007525468543178676185089859186550080677532355108510234998991838967281973483348896796755223_<394>] · C869

C869 = P29 · C840

P29 = 88069370339005814813332403179_<29>

C840 = [490891182024055768303752448641711254423965418035815948434540059825112526865794436891158692344525740667640215258095895206329386376678402738775497808175021519842805327426106442373856336850571315530961479638250093659953397539875582001392216062410162111734230403799329909279629474278117095074949361610801053309078179578765676913094212535145467716201912187985533289286101878598434483506183916691225899431281901210559325567363985600274656341045284488282414867400615456204294619663505148649829642437069440418643662744942039427890109652539672121197076171571860904552661826173448806554360971818577812524996561063671351439779588997281497543003882019346099698333311943121452149103038987112141501284299533953009969661940609519236049791940648085437210318272370951609760658678065732274533718045425407568887423257854476732620452773560574452704443488415877_<840>]

Mar 23, 2007 (4th)

By Yousuke Koide / GMP-ECM / Mar 15, 2007

10¹⁰⁴⁴+1 = 1(0)₁₀₄₃1_<1045> = 73 · 137 · 233 · 3169 · 13921 · 98641 · 355193 · 99990001 · 21591416633_<11> · 192346125251257_<15> · 3199044596370769_<16> · 11090099157944399977_<20> · 17468739848498438039329935679794457_<35> · 246900403017958787131873605843061988161_<39> · 320326994163169943384295066992439316655840979654890345228609_<60> · 2623709608263520547879954791214412810391703985166673562220208867630775121385164482905259044455273939230491414883050557483687370269811018178176841590586944036054473_<163> · C658

C658 = P31 · P628

P31 = 1625458218739290128864916634393_<31>

P628 = 3198458699783050536968283401478982683944528000068135835839586527370144819849764922320573399552615795836284837690553084192932370474126106776285338588228275657236279389210630068653431296486652949237156444521521152418640091807354686792087134015545130855986648074389240747528765978498126669434936092301530847500040330892702072177445595054747262623246459270677168775935422451177882409563066968720256690285465719695234904487207368361185299854596149960626836167373098838553773698029915536112232582904128376139462422005842249372344048254807991740818332936597022240787264242857005018741508465960721402060639401624790434299746509191318001_<628>

By Yousuke Koide / GMP-ECM / Mar 17, 2007

(10⁷¹⁹-1)/9 = (1)₇₁₉_<719> = 1439 · 1153277 · 6699643 · C702

C702 = P40 · C663

P40 = 3713656876665286297046096029015677459199_<40>

C663 = [269097479386038576036358324111351774806252265640747217262071077189387212219811678802485493254067295614358833851846346846112373614951579138009912107531825433722907258144026470897326730436327972589621793493828435956171945704741239221872251269735271946392127516869504289440634603138735776750777050975850022700923009814235995356036666401273827145316553631769106025832008477594679623338432757544279350895770964184294952891206974288204046187565654983102962849566418022038627835250348032633372718008292520671008293816721752400771336200089796153543716360753236555894101881377432325335995230001091002680143876905641146960653145348907542114406930665370204654545512135947241_<663>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 23, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

3·10¹⁴⁵+1 = 3(0)₁₄₄1_<146> = 23 · 163365916333_<12> · C133

C133 = P43 · P91

P43 = 1512111483928357227059586147307533255856999_<43>

P91 = 5280173022660233758936952412889720282802454835751048118163212654450579862340614890525644261_<91>

Number: 30001_145
N=7984210264693245460064507559711094683106232413676197102921955777594960957994230311233711913285244527822227900636517028122986161032739
  ( 133 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=1512111483928357227059586147307533255856999 (pp43)
 r2=5280173022660233758936952412889720282802454835751048118163212654450579862340614890525644261 (pp91)
Version: GGNFS-0.77.1-20050930-k8
Total time: 9.90 hours.
Scaled time: 8.99 units (timescale=0.908).
Factorization parameters were as follows:
n: 7984210264693245460064507559711094683106232413676197102921955777594960957994230311233711913285244527822227900636517028122986161032739
m: 100000000000000000000000000000
c5: 3
c0: 1
skew: 1
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 1300001)
Primes: RFBsize:114155, AFBsize:114062, largePrimes:2646018 encountered
Relations: rels:2633399, finalFF:294706
Max relations in full relation-set: 28
Initial matrix: 228282 x 294706 with sparse part having weight 19441463.
Pruned matrix : 198508 x 199713 with weight 10628700.
Total sieving time: 9.68 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000
total time: 9.90 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335813)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334235)
Total of 2 processors activated (9340.09 BogoMIPS).

Mar 23, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(71·10¹⁵⁴-17)/9 = 7(8)₁₅₃7_<155> = 197 · 520867 · 5751145261_<10> · C138

C138 = P47 · P91

P47 = 53701924431312439410408177111495360811709318993_<47>

P91 = 2489307707460823521893037761555514767129507905859057023337340854513007304174704820222113581_<91>

Number: n
N=133680614392344757498170778665032531414430724998130071499961029024244849458358250472303926326253296322462495221636126193770469832606543933
  ( 138 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=53701924431312439410408177111495360811709318993 (pp47)
 r2=2489307707460823521893037761555514767129507905859057023337340854513007304174704820222113581 (pp91)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 44.09 hours.
Scaled time: 52.56 units (timescale=1.192).
Factorization parameters were as follows:
name: KA_7_8_153_7
n: 133680614392344757498170778665032531414430724998130071499961029024244849458358250472303926326253296322462495221636126193770469832606543933
type: snfs
skew: 1
deg: 5
c5: 71
c0: -170
m: 10000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [1600000, 3100001)
Primes: RFBsize:230209, AFBsize:229943, largePrimes:7474870 encountered
Relations: rels:6962838, finalFF:520544
Max relations in full relation-set: 28
Initial matrix: 460217 x 520544 with sparse part having weight 39980357.
Pruned matrix : 426050 x 428415 with weight 29284340.
Total sieving time: 36.86 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 6.44 hours.
Total square root time: 0.58 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 44.09 hours.
 --------- CPU info (if available) ----------

Cygwin on Amd XP 2700+

Mar 23, 2007

By Shaopu Lin / Msieve v. 1.17, GGNFS-0.77.1-20060722-pentium4 gnfs

3·10¹⁵¹+1 = 3(0)₁₅₀1_<152> = 31 · 397 · 38197 · 60017 · 2703403 · 2730124326417233_<16> · 373344263955479291_<18> · C99

C99 = P35 · P64

P35 = 62705195924448530372188252023190597_<35>

P64 = 6154025449218468087679049299048266043351577284513852625291792459_<64>

Wed Mar 21 14:15:09 2007  
Wed Mar 21 14:15:09 2007  
Wed Mar 21 14:15:09 2007  Msieve v. 1.17
Wed Mar 21 14:15:09 2007  random seeds: 98c0ffc5 75556fe9
Wed Mar 21 14:15:09 2007  factoring 385889371517286421442250331069095000754556604021618402863747194455031301300113592412525634324308023 (99 digits)
Wed Mar 21 14:15:09 2007  commencing quadratic sieve (99-digit input)
Wed Mar 21 14:15:09 2007  using multiplier of 47
Wed Mar 21 14:15:09 2007  sieve interval: 9 blocks of size 65536
Wed Mar 21 14:15:09 2007  processing polynomials in batches of 6
Wed Mar 21 14:15:09 2007  using a sieve bound of 2611159 (95294 primes)
Wed Mar 21 14:15:09 2007  using large prime bound of 391673850 (28 bits)
Wed Mar 21 14:15:09 2007  using double large prime bound of 2932676752219800 (43-52 bits)
Wed Mar 21 14:15:09 2007  using trial factoring cutoff of 57 bits
Wed Mar 21 14:15:09 2007  polynomial 'A' values have 13 factors
Wed Mar 21 14:34:52 2007  535 relations (527 full + 8 combined from 29903 partial), need 95390
Wed Mar 21 14:34:52 2007  c99 factor: 385889371517286421442250331069095000754556604021618402863747194455031301300113592412525634324308023
Wed Mar 21 14:34:52 2007  elapsed time 00:19:43
Wed Mar 21 14:47:22 2007  
Wed Mar 21 14:47:22 2007  
Wed Mar 21 14:47:22 2007  Msieve v. 1.17
Wed Mar 21 14:47:22 2007  random seeds: 74180741 05ba4e00
Wed Mar 21 14:47:22 2007  factoring 385889371517286421442250331069095000754556604021618402863747194455031301300113592412525634324308023 (99 digits)
Wed Mar 21 14:47:23 2007  commencing quadratic sieve (99-digit input)
Wed Mar 21 14:47:23 2007  using multiplier of 47
Wed Mar 21 14:47:23 2007  sieve interval: 9 blocks of size 65536
Wed Mar 21 14:47:23 2007  processing polynomials in batches of 6
Wed Mar 21 14:47:23 2007  using a sieve bound of 2611159 (95294 primes)
Wed Mar 21 14:47:23 2007  using large prime bound of 391673850 (28 bits)
Wed Mar 21 14:47:23 2007  using double large prime bound of 2932676752219800 (43-52 bits)
Wed Mar 21 14:47:23 2007  using trial factoring cutoff of 57 bits
Wed Mar 21 14:47:23 2007  polynomial 'A' values have 13 factors
Wed Mar 21 14:47:23 2007  restarting with 527 full and 29903 partial relations
Wed Mar 21 17:41:13 2007  6172 relations (5073 full + 1099 combined from 300728 partial), need 95390
Wed Mar 21 17:41:13 2007  c99 factor: 385889371517286421442250331069095000754556604021618402863747194455031301300113592412525634324308023
Wed Mar 21 17:41:13 2007  elapsed time 02:53:51
Wed Mar 21 18:24:55 2007  
Wed Mar 21 18:24:55 2007  
Wed Mar 21 18:24:55 2007  Msieve v. 1.17
Wed Mar 21 18:24:55 2007  random seeds: b2ab1b94 1f8bf804
Wed Mar 21 18:24:55 2007  factoring 385889371517286421442250331069095000754556604021618402863747194455031301300113592412525634324308023 (99 digits)
Wed Mar 21 18:24:55 2007  commencing quadratic sieve (99-digit input)
Wed Mar 21 18:24:56 2007  using multiplier of 47
Wed Mar 21 18:24:56 2007  sieve interval: 9 blocks of size 65536
Wed Mar 21 18:24:56 2007  processing polynomials in batches of 6
Wed Mar 21 18:24:56 2007  using a sieve bound of 2611159 (95294 primes)
Wed Mar 21 18:24:56 2007  using large prime bound of 391673850 (28 bits)
Wed Mar 21 18:24:56 2007  using double large prime bound of 2932676752219800 (43-52 bits)
Wed Mar 21 18:24:56 2007  using trial factoring cutoff of 57 bits
Wed Mar 21 18:24:56 2007  polynomial 'A' values have 13 factors
Wed Mar 21 18:24:57 2007  restarting with 5073 full and 300728 partial relations
Thu Mar 22 06:26:27 2007  95394 relations (23334 full + 72060 combined from 1407826 partial), need 95390
Thu Mar 22 06:26:31 2007  begin with 1431160 relations
Thu Mar 22 06:26:34 2007  reduce to 248028 relations in 12 passes
Thu Mar 22 06:26:34 2007  attempting to read 248028 relations
Thu Mar 22 06:26:39 2007  recovered 248028 relations
Thu Mar 22 06:26:39 2007  recovered 237984 polynomials
Thu Mar 22 06:26:39 2007  attempting to build 95394 cycles
Thu Mar 22 06:26:40 2007  found 95394 cycles in 6 passes
Thu Mar 22 06:26:40 2007  distribution of cycle lengths:
Thu Mar 22 06:26:40 2007     length 1 : 23334
Thu Mar 22 06:26:40 2007     length 2 : 17078
Thu Mar 22 06:26:40 2007     length 3 : 15986
Thu Mar 22 06:26:40 2007     length 4 : 13025
Thu Mar 22 06:26:40 2007     length 5 : 9632
Thu Mar 22 06:26:40 2007     length 6 : 6464
Thu Mar 22 06:26:40 2007     length 7 : 4197
Thu Mar 22 06:26:40 2007     length 9+: 5678
Thu Mar 22 06:26:40 2007  largest cycle: 20 relations
Thu Mar 22 06:26:41 2007  matrix is 95294 x 95394 with weight 6270112 (avg 65.73/col)
Thu Mar 22 06:26:42 2007  filtering completed in 3 passes
Thu Mar 22 06:26:42 2007  matrix is 93740 x 93804 with weight 6115800 (avg 65.20/col)
Thu Mar 22 06:26:43 2007  saving the first 48 matrix rows for later
Thu Mar 22 06:26:43 2007  matrix is 93692 x 93804 with weight 4698380 (avg 50.09/col)
Thu Mar 22 06:26:43 2007  matrix includes 32 packed rows
Thu Mar 22 06:32:36 2007  lanczos halted after 1483 iterations
Thu Mar 22 06:32:37 2007  recovered 16 nontrivial dependencies
Thu Mar 22 06:32:38 2007  prp35 factor: 62705195924448530372188252023190597
Thu Mar 22 06:32:38 2007  prp64 factor: 6154025449218468087679049299048266043351577284513852625291792459
Thu Mar 22 06:32:38 2007  elapsed time 12:07:43

3·10¹⁴³+1 = 3(0)₁₄₂1_<144> = 13 · 47 · 2099 · 4231 · 4259 · 17736799 · 74115735887240684807_<20> · C103

C103 = P33 · P71

P33 = 120940167904876203213061027933433_<33>

P71 = 81650848796699811506688800647364367461674661533783095495619303656848309_<71>

Number: 3.143.+1
N=9874867363048534300768923310572398538246738841229883690278000169463929671639994810806096769076230614797
  ( 103 digits)
Divisors found:
 r1=120940167904876203213061027933433 (pp33)
 r2=81650848796699811506688800647364367461674661533783095495619303656848309 (pp71)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 13.81 hours.
Scaled time: 17.13 units (timescale=1.241).
Factorization parameters were as follows:
name: 3.143.+1
n: 9874867363048534300768923310572398538246738841229883690278000169463929671639994810806096769076230614797
skew: 6749.35
# norm 4.00e+13
c5: 48600
c4: -371210235
c3: -5500894816123
c2: 14026046391797824
c1: 138005832591685066335
c0: -1470412156833659345697
# alpha -4.71
Y1: 37579168649
Y0: -45875366177130951970
# Murphy_E 2.38e-09
# M 9655638943442329929065301975488399586430887237464357172778108578355126427732345746409409778290330587088
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1950001)
Primes: RFBsize:169511, AFBsize:169084, largePrimes:4511450 encountered
Relations: rels:4703975, finalFF:560178
Max relations in full relation-set: 32
Initial matrix: 338670 x 560178 with sparse part having weight 43990815.
Pruned matrix : 196015 x 197772 with weight 20038421.
Total sieving time: 12.47 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.82 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 13.81 hours.
 --------- CPU info (if available) ----------

Mar 22, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

3·10¹⁵⁰+1 = 3(0)₁₄₉1_<151> = C151

C151 = P61 · P90

P61 = 3757884014173930271262822327673582373969961097805606684684809_<61>

P90 = 798321605638876885936868160206937968803884648888029502380986396890251623546215931267628089_<90>

Number: 30001_150
N=3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
  ( 151 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=3757884014173930271262822327673582373969961097805606684684809 (pp61)
 r2=798321605638876885936868160206937968803884648888029502380986396890251623546215931267628089 (pp90)
Version: GGNFS-0.77.1-20050930-k8
Total time: 16.21 hours.
Scaled time: 14.65 units (timescale=0.904).
Factorization parameters were as follows:
n: 3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
m: 1000000000000000000000000000000
c5: 3
c0: 1
skew: 1
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [900000, 1800001)
Primes: RFBsize:135072, AFBsize:134928, largePrimes:2726191 encountered
Relations: rels:2710347, finalFF:316135
Max relations in full relation-set: 28
Initial matrix: 270065 x 316135 with sparse part having weight 18817652.
Pruned matrix : 250350 x 251764 with weight 12558643.
Total sieving time: 15.84 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,45,45,2.3,2.3,75000
total time: 16.21 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335812)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238)
Total of 2 processors activated (9340.10 BogoMIPS).

3·10¹⁴²+1 = 3(0)₁₄₁1_<143> = 97 · 203543020951_<12> · C130

C130 = P47 · P83

P47 = 33690430121780543888212711166213824692220327981_<47>

P83 = 45101059976427355505564135250839549784926008407968873075769527543445669278405405443_<83>

Number: 30001_142
N=1519474109554059084609548420833139409946353621611335173749042270509374517238216006850359020183147921673643448703289388436742600583
  ( 130 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=33690430121780543888212711166213824692220327981 (pp47)
 r2=45101059976427355505564135250839549784926008407968873075769527543445669278405405443 (pp83)
Version: GGNFS-0.77.1-20050930-k8
Total time: 9.87 hours.
Scaled time: 8.98 units (timescale=0.909).
Factorization parameters were as follows:
n: 1519474109554059084609548420833139409946353621611335173749042270509374517238216006850359020183147921673643448703289388436742600583
m: 10000000000000000000000000000
c5: 300
c0: 1
skew: 1
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 1300001)
Primes: RFBsize:114155, AFBsize:114347, largePrimes:2642238 encountered
Relations: rels:2618585, finalFF:286160
Max relations in full relation-set: 28
Initial matrix: 228568 x 286160 with sparse part having weight 18940398.
Pruned matrix : 202223 x 203429 with weight 10814074.
Total sieving time: 9.64 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000
total time: 9.87 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335812)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238)
Total of 2 processors activated (9340.10 BogoMIPS).

Mar 21, 2007 (6th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

3·10¹³⁵+1 = 3(0)₁₃₄1_<136> = 523 · 13477 · 1075774213_<10> · 5752978421_<10> · C110

C110 = P36 · P75

P36 = 147095946235219350911667697013541493_<36>

P75 = 467532449005166182402814318007788918674002841796260849988478421239468688979_<75>

Number: 30001_135
N=68772127982084357672888092300112850412086888448042124154539344177097592160142571052867879456959527938528305647
  ( 110 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=147095946235219350911667697013541493 (pp36)
 r2=467532449005166182402814318007788918674002841796260849988478421239468688979 (pp75)
Version: GGNFS-0.77.1-20050930-k8
Total time: 4.34 hours.
Scaled time: 3.93 units (timescale=0.907).
Factorization parameters were as follows:
n: 68772127982084357672888092300112850412086888448042124154539344177097592160142571052867879456959527938528305647
m: 1000000000000000000000000000
c5: 3
c0: 1
skew: 1
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [650000, 1300001)
Primes: RFBsize:100021, AFBsize:99933, largePrimes:1571319 encountered
Relations: rels:1618924, finalFF:241524
Max relations in full relation-set: 28
Initial matrix: 200019 x 241524 with sparse part having weight 8834742.
Pruned matrix : 176061 x 177125 with weight 5550943.
Total sieving time: 4.21 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1300000,1300000,25,25,43,43,2.3,2.3,50000
total time: 4.34 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335812)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238)
Total of 2 processors activated (9340.10 BogoMIPS).

Mar 21, 2007 (5th)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(67·10¹⁵⁴+23)/9 = 7(4)₁₅₃7_<155> = 233168882957420675233_<21> · C135

C135 = P41 · P43 · P53

P41 = 11379813213676719854455664457933030998149_<41>

P43 = 1587248342657233076523061352021858322701023_<43>

P53 = 17675906074957204594524237615101714309571956136443117_<53>

Number: trial
N=319272638356460530808654765903576271179526029216138353262035954538553273441603920608246228075825386906312739402331673810547706147712959
  ( 135 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=11379813213676719854455664457933030998149 (pp41)
 r2=1587248342657233076523061352021858322701023 (pp43)
 r3=17675906074957204594524237615101714309571956136443117 (pp53)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 71.79 hours.
Scaled time: 36.11 units (timescale=0.503).
Factorization parameters were as follows:
n: 319272638356460530808654765903576271179526029216138353262035954538553273441603920608246228075825386906312739402331673810547706147712959
m: 10000000000000000000000000000000
c5: 67
c0: 230
skew: 1.28
type: snfsFactor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 1
)
Primes: RFBsize:216816, AFBsize:216516, largePrimes:5701357 encountered
Relations: rels:5685937, finalFF:503412
Max relations in full relation-set: 0
Initial matrix: 433397 x 503412 with sparse part having weight 33046809.
Pruned matrix : 393045 x 395275 with weight 24591541.
Total sieving time: 63.79 hours.
Total relation processing time: 0.59 hours.
Matrix solve time: 7.10 hours.
Time per square root: 0.32 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 71.79 hours.
 --------- CPU info (if available) ----------

Mar 21, 2007 (4th)

By suberi / GMP-ECM 6.1.2 B1=1500000

(5·10¹⁷⁰+1)/3 = 1(6)₁₆₉7_<171> = 7487 · 169321 · 3120931921_<10> · 2094038676000833609_<19> · C134

C134 = P34 · P100

P34 = 6330148428935272130730269808330421_<34>

P100 = 3177951057107386168338512979344112428416946032503776796031417480994030657221820623388204144977247009_<100>

Mar 21, 2007 (3rd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(5·10¹⁵¹+1)/3 = 1(6)₁₅₀7_<152> = 19 · 9241 · 131331427 · C138

C138 = P37 · P39 · P63

P37 = 1738813535312938111598190623296264579_<37>

P39 = 559577859531754734428273075732784737987_<39>

P63 = 742837774773700873641647036143752794028585520948746579669338563_<63>

Number: n
N=722782310870289627746169413515506430457992195423434849290341876222067869070125129260611987346780261939106059985584469415989129554547446299
  ( 138 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=1738813535312938111598190623296264579 (pp37)
 r2=559577859531754734428273075732784737987 (pp39)
 r3=742837774773700873641647036143752794028585520948746579669338563 (pp63)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 22.24 hours.
Scaled time: 26.69 units (timescale=1.200).
Factorization parameters were as follows:
name: KA_1_6_150_7
n: 722782310870289627746169413515506430457992195423434849290341876222067869070125129260611987346780261939106059985584469415989129554547446299
type: snfs
skew: 1
deg: 5
c5: 50
c0: 1
m: 1000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [1600000, 1600000)
Primes: RFBsize:230209, AFBsize:230262, largePrimes:7152336 encountered
Relations: rels:6642883, finalFF:526015
Max relations in full relation-set: 28
Initial matrix: 460536 x 526015 with sparse part having weight 34370220.
Pruned matrix : 407274 x 409640 with weight 22436194.
Total sieving time: 17.08 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 4.77 hours.
Total square root time: 0.22 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 22.24 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Mar 21, 2007 (2nd)

By Shaopu Lin / GGNFS-0.77.1-20060722-pentium4

(5·10¹⁷²+1)/3 = 1(6)₁₇₁7_<173> = 7 · 23 · 787 · 3592897283321_<13> · 13409369737723_<14> · 720221664378281653603080022761581_<33> · C109

C109 = P35 · P75

P35 = 11187158312418767561564578896159263_<35>

P75 = 338851185355906112703584873042435753235342294622312755124422330024404931569_<75>

Number: 5.172.+1
N=3790781854927277631648278252606516515296395111422830767220826618421065775857484773239829096077858370440473647
  ( 109 digits)
Divisors found:
 r1=11187158312418767561564578896159263 (pp35)
 r2=338851185355906112703584873042435753235342294622312755124422330024404931569 (pp75)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 25.37 hours.
Scaled time: 32.65 units (timescale=1.287).
Factorization parameters were as follows:
name: 5.172.+1
n: 3790781854927277631648278252606516515296395111422830767220826618421065775857484773239829096077858370440473647
skew: 32948.05
# norm 1.51e+15
c5: 17220
c4: 14458390
c3: -103341475597152
c2: 281584288696052283
c1: 39073308390551941890838
c0: -86019664049948734884907152
# alpha -6.16
Y1: 177045558749
Y0: -738820796836376918465
# Murphy_E 1.15e-09
# M 2907907167967925298903030487242863143011263020191204105775196844047268453970546110481020997988859280422515842
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2900001)
Primes: RFBsize:230209, AFBsize:229950, largePrimes:7404566 encountered
Relations: rels:7327936, finalFF:671556
Max relations in full relation-set: 32
Initial matrix: 460245 x 671556 with sparse part having weight 56363648.
Pruned matrix : 300813 x 303178 with weight 28748107.
Total sieving time: 21.88 hours.
Total relation processing time: 0.47 hours.
Matrix solve time: 2.60 hours.
Time per square root: 0.42 hours.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 25.37 hours.
 --------- CPU info (if available) ----------

Mar 21, 2007

The factor table of 300...001 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Mar 20, 2007 (4th)

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000, GMP-ECM 6.1 B1=11000000

10¹⁷³+3 = 1(0)₁₇₂3_<174> = 8753 · 14107 · 2625274331_<10> · C156

C156 = P34 · P122

P34 = 4654165597283817538340682232414823_<34>

P122 = 66281431794713202969955544003490886754601337940508012963182198582216786419780605860128839549004095099134596062756894253661_<122>

(5·10¹⁹⁷+1)/3 = 1(6)₁₉₆7_<198> = 43 · 1108021631163049657_<19> · C178

C178 = P31 · C147

P31 = 3724929267509920843996372775497_<31>

C147 = [939104723049981509289811750930030691770734096377436694089298811115147192934297884941625038686793082121971137561628863866898691665347893823937479361_<147>]

Mar 20, 2007 (3rd)

By Kenichiro Yamaguchi / GGNFS-0.77.1

(5·10¹⁴³+1)/3 = 1(6)₁₄₂7_<144> = 390953 · C138

C138 = P31 · P45 · P63

P31 = 6125134479493857489788596359529_<31>

P45 = 124754495274432898134178118407138197155338843_<45>

P63 = 557894869819739178785330732398794202349486582304975230797045537_<63>

Number: 16667.143
N=426308703774281477995223637282912950320541514367882243304608652873022247346015164653210658740735246095225427779468802302749094307158831539
  ( 138 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=6125134479493857489788596359529 (pp31)
 r2=124754495274432898134178118407138197155338843 (pp45)
 r3=557894869819739178785330732398794202349486582304975230797045537 (pp63)
Version: GGNFS-0.77.1
Total time: 27.46 hours.
Scaled time: 32.98 units (timescale=1.201).
Factorization parameters were as follows:
name: 16667_143
n: 426308703774281477995223637282912950320541514367882243304608652873022247346015164653210658740735246095225427779468802302749094307158831539 
m: 1000000000000000000000000
c6: 1
c0: 2
type: snfs
skew: 1
qintsize: 200000
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Sieved special-q in [650000, 3850001)
Relations: rels:3273771, finalFF:255803
Initial matrix: 199682 x 255803 with sparse part having weight 32662078.
Pruned matrix : 193403 x 194465 with weight 20914869.
Total sieving time: 26.78 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.41 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,144,6,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 27.46 hours.
 --------- CPU info (if available) ----------

The factor table of 166...667 was completed up to n=150.

Mar 20, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(5·10¹⁴⁷+1)/3 = 1(6)₁₄₆7_<148> = 131 · 1571 · 128991859 · 10296803609_<11> · C124

C124 = P36 · P89

P36 = 327551454911584926725646090308651051_<36>

P89 = 18614741295214149817808628598816185490713815805914154383801682093489728139240162417517307_<89>

Number: n
N=6097285594050155593811700550087359412458342325601225900151084559740331348920054275523792364740957682431413803457047616239657
  ( 124 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=327551454911584926725646090308651051 (pp36)
 r2=18614741295214149817808628598816185490713815805914154383801682093489728139240162417517307 (pp89)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 16.83 hours.
Scaled time: 19.86 units (timescale=1.180).
Factorization parameters were as follows:
name: KA_1_6_146_7
n: 6097285594050155593811700550087359412458342325601225900151084559740331348920054275523792364740957682431413803457047616239657
type: snfs
skew: 1
deg: 5
c5: 500
c0: 1
m: 100000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [1600000, 1600000)
Primes: RFBsize:230209, AFBsize:229657, largePrimes:7379076 encountered
Relations: rels:6932372, finalFF:607364
Max relations in full relation-set: 28
Initial matrix: 459932 x 607364 with sparse part having weight 37170701.
Pruned matrix : 343861 x 346224 with weight 21575208.
Total sieving time: 12.31 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.86 hours.
Total square root time: 0.47 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 16.83 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Mar 20, 2007

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(5·10¹⁷⁸+1)/3 = 1(6)₁₇₇7_<179> = 7 · 227 · 11827 · 533310941 · 28380115229_<11> · C152

C152 = P31 · P122

P31 = 3220880018492646919471597460249_<31>

P122 = 18192025687327268232347237399252291090017208324941923677752372262674478864504639217167680287671601149803384330379323729349_<122>

(5·10¹⁸¹+1)/3 = 1(6)₁₈₀7_<182> = 1127133396136907_<16> · 18168259852882193_<17> · 72958897769204360339_<20> · C131

C131 = P41 · P90

P41 = 18041178939320340671069908987346459308697_<41>

P90 = 618325163147533482267971198200954906059845807104977100519107654516931740581366986358909699_<90>

Mar 19, 2007 (4th)

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000

10¹⁷⁰+3 = 1(0)₁₆₉3_<171> = 1447 · 101377 · 5131069 · 10740883 · 91413901 · 1019392014671857_<16> · C126

C126 = P36 · P90

P36 = 979614353591462245935054061765020517_<36>

P90 = 135498841902904458414080769423196258648267894198367246061470273791512538221196685877755299_<90>

Mar 19, 2007 (3rd)

By suberi / GMP-ECM 6.1.2 B1=1500000, B1=1000000

(5·10¹⁵⁹+1)/3 = 1(6)₁₅₈7_<160> = 39161 · 286393 · 208426562849_<12> · 113625146795456899764043_<24> · C115

C115 = P34 · P82

P34 = 1779063191475882495566028532059457_<34>

P82 = 3527066754417390898547821450334261762905883906849574519258881288012421214812083921_<82>

(5·10¹⁷²+1)/3 = 1(6)₁₇₁7_<173> = 7 · 23 · 787 · 3592897283321_<13> · 13409369737723_<14> · C142

C142 = P33 · C109

P33 = 720221664378281653603080022761581_<33>

C109 = [3790781854927277631648278252606516515296395111422830767220826618421065775857484773239829096077858370440473647_<109>]

(16·10²³⁵-61)/9 = 1(7)₂₃₄1_<236> = 11 · 29 · 37037719357719760261079_<23> · 713567298076051856522358950335091_<33> · C178

C178 = P30 · C148

P30 = 386429589610739568586536276533_<30>

C148 = [5456790006598550442100281169561982842187688146957656961433830490109471823566646007637536015206945208419922672451393758392495497829432520817568779357_<148>]

Mar 19, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(5·10¹³⁸+1)/3 = 1(6)₁₃₇7_<139> = 367 · 292141 · 6732116563_<10> · C121

C121 = P52 · P69

P52 = 5548241825186025128783144564510863551756594191888167_<52>

P69 = 416181877384096850179759514496060513542552738308357607455754502385541_<69>

Number: n
N=2309077698986888021355688003609105465986085718091745417948908205191294380281367690505515257298840643484242072112589793347
  ( 121 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=5548241825186025128783144564510863551756594191888167 (pp52)
 r2=416181877384096850179759514496060513542552738308357607455754502385541 (pp69)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.99 hours.
Scaled time: 10.78 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_1_6_137_7
n: 2309077698986888021355688003609105465986085718091745417948908205191294380281367690505515257298840643484242072112589793347
type: snfs
skew: 1
deg: 5
c5: 1
c0: 20
m: 10000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [1600000, 2200001)
Primes: RFBsize:230209, AFBsize:229762, largePrimes:7160178 encountered
Relations: rels:6743778, finalFF:629465
Max relations in full relation-set: 28
Initial matrix: 460035 x 629465 with sparse part having weight 33199001.
Pruned matrix : 307762 x 310126 with weight 14695744.
Total sieving time: 6.80 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.95 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,75000
total time: 8.99 hours.
 --------- CPU info (if available) ----------

Cygwin on Athlon Xp 2700+

Mar 19, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

(5·10¹⁴⁶+1)/3 = 1(6)₁₄₅7_<147> = 109 · 4129 · 50372423 · 53207489069674132147_<20> · C114

C114 = P56 · P58

P56 = 55066090111194564517518085962596060838780437707542837161_<56>

P58 = 2509155181218576475680066474978312365041289615110565064467_<58>

Number: 16667_146
N=138169365311952859564155138398408649511921930828779762166404664699158735354281554235583735296178334497870048258187
  ( 114 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=55066090111194564517518085962596060838780437707542837161 (pp56)
 r2=2509155181218576475680066474978312365041289615110565064467 (pp58)
Version: GGNFS-0.77.1-20050930-k8
Total time: 12.66 hours.
Scaled time: 11.49 units (timescale=0.907).
Factorization parameters were as follows:
n: 138169365311952859564155138398408649511921930828779762166404664699158735354281554235583735296178334497870048258187
m: 100000000000000000000000000000
c5: 50
c0: 1
skew: 1
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [900000, 1575001)
Primes: RFBsize:135072, AFBsize:135393, largePrimes:2813371 encountered
Relations: rels:2890053, finalFF:395475
Max relations in full relation-set: 28
Initial matrix: 270530 x 395475 with sparse part having weight 22426642.
Pruned matrix : 198270 x 199686 with weight 11742078.
Total sieving time: 12.41 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,45,45,2.3,2.3,75000
total time: 12.66 hours.
 --------- CPU info (if available) ----------

Mar 18, 2007 (6th)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(5·10¹⁴⁵+1)/3 = 1(6)₁₄₄7_<146> = 17 · 89 · 95083 · 147933658601_<12> · 545549849591657_<15> · C112

C112 = P46 · P66

P46 = 9821450547370350820743186696589047734433957809_<46>

P66 = 146160450531063005964151508951960723735329958138243051493844149721_<66>

Number: n
N=1435507636872205843232453222119746091816963578756254265764847729490824807382928031939507196894054566414393121289
  ( 112 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=9821450547370350820743186696589047734433957809 (pp46)
 r2=146160450531063005964151508951960723735329958138243051493844149721 (pp66)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 11.15 hours.
Scaled time: 13.33 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_1_6_144_7
n: 1435507636872205843232453222119746091816963578756254265764847729490824807382928031939507196894054566414393121289
type: snfs
skew: 1
deg: 5
c5: 5
c0: 1
m: 100000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [1600000, 2400001)
Primes: RFBsize:230209, AFBsize:229802, largePrimes:6958890 encountered
Relations: rels:6414597, finalFF:521730
Max relations in full relation-set: 28
Initial matrix: 460076 x 521730 with sparse part having weight 27949889.
Pruned matrix : 404635 x 406999 with weight 17520948.
Total sieving time: 7.73 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 3.16 hours.
Total square root time: 0.10 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 11.15 hours.
 --------- CPU info (if available) ----------

Cygwin on Athlon XP 2700+

Mar 18, 2007 (5th)

By Shaopu Lin / Msieve v. 1.17

(5·10¹⁵⁴+1)/3 = 1(6)₁₅₃7_<155> = 7 · 3301 · 888048827 · 186987050313163_<15> · 400255206926456710904556653969_<30> · C98

C98 = P45 · P53

P45 = 263599823092139043940210571668030772184899849_<45>

P53 = 41169415837319584505469666667843139597894309850912601_<53>

Sun Mar 18 10:36:11 2007  
Sun Mar 18 10:36:11 2007  
Sun Mar 18 10:36:11 2007  Msieve v. 1.17
Sun Mar 18 10:36:11 2007  random seeds: abffae1c f2f3b328
Sun Mar 18 10:36:11 2007  factoring 10852250731524149884902936866649181051649532146672309543153103356807939508754099359950924437097249 (98 digits)
Sun Mar 18 10:36:11 2007  commencing quadratic sieve (97-digit input)
Sun Mar 18 10:36:12 2007  using multiplier of 41
Sun Mar 18 10:36:12 2007  sieve interval: 9 blocks of size 65536
Sun Mar 18 10:36:12 2007  processing polynomials in batches of 6
Sun Mar 18 10:36:12 2007  using a sieve bound of 2435183 (89412 primes)
Sun Mar 18 10:36:12 2007  using large prime bound of 365277450 (28 bits)
Sun Mar 18 10:36:12 2007  using double large prime bound of 2586551540097000 (43-52 bits)
Sun Mar 18 10:36:12 2007  using trial factoring cutoff of 57 bits
Sun Mar 18 10:36:12 2007  polynomial 'A' values have 13 factors
Sun Mar 18 12:50:27 2007  5404 relations (4490 full + 914 combined from 274893 partial), need 89508
Sun Mar 18 12:50:27 2007  c98 factor: 10852250731524149884902936866649181051649532146672309543153103356807939508754099359950924437097249
Sun Mar 18 12:50:27 2007  elapsed time 02:14:16
Sun Mar 18 13:08:15 2007  
Sun Mar 18 13:08:15 2007  
Sun Mar 18 13:08:15 2007  Msieve v. 1.17
Sun Mar 18 13:08:15 2007  random seeds: fdcc0646 c4cb6867
Sun Mar 18 13:08:15 2007  factoring 10852250731524149884902936866649181051649532146672309543153103356807939508754099359950924437097249 (98 digits)
Sun Mar 18 13:08:15 2007  commencing quadratic sieve (97-digit input)
Sun Mar 18 13:08:15 2007  using multiplier of 41
Sun Mar 18 13:08:15 2007  sieve interval: 9 blocks of size 65536
Sun Mar 18 13:08:15 2007  processing polynomials in batches of 6
Sun Mar 18 13:08:15 2007  using a sieve bound of 2435183 (89412 primes)
Sun Mar 18 13:08:15 2007  using large prime bound of 365277450 (28 bits)
Sun Mar 18 13:08:15 2007  using double large prime bound of 2586551540097000 (43-52 bits)
Sun Mar 18 13:08:15 2007  using trial factoring cutoff of 57 bits
Sun Mar 18 13:08:15 2007  polynomial 'A' values have 13 factors
Sun Mar 18 13:08:17 2007  restarting with 4490 full and 274893 partial relations
Sun Mar 18 18:26:23 2007  36017 relations (14885 full + 21132 combined from 912309 partial), need 89508
Sun Mar 18 18:26:23 2007  c98 factor: 10852250731524149884902936866649181051649532146672309543153103356807939508754099359950924437097249
Sun Mar 18 18:26:23 2007  elapsed time 05:18:08
Sun Mar 18 18:29:05 2007  
Sun Mar 18 18:29:05 2007  
Sun Mar 18 18:29:05 2007  Msieve v. 1.17
Sun Mar 18 18:29:05 2007  random seeds: 3dc363ff e8b00b47
Sun Mar 18 18:29:05 2007  factoring 10852250731524149884902936866649181051649532146672309543153103356807939508754099359950924437097249 (98 digits)
Sun Mar 18 18:29:05 2007  commencing quadratic sieve (97-digit input)
Sun Mar 18 18:29:06 2007  using multiplier of 41
Sun Mar 18 18:29:06 2007  sieve interval: 9 blocks of size 65536
Sun Mar 18 18:29:06 2007  processing polynomials in batches of 6
Sun Mar 18 18:29:06 2007  using a sieve bound of 2435183 (89412 primes)
Sun Mar 18 18:29:06 2007  using large prime bound of 365277450 (28 bits)
Sun Mar 18 18:29:06 2007  using double large prime bound of 2586551540097000 (43-52 bits)
Sun Mar 18 18:29:06 2007  using trial factoring cutoff of 57 bits
Sun Mar 18 18:29:06 2007  polynomial 'A' values have 13 factors
Sun Mar 18 18:29:07 2007  restarting with 14885 full and 912309 partial relations
Sun Mar 18 21:53:48 2007  89522 relations (21678 full + 67844 combined from 1325295 partial), need 89508
Sun Mar 18 21:53:49 2007  begin with 1346973 relations
Sun Mar 18 21:53:52 2007  reduce to 233154 relations in 11 passes
Sun Mar 18 21:53:52 2007  attempting to read 233154 relations
Sun Mar 18 21:53:56 2007  recovered 233154 relations
Sun Mar 18 21:53:56 2007  recovered 221559 polynomials
Sun Mar 18 21:53:56 2007  attempting to build 89522 cycles
Sun Mar 18 21:53:57 2007  found 89522 cycles in 6 passes
Sun Mar 18 21:53:57 2007  distribution of cycle lengths:
Sun Mar 18 21:53:57 2007     length 1 : 21678
Sun Mar 18 21:53:57 2007     length 2 : 15736
Sun Mar 18 21:53:57 2007     length 3 : 15185
Sun Mar 18 21:53:57 2007     length 4 : 12099
Sun Mar 18 21:53:57 2007     length 5 : 9330
Sun Mar 18 21:53:57 2007     length 6 : 6140
Sun Mar 18 21:53:57 2007     length 7 : 3886
Sun Mar 18 21:53:57 2007     length 9+: 5468
Sun Mar 18 21:53:57 2007  largest cycle: 20 relations
Sun Mar 18 21:53:57 2007  matrix is 89412 x 89522 with weight 5818568 (avg 65.00/col)
Sun Mar 18 21:53:58 2007  filtering completed in 3 passes
Sun Mar 18 21:53:58 2007  matrix is 87956 x 88020 with weight 5671841 (avg 64.44/col)
Sun Mar 18 21:54:00 2007  saving the first 48 matrix rows for later
Sun Mar 18 21:54:00 2007  matrix is 87908 x 88020 with weight 4314822 (avg 49.02/col)
Sun Mar 18 21:54:00 2007  matrix includes 32 packed rows
Sun Mar 18 21:58:43 2007  lanczos halted after 1392 iterations
Sun Mar 18 21:58:44 2007  recovered 13 nontrivial dependencies
Sun Mar 18 21:58:47 2007  prp45 factor: 263599823092139043940210571668030772184899849
Sun Mar 18 21:58:47 2007  prp53 factor: 41169415837319584505469666667843139597894309850912601
Sun Mar 18 21:58:47 2007  elapsed time 03:29:42

Mar 18, 2007 (4th)

By suberi / GMP-ECM 6.1.2 B1=1000000

(16·10²¹⁴-61)/9 = 1(7)₂₁₃1_<215> = 13 · 863 · 18661 · 369819256019_<12> · 584833068852155422531_<21> · C174

C174 = P34 · C140

P34 = 4516565897012282883697690057920883_<34>

C140 = [86927786155318407263273710266523202940690097929584601977940218641236715258445415008714444666356629075405450626239173034367866144188409959887_<140>]

(10¹⁸⁵+53)/9 = (1)₁₈₄7_<185> = 8527 · C181

C181 = P29 · C152

P29 = 29587001068429855351442206649_<29>

C152 = [44041315240731342627152033825315210424898830618066156602341326236451254516042808567074969782491829929498528258973637320140692358628653317197742809301179_<152>]

Mar 18, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

(5·10¹³¹+1)/3 = 1(6)₁₃₀7_<132> = 295411 · 545641 · 21429691 · C113

C113 = P38 · P75

P38 = 71278904279841751639280680665781860691_<38>

P75 = 676921279683403714414286009774964550351851826502560543637491151314943810657_<75>

Number: 16667_131
N=48250207099541320381486426234048916572401910715200651510201078518073780540340990694316873955109328373331455183987
  ( 113 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=71278904279841751639280680665781860691 (pp38)
 r2=676921279683403714414286009774964550351851826502560543637491151314943810657 (pp75)
Version: GGNFS-0.77.1-20050930-k8
Total time: 2.80 hours.
Scaled time: 2.54 units (timescale=0.907).
Factorization parameters were as follows:
n: 48250207099541320381486426234048916572401910715200651510201078518073780540340990694316873955109328373331455183987
m: 100000000000000000000000000
c5: 50
c0: 1
skew: 1
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [500000, 950001)
Primes: RFBsize:78498, AFBsize:78411, largePrimes:1554495 encountered
Relations: rels:1599498, finalFF:217269
Max relations in full relation-set: 28
Initial matrix: 156974 x 217269 with sparse part having weight 10967430.
Pruned matrix : 130993 x 131841 with weight 5274102.
Total sieving time: 2.71 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000
total time: 2.80 hours.
 --------- CPU info (if available) ----------

Mar 18, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

8·10¹⁵⁵-1 = 7(9)₁₅₅_<156> = 24391 · 918839 · 3132989706569_<13> · C134

C134 = P44 · P90

P44 = 25299121414677623214283953730819328916466561_<44>

P90 = 450356622042797048454591109679905092704867767939346295702116218557105008704105348263325639_<90>

Number: n
N=11393626860964803334816245374068666021838036458519996173075889805142698696785738778530768098113617739706030753107072643747962797457479
  ( 134 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=25299121414677623214283953730819328916466561 (pp44)
 r2=450356622042797048454591109679905092704867767939346295702116218557105008704105348263325639 (pp90)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 30.40 hours.
Scaled time: 36.30 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_7_9_155
n: 11393626860964803334816245374068666021838036458519996173075889805142698696785738778530768098113617739706030753107072643747962797457479
type: snfs
skew: 1
deg: 5
c5: 8
c0: -1
m: 10000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [1600000, 2600001)
Primes: RFBsize:230209, AFBsize:230077, largePrimes:7417752 encountered
Relations: rels:6972041, finalFF:576947
Max relations in full relation-set: 28
Initial matrix: 460351 x 576947 with sparse part having weight 41539673.
Pruned matrix : 373294 x 375659 with weight 25838093.
Total sieving time: 25.61 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 4.49 hours.
Total square root time: 0.11 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 30.40 hours.
 --------- CPU info (if available) ----------

Mar 18, 2007

The factor table of 166...667 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Mar 17, 2007 (2nd)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

3·10¹⁵⁴-1 = 2(9)₁₅₄_<155> = 169973521 · 3541566709633_<13> · C134

C134 = P44 · P90

P44 = 62282513633822346544465252554897044469175211_<44>

P90 = 800162926125406274759982565017119197917086497848155175255046781462749015168218472947165613_<90>

Number: trial
N=49836158355684799392710790914879561735438604550081498928621816209020362192917352507673034351473382284833557383946745371232190331219343
  ( 134 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=62282513633822346544465252554897044469175211 (pp44)
 r2=800162926125406274759982565017119197917086497848155175255046781462749015168218472947165613 (pp90)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 63.81 hours.
Scaled time: 33.88 units (timescale=0.531).
Factorization parameters were as follows:
n: 49836158355684799392710790914879561735438604550081498928621816209020362192917352507673034351473382284833557383946745371232190331219343
m: 10000000000000000000000000000000
c5: 3
c0: -10
skew: 1.27
type: snfsFactor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2700001)
Primes: RFBsize:216816, AFBsize:216741, largePrimes:5681901 encountered
Relations: rels:5682246, finalFF:509993
Max relations in full relation-set: 0
Initial matrix: 433622 x 509993 with sparse part having weight 32711006.
Pruned matrix : 380977 x 383209 with weight 23958820.
Total sieving time: 51.96 hours.
Total relation processing time: 0.48 hours.
Matrix solve time: 11.09 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 63.81 hours.
 --------- CPU info (if available) ----------

Mar 17, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

(2·10¹⁶⁸-17)/3 = (6)₁₆₇1_<168> = C168

C168 = P54 · P115

P54 = 386717692502497012381472407394111919698336364510087247_<54>

P115 = 1723910438006045045271405706885467846235237280071891245137997281599442943976319787475472022679721558948263592668363_<115>

Number: 66661_168
N=666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661
  ( 168 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=386717692502497012381472407394111919698336364510087247 (pp54)
 r2=1723910438006045045271405706885467846235237280071891245137997281599442943976319787475472022679721558948263592668363 (pp115)
Version: GGNFS-0.77.1-20050930-k8
Total time: 129.30 hours.
Scaled time: 117.14 units (timescale=0.906).
Factorization parameters were as follows:
n: 666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661
m: 2000000000000000000000000000000000
c5: 125
c0: -34
skew: 1
type: snfs
Factor base limits: 7200000/7200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3600000, 8200001)
Primes: RFBsize:489319, AFBsize:489193, largePrimes:6257089 encountered
Relations: rels:6681474, finalFF:1112392
Max relations in full relation-set: 28
Initial matrix: 978577 x 1112392 with sparse part having weight 52925354.
Pruned matrix : 861071 x 866027 with weight 38066993.
Total sieving time: 123.69 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 5.37 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,7200000,7200000,27,27,48,48,2.6,2.6,100000
total time: 129.30 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335817)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334239)
Total of 2 processors activated (9340.11 BogoMIPS).

Mar 16, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

3·10¹⁵⁵-1 = 2(9)₁₅₅_<156> = 7² · 844643 · 159010443754010418818537_<24> · C125

C125 = P43 · P82

P43 = 5423853441107577188852485479594908047413233_<43>

P82 = 8404625993321570476494919510450078586561494231252473102406403901939727050282602317_<82>

Number: n
N=45585459615099389086179041758110407185275001961176861368273277748048769706955256547000294966297413952381207813653575502260861
  ( 125 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=5423853441107577188852485479594908047413233 (pp43)
 r2=8404625993321570476494919510450078586561494231252473102406403901939727050282602317 (pp82)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 27.74 hours.
Scaled time: 32.59 units (timescale=1.175).
Factorization parameters were as follows:
name: KA_2_9_155
n: 45585459615099389086179041758110407185275001961176861368273277748048769706955256547000294966297413952381207813653575502260861
type: snfs
skew: 1
deg: 5
c5: 3
c0: -1
m: 10000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [1600000, 2500001)
Primes: RFBsize:230209, AFBsize:230192, largePrimes:7224662 encountered
Relations: rels:6717869, finalFF:525864
Max relations in full relation-set: 28
Initial matrix: 460466 x 525864 with sparse part having weight 36596595.
Pruned matrix : 410679 x 413045 with weight 24697501.
Total sieving time: 22.73 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 4.69 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 27.74 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Mar 16, 2007

By suberi / GGNFS-0.77.1-20060513-pentium4, GMP-ECM 6.1.2 B1=1000000

(8·10¹⁵⁴+1)/9 = (8)₁₅₃9_<154> = 3² · 17 · 111479075100979_<15> · C138

C138 = P56 · P83

P56 = 32177707529893710433902536146572371561641868491685058673_<56>

P83 = 16195993354003447450979603450797475454295102425384430441701793883484636403132310539_<83>

Number: 88889_154
N=521149937301225221583231257120702045795537650550148843910205812236172301369042097361478079470627378071760856736045886848228640350271254747
  ( 138 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=32177707529893710433902536146572371561641868491685058673 (pp56)
 r2=16195993354003447450979603450797475454295102425384430441701793883484636403132310539 (pp83)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 32.41 hours.
Scaled time: 20.03 units (timescale=0.618).
Factorization parameters were as follows:
n: 521149937301225221583231257120702045795537650550148843910205812236172301369042097361478079470627378071760856736045886848228640350271254747
m: 10000000000000000000000000000000
c5: 4
c0: 5
skew: 1.05
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2400001)
Primes: RFBsize:216816, AFBsize:216926, largePrimes:5533675 encountered
Relations: rels:5520996, finalFF:582833
Max relations in full relation-set: 28
Initial matrix: 433806 x 582833 with sparse part having weight 41783728.
Pruned matrix : 323178 x 325411 with weight 25316982.
Total sieving time: 26.72 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 5.18 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.41 hours.
 --------- CPU info (if available) ----------

(7·10¹⁸⁸+11)/9 = (7)₁₈₇9_<188> = 17 · 41 · 337511 · 321348211 · 16826529918033630069673_<23> · C149

C149 = P36

P36 = 335115240990780875742167474614245799_<36>

P114 = 182461059486518113964270665145747212245055354341456620345081920388280026228471754639932704349932407082619966553521_<114>

(7·10¹⁵⁶+11)/9 = (7)₁₅₅9_<156> = 17 · 22067 · 40360471134589043064933745786051_<32> · C119

C119 = P30 · P90

P30 = 180456851647834561315931550073_<30>

P90 = 284664762455700346404377228916434989848075119780853356972582547306819635356646779045237907_<90>

Mar 15, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=1000000, GGNFS-0.77.1-20060722-pentium4

(7·10¹⁹⁰+11)/9 = (7)₁₈₉9_<190> = 3² · 187603427717_<12> · C178

C178 = P37 · P141

P37 = 6177774173350487484434222587767501487_<37>

P141 = 745658929842245053745336194347900728624922448846406553486583278902680688904222161398693614637129510927532193940569066916225861802470289225489_<141>

(16·10²⁴⁵-61)/9 = 1(7)₂₄₄1_<246> = 3² · 11 · 23 · 661 · 3593 · 10301 · 4840133 · 5764841 · 679164323 · 3629375857_<10> · 334689967902904368763_<21> · C180

C180 = P34 · P146

P34 = 6805943732941698014429478017066561_<34>

P146 = 20370134213368423426672455205813626417541067572894236720844778196943084983955699624795881283538877410006319344463020634482928235221594799195308979_<146>

(68·10¹⁵⁴+13)/9 = 7(5)₁₅₃7_<155> = 47 · 498630726983_<12> · 481480518643109_<15> · C127

C127 = P36 · P41 · P52

P36 = 180048411580101335807564711501968399_<36>

P41 = 12885467681488848348054410283777960509393_<41>

P52 = 2886166011333284120917867347222492944354289914055239_<52>

Number: 75557_154
N=6695928202484655635452379415298947471387647632758248358468768790611612165249036732543960482350604990882306999581263998199946873
  ( 127 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=180048411580101335807564711501968399 (pp36)
 r2=12885467681488848348054410283777960509393 (pp41)
 r3=2886166011333284120917867347222492944354289914055239 (pp52)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 35.03 hours.
Scaled time: 23.96 units (timescale=0.684).
Factorization parameters were as follows:
n: 6695928202484655635452379415298947471387647632758248358468768790611612165249036732543960482350604990882306999581263998199946873
m: 10000000000000000000000000000000
c5: 34
c0: 65
skew: 1.14
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2700001)
Primes: RFBsize:216816, AFBsize:216756, largePrimes:5724145 encountered
Relations: rels:5759916, finalFF:625672
Max relations in full relation-set: 32
Initial matrix: 433638 x 625672 with sparse part having weight 52507304.
Pruned matrix : 324341 x 326573 with weight 31231916.
Total sieving time: 29.41 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 5.20 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 35.03 hours.
 --------- CPU info (if available) ----------

Mar 15, 2007

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(4·10¹⁵⁴-13)/9 = (4)₁₅₃3_<154> = 3 · 491279 · 233281879 · 2378170747_<10> · C130

C130 = P42 · P88

P42 = 623157291540903823369569922445206459369843_<42>

P88 = 8722607053645853108078000019436196832381880430877361385183603912492573372633755625577521_<88>

Number: n
N=5435556186725533001281237955401538909720919357929426277835504923537027699853207670533178790001606769710481300713046036238606099203
  ( 130 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=623157291540903823369569922445206459369843 (pp42)
 r2=8722607053645853108078000019436196832381880430877361385183603912492573372633755625577521 (pp88)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 38.86 hours.
Scaled time: 46.52 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_4_153_3
n: 5435556186725533001281237955401538909720919357929426277835504923537027699853207670533178790001606769710481300713046036238606099203
type: snfs
skew: 1
deg: 5
c5: 2
c0: -65
m: 10000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [1600000, 2900001)
Primes: RFBsize:230209, AFBsize:229447, largePrimes:7489861 encountered
Relations: rels:6997333, finalFF:538310
Max relations in full relation-set: 28
Initial matrix: 459721 x 538310 with sparse part having weight 40517081.
Pruned matrix : 409453 x 411815 with weight 28003554.
Total sieving time: 33.07 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 5.47 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 38.86 hours.
 --------- CPU info (if available) ----------

AMD XP 2700+

Mar 14, 2007 (4th)

By NFSNET / SNFS / Mar 7, 2007

10²²⁹+1 = 1(0)₂₂₈1_<230> = 11 · 2317091604522004723965449_<25> · 22122368173743271094350225612207534262957_<41> · C164

C164 = P59 · P106

P59 = 13270807703600518273110858480695033043595534787235597140531_<59>

P106 = 1336395914067475494619360928220680511145198857935330550248985354190742963795052553003443246310484435548877_<106>

By Yousuke Koide / GMP-ECM / Mar 9, 2007

(10¹²²¹-1)/9 = (1)₁₂₂₁_<1221> = 3 · 37² · 67 · 21649 · 46399 · 390721 · 513239 · 2028119 · 247629013 · 3306121237_<10> · 37232500009_<11> · 2377517312347_<13> · 171055055020477_<15> · 30557051518647307_<17> · 1344628210313298373_<19> · 2212394296770203368013_<22> · 14922184078787276001107_<23> · 8845981170865629119271997_<25> · 90077814396055017938257237117_<29> · [1399300708003111495578140482186320347277273505089781034200096366442134264784657534390363164267749971684437448447281946338001226312001060024115902223232728865313091486857448782879187621243824754236824516208584519649679801623269793676780347076796179020835671903144327739679125772035571304791326088307189347498475947401_<316>] · C686

C686 = P31 · C655

P31 = 9557310079389075405641287553803_<31>

C655 = [5515824196307780952584504442192890690575562875540825114944734663606474647281575002887478680286288052210526929443365680648852789555336764321822510527238695441418410283165718247242678059529341629517493669953736654452852386489889645013663965799353193599363460281027545061024040407073689527881928488768231400642687569429481473171385035979460579452200774729679752710793572101391827980965952297964933833022089122319372818564966309988014980282039713988319062537834423629632975228839285882370287649636569520965917059633562233758023513111518386548144522612870452249743261736259162946084327556981920462966793150850301959340294903413186803082903485275606383479206757_<655>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 14, 2007 (3rd)

By Jo Yeong Uk / GMP-ECM 6.1.1 B1=1000000

(83·10¹⁵⁴+61)/9 = 9(2)₁₅₃9_<155> = 3⁴ · 43 · 2137 · 11165990385401_<14> · C136

C136 = P34 · P103

P34 = 1080410951908217088203068529610239_<34>

P103 = 1027049460661970594903506561912251124101625777138266370978214953652943793348367291441285157423461027041_<103>

Mar 14, 2007 (2nd)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(25·10¹⁵⁴-7)/9 = 2(7)₁₅₄_<155> = 3² · 768787 · 1165904386753975531948451_<25> · C124

C124 = P52 · P73

P52 = 1229703685613870565482097442621203311966911738729487_<52>

P73 = 2800177411079931025313554235270821858708785199889560692524686905876053087_<73>

Number: trial
N=3443388482777697502163738810997444139894472237224630200880616654110118907544360097930000698844817572230384236838239544276369
  ( 124 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=1229703685613870565482097442621203311966911738729487 (pp52)
 r2=2800177411079931025313554235270821858708785199889560692524686905876053087 (pp73)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 63.39 hours.
Scaled time: 32.45 units (timescale=0.512).
Factorization parameters were as follows:
n: 3443388482777697502163738810997444139894472237224630200880616654110118907544360097930000698844817572230384236838239544276369
m: 10000000000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfsFactor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:217381, largePrimes:5516679 encountered
Relations: rels:5409954, finalFF:500848
Max relations in full relation-set: 0
Initial matrix: 434262 x 500848 with sparse part having weight 38610131.
Pruned matrix : 391194 x 393429 with weight 26929819.
Total sieving time: 48.84 hours.
Total relation processing time: 0.47 hours.
Matrix solve time: 13.72 hours.
Time per square root: 0.35 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 63.39 hours.
 --------- CPU info (if available) ----------

Mar 14, 2007

By suberi / GMP-ECM 6.1.2 B1=1000000

(2·10¹⁸¹+1)/3 = (6)₁₈₀7_<181> = 7 · C180

C180 = P32 · P149

P32 = 67255070283668769619862559473201_<32>

P149 = 14160730906443116746495111115047641558481701837678541313334391465479394184166860056522357072852820398128709983357170191950212503099674765380256703181_<149>

(7·10¹⁷⁵+11)/9 = (7)₁₇₄9_<175> = 3 · 506195919767_<12> · 18822712509076627_<17> · C147

C147 = P32 · C116

P32 = 12007442890556404705517171537299_<32>

C116 = [22661199643274826616506037502975050665929602295137054181268069957443993666880701283713935646994058586764830130031423_<116>]

(7·10¹⁵⁶+11)/9 = (7)₁₅₅9_<156> = 17 · 22067 · C151

C151 = P32 · C119

P32 = 40360471134589043064933745786051_<32>

C119 = [51369706807834383019335582860585395422013721864161473338139081911966650927257577175840142699944608709208573947568217211_<119>]

(16·10²⁴⁶-61)/9 = 1(7)₂₄₅1_<247> = 7873 · 73735471 · C235

C235 = P29 · P206

P29 = 50471251208266401221148968621_<29>

P206 = 60675964949918263205609110309720019624586192956489493080965555374327360718253084322742804690412945082154262349245969473440450190732883309700083469169362728986304992360444260458290295833946365316166058187897_<206>

Mar 13, 2007 (2nd)

By Robert Backstrom / GGNFS-0.77.1-20051202-athlon

(79·10¹⁵³-7)/9 = 8(7)₁₅₃_<154> = 1609 · 194886308091743_<15> · C137

C137 = P53 · P84

P53 = 33189147649745737114986138374689356517744711840673371_<53>

P84 = 843434011803161407008535388292933087394417867330522649337638124595057972951922937301_<84>

Number: n
N=27992855950552512708828138574591719985934225428898365721529634560471152640342015896190558043914185790452999492624622285097241644053311671
  ( 137 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=33189147649745737114986138374689356517744711840673371 (pp53)
 r2=843434011803161407008535388292933087394417867330522649337638124595057972951922937301 (pp84)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 50.61 hours.
Scaled time: 60.58 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_87_153
n: 27992855950552512708828138574591719985934225428898365721529634560471152640342015896190558043914185790452999492624622285097241644053311671
type: snfs
skew: 1
deg: 5
c5: 79
c0: -700
m: 10000000000000000000000000000000
rlim: 3600000
alim: 3600000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [1800000, 3500001)
Primes: RFBsize:256726, AFBsize:256641, largePrimes:7837103 encountered
Relations: rels:7422443, finalFF:649186
Max relations in full relation-set: 28
Initial matrix: 513434 x 649186 with sparse part having weight 47166009.
Pruned matrix : 421054 x 423685 with weight 31807317.
Total sieving time: 43.89 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 6.34 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3600000,3600000,28,28,48,48,2.3,2.3,100000
total time: 50.61 hours.
 --------- CPU info (if available) ----------

Mar 13, 2007

By Shaopu Lin / GGNFS-0.77.1-20060722-pentium4 gnfs

(2·10¹⁷³+1)/3 = (6)₁₇₂7_<173> = 3229 · 11430617272077882869154127363_<29> · 12285208461573705537910016528766093075163_<41> · C102

C102 = P44 · P58

P44 = 66429507839354412739936008855315386915039609_<44>

P58 = 2213234580595026489302987004215298111708002099947957511663_<58>

Number: 2_173_+1
N=147024083921967587987395231596813878970053978418196045340299325824837867451060084011196308738724459767
  ( 102 digits)
Divisors found:
 r1=66429507839354412739936008855315386915039609 (pp44)
 r2=2213234580595026489302987004215298111708002099947957511663 (pp58)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 11.33 hours.
Scaled time: 14.45 units (timescale=1.275).
Factorization parameters were as follows:
name: 2_173_+1
n: 147024083921967587987395231596813878970053978418196045340299325824837867451060084011196308738724459767
skew: 8504.53
# norm 7.18e+13
c5: 27720
c4: 928856
c3: 838999784614
c2: 13811724910760072
c1: -145254733038042269233
c0: 586307634080437791242630
# alpha -6.12
Y1: 9676492943
Y0: -22126822396585063233
# Murphy_E 2.89e-09
# M 27762482580871199612752955659640071218869230702763312386995455804620665012658065600234887922006868397
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1750001)
Primes: RFBsize:169511, AFBsize:169435, largePrimes:4472688 encountered
Relations: rels:4713994, finalFF:404523
Max relations in full relation-set: 0
Initial matrix: 339029 x 404523 with sparse part having weight 16607813.
Pruned matrix : 274559 x 276318 with weight 10059418.
Total sieving time: 9.84 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 1.03 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 11.33 hours.
 --------- CPU info (if available) ----------

Mar 12, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=1000000

(2·10¹⁸²+1)/3 = (6)₁₈₁7_<182> = 14376697 · C175

C175 = P31 · P145

P31 = 1585124564388882215739248989409_<31>

P145 = 2925406520016824459793686144437048199244743707159174486289472705344922902509467003357759004945188155785099130434982841704107321288453540961497379_<145>

(2·10¹⁷³+1)/3 = (6)₁₇₂7_<173> = 3229 · 12285208461573705537910016528766093075163_<41> · C130

C130 = P29 · C102

P29 = 11430617272077882869154127363_<29>

C102 = [147024083921967587987395231596813878970053978418196045340299325824837867451060084011196308738724459767_<102>]

(7·10¹⁹³+11)/9 = (7)₁₉₂9_<193> = 3 · 41 · 1645791483541_<13> · C179

C179 = P31 · C148

P31 = 6062012711580861138593484137483_<31>

C148 = [6338095311422806628041681278497479626715196088761396462118763294477096960206884824639260108850297771297395071653505161859348368210705651421925743791_<148>]

Mar 12, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 gnfs

(82·10¹⁵³-1)/9 = 9(1)₁₅₃_<154> = 3⁴ · 688622185393_<12> · 1797980043765438104625447953831_<31> · C110

C110 = P46 · P65

P46 = 5439400968192000070068961568453812223828872829_<46>

P65 = 16702034347162201771602568558900760327009737339991475475328660533_<65>

Number: 91111_153
N=90849061798730120134415671857022727048215492925996768275275430895716965482161611441749945949212881419768357857
  ( 110 digits)
Divisors found:
 r1=5439400968192000070068961568453812223828872829 (pp46)
 r2=16702034347162201771602568558900760327009737339991475475328660533 (pp65)
Version: GGNFS-0.77.1-20050930-k8
Total time: 19.93 hours.
Scaled time: 18.12 units (timescale=0.909).
Factorization parameters were as follows:
name: 91111_153
n: 90849061798730120134415671857022727048215492925996768275275430895716965482161611441749945949212881419768357857
skew: 18321.44
# norm 7.82e+14
c5: 74040
c4: -141551270
c3: -75674640805143
c2: 234083487897747316
c1: 11789311970640685195440
c0: 30586280943535814825544832
# alpha -5.50
Y1: 590458278671
Y0: -1041767732293455366015
# Murphy_E 1.00e-09
# M 28565350679692008008041514640150531919897960650683454797846857629211816849063124324921802901586270592034102610
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1200000, 2040001)
Primes: RFBsize:176302, AFBsize:175819, largePrimes:7573923 encountered
Relations: rels:7368554, finalFF:446585
Max relations in full relation-set: 28
Initial matrix: 352201 x 446585 with sparse part having weight 44352998.
Pruned matrix : 290898 x 292723 with weight 27846011.
Total sieving time: 18.94 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.72 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000
total time: 19.93 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335814)
Calibrating delay using timer specific routine.. 4668.46 BogoMIPS (lpj=2334234)
Total of 2 processors activated (9340.09 BogoMIPS).

Mar 11, 2007 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

(23·10¹⁵³+1)/3 = 7(6)₁₅₂7_<154> = 11 · 41 · 36217 · C147

C147 = P65 · P82

P65 = 66701654924490943009481067725328090047586712513646273561735978657_<65>

P82 = 7036893156669408344386011389295761191203948118542807066538803903115219196386336993_<82>

Number: 76667_153
N=469372419076674658038213894276638022500530135739850622431703813106024841923022066156573129110618242861085293927437187205373146889629177626257558401
  ( 147 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=66701654924490943009481067725328090047586712513646273561735978657 (pp65)
 r2=7036893156669408344386011389295761191203948118542807066538803903115219196386336993 (pp82)
Version: GGNFS-0.77.1-20050930-k8
Total time: 21.84 hours.
Scaled time: 18.68 units (timescale=0.855).
Factorization parameters were as follows:
n: 469372419076674658038213894276638022500530135739850622431703813106024841923022066156573129110618242861085293927437187205373146889629177626257558401
m: 5000000000000000000000000000000
c5: 184
c0: 25
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2500001)
Primes: RFBsize:216816, AFBsize:217116, largePrimes:5508950 encountered
Relations: rels:5404912, finalFF:505602
Max relations in full relation-set: 28
Initial matrix: 433999 x 505602 with sparse part having weight 37622010.
Pruned matrix : 382479 x 384712 with weight 25700698.
Total sieving time: 20.53 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.17 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 21.84 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.62 BogoMIPS (lpj=2335814)
Calibrating delay using timer specific routine.. 4668.46 BogoMIPS (lpj=2334234)
Total of 2 processors activated (9340.09 BogoMIPS).

Mar 11, 2007 (2nd)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(35·10¹⁵³-53)/9 = 3(8)₁₅₂3_<154> = 11 · 5119 · 29729852380307_<14> · C136

C136 = P64 · P73

P64 = 1336857265227055891602255144595312710366914084138447152868661721_<64>

P73 = 1737680497099652281480746842090914423799196760175286953572897766236908421_<73>

Number: trial
N=2323030797191032176060172857078046465138870277980828896592371826135653611090689420139183547157987504868205237165243564748675554705252541
  ( 136 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=1336857265227055891602255144595312710366914084138447152868661721 (pp64)
 r2=1737680497099652281480746842090914423799196760175286953572897766236908421 (pp73)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 65.51 hours.
Scaled time: 34.79 units (timescale=0.531).
Factorization parameters were as follows:
n: 2323030797191032176060172857078046465138870277980828896592371826135653611090689420139183547157987504868205237165243564748675554705252541
m: 5000000000000000000000000000000
c5: 56
c0: -265
skew: 1.36
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2700001)
Primes: RFBsize:216816, AFBsize:216291, largePrimes:5713559 encountered
Relations: rels:5732506, finalFF:501309
Max relations in full relation-set: 0
Initial matrix: 433173 x 501309 with sparse part having weight 30175485.
Pruned matrix : 383318 x 385547 with weight 22673806.
Total sieving time: 54.21 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 10.52 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 65.51 hours.
 --------- CPU info (if available) ----------

Mar 11, 2007

By Jo Yeong Uk / GMP-ECM 6.1.1 B1=1000000

(82·10¹⁵³-1)/9 = 9(1)₁₅₃_<154> = 3⁴ · 688622185393_<12> · C141

C141 = P31 · C110

P31 = 1797980043765438104625447953831_<31>

C110 = [90849061798730120134415671857022727048215492925996768275275430895716965482161611441749945949212881419768357857_<110>]

Mar 10, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 snfs, gnfs

(34·10¹⁵³-7)/9 = 3(7)₁₅₃_<154> = 3 · 14556803 · C146

C146 = P34 · P43 · P70

P34 = 8594268236093335921513615334779403_<34>

P43 = 2721524007350718785531830805984150175159193_<43>

P70 = 3698520874245273856922213592778507670368184847406373387779530756679507_<70>

Number: 37777_153
N=86506581098834631426918345962314613947805658925195268443164289525609384097542520789713184911498717078142725381339519347706997151727564030320342953
  ( 146 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=8594268236093335921513615334779403 (pp34)
 r2=2721524007350718785531830805984150175159193 (pp43)
 r3=3698520874245273856922213592778507670368184847406373387779530756679507 (pp70)
Version: GGNFS-0.77.1-20050930-k8
Total time: 29.32 hours.
Scaled time: 26.56 units (timescale=0.906).
Factorization parameters were as follows:
n: 86506581098834631426918345962314613947805658925195268443164289525609384097542520789713184911498717078142725381339519347706997151727564030320342953
m: 2000000000000000000000000000000
c5: 2125
c0: -14
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2900001)
Primes: RFBsize:216816, AFBsize:216796, largePrimes:5647466 encountered
Relations: rels:5576706, finalFF:516040
Max relations in full relation-set: 28
Initial matrix: 433678 x 516040 with sparse part having weight 42818916.
Pruned matrix : 393255 x 395487 with weight 29312729.
Total sieving time: 27.82 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.34 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 29.32 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335817)
Calibrating delay using timer specific routine.. 4668.49 BogoMIPS (lpj=2334245)
Total of 2 processors activated (9340.12 BogoMIPS).

(4·10¹⁸¹-1)/3 = 1(3)₁₈₁_<182> = 13 · 208003 · 947369 · 6213997 · 422657489810930235663875844391_<30> · 95889960353472897975804675641271719639_<38> · C95

C95 = P44 · P52

P44 = 18428292279714960219702287943095725613326919_<44>

P52 = 1121472882089843997692184363087036030254868910061009_<52>

Number: 13333_181
N=20666830054925958025154487842787710069959392668108893582404651266727653619739610443131752001271
  ( 95 digits)
Divisors found:
 r1=18428292279714960219702287943095725613326919 (pp44)
 r2=1121472882089843997692184363087036030254868910061009 (pp52)
Version: GGNFS-0.77.1-20050930-k8
Total time: 4.51 hours.
Scaled time: 4.08 units (timescale=0.905).
Factorization parameters were as follows:
name: 13333_181
n:  20666830054925958025154487842787710069959392668108893582404651266727653619739610443131752001271
m:  3520571363530624627796
deg: 4
c4: 134530656
c3: -818416215523
c2: 77204166447062888
c1: 3032188238699940176
c0: -27449618853113239775241
skew: 1635.250
type: gnfs
# adj. I(F,S) = 53.726
# E(F1,F2) = 4.428722e-05
# GGNFS version 0.77.1-20050930-k8 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=58.00000000, seed=1173454162.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 50000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1200001)
Primes: RFBsize:92938, AFBsize:93069, largePrimes:1870373 encountered
Relations: rels:1942169, finalFF:238237
Max relations in full relation-set: 28
Initial matrix: 186084 x 238237 with sparse part having weight 16401459.
Pruned matrix : 161680 x 162674 with weight 8895346.
Polynomial selection time: 0.08 hours.
Total sieving time: 4.26 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,50000
total time: 4.51 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335817)
Calibrating delay using timer specific routine.. 4668.49 BogoMIPS (lpj=2334245)
Total of 2 processors activated (9340.12 BogoMIPS).

Mar 9, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=1000000

(4·10¹⁸¹-1)/3 = 1(3)₁₈₁_<182> = 13 · 208003 · 947369 · 6213997 · 422657489810930235663875844391_<30> · C133

C133 = P38 · C95

P38 = 95889960353472897975804675641271719639_<38>

C95 = [20666830054925958025154487842787710069959392668108893582404651266727653619739610443131752001271_<95>]

Mar 9, 2007

By Philippe Strohl / gmp-ecm 6.1.1, msieve

(31·10¹⁵⁹-13)/9 = 3(4)₁₅₈3_<160> = 11 · 29 · 103 · 31495525256123412108590573_<26> · C130

C130 = P32 · P99

P32 = 18220801332111452637905105535377_<32>

P99 = 182673246922664922215116667618385192896049286094122406240480789269739834481068876099995763335349519_<99>

(31·10¹⁶¹-13)/9 = 3(4)₁₆₀3_<162> = 11 · 71160562589767531_<17> · 35346772348313233757_<20> · C125

C125 = P31 · P94

P31 = 9214711542428400460620693533887_<31>

P94 = 1351000839508368862206252121522886281976194919602387289398936256144347787863519361665877324497_<94>

(31·10¹⁶⁹-13)/9 = 3(4)₁₆₈3_<170> = 3 · 11 · 17 · 79531 · C162

C162 = P39 · P124

P39 = 522235888582298378420929116637405995083_<39>

P124 = 1478267967438312308101056504254553548511855058325922241446036981530842781007936900982261738169354345327696013073609676251331_<124>

(31·10¹⁷⁴-13)/9 = 3(4)₁₇₃3_<175> = 293617 · 1436471 · 7557443 · 130775549186455666311890896219_<30> · C127

C127 = P27 · P46 · P56

P27 = 527793365692251166832991629_<27>

P46 = 1413255507990492806168595079438433390439397411_<46>

P56 = 11077839744989375386501684687854942571016255668118907163_<56>

(31·10¹⁷⁷-13)/9 = 3(4)₁₇₆3_<178> = 11 · 173 · 227 · 223461044467_<12> · C161

C161 = P35 · P36 · P90

P35 = 65219477847426587077518315943625357_<35>

P36 = 719038817915347421940630071846579687_<36>

P90 = 760892074198757200697890675804603439092610757105817352711491913696740817887672336986109351_<90>

(31·10¹⁸⁴-13)/9 = 3(4)₁₈₃3_<185> = 3² · C184

C184 = P29 · P155

P29 = 50860390743863081094178433417_<29>

P155 = 75248350196541765986731032991141074676843238579485128560091333022256455922893727877575862591799754153933049498279895799619706673770461385880459855652498731_<155>

(31·10¹⁸⁵-13)/9 = 3(4)₁₈₄3_<186> = 11² · 17 · 181 · 41131 · 1592243039_<10> · 2417267440429797889605030637_<28> · C139

C139 = P41 · P99

P41 = 17757128990144490057865326416335009059131_<41>

P99 = 329101785627995503144769772900089826205540526094392828018012426909891788968440162312882573944829573_<99>

(31·10¹⁹²-13)/9 = 3(4)₁₉₁3_<193> = 157 · 1936999 · C185

C185 = P32 · P36 · P118

P32 = 12156616229645126390322167911417_<32>

P36 = 606268239934794595379364961442940829_<36>

P118 = 1536783223791944940826326054744739537580422334052791100435400818238680780875852116995008930134240059957027789762086957_<118>

(31·10¹⁹⁴-13)/9 = 3(4)₁₉₃3_<195> = 7 · 24851 · 578959 · C184

C184 = P33 · P34 · P119

P33 = 117602516565159674781337594954997_<33>

P34 = 1736648356153263282151812902240569_<34>

P119 = 16745609548147609812124124983067904018895063174524086172259099007693123279142523007585234586580156877839035349260578677_<119>

(31·10¹⁹⁵-13)/9 = 3(4)₁₉₄3_<196> = 11 · 409 · 433 · 1231 · 9857 · 29106199 · 226024859 · C167

C167 = P34 · C133

P34 = 5027043972621015155274153602261603_<34>

C133 = [4406138049467862108822304886904684665095340472558491300911579282015207482952828657413786426677152881312064869462756319604850096004769_<133>]

(31·10¹⁹⁷-13)/9 = 3(4)₁₉₆3_<198> = 11 · 8529173 · 16832693 · C183

C183 = P35 · C148

P35 = 31718978554313454335064248296767941_<35>

P148 = [6876172764021503279846353192025765375761066473830933599403773173852114080803102720428674084422381287992997630233231841600216245045225929329829236037_<148>]

Note: for all the composites submitted today gmp-ecm 6.1.1 option -I between 1e6 and 3e6 plus a few extra curves at 10e6 (so level 35 digits should be complete) pp1 done at 10e9 one time for the ten first remaining composites of the list, one time

(Philippe Strohl)

Mar 8, 2007 (4th)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

(68·10¹⁵³+13)/9 = 7(5)₁₅₂7_<154> = 3² · 11 · 1129 · 1375013 · C143

C143 = P38 · P105

P38 = 61065373075425676577973996838542929633_<38>

P105 = 805073344781424198084009165594160318465099225536810480321303682980714430410153103765571332168602554390323_<105>

Number: 75557_153
N=49162104152158473852257356247164514014169615600587153399576969092026274841248343978397668819540045798313854721876473148828889098776674605141459
  ( 143 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=61065373075425676577973996838542929633 (pp38)
 r2=805073344781424198084009165594160318465099225536810480321303682980714430410153103765571332168602554390323 (pp105)
Version: GGNFS-0.77.1-20050930-k8
Total time: 25.50 hours.
Scaled time: 23.18 units (timescale=0.909).
Factorization parameters were as follows:
n: 49162104152158473852257356247164514014169615600587153399576969092026274841248343978397668819540045798313854721876473148828889098776674605141459
m: 2000000000000000000000000000000
c5: 2125
c0: 13
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2700001)
Primes: RFBsize:216816, AFBsize:216466, largePrimes:5605113 encountered
Relations: rels:5534336, finalFF:522965
Max relations in full relation-set: 28
Initial matrix: 433348 x 522965 with sparse part having weight 41494477.
Pruned matrix : 379741 x 381971 with weight 27448128.
Total sieving time: 24.12 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.23 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 25.50 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1299k data, 196k init)
Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335817)
Calibrating delay using timer specific routine.. 4668.49 BogoMIPS (lpj=2334245)
Total of 2 processors activated (9340.12 BogoMIPS).

Mar 8, 2007 (3rd)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(82·10¹⁵³+71)/9 = 9(1)₁₅₂9_<154> = 11 · 65519 · 237466693823083_<15> · C134

C134 = P51 · P84

P51 = 146390585269811370845985545630132602549881181957493_<51>

P84 = 363660008608730922630636735619631543462580645365161805226770939783787413528491520389_<84>

Number: trial
N=53236401499456761316073245652900249749764555961276757346582245881790826230770824257629997843337224692510634933036878499624830740824777
  ( 134 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=146390585269811370845985545630132602549881181957493 (pp51)
 r2=363660008608730922630636735619631543462580645365161805226770939783787413528491520389 (pp84)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 75.52 hours.
Scaled time: 38.14 units (timescale=0.505).
Factorization parameters were as follows:
n: 53236401499456761316073245652900249749764555961276757346582245881790826230770824257629997843337224692510634933036878499624830740824777
m: 2000000000000000000000000000000
c5: 5125
c0: 142
skew: 1
type: snfsFactor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 1
)
Primes: RFBsize:216816, AFBsize:216828, largePrimes:5610853 encountered
Relations: rels:5499955, finalFF:500031
Max relations in full relation-set: 0
Initial matrix: 433710 x 500031 with sparse part having weight 46174110.
Pruned matrix : 407069 x 409301 with weight 32384029.
Total sieving time: 66.29 hours.
Total relation processing time: 0.59 hours.
Matrix solve time: 8.29 hours.
Time per square root: 0.35 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 75.52 hours.
 --------- CPU info (if available) ----------

Mar 8, 2007 (2nd)

By Bruce Dodson / GMP-ECM / Feb 25, 2007

10³⁷⁹+1 = 1(0)₃₇₈1_<380> = 11 · 10613 · 30817249 · 4918445244727502358176820280164673127_<37> · C330

C330 = P53 · C278

P53 = 33584520860278767011970207517032237108309731086439023_<53>

C278 = [16827061636858301807417830743016139436111697678133727198462189350037543615130040061453939200050698409557403053836355657478868125072163055516431199446323056297229473485500285538897823057447955700947790298371668529982572265464316125827004742058791596076336326778009636479204734783_<278>]

By Bruce Dodson / GMP-ECM / Mar 2, 2007

10³⁹⁴+1 = 1(0)₃₉₃1_<395> = 101 · 27581 · 39183683903547299202471125940449908897423309_<44> · C344

C344 = P53 · P291

P53 = 95857172574244109092139928579854506165297073472804809_<53>

P291 = 955737746910848289298542541424663089706331830294404692746411509225952770622079883261039291690273699630517609797375668184351088065578009261657806563698330735168868137570443380377516027002412525522935434804743886172764249065452729071714341068915031993169251851872703748461050312064423743542541_<291>

By Yousuke Koide / GMP-ECM / Mar 6, 2007

(10¹⁰¹¹-1)/9 = (1)₁₀₁₁_<1011> = 3 · 37 · 248707 · 427991 · 282549563 · 288525099368866187_<18> · 16917315519781128734365649437223631827_<38> · [1882405423818571330780209095519806749563519430700453721593179952656343963131813810925373770836559341617884038513747354594918124525467950655542193487570841729702485413334783631101246494629336094540357234595856835370463421588982989455925674466916759281841736587368701683_<268>] · C667

C667 = P32 · C636

P32 = 12652477149085504014830875594123_<32>

C636 = [286294793881282912130855648097538698206027889766121394515256725961872922751483459413620078771040119414455975097318456561036922025364700573661111764253749922304265639740420941814888613838229170105845271060995650346929300836861427222478412662698349880700722276694945914794152736979267379128349311405152497674634320275965800024192769244850307821227101765226856267317872753791085432843605201253802719836972476742620905073236547193718736530795849658690715813666409811296034926060045018355572062333758848573919367583116604677220526788431409580883989472938335069801691982943912731447595279635026489033797287399458502618926938385063431899021231_<636>]

(10¹⁰⁴¹-1)/9 = (1)₁₀₄₁_<1041> = 3 · 37 · 2083 · 8329 · 27067 · 387498606374535498907_<21> · 410503975731004954782987073229804230653973883737063993464776706362401119854845794181516647988735770905941224040754834710574171910854956630254964019326527177415713271183031407659183179189090446340972812321687335541844722766139990065803787309680094251712827838737618173832013563051358152403706029892899512731780807297118672594344076222378213733_<342> · C665

C665 = P36 · C629

P36 = 577252559308332845030620001242246603_<36>

C629 = [23214475573112864700395259491972658202333453156514809632205180386220897847773687197971996181780712132346732719148680085001157370374533487762518892347421470715193616477326444632942199942405300688391126791278435320093415489210733243143059636998103080857040663665750148760924967727020431499198996537173570939491700490193438339980421604001945908933355246620462076573217246166796652564502969051366151263217279284957832647067808529306065284071704810178613972436255263012347169862879437715552991430838967498025200325707172390079310740595199412531636776504037915756237589195211740726755394516519375380035197743847351595531386777246611253_<629>]

By Yousuke Koide / GMP-ECM / Mar 7, 2007

(10¹⁰⁵⁹-1)/9 = (1)₁₀₅₉_<1059> = 3 · 37 · 137079079 · 1781225293_<10> · 1044667255801249_<16> · 276218418252581926399_<21> · [5971186761077908392402271407138469531337493584613277755428999212784863535602930319390757965057266944400930822994221431803426200382259169609623749938890624018856064323434210138683794638398181555480636589432967847046558303900493221643545118097808466487261074656366822115475153656260621410869928975265101194270553763134331528776323_<328>] · C676

C676 = P34 · C642

P34 = 2691389034550013371833520881354751_<34>

C642 = [884049801030082601270977336088490220653550515011911834288189327905733002820208844890522745337342941036583290341313709289759140020077635739025637834248112703394232284208374017876926369421341920680738712424467307084277330820948742870649808872849518268665410142792357137992362367708470343491917411114590672611542431152126603857084300670009823350599290435359606828975158445248233289321388028791829142849297518966358279310536561694746192762490653696178155614179174376659813367065368915000672478855509803415476012840941116146020460058072391134226210532777512274239989720039594198159975070372096719717717606732379981908825888205585620356444445343321_<642>]

By Yousuke Koide / GMP-ECM / Mar 8, 2007

(10¹¹⁰⁷-1)/9 = (1)₁₁₀₇_<1107> = 3³ · 37 · 83 · 757 · 1231 · 333667 · 538987 · 1811791 · 626920594693_<12> · 440334654777631_<15> · 9425856976319889649_<19> · 3244514648940691294717_<22> · 1900016393894413508477719_<25> · 201763709900322803748657942361_<30> · 3151445759294008336434146467746716852125711_<43> · 8414640003465161203119978906558054839526493_<43> · 4624740815741021164555032450406356165555243059597323_<52> · 36075379229129405137442680972370788324414060277012433191198831287911648192680373281921936535843435181632954359677168188643_<122> · C699

C699 = P29

P29 = 36598745651481177932875978009_<29>

C670 = [8421395407701451357967778582252244520221237772223889951133870001343239320459225863280237771550205743834888122813777081705029318772145397879204796376432965690632959491597520423303205670492188492743468799736285667411811792446094603419983097940429401208865957790402408688555656858847087828907487521626755717445454039822609326576086912994025567567275380187461141741370039005225985561644299683996212863959980256694546773043469777628715362669884539629551914663581747854969463992070819901996738139264576576055976866608541775357637709419786900480317302741392460029144631200537648005105676799674440167889384770969409630530611228585776516841744339495137905408376149866733190857117_<670>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 8, 2007

By suberi / GMP-ECM 6.1.2 B1=1000000

10¹⁹⁷+3 = 1(0)₁₉₆3_<198> = 19106066785697_<14> · 23966692732375924083199_<23> · C162

C162 = P40 · P123

P40 = 1506740400796917587901655344160313161129_<40>

P123 = 144937967623748042799512511778911106094684897095036555622767428355565706896710086626493506929331448785972737501085874126869_<123>

Mar 7, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

(4·10¹⁵³-31)/9 = (4)₁₅₂1_<153> = 3 · 7 · 173 · 3385201 · C143

C143 = P67 · P76

P67 = 4560488305057311382507435593928027003772055069381323048336055152141_<67>

P76 = 7924215490068690146402503872065403399730977147986139905338185035670928531997_<76>

Number: 44441_153
N=36138292069212252804360029632108275578414345782524514470030745613346797095292264523197204403608737079442116410293774845823464966686989621555577
  ( 143 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=4560488305057311382507435593928027003772055069381323048336055152141 (pp67)
 r2=7924215490068690146402503872065403399730977147986139905338185035670928531997 (pp76)
Version: GGNFS-0.77.1-20050930-k8
Total time: 24.08 hours.
Scaled time: 21.67 units (timescale=0.900).
Factorization parameters were as follows:
n: 36138292069212252804360029632108275578414345782524514470030745613346797095292264523197204403608737079442116410293774845823464966686989621555577
m: 2000000000000000000000000000000
c5: 125
c0: -31
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2500001)
Primes: RFBsize:176302, AFBsize:175914, largePrimes:5665459 encountered
Relations: rels:5608318, finalFF:477939
Max relations in full relation-set: 28
Initial matrix: 352281 x 477939 with sparse part having weight 46352456.
Pruned matrix : 305368 x 307193 with weight 27517089.
Total sieving time: 23.11 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.82 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 24.08 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init)
Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334236)
Total of 2 processors activated (9340.10 BogoMIPS).

Mar 6, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=1000000

(10¹⁸⁹-7)/3 = (3)₁₈₈1_<189> = 6271 · 32299 · 49499 · C176

C176 = P39 · C137

P39 = 390260975373901404701261090769277737521_<39>

C137 = [85192491022602890603074871079556893265640713223062077079739053971510944948117291577066638568041553214076814786971563038486205148193680341_<137>]

(10¹⁹⁸-7)/3 = (3)₁₉₇1_<198> = 5227 · 46166297 · 22914711330208754233_<20> · 23718216221212076013091_<23> · C145

C145 = P31 · P114

P31 = 7696067714948962015077813118481_<31>

P114 = 330244740180740509985313674081442941277435825012140259779350607572345764737082477798183352202923318056811684612243_<114>

2·10¹⁹⁷-1 = 1(9)₁₉₇_<198> = 3489781 · 1544884849_<10> · C182

C182 = P29 · C153

P29 = 99635152957880897351925251119_<29>

C153 = [372325786866169441250327851059588119485775841500993243856730119954248515508380134433190793829593497441299946322830257214959074704367324446826072083886109_<153>]

Mar 6, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

(8·10¹⁵³-17)/9 = (8)₁₅₂7_<153> = 89 · 22286723 · 94976111 · C136

C136 = P33 · P104

P33 = 217268134271750274716736715143719_<33>

P104 = 21717050344389871464856176217536012976372677149540834313494789291293540788172416316018723197631883531069_<104>

Number: 88887_153
N=4718423010211259138794297245007442786322594410737558694288228071792107072248790299828640538720776084278326199636955123467452167536705611
  ( 136 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=217268134271750274716736715143719 (pp33)
 r2=21717050344389871464856176217536012976372677149540834313494789291293540788172416316018723197631883531069 (pp104)
Version: GGNFS-0.77.1-20050930-k8
Total time: 25.48 hours.
Scaled time: 23.11 units (timescale=0.907).
Factorization parameters were as follows:
n: 4718423010211259138794297245007442786322594410737558694288228071792107072248790299828640538720776084278326199636955123467452167536705611
m: 2000000000000000000000000000000
c5: 250
c0: -17
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2500001)
Primes: RFBsize:176302, AFBsize:176403, largePrimes:5745221 encountered
Relations: rels:5725835, finalFF:503365
Max relations in full relation-set: 28
Initial matrix: 352771 x 503365 with sparse part having weight 49566596.
Pruned matrix : 300196 x 302023 with weight 28750459.
Total sieving time: 24.47 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.87 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 25.48 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init)
Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334236)
Total of 2 processors activated (9340.10 BogoMIPS).

Mar 4, 2007 (2nd)

By suberi / GMP-ECM 6.1.2 B1=11000000

(10¹⁹¹-7)/3 = (3)₁₉₀1_<191> = 38299 · C186

C186 = P32 · P155

P32 = 47001744539769751968602827241659_<32>

P155 = 18517285944918351763957129214874859790396179101241321575840473185447049981337656206617185899986468939901439768367561621500456875804784348671181349229107691_<155>

(10¹⁹⁶-7)/3 = (3)₁₉₅1_<196> = 109 · 11741231 · 633752989 · 28326817297_<11> · 527066786539_<12> · C156

C156 = P29 · C127

P29 = 67704288545514248426941515407_<29>

C127 = [4065734211912069651889418786821571190367441227208124424697089378343489919175810203932388911072813673779896556294261144324891921_<127>]

Mar 4, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

8·10¹⁵³-3 = 7(9)₁₅₂7_<154> = 11 · 678555051229694470501_<21> · C133

C133 = P37 · P96

P37 = 3958588948165095373557421558315246987_<37>

P96 = 270752082824477123437977810221348106655215927606556266395115229672809633068748701952340775747521_<96>

Number: trial
N=1071796202761655680975767715160548894626826466165230156972830778309328057835702269408135222770727052795304362435081217609366667969227
  ( 133 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=3958588948165095373557421558315246987 (pp37)
 r2=270752082824477123437977810221348106655215927606556266395115229672809633068748701952340775747521 (pp96)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 49.08 hours.
Scaled time: 25.13 units (timescale=0.512).
Factorization parameters were as follows:
n: 1071796202761655680975767715160548894626826466165230156972830778309328057835702269408135222770727052795304362435081217609366667969227
m: 2000000000000000000000000000000
c5: 250
c0: -3
skew: 1
type: snfsFactor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176393, largePrimes:5374741 encountered
Relations: rels:5178886, finalFF:405889
Max relations in full relation-set: 0
Initial matrix: 352761 x 405889 with sparse part having weight 35888798.
Pruned matrix : 327530 x 329357 with weight 25113503.
Total sieving time: 38.95 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 9.27 hours.
Time per square root: 0.50 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 49.08 hours.
 --------- CPU info (if available) ----------

Mar 2, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

(2·10¹⁵³+1)/3 = (6)₁₅₂7_<153> = 57301 · 45531221 · C141

C141 = P31 · P111

P31 = 1246958727165838831404081235523_<31>

P111 = 204920385309652616260714333673676048692818683964619270985352641874084886153793092233456525778430057468791514049_<111>

Number: 66667_153
N=255527262836057684415306691004922423526332419823667789088261154131521107217490488391670035818390945946835122826285976260835405729617732362627
  ( 141 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=1246958727165838831404081235523 (pp31)
 r2=204920385309652616260714333673676048692818683964619270985352641874084886153793092233456525778430057468791514049 (pp111)
Version: GGNFS-0.77.1-20050930-k8
Total time: 18.10 hours.
Scaled time: 16.02 units (timescale=0.885).
Factorization parameters were as follows:
n: 255527262836057684415306691004922423526332419823667789088261154131521107217490488391670035818390945946835122826285976260835405729617732362627
m: 2000000000000000000000000000000
c5: 125
c0: 2
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176703, largePrimes:5568032 encountered
Relations: rels:5511902, finalFF:508441
Max relations in full relation-set: 28
Initial matrix: 353070 x 508441 with sparse part having weight 44296531.
Pruned matrix : 286818 x 288647 with weight 23160247.
Total sieving time: 17.32 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.65 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 18.10 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init)
Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238)
Total of 2 processors activated (9340.10 BogoMIPS).

Mar 1, 2007 (3rd)

By Shaopu Lin / Msieve v. 1.16

10¹⁹⁰+3 = 1(0)₁₈₉3_<191> = 7 · 109 · 1999 · 9733 · 3233311 · 754010347 · 2866919243941_<13> · 17720582280902798851_<20> · 655722163172284079918744219522347_<33> · C100

C100 = P45 · P56

P45 = 623346172585568150454866799443866912070379169_<45>

P56 = 13306031615599752194914775123337309874878370542863648083_<56>

Wed Feb 28 11:34:08 2007  
Wed Feb 28 11:34:08 2007  
Wed Feb 28 11:34:08 2007  Msieve v. 1.16
Wed Feb 28 11:34:08 2007  random seeds: fd3e5e78 9c85d5b5
Wed Feb 28 11:34:08 2007  factoring 8294263879886669337889452986894589163143089933573829537603544076933357431118781123536752128389983027 (100 digits)
Wed Feb 28 11:34:08 2007  using multiplier of 3
Wed Feb 28 11:34:08 2007  sieve interval: 9 blocks of size 65536
Wed Feb 28 11:34:08 2007  processing polynomials in batches of 6
Wed Feb 28 11:34:08 2007  using a sieve bound of 2751557 (99744 primes)
Wed Feb 28 11:34:08 2007  using large prime bound of 412733550 (28 bits)
Wed Feb 28 11:34:08 2007  using double large prime bound of 3222593841584400 (43-52 bits)
Wed Feb 28 11:34:08 2007  using trial factoring cutoff of 57 bits
Wed Feb 28 11:34:08 2007  polynomial 'A' values have 13 factors
Wed Feb 28 13:55:54 2007  3251 relations (2946 full + 305 combined from 185074 partial), need 99840
Wed Feb 28 13:55:54 2007  elapsed time 02:21:46
Wed Feb 28 20:46:51 2007  
Wed Feb 28 20:46:51 2007  
Wed Feb 28 20:46:51 2007  Msieve v. 1.16
Wed Feb 28 20:46:51 2007  random seeds: 6c76c7ad 23a675ba
Wed Feb 28 20:46:51 2007  factoring 8294263879886669337889452986894589163143089933573829537603544076933357431118781123536752128389983027 (100 digits)
Wed Feb 28 20:46:51 2007  using multiplier of 3
Wed Feb 28 20:46:51 2007  sieve interval: 9 blocks of size 65536
Wed Feb 28 20:46:51 2007  processing polynomials in batches of 6
Wed Feb 28 20:46:51 2007  using a sieve bound of 2751557 (99744 primes)
Wed Feb 28 20:46:51 2007  using large prime bound of 412733550 (28 bits)
Wed Feb 28 20:46:51 2007  using double large prime bound of 3222593841584400 (43-52 bits)
Wed Feb 28 20:46:51 2007  using trial factoring cutoff of 57 bits
Wed Feb 28 20:46:51 2007  polynomial 'A' values have 13 factors
Wed Feb 28 20:46:52 2007  restarting with 2946 full and 185074 partial relations
Wed Feb 28 21:53:31 2007  4826 relations (4151 full + 675 combined from 263698 partial), need 99840
Wed Feb 28 21:53:31 2007  elapsed time 01:06:40
Wed Feb 28 22:39:39 2007  
Wed Feb 28 22:39:39 2007  
Wed Feb 28 22:39:39 2007  Msieve v. 1.16
Wed Feb 28 22:39:39 2007  random seeds: 101005eb 187da084
Wed Feb 28 22:39:39 2007  factoring 8294263879886669337889452986894589163143089933573829537603544076933357431118781123536752128389983027 (100 digits)
Wed Feb 28 22:39:40 2007  using multiplier of 3
Wed Feb 28 22:39:40 2007  sieve interval: 9 blocks of size 65536
Wed Feb 28 22:39:40 2007  processing polynomials in batches of 6
Wed Feb 28 22:39:40 2007  using a sieve bound of 2751557 (99744 primes)
Wed Feb 28 22:39:40 2007  using large prime bound of 412733550 (28 bits)
Wed Feb 28 22:39:40 2007  using double large prime bound of 3222593841584400 (43-52 bits)
Wed Feb 28 22:39:40 2007  using trial factoring cutoff of 57 bits
Wed Feb 28 22:39:40 2007  polynomial 'A' values have 13 factors
Wed Feb 28 22:39:40 2007  restarting with 4151 full and 263698 partial relations
Thu Mar  1 02:26:09 2007  12719 relations (8672 full + 4047 combined from 550728 partial), need 99840
Thu Mar  1 02:26:09 2007  elapsed time 03:46:30
Thu Mar  1 02:40:22 2007  
Thu Mar  1 02:40:22 2007  
Thu Mar  1 02:40:22 2007  Msieve v. 1.16
Thu Mar  1 02:40:22 2007  random seeds: e3b4d815 047781cd
Thu Mar  1 02:40:22 2007  factoring 8294263879886669337889452986894589163143089933573829537603544076933357431118781123536752128389983027 (100 digits)
Thu Mar  1 02:40:22 2007  using multiplier of 3
Thu Mar  1 02:40:22 2007  sieve interval: 9 blocks of size 65536
Thu Mar  1 02:40:22 2007  processing polynomials in batches of 6
Thu Mar  1 02:40:22 2007  using a sieve bound of 2751557 (99744 primes)
Thu Mar  1 02:40:22 2007  using large prime bound of 412733550 (28 bits)
Thu Mar  1 02:40:22 2007  using double large prime bound of 3222593841584400 (43-52 bits)
Thu Mar  1 02:40:22 2007  using trial factoring cutoff of 57 bits
Thu Mar  1 02:40:22 2007  polynomial 'A' values have 13 factors
Thu Mar  1 02:40:25 2007  restarting with 8672 full and 550728 partial relations
Thu Mar  1 07:20:08 2007  30190 relations (14336 full + 15854 combined from 903383 partial), need 99840
Thu Mar  1 07:20:08 2007  elapsed time 04:39:46
Thu Mar  1 07:30:56 2007  
Thu Mar  1 07:30:56 2007  
Thu Mar  1 07:30:56 2007  Msieve v. 1.16
Thu Mar  1 07:30:56 2007  random seeds: 38d2b3b4 69611d54
Thu Mar  1 07:30:56 2007  factoring 8294263879886669337889452986894589163143089933573829537603544076933357431118781123536752128389983027 (100 digits)
Thu Mar  1 07:30:57 2007  using multiplier of 3
Thu Mar  1 07:30:57 2007  sieve interval: 9 blocks of size 65536
Thu Mar  1 07:30:57 2007  processing polynomials in batches of 6
Thu Mar  1 07:30:57 2007  using a sieve bound of 2751557 (99744 primes)
Thu Mar  1 07:30:57 2007  using large prime bound of 412733550 (28 bits)
Thu Mar  1 07:30:57 2007  using double large prime bound of 3222593841584400 (43-52 bits)
Thu Mar  1 07:30:57 2007  using trial factoring cutoff of 57 bits
Thu Mar  1 07:30:57 2007  polynomial 'A' values have 13 factors
Thu Mar  1 07:31:00 2007  restarting with 14336 full and 903383 partial relations
Thu Mar  1 15:05:37 2007  100015 relations (23609 full + 76406 combined from 1496872 partial), need 99840
Thu Mar  1 15:05:39 2007  begin with 1520481 relations
Thu Mar  1 15:05:42 2007  reduce to 264112 relations in 11 passes
Thu Mar  1 15:05:42 2007  attempting to read 264112 relations
Thu Mar  1 15:05:46 2007  recovered 264112 relations
Thu Mar  1 15:05:46 2007  recovered 255700 polynomials
Thu Mar  1 15:05:47 2007  attempting to build 100015 cycles
Thu Mar  1 15:05:47 2007  found 100015 cycles in 6 passes
Thu Mar  1 15:05:47 2007  distribution of cycle lengths:
Thu Mar  1 15:05:47 2007     length 1 : 23609
Thu Mar  1 15:05:47 2007     length 2 : 17124
Thu Mar  1 15:05:47 2007     length 3 : 16634
Thu Mar  1 15:05:47 2007     length 4 : 13670
Thu Mar  1 15:05:47 2007     length 5 : 10309
Thu Mar  1 15:05:47 2007     length 6 : 7296
Thu Mar  1 15:05:47 2007     length 7 : 4705
Thu Mar  1 15:05:47 2007     length 9+: 6668
Thu Mar  1 15:05:47 2007  largest cycle: 23 relations
Thu Mar  1 15:05:48 2007  matrix is 99744 x 100015 with weight 6892518 (avg 68.91/col)
Thu Mar  1 15:05:49 2007  filtering completed in 3 passes
Thu Mar  1 15:05:49 2007  matrix is 98293 x 98357 with weight 6706543 (avg 68.19/col)
Thu Mar  1 15:05:51 2007  saving the first 48 matrix rows for later
Thu Mar  1 15:05:51 2007  matrix is 98245 x 98357 with weight 5288937 (avg 53.77/col)
Thu Mar  1 15:05:51 2007  matrix includes 32 packed rows
Thu Mar  1 15:12:18 2007  lanczos halted after 1555 iterations
Thu Mar  1 15:12:18 2007  recovered 15 nontrivial dependencies
Thu Mar  1 15:12:20 2007  prp45 factor: 623346172585568150454866799443866912070379169
Thu Mar  1 15:12:20 2007  prp56 factor: 13306031615599752194914775123337309874878370542863648083
Thu Mar  1 15:12:21 2007  elapsed time 07:41:25

Mar 1, 2007 (2nd)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(23·10¹⁷⁴+1)/3 = 7(6)₁₇₃7_<175> = C175

C175 = P82 · P94

P82 = 1160607580637197436909970824725037202415122085752327758687078618700131481703406693_<82>

P94 = 6605735473877836429266158816256245412965621347106431956774582202198506986337160850347488301519_<94>

Number: trial
N=7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667
  ( 175 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=1160607580637197436909970824725037202415122085752327758687078618700131481703406693 (pp82)
 r2=6605735473877836429266158816256245412965621347106431956774582202198506986337160850347488301519 (pp94)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 524.24 hours.
Scaled time: 261.59 units (timescale=0.499).
Factorization parameters were as follows:
n: 7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667
m: 100000000000000000000000000000000000
c5: 23
c0: 10
skew: 1
type: snfsFactor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 12000001)
Primes: RFBsize:501962, AFBsize:502936, largePrimes:6573231 encountered
Relations: rels:7075654, finalFF:1156659
Max relations in full relation-set: 0
Initial matrix: 1004963 x 1156659 with sparse part having weight 73670169.
Pruned matrix : 875281 x 880369 with weight 56635738.
Total sieving time: 421.19 hours.
Total relation processing time: 2.85 hours.
Matrix solve time: 99.19 hours.
Time per square root: 1.01 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 524.24 hours.
 --------- CPU info (if available) ----------

ggnfs.log

P82 is the largest factor found by GGNFS so far in our tables. Congratulations!

Mar 1, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

2·10¹⁵³-1 = 1(9)₁₅₃_<154> = 15691768246211_<14> · C141

C141 = P69 · P72

P69 = 353513036560672278720383066571230366372013904846573971289155955705721_<69>

P72 = 360539354070797054614614477395854393904128587102075385793873356333263229_<72>

Number: 19999_153
N=127455361857190846931918977265359562320737650559762438370891685772080440799934245153725798549661033306725368901569294000250485152745554233109
  ( 141 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=353513036560672278720383066571230366372013904846573971289155955705721 (pp69)
 r2=360539354070797054614614477395854393904128587102075385793873356333263229 (pp72)
Version: GGNFS-0.77.1-20050930-k8
Total time: 18.09 hours.
Scaled time: 16.28 units (timescale=0.900).
Factorization parameters were as follows:
n: 127455361857190846931918977265359562320737650559762438370891685772080440799934245153725798549661033306725368901569294000250485152745554233109
m: 2000000000000000000000000000000
c5: 125
c0: -2
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176703, largePrimes:5510413 encountered
Relations: rels:5411193, finalFF:473639
Max relations in full relation-set: 28
Initial matrix: 353070 x 473639 with sparse part having weight 41868614.
Pruned matrix : 299602 x 301431 with weight 23572181.
Total sieving time: 17.27 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.69 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 18.09 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init)
Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238)
Total of 2 processors activated (9340.10 BogoMIPS).

February 2007

Feb 28, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

(10¹⁵³+11)/3 = (3)₁₅₂7_<153> = 21713 · 1958639 · C142

C142 = P47 · P96

P47 = 56012047933977242644746128635736463158657930621_<47>

P96 = 139933940296037326170860171696111127188198457902149369986513673643425230148449166105666454124371_<96>

Number: 33337_153
N=7837986571451952337344021664199398173461416743422190003615130300703792594977381173662233460335937902016270973969313815005514673204533423264391
  ( 142 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=56012047933977242644746128635736463158657930621 (pp47)
 r2=139933940296037326170860171696111127188198457902149369986513673643425230148449166105666454124371 (pp96)
Version: GGNFS-0.77.1-20050930-k8
Total time: 23.71 hours.
Scaled time: 21.41 units (timescale=0.903).
Factorization parameters were as follows:
n: 7837986571451952337344021664199398173461416743422190003615130300703792594977381173662233460335937902016270973969313815005514673204533423264391
m: 2000000000000000000000000000000
c5: 125
c0: 44
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2400001)
Primes: RFBsize:176302, AFBsize:176309, largePrimes:5522255 encountered
Relations: rels:5355675, finalFF:397759
Max relations in full relation-set: 28
Initial matrix: 352677 x 397759 with sparse part having weight 36285588.
Pruned matrix : 338033 x 339860 with weight 27748899.
Total sieving time: 22.55 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.02 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 23.71 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init)
Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238)
Total of 2 processors activated (9340.10 BogoMIPS).

Feb 27, 2007 (2nd)

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000

10¹⁹⁰+3 = 1(0)₁₈₉3_<191> = 7 · 109 · 1999 · 9733 · 3233311 · 754010347 · 2866919243941_<13> · 17720582280902798851_<20> · C133

C133 = P33 · C100

P33 = 655722163172284079918744219522347_<33>

C100 = [8294263879886669337889452986894589163143089933573829537603544076933357431118781123536752128389983027_<100>]

Feb 27, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 gnfs

10¹⁷⁸+3 = 1(0)₁₇₇3_<179> = 7 · 157 · 24245477791_<11> · 5078466902270143_<16> · 4569709099059178801353087954144739_<34> · C116

C116 = P57 · P59

P57 = 841050813852720381404892919400005717849954152346218888253_<57>

P59 = 19227735730244777938096884405431184217580235872014168819807_<59>

Number: 10003_178
N=16171502784467401319287662621859897744129487788677630030766407486502790213752219467024595149277155013321436626027171
  ( 116 digits)
Divisors found:
 r1=841050813852720381404892919400005717849954152346218888253 (pp57)
 r2=19227735730244777938096884405431184217580235872014168819807 (pp59)
Version: GGNFS-0.77.1-20050930-k8
Total time: 31.02 hours.
Scaled time: 28.04 units (timescale=0.904).
Factorization parameters were as follows:
name: 10003_178
n: 16171502784467401319287662621859897744129487788677630030766407486502790213752219467024595149277155013321436626027171
skew: 59320.44
# norm 8.29e+15
c5: 18360
c4: -5896211018
c3: -169978952505995
c2: 19216375200484044757
c1: 295044772439832950255035
c0: -5091579523182641313914445475
# alpha -6.33
Y1: 648790286489
Y0: -15451715806320998022694
# Murphy_E 5.24e-10
# M 2075202453831472643899126093394648510121006128741731540160248918241614765343065675054342930282131187537282500185585
type: gnfs
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1800000, 3075001)
Primes: RFBsize:256726, AFBsize:257167, largePrimes:7603714 encountered
Relations: rels:7597769, finalFF:672489
Max relations in full relation-set: 28
Initial matrix: 513974 x 672489 with sparse part having weight 59145054.
Pruned matrix : 388056 x 390689 with weight 34744662.
Total sieving time: 29.17 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.52 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000
total time: 31.02 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init)
Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238)
Total of 2 processors activated (9340.10 BogoMIPS).

Feb 25, 2007 (2nd)

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000

10¹⁷⁸+3 = 1(0)₁₇₇3_<179> = 7 · 157 · 24245477791_<11> · 5078466902270143_<16> · C149

C149 = P34 · C116

P34 = 4569709099059178801353087954144739_<34>

C116 = [16171502784467401319287662621859897744129487788677630030766407486502790213752219467024595149277155013321436626027171_<116>]

Feb 25, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

(55·10¹⁵³-1)/9 = 6(1)₁₅₃_<154> = 3 · 7² · 59 · 499 · 4433601500999501_<16> · C132

C132 = P36 · P96

P36 = 443171310398193925665075725975649587_<36>

P96 = 718657553936836885321598272947467364542248403492347369865271322934439134580238588061966073028939_<96>

Number: 61111_153
N=318488409905748732335262453779275118109518084807264340557733279354756102540104018347999743339896897734455486744819880964471174398193
  ( 132 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=443171310398193925665075725975649587 (pp36)
 r2=718657553936836885321598272947467364542248403492347369865271322934439134580238588061966073028939 (pp96)
Version: GGNFS-0.77.1-20050930-k8
Total time: 23.26 hours.
Scaled time: 21.07 units (timescale=0.906).
Factorization parameters were as follows:
n: 318488409905748732335262453779275118109518084807264340557733279354756102540104018347999743339896897734455486744819880964471174398193
m: 10000000000000000000000000000000
c5: 11
c0: -20
skew: 1.13
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:217532, largePrimes:5648529 encountered
Relations: rels:5672716, finalFF:610597
Max relations in full relation-set: 28
Initial matrix: 434414 x 610597 with sparse part having weight 46505927.
Pruned matrix : 319951 x 322187 with weight 28817513.
Total sieving time: 22.20 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.91 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 23.26 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init)
Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238)
Total of 2 processors activated (9340.10 BogoMIPS).

Feb 24, 2007 (2nd)

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000

10¹⁸⁰+3 = 1(0)₁₇₉3_<181>= 28123846354801856041_<20> · 846519155191153820587_<21> · C140

C140 = P35 · P105

P35 = 77061435151581887669779157560546231_<35>

P105 = 545068896844122913071888795078742584270297590744667404658731433888121502839542622364777079658746154067239_<105>

Feb 24, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

(28·10¹⁵³-1)/9 = 3(1)₁₅₃_<154> = 3 · 2156207 · 8622287 · 599155396153_<12> · C128

C128 = P51 · P78

P51 = 758789025710646472692249434850475074640894740293827_<51>

P78 = 122693293575279404068194860876165197135028729140976454096131624341950993818503_<78>

Number: 31111_153
N=93098324693216579417753550046991752832637021075594278760522148525511109448795692087399923815341074215583301555795522034929280981
  ( 128 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=758789025710646472692249434850475074640894740293827 (pp51)
 r2=122693293575279404068194860876165197135028729140976454096131624341950993818503 (pp78)
Version: GGNFS-0.77.1-20050930-k8
Total time: 19.61 hours.
Scaled time: 17.77 units (timescale=0.906).
Factorization parameters were as follows:
n: 93098324693216579417753550046991752832637021075594278760522148525511109448795692087399923815341074215583301555795522034929280981
m: 10000000000000000000000000000000
c5: 7
c0: -25
skew: 1.29
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2400001)
Primes: RFBsize:216816, AFBsize:216906, largePrimes:5406288 encountered
Relations: rels:5274106, finalFF:488668
Max relations in full relation-set: 28
Initial matrix: 433788 x 488668 with sparse part having weight 34023429.
Pruned matrix : 393569 x 395801 with weight 23880608.
Total sieving time: 18.36 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.12 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 19.61 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init)
Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238)
Total of 2 processors activated (9340.10 BogoMIPS).

Feb 23, 2007 (2nd)

By Yousuke Koide / GMP-ECM

10⁸¹²+1 = 1(0)₈₁₁1_<813> = 73 · 137 · 233 · 7841 · 355193 · 17456377 · 21591416633_<11> · 127522001020150503761_<21> · 17468739848498438039329935679794457_<35> · 320326994163169943384295066992439316655840979654890345228609_<60> · C665

C665 = P33 · C633

P33 = 144919694966021542240510318821809_<33>

C633 = [395331939737645320291413064117561097049246687109905814427194810304353495921929416126294305229072789125855534815576659488174603154390875860634149548209175383448724590281810799154139648183136729921980128112325848586411749334562196253224749514725985439259582812608720279719207754040268684455927656154375997917489451629418896999620634088684149924321190877325892101533587902648474485664803938673414481754826326389029692982503772120395159833178519597418300782371333265894526366450300708586722070814774924029567261873002611140424872633891019926511850875956451902172967028046865109519247953630446750690804572155699886510959628554374758738857_<633>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 23, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

(86·10¹⁵³+31)/9 = 9(5)₁₅₂9_<154> = 11 · 157 · 593447 · 355701609695516717_<18> · C128

C128 = P43 · P86

P43 = 2333147258247029252947881169964585045658781_<43>

P86 = 11234498342156787134685645268358398193131468455122513168368272096894919519757431168343_<86>

Number: 95559_153
N=26211739004783903442088690574964455578189548285351447620659647136122658039301734190181588545726298787223130741712855492947169883
  ( 128 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=2333147258247029252947881169964585045658781 (pp43)
 r2=11234498342156787134685645268358398193131468455122513168368272096894919519757431168343 (pp86)
Version: GGNFS-0.77.1-20050930-k8
Total time: 28.68 hours.
Scaled time: 25.98 units (timescale=0.906).
Factorization parameters were as follows:
n: 26211739004783903442088690574964455578189548285351447620659647136122658039301734190181588545726298787223130741712855492947169883
m: 2000000000000000000000000000000
c5: 5375
c0: 62
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:216097, largePrimes:5600692 encountered
Relations: rels:5519089, finalFF:512518
Max relations in full relation-set: 28
Initial matrix: 432979 x 512518 with sparse part having weight 41128559.
Pruned matrix : 389202 x 391430 with weight 27957400.
Total sieving time: 27.31 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 1.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 28.68 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init)
Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238)
Total of 2 processors activated (9340.10 BogoMIPS).

Feb 22, 2007 (2nd)

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000

10¹⁹⁹+3 = 1(0)₁₉₈3_<200> = 13 · 4533299 · 259556761 · 111011352372742720485057131_<27> · 505135145839533539009957298516389_<33> · C125

C125 = P41 · P84

P41 = 16093036459190114862200718359175889466551_<41>

P84 = 724430892695841602220008780254282449815290128891715782166558993784367540920500492781_<84>

Feb 22, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 gnfs

(52·10¹⁹⁹-7)/9 = 5(7)₁₉₉_<200> = 3 · 19 · 13119178847_<11> · 21322941493829819_<17> · 27313233753447177563_<20> · 411351101494831873367498992021260976263151_<42> · C111

C111 = P46 · P66

P46 = 1272101379026747903707298354196236477819089199_<46>

P66 = 253527282351532668908867579235496341067847640059655454647818415871_<66>

Number: 57777_199
N=322512405500288394218032710154255774087278705689799529635356287413030666368619768153870436563708339820226277329
  ( 111 digits)
Divisors found:
 r1=1272101379026747903707298354196236477819089199 (pp46)
 r2=253527282351532668908867579235496341067847640059655454647818415871 (pp66)
Version: GGNFS-0.77.1-20050930-k8
Total time: 19.89 hours.
Scaled time: 17.98 units (timescale=0.904).
Factorization parameters were as follows:
name: 57777_199
n: 322512405500288394218032710154255774087278705689799529635356287413030666368619768153870436563708339820226277329
skew: 19049.31
# norm 4.62e+15
c5: 56940
c4: 8333311569
c3: 130378450823455
c2: -3457389236060032737
c1: 7122233774699597553648
c0: 26218571313762820195500400
# alpha -5.75
Y1: 129261245377
Y0: -1414570610242647704179
# Murphy_E 8.37e-10
# M 244908670307495451176391156578070089225011585752165573221271866723377090566827216829777892597738977141074837489
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1200000, 2040001)
Primes: RFBsize:176302, AFBsize:176810, largePrimes:7526749 encountered
Relations: rels:7290349, finalFF:434299
Max relations in full relation-set: 28
Initial matrix: 353195 x 434299 with sparse part having weight 42494161.
Pruned matrix : 299074 x 300903 with weight 27376589.
Total sieving time: 18.86 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.75 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000
total time: 19.89 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init)
Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238)
Total of 2 processors activated (9340.10 BogoMIPS).

Feb 21, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

(2·10¹⁵⁷-17)/3 = (6)₁₅₆1_<157> = C157

C157 = P60 · P98

P60 = 628486628437275763243226019561267587348336747741014522686317_<60>

P98 = 10607491655380562300466288136354207234632798963479344661061680154739676571597744074392683606884633_<98>

Number: 66661_157
N=6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661
  ( 157 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=628486628437275763243226019561267587348336747741014522686317 (pp60)
 r2=10607491655380562300466288136354207234632798963479344661061680154739676571597744074392683606884633 (pp98)
Version: GGNFS-0.77.1-20050930-k8
Total time: 27.11 hours.
Scaled time: 24.59 units (timescale=0.907).
Factorization parameters were as follows:
n: 6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661
m: 10000000000000000000000000000000
c5: 200
c0: -17
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:216541, largePrimes:5667132 encountered
Relations: rels:5652586, finalFF:569599
Max relations in full relation-set: 28
Initial matrix: 433422 x 569599 with sparse part having weight 46045150.
Pruned matrix : 356719 x 358950 with weight 28863014.
Total sieving time: 25.81 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.15 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 27.11 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init)
Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238)
Total of 2 processors activated (9340.10 BogoMIPS).

Feb 21, 2007

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(52·10¹⁹⁹-7)/9 = 5(7)₁₉₉_<200> = 3 · 19 · 13119178847_<11> · 21322941493829819_<17> · 27313233753447177563_<20> · C153

C153 = P42 · C111

P42 = 411351101494831873367498992021260976263151_<42>

C111 = [322512405500288394218032710154255774087278705689799529635356287413030666368619768153870436563708339820226277329_<111>]

Feb 17, 2007 (2nd)

By Yousuke Koide / GMP-ECM

(10¹⁴⁸⁵-1)/9 = (1)₁₄₈₅_<1485> = 3³ · 31 · 37 · 41 · 67 · 199 · 271 · 397 · 757 · 991 · 1321 · 21649 · 34849 · 55243 · 62921 · 198397 · 238681 · 333667 · 471241 · 513239 · 1577071 · 2906161 · 16357951 · 18679321 · 60834511 · 83251631 · 310362841 · 1981560241_<10> · 31351842721_<11> · 258360989311_<12> · 31600574312077_<14> · 440334654777631_<15> · 545431981101481_<15> · 596298133647227881_<18> · 1344628210313298373_<19> · 4185502830133110721_<19> · 165426670443186506567467_<24> · 1300635692678058358830121_<25> · 138267770127916457629034873443951_<33> · 483418418597220677238517353915231961831_<39> · 16860090181450569942798606214497570829921_<41> · 1703548913892494075097664562023844278044121_<43> · 362853724342990469324766235474268869786311886053883_<51> · 7907009307594694001053552000588658391100974093457603716419437_<61> · 1113954903312329460800701782039373182801635744784098645224633477_<64> · [88415092713367678139008031849456036531214635443710603842417450647749425991456343388066542975721610469026836129783834813518385505575072089337317444944320083700084281_<164>] · C695

C695 = P34 · C662

P34 = 4035237932666608861051093768608241_<34>

C662 = [14491961854759997987318745440205865717215092235131607457539451297044985828137745987618751910779935337450743029169715116165130001535712858818542505553012159022658570403931283147158358096058156927519056819695880820440205164069148370546551136152026451401191468202488142651601966386910139935847132556803499130069122366612387262070859275372869822375695150111399077632325143331047045000707169517942466827613230622811019760241780737321155276049750304376977883406746688008002436878234529678022439754363890579416396792468847348438177735168318288241130782120589812040887053417704682926423525859672694505398099632321848048462247957579965155055393914376032729548547886567561_<662>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 17, 2007

By Thomas Womack / gmp-ecm 6.1.2 B1=10^7

(52·10¹⁸⁰-7)/9 = 5(7)₁₈₀_<181> = C181

C181 = P40 · C142

P40 = 1907145664709063958354268537876114943171_<40>

C142 = [3029541940446998167772966488018297475181566383829140811226747765285330708447334102021603405973003072683807287017514072821950182110331738508987_<142>]

Feb 16, 2007 (2nd)

By Thomas Womack / gmp-ecm 6.1.2 B1=10000000

(4·10¹⁷⁴-13)/9 = (4)₁₇₃3_<174> = C174

C174 = P35 · P139

P35 = 87397362083737992740080811306657947_<35>

P139 = 5085330195877183357332537501058300188350678694002609720879352861143821239003179780252075511657845817249891108582299028154671201878554346369_<139>

Feb 16, 2007

By Thomas Womack / ggnfs-0.77.0

8·10¹⁶¹-3 = 7(9)₁₆₀7_<162> = 11² · C160

C160 = P51 · P110

P51 = 250747836796484155922888159263112237486391376320671_<51>

P110 = 26367406923235271511544763325616291041131768180892905671230128715401910040795595415317934691655387997292702267_<110>

r1 = 26367406923235271511544763325616291041131768180892905671230128715401910040795595415317934691655387997292702267
r2 = 250747836796484155922888159263112237486391376320671

Total time: 42.61 hours.
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [2250000, 3850001)
Relations: rels:5942000, finalFF:809129
Initial matrix: 631709 x 809129 with sparse part having weight 46075762.
Pruned matrix : 557525 x 560747 with weight 22467359.
Total sieving time: 39.60 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 2.76 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 42.61 hours.

Feb 15, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8

2·10¹⁶⁶-9 = 1(9)₁₆₅1_<167> = C167

C167 = P43 · P124

P43 = 4342608369450320053307697679764984011450663_<43>

P124 = 4605526977909722451833107953713650779997398871974627226660275324682668177795505331963035514480056136584527504258436835169457_<124>

Number: 19991_166
N=19999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
  ( 167 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=4342608369450320053307697679764984011450663 (pp43)
 r2=4605526977909722451833107953713650779997398871974627226660275324682668177795505331963035514480056136584527504258436835169457 (pp124)
Version: GGNFS-0.77.1-20050930-k8
Total time: 69.64 hours.
Scaled time: 63.03 units (timescale=0.905).
Factorization parameters were as follows:
n: 19999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
m: 1000000000000000000000000000000000
c5: 20
c0: -9
skew: 1
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 5700001)
Primes: RFBsize:412849, AFBsize:412306, largePrimes:5923360 encountered
Relations: rels:6223470, finalFF:960819
Max relations in full relation-set: 28
Initial matrix: 825222 x 960819 with sparse part having weight 43152556.
Pruned matrix : 703215 x 707405 with weight 28666743.
Total sieving time: 66.35 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 3.11 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.5,2.5,100000
total time: 69.64 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init)
Calibrating delay using timer specific routine.. 4671.60 BogoMIPS (lpj=2335804)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238)
Total of 2 processors activated (9340.08 BogoMIPS).

Feb 14, 2007 (3rd)

(10³⁹⁵-1)/9 = (1)₃₉₅_<395> = 41 · 271 · 317 · 6163 · 10271 · 307627 · 870801991 · 25439781075319591_<17> · 49172195536083790769_<20> · 4706625334158237778391951_<25> · 3660574762725521461527140564875080461079917_<43> · C262

C262 = P54 · P209

P54 = 388603184868446209952357338208961774763421470820867551_<54>

P209 = 22212532982654486103266742473370118653419410820133470750925842805231785671919088995453275587554965715421794773862472837122581772057977997807066409510062713778700204701764277608437512924874155027264480537635511_<209>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 14, 2007 (2nd)

By Shusuke Kubota / GGNFS-0.77.0

(73·10¹⁵⁴-1)/9 = 8(1)₁₅₄_<155> = 3² · C154

C154 = P41 · P113

P41 = 93458549042255332010768816824559015680981_<41>

P113 = 96431474395537659290440617511664931557542477458136745046691918305873367117076472604700705384745959369588944243859_<113>

Number: 88881-155
N=9012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679
  ( 154 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=93458549042255332010768816824559015680981 (pp41)
 r2=96431474395537659290440617511664931557542477458136745046691918305873367117076472604700705384745959369588944243859 (pp113)
Version: GGNFS-0.77.0
Total time: 56.41 hours.
Scaled time: 46.48 units (timescale=0.824).
Factorization parameters were as follows:
n: 9012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679
m: 10000000000000000000000000000000
c5: 73
c0: -10
skew: 1
type: snfs
qintsize: 25000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1500000, 2875000)
Relations: rels:5526542, finalFF:505041
Initial matrix: 433502 x 505041 with sparse part having weight 40814331.
Pruned matrix : 418963 x 421194 with weight 26453378.
Total sieving time: 51.15 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 4.69 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 56.41 hours.
 --------- CPU info (if available) ----------

Feb 14, 2007

By Thomas Womack / GGNFS-0.77.0

(5·10¹⁵³+13)/9 = (5)₁₅₂7_<153> = 109 · 1756903 · 1035843636655735339_<19> · C127

C127 = P35 · P92

P35 = 50145955190901622584127136372141099_<35>

P92 = 55849990274513738302544705045190770656055373081642160005471409653566216764003101702841243831_<92>

r1 = 50145955190901622584127136372141099
r2 = 55849990274513738302544705045190770656055373081642160005471409653566216764003101702841243831
SNFS difficulty: 154 digits.
Divisors found:
 r1=50145955190901622584127136372141099 (pp35)
 r2=55849990274513738302544705045190770656055373081642160005471409653566216764003101702841243831 (pp92)
Version: GGNFS-0.77.0
Total time: 26.69 hours.
Scaled time: 42.86 units (timescale=1.606).
Sieved special-q in [1200000, 2300001)
Relations: rels:5620503, finalFF:527326
Initial matrix: 352875 x 527326 with sparse part having weight 48316105.
Pruned matrix : 321712 x 323540 with weight 19282768.
Total sieving time: 24.69 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.79 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 26.69 hours.

Feb 12, 2007 (2nd)

By Yousuke Koide / GMP-ECM

(10⁸²⁵-1)/9 = (1)₈₂₅_<825> = 3 · 31 · 37 · 41 · 67 · 151 · 271 · 1321 · 4201 · 7151 · 15401 · 21401 · 21649 · 25601 · 59951 · 62921 · 143551 · 471241 · 513239 · 2906161 · 83251631 · 182521213001_<12> · 1344628210313298373_<19> · 155460646275454423201_<21> · 1300635692678058358830121_<25> · 138267770127916457629034873443951_<33> · 2495283264895779020253203931608951_<34> · 15763985553739191709164170940063151_<35> · 1703548913892494075097664562023844278044121_<43> · 6069650333889644423896816835276507778804898705650161138729963603757211141984131085449988328049514249213169785004014797295919583814686411189300687347453551_<154> · C375

C375 = P43 · P333

P43 = 2088776436021648629103222560680031099644951_<43>

P333 = 214528843968953631928063476651039061041063809962416030964828547787541153707714846521305533494862873734486298787721809249575564868485587852627557513243818964260757025571864734011221992206979184553651791551471337682785524853615509168758324340944481464694072720676919519406523000680246989690635604205812979868199506676258154640779755801_<333>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 12, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 gnfs

(7·10¹⁸⁴-43)/9 = (7)₁₈₃3_<184> = 3 · 2087 · 173267 · 92637580320041260534335543461_<29> · 54923797941083258665408610502743_<32> · C115

C115 = P49 · P67

P49 = 1383615489945228484659595198563915740434096933951_<49>

P67 = 1018433770708324513989795221242712535071162592913196540345250819023_<67>

Number: 77773_184
N=1409120740635364908607465067802764562290036915063588145837948055243262006073639575459991601899495173541955885349873
  ( 115 digits)
Divisors found:
 r1=1383615489945228484659595198563915740434096933951 (pp49)
 r2=1018433770708324513989795221242712535071162592913196540345250819023 (pp67)
Version: GGNFS-0.77.1-20050930-k8
Total time: 31.91 hours.
Scaled time: 28.94 units (timescale=0.907).
Factorization parameters were as follows:
name: 77773_184
n: 1409120740635364908607465067802764562290036915063588145837948055243262006073639575459991601899495173541955885349873
skew: 57408.89
# norm 1.21e+16
c5: 14280
c4: -8199350774
c3: -148304488649521
c2: 21405458101595154052
c1: 142537809412331697636336
c0: -11062522908965943983877268608
# alpha -6.44
Y1: 1229138586269
Y0: -9973558664403551923037
# Murphy_E 5.60e-10
# M 936351327745923239120694157973164494754818427960473456494344742826592099052997543653036754399328806873797529005227
type: gnfs
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1800000, 3075001)
Primes: RFBsize:256726, AFBsize:256781, largePrimes:7532171 encountered
Relations: rels:7446703, finalFF:614994
Max relations in full relation-set: 28
Initial matrix: 513590 x 614994 with sparse part having weight 53608083.
Pruned matrix : 430894 x 433525 with weight 34153324.
Polynomial selection time: 1.31 hours.
Total sieving time: 28.56 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.72 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000
total time: 31.91 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Intel(R) Core(TM)2 CPU          6300  @ 1.86GHz stepping 06
Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init)
Calibrating delay using timer specific routine.. 4671.60 BogoMIPS (lpj=2335804)
Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238)
Total of 2 processors activated (9340.08 BogoMIPS).

Feb 11, 2007

By Yousuke Koide / GMP-ECM

(10⁷⁶⁵-1)/9 = (1)₇₆₅_<765> = 3² · 31 · 37 · 41 · 271 · 307 · 613 · 18973 · 210631 · 238681 · 333667 · 2071723 · 2906161 · 11910133 · 52986961 · 262533041 · 5363222357_<10> · 8119594779271_<13> · 25332185271529_<14> · 77967508765681_<14> · 13168164561429877_<17> · 41331541464123787_<17> · 4185502830133110721_<19> · 17452955481423492661946457391_<29> · 34194473116159546979818689031_<29> · 4222100119405530170179331190291488789678081_<43> · 13753721844250167674053932561585423251305429858083649_<53> · 2385503624916094046163570223793978575506412147454036200711_<58> · C385

C385 = P39 · P346

P39 = 513179642980665929403935269209265889161_<39>

P346 = 1950585947224940419950248867026805880899314052934810675053013776673117345436439511928719471294613511792179585771032825256940078928817403205519252806576240803441065824757216160174665670758508088069382574508854177932682656221426002932789572902329615434652326605290218636214671926683628663404694204326895954873066839725116831163068208522081531521441_<346>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 10, 2007 (2nd)

By Philippe Strohl / GMP-ECM, GGNFS-0.77.1-20060722-pentium-m

(7·10¹⁸¹-43)/9 = (7)₁₈₀3_<181> = 3 · 60487457 · 63749185262142707_<17> · C156

C156 = P35 · P122

P35 = 64777876741657802572555583806019627_<35>

P122 = 10379288937582466970916981607412631488017397024321519329007965704922134757985272848817679210368742928554294200964291659967_<122>

(7·10¹⁸⁴-43)/9 = (7)₁₈₃3_<184> = 3 · 2087 · 173267 · 92637580320041260534335543461_<29> · C146

C146 = P32 · C115

P32 = 54923797941083258665408610502743_<32>

C115 = [1409120740635364908607465067802764562290036915063588145837948055243262006073639575459991601899495173541955885349873_<115>]

(7·10¹⁹⁰-43)/9 = (7)₁₈₉3_<190> = 3 · 379853 · 1653502611689_<13> · 223033235529943_<15> · C158

C158 = P32 · P126

P32 = 30617702251306471516292760426167_<32>

P126 = 604465682901527770286687448552777681175592272944031753571377173281664702601341986824877637011967643421219608087996220150348483_<126>

(7·10¹⁷¹-43)/9 = (7)₁₇₀3_<171> = 199 · 151305076042521491_<18> · C152

C152 = P42 · P43 · P68

P42 = 121495956675387278043299989858967591123701_<42>

P43 = 7068538249965126094045281972629883093163147_<43>

P68 = 30078593090070246841437934832118520753770865013385674443419876087151_<68>

Feb 10, 2007

By Philippe Strohl / GMP-ECM

(7·10¹⁹¹-43)/9 = (7)₁₉₀3_<191> = 896542069 · 151215945352530419_<18> · 834957171990917126025520458563_<30> · C152

C152 = P37 · P99

P37 = 1555638964216566815934684090827554843_<37>

P99 = 441686633572614353856740837849121421170592905576897104142793452892615860092900755744822879464359827_<99>

Feb 9, 2007

By Shusuke Kubota / GMP-ECM 6.0.1 B1=1000000, GGNFS-0.77.0 gnfs

(17·10¹⁵³-71)/9 = 1(8)₁₅₂1_<154> = 3 · 11 · 458033732131576820267_<21> · C132

C132 = P34 · P45 · P53

P34 = 2487441325075200197121778501595359_<34>

P45 = 935061187428302940375031505062267678199121469_<45>

P53 = 53728180464604315513396648915975156149011893915038001_<53>

Number: 18881-153
N=50239136223595060423269539592167071615943681788416865006866027868792606935588881818866205949943469
  ( 98 digits)
Divisors found:
 r1=935061187428302940375031505062267678199121469 (pp45)
 r2=53728180464604315513396648915975156149011893915038001 (pp53)
Version: GGNFS-0.77.0
Total time: 16.77 hours.
Scaled time: 13.76 units (timescale=0.820).
Factorization parameters were as follows:
name: 18881-153
n:  50239136223595060423269539592167071615943681788416865006866027868792606935588881818866205949943469
m:  1709282966443362906
deg: 5
c5: 3443280
c4: 4131057000
c3: -144180038412326
c2: -1723950652316668
c1: 5865605519247624248
c0: -848169666955669766435
skew: 725.838
type: gnfs
# adj. I(F,S) = 47.844
# E(F1,F2) = 2.926012e-03
# GGNFS version 0.77.0 polyselect.
# Options were: 
# lcd=1, enumLCD=2, maxS1=58.00000000, seed=1170826781.
# maxskew=1500.0
# These parameters should be manually set:
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000

type: gnfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Sieved special-q in [900000, 1950001)
Relations: rels:3911307, finalFF:340161
Initial matrix: 270265 x 340161 with sparse part having weight 28787639.
Pruned matrix : 247996 x 249411 with weight 15276957.
Total sieving time: 14.69 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 1.51 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 16.77 hours.
 --------- CPU info (if available) ----------

Feb 8, 2007

By Bruce Dodson / GMP-ECM

10²⁶⁶+1 = 1(0)₂₆₅1_<267> = 29 · 101 · 281 · 2129 · 121499449 · 14691812549_<11> · 722817036322379041_<18> · 1369778187490592461_<19> · 1728095716605342484009_<22> · C182

C182 = P52 · P130

P52 = 3845225778323318739662926792353902964405172909187389_<52>

P130 = 4859378131018035310593858490137688922829468686775068797577396520148545290055799616742354372616293735785798821073310265896384033181_<130>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 6, 2007 (2nd)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(13·10¹⁵³-1)/3 = 4(3)₁₅₃_<154> = 7 · 661 · 797 · 460916575998112074071727299_<27> · C121

C121 = P54 · P68

P54 = 199795892670038144209829374746205946009729446983267859_<54>

P68 = 12760138661362256349935504330320109597229231443037841109860164508027_<68>

Number: trial
N=2549423294440337571087290903497700361859461239948612878825560392658318637774911572584694853772175150748353008237496604193
  ( 121 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=199795892670038144209829374746205946009729446983267859 (pp54)
 r2=12760138661362256349935504330320109597229231443037841109860164508027 (pp68)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 70.94 hours.
Scaled time: 38.88 units (timescale=0.548).
Factorization parameters were as follows:
n: 2549423294440337571087290903497700361859461239948612878825560392658318637774911572584694853772175150748353008237496604193
m: 1000000000000000000000000000000
c5: 13000
c0: -1
skew: 1
type: snfsFactor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2600001)
Primes: RFBsize:176302, AFBsize:176953, largePrimes:5649921 encountered
Relations: rels:5555582, finalFF:412943
Max relations in full relation-set: 0
Initial matrix: 353322 x 412943 with sparse part having weight 38504182.
Pruned matrix : 331910 x 333740 with weight 28482681.
Total sieving time: 59.58 hours.
Total relation processing time: 0.57 hours.
Matrix solve time: 10.38 hours.
Time per square root: 0.41 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 70.94 hours.
 --------- CPU info (if available) ----------

Feb 6, 2007

By suberi / GGNFS-0.77.1-20060513-pentium4

(8·10¹⁵⁴-53)/9 = (8)₁₅₃3_<154> = 3 · 7 · 19 · C152

C152 = P49 · P104

P49 = 2109117000218396790445988790435409265621492648171_<49>

P104 = 10562674812469988978662532655660065618933586481087912099926424984662629593973290757990833266941366306327_<104>

Number: 88883_154
N=22277917014759120022277917014759120022277917014759120022277917014759120022277917014759120022277917014759120022277917014759120022277917014759120022277917
  ( 152 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=2109117000218396790445988790435409265621492648171 (pp49)
 r2=10562674812469988978662532655660065618933586481087912099926424984662629593973290757990833266941366306327 (pp104)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 53.54 hours.
Scaled time: 33.84 units (timescale=0.632).
Factorization parameters were as follows:
n: 22277917014759120022277917014759120022277917014759120022277917014759120022277917014759120022277917014759120022277917014759120022277917014759120022277917
m: 10000000000000000000000000000000
c5: 4
c0: -265
skew: 2.31
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:216371, largePrimes:5634709 encountered
Relations: rels:5587850, finalFF:541403
Max relations in full relation-set: 28
Initial matrix: 433251 x 541403 with sparse part having weight 43022066.
Pruned matrix : 372854 x 375084 with weight 27680522.
Total sieving time: 46.09 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 6.91 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 53.54 hours.
 --------- CPU info (if available) ----------

Feb 2, 2007 (3rd)

By Anonymous

10¹⁰⁰¹+1 = 1(0)₁₀₀₀1_<1002> = 11² · 23 · 463 · 859 · 4093 · 8009 · 8779 · 24179 · 51767 · 590437 · 909091 · 7444361 · 21705503 · 1058313049_<10> · 22144088539_<11> · 109313560357_<12> · 264752347289_<12> · 4539402627853030477_<19> · 104730101107272149081_<21> · 216031795247629116757_<21> · 4924630160315726207887_<22> · 50678387411703889101759125785290439894389920385627096501794498837_<65> · 34607524609209512562213651270561528862879196390936320471942325254862879783_<74> · C685

C685 = P32 · C653

P32 = 82618024434905595106111659338321_<32>

C653 = [58178503308788154426291302030707350928236341702129983308363771602879105119870038450937896434351306926832195838172811764529737671608235809780061534507676893306702862878665952965468559129218515193819486430054025214904255822372500866194419422851643203261474792811499761645758008369734627788354249782503720864053338330703456736872798891065209921648587941030445907386080167626025743023118127792717574879066917697833440606515276780249741342049676747757046612644216010177666746964557488809230177420595138964543098172211888391402341224671422980295129401586274555426919525435497071806104833893258096563326906555680874384650491265582875651844594074431054692116931_<653>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 2, 2007 (2nd)

By Kurt Beschorner / GMP-ECM

(10¹³⁶³-1)/9 = (1)₁₃₆₃_<1363> = 3191 · 16763 · 43037 · 62003 · 580639 · 35121409 · 569205157 · 77843839397_<11> · 509649121665126339920293_<24> · 221693470933128952318104031_<27> · 316362908763458525001406154038726382279_<39> · C1224

C1224 = P30 · C1194

P30 = 795287068884583505529998090507_<30>

C1194 = [303053550423437757744577970664347139058174265460996097827735855091960961366617190860861899538339427405302065921323308004694332410780453265553794004513756822368209038844441902309599726063212073788915315822866313526643695616771407660238952357090919109445769850894110083406400864937888101833288067278306468763556061991141637735812818752063838929845320254221932028730902118799572921376401194490286744053625633974823222256070386822901071470266212047977758083287736560454805962821410294269221218466138883248534724699124803763016999874119320088188873423380603419044661818905203746741225061226597240721791112435539530002691526296718763907292498223321401320012291219342972873336424886111381568035786397233783154826935657629585333161391381414575770495792384239420277817996166704389686399904195136501855409808019538835646562852044459239211575894673645778708008519647683157375573098405948287435014337255947307010911001292419835690084361858589494681751918742740383645957261693219402585237639569461609996150772869934210727941413121840947487571997838497930100990291001100537076969586874801586276569972001567327069012872244703569759943095969578175595127498839339587510269198005621059667948789447437782642986957_<1194>]

(10¹⁴¹⁷-1)/9 = (1)₁₄₁₇_<1417> = 53 · 79 · 592307 · 1192679 · 74383999 · 265371653 · 35224702898191_<14> · 712767480971213008079_<21> · 5295275348767234696493_<22> · 246829743984355435962408390910378218537282105150086881669547_<60> · C1269

C1269 = P27 · C1243

P27 = 320759296668278219098942271_<27>

C1243 = [1807962964739891266189097056530234806062431767311423328744246983012018469480509986030486092575806531205340633799701714501165255757647960636778704332848091002970907847614870031786506197311736491694548091615354728702238276470555753505102286480946750577799105829175873448773931411486194802387560478953556109800421252377051910887848432972004805875176348604596991067283393186015327300001219122275166001470317555037985576878046909924066826046595406861138007407044607947349804561692439601682308891050632770431801025387194322134807435474333209341495146357837941837551706663872277184691379667841049800124927701696945137899749848756941018168966978497219949386544439607730078717943844176715497535766483923175904691169486082589380849466712498419529363740988161052645728327293980736354239984569025476919263028684103495974518096875427430007362125003715323349166458392306648079506655261994595408652409837318999606971784596145004271200346154069050284165284502300089336496441994324497430903465478316042118552841508288916762534034593841431651854367051273254973426855748143399608480280391066558807548859322585665145716396172940250714548218710694760335882280800696008224923355890289479592821583051861272228680196273820468893343061082725120024319369835150920080067_<1243>]

(10¹⁵⁴¹-1)/9 = (1)₁₅₄₁_<1541> = 3083 · 416071 · 493121 · 73169879117_<11> · 79863595778924342083_<20> · 11111111111111111111111_<23> · 28213380943176667001263153660999177245677_<41> · C1432

C1432 = P27 · C1406

P27 = 453705568156105320101001973_<27>

C1406 = [21134651516625743546890394107470844907479101338767920175606829641381409740006066105359778875852557693330672741609769971903490143459321853791621927150388840080978939724048850901854316724028594840222545578756237289839719333944013510117329696331418528887043082498707522884927211722756355953420758843956706414456395748205730175240795380943328077101500432000606746309699225335852275849208810579013996932425337858730804408430076455488292782663754279650536042416841571872994763623564370557928084924692369433971807291184955462748659972340620316419998766214376110878039100970605546328475282329672793112780945215005900449423748649485575832923817067261319677247616470177480667543260307649641155900211417251124900673058337339052575004426303516852740850083831820888199155367665484662813601732714457812587267307725453146328707543884479978031437792448373540869436638720441463327503700034899467797981715427485727388369367494620211186531624606909762218646618344073281919148141141103101374642913607603429301308817846134680270940432922295257930326912840385952450105869326719027661322184642246076759572589955126651100077599548810133757709419575105659702183751467048010072475380106330080726264759988336691270828091597604129022525679595125180138288946082224994462694280827181587124958906971098972669340113833079048056605666830126595568874371693442218186856330033320899529202798532949224792235565371115950824730876872577562530307_<1406>]

(10¹⁷⁸⁹-1)/9 = (1)₁₇₈₉_<1789> = 39359 · 15367511 · 1553903933_<10> · 1036330801552389631_<19> · C1750

C1750 = P24 · C1726

P24 = 289319996763559834545559_<24>

C1726 = [3942837499439788061006944005045960718031486305577669627347253650039890321211994289379151938973310874850909435607956123122373090697532769795751167924693837794161082874840439638501132104303263899086924115533649057636244015830444657773516604004037438543727777073203302412364862600498176849479949473377539411452728745169933045051932389267734062359088160828713934870961080362842267605776193414549899550396053896313811933135608302426066443951706346413481958933433688342021908673459058683089585505795767461215484375046250361597762305765392896560557743728592263890398335486220705008931781533659816577900022386517954802174214486603572948890913445984059319713144031993677879920870496666548344818537213927754061002698478647910543381380073623428605053342609122482475738206920326824464327619038724816610030642905609614072435312429524191225206369486913501903002277803975049628855245626076186828913477216013920331439226922420525254233442729472850030206453751204580226244005963622625739486689341400829788024746459418073871675281540798930149401936448596412966292470988929859007344438577764846698397140012506376736645041912539548266216913362399399032412908581595079247559109902038049591748329385786055846889351909274757252136756090688205433305699729684759624710529568581942894558580807538053455910285653760969235114134103679010678018567507583541013942437863524408140562028399790265985729515306715849629150272650273129300704875740641586416956958650682921949181587381455061374245833631347378093122836134452241005704894394879066045192375148941067473715818860137578458100687319496055787232337883524420144853590949474086092966954941929991699950779540584381552340206530079269381878652437099530645734013689177173442931238693436585294711171175497278627_<1726>]

10¹¹⁷³+1 = 1(0)₁₁₇₂1_<1174> = 7 · 11 · 13 · 47 · 103 · 139 · 2531 · 4013 · 31051 · 2955961 · 2140571729_<10> · 21993833369_<11> · 37633218241_<11> · 291078844423_<12> · 837042695779_<12> · 9101279023169_<13> · 143574021480139_<15> · 549797184491917_<15> · 377526955309799110357_<21> · 24649445347649059192745899_<26> · 473608692432035450677211738101499095303_<39> · 10716938719047367538834654373404752406351326801836497222088230040131663586216274781916394062442922695303181507242106723273347077744999936956310904046369389147208937313522359019479619429347564668082983985444056247726866683751993403229947286059050999830315193876492518147194037_<275> · C693

C693 = P28 · C665

P28 = 5718695187661520881538869249_<28>

C665 = [19010644145695322442596197267125042884422868255022599767493290364039234062415429333907999864691739173795260320378861055964127145682409009427107712529810252464517289298080164319904869840576256342883389125818582402079952512042858297115608946297491656759114204785207287207243576094138786865390191547258635907677241328093726205037638267062013156683163911676808858057446736948956303893626662973050170317203867973298049356744746481831901972743222598577141036541608397443502337218886325093431887273649028091617509913303741217594022418581681618959379282154580275142153998626983832153956552170243293669205787041806706605636159791777704358392669878320221138319342230431351721_<665>]

10¹¹⁹³+1 = 1(0)₁₁₉₂1_<1194> = 11 · 59651 · 53979914146049857432194823_<26> · C1162

C1162 = P30 · C1133

P30 = 198967330445464802733582366889_<30>

C1133 = [14189778742392371822642464950295420598664613116648809753042689444870476667678262283972005038116540843336863837863764148879121448975368096535914316580611824820280358541845177484282962523673492504056748411707282673481645254762423336182533392931917615081877746791397835188974222778151311424184745536567736162654982777184515925485753546325716404087091870903092275328177951082186392981158347804800448785726152060403108870700513166920826189555108851673010918501338004327589779330197106265408955344060922120410917888447706962950356306376942817414547580241131328456968130947355118062783781411462622375933899030723810309604218581357118013526489734378995893972825454915362359640168679374586440064527973918906860115103631093524224684768949076317452365838495117769189761295766298889392238273398605877114850710885226216618560741198378653014548830718195754193150403671240372569916849086223167646058546438327863231841205948476087420301663949934620211238040821675676819201872339480134979460270733168740906651295908694282683598843883004034032243280079564829227845090271498824504246761717903627496937462197957747979655626804393725202656530686491589503_<1133>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 2, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(67·10¹⁵³+23)/9 = 7(4)₁₅₂7_<154> = 11 · 6030653 · 8193403 · 326176421242447441543_<21> · C119

C119 = P43 · P76

P43 = 5154315594748468038755725836892835668230311_<43>

P76 = 8146806128868512010643223189999358487179665174602492096290584650206693233411_<76>

Number: trial
N=41991209877419369037432001482964525746811820171841723098290931984019537579033702205003427059699691239093343828828120821
  ( 119 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=5154315594748468038755725836892835668230311 (pp43)
 r2=8146806128868512010643223189999358487179665174602492096290584650206693233411 (pp76)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 67.72 hours.
Scaled time: 34.88 units (timescale=0.515).
Factorization parameters were as follows:
n: 41991209877419369037432001482964525746811820171841723098290931984019537579033702205003427059699691239093343828828120821
m: 1000000000000000000000000000000
c5: 67000
c0: 23
skew: 1
type: snfsFactor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2700001)
Primes: RFBsize:216816, AFBsize:217321, largePrimes:5617548 encountered
Relations: rels:5590468, finalFF:508481
Max relations in full relation-set: 0
Initial matrix: 434204 x 508481 with sparse part having weight 32443032.
Pruned matrix : 382267 x 384502 with weight 23492975.
Total sieving time: 55.64 hours.
Total relation processing time: 0.56 hours.
Matrix solve time: 11.02 hours.
Time per square root: 0.50 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 67.72 hours.
 --------- CPU info (if available) ----------

January 2007

Jan 31, 2007 (2nd)

By suberi / GGNFS-0.77.1-20060513-pentium4

(5·10¹⁵⁶-23)/9 = (5)₁₅₅3_<156> = C156

C156 = P49 · P108

P49 = 2560846149716872439579858329726586825671575032531_<49>

P108 = 216942183589192918421663964578069355218853581414103484953743923902937473987096413182058653625995214621863163_<108>

Number: 55553_156
N=555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553
  ( 156 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=2560846149716872439579858329726586825671575032531 (pp49)
 r2=216942183589192918421663964578069355218853581414103484953743923902937473987096413182058653625995214621863163 (pp108)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 62.22 hours.
Scaled time: 37.96 units (timescale=0.610).
Factorization parameters were as follows:
n: 555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553
m: 10000000000000000000000000000000
c5: 50
c0: -23
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 
)
Primes: RFBsize:216816, AFBsize:217086, largePrimes:5742807 encountered
Relations: rels:5740934, finalFF:571746
Max relations in full relation-set: 28
Initial matrix: 433967 x 571746 with sparse part having weight 48670665.
Pruned matrix : 367071 x 369304 with weight 30938760.
Total sieving time: 53.91 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 7.68 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 62.22 hours.
 --------- CPU info (if available) ----------

Jan 31, 2007

By Kurt Beschorner / GMP-ECM

(10¹⁰⁷⁵-1)/9 = (1)₁₀₇₅_<1075> = 41 · 173 · 271 · 431 · 21401 · 25601 · 1527791 · 182521213001_<12> · 1963506722254397_<16> · 2140992015395526641_<19> · 41398275939670867448911914339156680381343777006826487831_<56> · C840

C840 = P32 · C809

P32 = 28808518895110018881804272718751_<32>

C809 = [34711607481137779185343172568717063853649585607981256386198377523802955101674937658780544823861348911920227642123216535679247669103837522475155674109571330827877424273413589767269899876630170875051449423734879644153648797148657214133378174948653045435306621735367968242996150776676173929074851994253401369223360251902080671630146157701604684771369403136781086510374585437847110162407898647867517026085273167889611696348163648367323493946325384541861626251628996810055789736484792164758749290264880489129700245642965069450249435987606544165556441089849084572024845424821961153276851461743602388067096595478280474790653411469219889993269156750027876209726144359277423206345399199574980124591526006741368479442403172140074454806048167074796407295825522453850061099531834063042167111891660292294188880701000618751_<809>]

(10¹³³⁹-1)/9 = (1)₁₃₃₉_<1339> = 53 · 79 · 1031 · 2948479 · 7034077 · 265371653 · 376778533 · 134914656772016146559_<21> · 153211620887015423991278431667808361439217294295901387715486473457925534859044796980526236853_<93> · C1189

C1189 = P34 · C1155

P34 = 9493900906734104973632584503630517_<34>

C1155 = [632491207186448318890356683644297741034601907694816173005638750740737186940122497932594560862737202522189814350559651835868449534354515462709460091660741392814285242480113401500238396839063375106786760174836622425912148172669874591463607503550390352096721622033738764417670476128739126566593652232366036313115036262621351370531942058662970675263252135456180530041111456576490840059497947547656297180150865169781921026697092535326559189090901016073621062270288251905350095113048701395892474088679773730180957620791457786874975077274963046507870295886492068449779576980621429573621987926862106957358529979871749003078012483311918918056897022178680906927333023672650547467196330473015376365169819270298135302424463054955275154178508872212669165606005556186097344135313836949668943436468735757706714806656076555645025638238949490301337481793952710831287244059417539551759685294285676541444031993261039619459300689558717767780552414413207728044156319556290785341776021015215167915759238562759219794577748280605771163176444321516668102067580717790586331168633043863180135666797505171251204514617530287681136978427097385346931445452216068468197848426615040752671_<1155>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 30, 2007 (3rd)

By Wataru Sakai / GGNFS-0.77.1-20060513-pentium4

(2·10¹⁹²-11)/9 = (2)₁₉₁1_<192> = C192

C192 = P51 · P141

P51 = 558618399051833370115786772061914616637233905518207_<51>

P141 = 397806843812179113084158478278673278462548559737123328190563207638690256907455600564416540019096658258610880726309405139019884843047677986803_<141>

Number: 22221_192
N=222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
  ( 192 digits)
SNFS difficulty: 192 digits.
Divisors found:
 r1=558618399051833370115786772061914616637233905518207 (pp51)
 r2=397806843812179113084158478278673278462548559737123328190563207638690256907455600564416540019096658258610880726309405139019884843047677986803 (pp141)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2650.61 hours.
Scaled time: 3353.02 units (timescale=1.265).
Factorization parameters were as follows:
n: 222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
m: 100000000000000000000000000000000000000
c5: 200
c0: -11
skew: 1
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 30100001)
Primes: RFBsize:501962, AFBsize:503807, largePrimes:7704137 encountered
Relations: rels:8480417, finalFF:1132965
Max relations in full relation-set: 28
Initial matrix: 1005834 x 1132965 with sparse part having weight 156672342.
Pruned matrix : 922746 x 927839 with weight 141023585.
Total sieving time: 2579.02 hours.
Total relation processing time: 2.88 hours.
Matrix solve time: 68.25 hours.
Time per square root: 0.45 hours.
Prototype def-par.txt line would be:
snfs,192,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 2650.61 hours.
 --------- CPU info (if available) ----------

Jan 30, 2007 (2nd)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(52·10¹⁵²-7)/9 = 5(7)₁₅₂_<153> = 1621 · 50957 · C145

C145 = P67 · P79

P67 = 2709042073446592170792934274741551206028921382492321254041066670097_<67>

P79 = 2582011769442852651209968987523621441279428819480352551729492154606092853851153_<79>

Number: trial
N=6994778517554969842395789230498133434609117309353844380649105034970307763784602289934718310510036879660349374148178058000442508521116536194071841
  ( 145 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=2709042073446592170792934274741551206028921382492321254041066670097 (pp67)
 r2=2582011769442852651209968987523621441279428819480352551729492154606092853851153 (pp79)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 62.87 hours.
Scaled time: 32.76 units (timescale=0.521).
Factorization parameters were as follows:
n: 6994778517554969842395789230498133434609117309353844380649105034970307763784602289934718310510036879660349374148178058000442508521116536194071841
m: 2000000000000000000000000000000
c5: 325
c0: -14
skew: 1
type: snfsFactor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2400001)
Primes: RFBsize:176302, AFBsize:176488, largePrimes:5582957 encountered
Relations: rels:5444690, finalFF:406954
Max relations in full relation-set: 0
Initial matrix: 352856 x 406954 with sparse part having weight 35869280.
Pruned matrix : 334041 x 335869 with weight 26580813.
Total sieving time: 51.60 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 10.36 hours.
Time per square root: 0.42 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 62.87 hours.
 --------- CPU info (if available) ----------

Jan 30, 2007

By anonymous / GMP-ECM B1=1000000

(5·10¹⁹⁷-41)/9 = (5)₁₉₆1_<197> = 3³ · 113 · 7057 · 98731 · 180990319 · 2368810349_<10> · 112482036837773_<15> · 5364655462624710751_<19> · C135

C135 = P32 · P103

P32 = 11964267951850715104560344952589_<32>

P103 = 8443351287853077133602447796951347937273196183236859341898751751641591112408103384212454905661287831579_<103>

Jan 29, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

(14·10¹⁷⁵-41)/9 = 1(5)₁₇₄1_<176> = 11 · 43 · C173

C173 = P46 · P128

P46 = 1971848954400133691125566917937107287858416479_<46>

P128 = 16678260045126227226173832334535265219726130696522534014568395028983269564908150799866271813714347853920132775969907902330680553_<128>

Number: 15551_175
N=32887009631195677707305614282358468404980032887009631195677707305614282358468404980032887009631195677707305614282358468404980032887009631195677707305614282358468404980032887
  ( 173 digits)
SNFS difficulty: 176 digits.
Divisors found:
 r1=1971848954400133691125566917937107287858416479 (pp46)
 r2=16678260045126227226173832334535265219726130696522534014568395028983269564908150799866271813714347853920132775969907902330680553 (pp128)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 390.89 hours.
Scaled time: 238.83 units (timescale=0.611).
Factorization parameters were as follows:
name: 15551_175
n: 32887009631195677707305614282358468404980032887009631195677707305614282358468404980032887009631195677707305614282358468404980032887009631195677707305614282358468404980032887
m: 100000000000000000000000000000000000
c5: 14
c0: -41
skew: 4
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 11300001)
Primes: RFBsize:501962, AFBsize:502607, largePrimes:6474994 encountered
Relations: rels:6944147, finalFF:1127040
Max relations in full relation-set: 0
Initial matrix: 1004635 x 1127040 with sparse part having weight 69379171.
Pruned matrix : 898670 x 903757 with weight 54223156.
Total sieving time: 335.51 hours.
Total relation processing time: 1.06 hours.
Matrix solve time: 53.90 hours.
Time per square root: 0.42 hours.
Prototype def-par.txt line would be:
snfs,176,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 390.89 hours.
 --------- CPU info (if available) ----------

Jan 28, 2007

By anonymous / GMP-ECM B1=250000

(28·10¹⁷⁰+17)/9 = 3(1)₁₆₉3_<171> = C171

C171 = P40 · C132

P40 = 1364116464566141004805456799576331094877_<40>

C132 = [228067851383980179396737331050460171350301360191884615279312516244379676595735991540084639749089760281280334949498526496536231019869_<132>]

Jan 27, 2007 (5th)

By anonymous / GMP-ECM B1=250000

(2·10¹⁶⁴-11)/9 = (2)₁₆₃1_<164> = 3 · 7 · C163

C163 = P28 · P135

P28 = 2705744860522788636251121991_<28>

P135 = 391094176557577793883311466250837928124679378240286597104225549984604139382887743727588795990566928192149494732283550828037750266209311_<135>

(89·10¹⁶⁶+1)/9 = 9(8)₁₆₅9_<167> = 3 · 7 · C166

C166 = P31 · C136

P31 = 2145267415169671460471822733293_<31>

C136 = [2195061872331785564833392556541334193678898931031362398283536977263473924321435784902869096812578999064592069887228245952439930289418313_<136>]

Jan 27, 2007 (4th)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(14·10¹⁵²-41)/9 = 1(5)₁₅₁1_<153> = 151 · 973057 · 847196941648551132106333324010269_<33> · C112

C112 = P36 · P77

P36 = 108123011159930669845571642420238883_<36>

P77 = 11557603368746529230971013510751174250574322894480256454543811212283540578959_<77>

Number: trial
N=1249642878021033284825168208794036075612473963907528490275936932677995158635356633750195668907903252864903462797
  ( 112 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=108123011159930669845571642420238883 (pp36)
 r2=11557603368746529230971013510751174250574322894480256454543811212283540578959 (pp77)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 47.63 hours.
Scaled time: 26.15 units (timescale=0.549).
Factorization parameters were as follows:
n: 1249642878021033284825168208794036075612473963907528490275936932677995158635356633750195668907903252864903462797
m: 1000000000000000000000000000000
c5: 1400
c0: -41
skew: 1
type: snfsFactor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176059, largePrimes:5528339 encountered
Relations: rels:5432457, finalFF:410172
Max relations in full relation-set: 0
Initial matrix: 352428 x 410172 with sparse part having weight 28109504.
Pruned matrix : 318706 x 320532 with weight 20499291.
Total sieving time: 39.98 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 6.94 hours.
Time per square root: 0.34 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 47.63 hours.
 --------- CPU info (if available) ----------

Jan 27, 2007 (3rd)

By Shaopu Lin / Msieve v. 1.16

2·10¹⁷⁹-9 = 1(9)₁₇₈1_<180> = 11 · 109 · 1531 · 197084090167072070444501_<24> · 30192185167289557139962813541_<29> · 11175180923359872868625684424731_<32> · C91

C91 = P44 · P47

P44 = 38745744185364135989275373176013064492968519_<44>

P47 = 42287395639301185430766513250585783292869637311_<47>

Fri Jan 26 22:27:14 2007  
Fri Jan 26 22:27:14 2007  
Fri Jan 26 22:27:14 2007  Msieve v. 1.16
Fri Jan 26 22:27:14 2007  random seeds: a6eb1203 b5238d3a
Fri Jan 26 22:27:14 2007  factoring 1638456613705646625512724389739829497429579295062517050049568260367385691018719269270812409 (91 digits)
Fri Jan 26 22:27:14 2007  using multiplier of 41
Fri Jan 26 22:27:14 2007  sieve interval: 9 blocks of size 65536
Fri Jan 26 22:27:14 2007  processing polynomials in batches of 6
Fri Jan 26 22:27:14 2007  using a sieve bound of 1648483 (62353 primes)
Fri Jan 26 22:27:14 2007  using large prime bound of 145066504 (27 bits)
Fri Jan 26 22:27:14 2007  using double large prime bound of 490705292959992 (42-49 bits)
Fri Jan 26 22:27:14 2007  using trial factoring cutoff of 51 bits
Fri Jan 26 22:27:14 2007  polynomial 'A' values have 12 factors
Sat Jan 27 01:15:16 2007  62806 relations (17263 full + 45543 combined from 679877 partial), need 62449
Sat Jan 27 01:15:17 2007  begin with 697140 relations
Sat Jan 27 01:15:19 2007  reduce to 149952 relations in 11 passes
Sat Jan 27 01:15:19 2007  attempting to read 149952 relations
Sat Jan 27 01:15:21 2007  recovered 149952 relations
Sat Jan 27 01:15:21 2007  recovered 133574 polynomials
Sat Jan 27 01:15:21 2007  attempting to build 62806 cycles
Sat Jan 27 01:15:21 2007  found 62806 cycles in 5 passes
Sat Jan 27 01:15:21 2007  distribution of cycle lengths:
Sat Jan 27 01:15:21 2007     length 1 : 17263
Sat Jan 27 01:15:21 2007     length 2 : 12770
Sat Jan 27 01:15:21 2007     length 3 : 11417
Sat Jan 27 01:15:21 2007     length 4 : 8177
Sat Jan 27 01:15:21 2007     length 5 : 5706
Sat Jan 27 01:15:21 2007     length 6 : 3337
Sat Jan 27 01:15:21 2007     length 7 : 1922
Sat Jan 27 01:15:21 2007     length 9+: 2214
Sat Jan 27 01:15:21 2007  largest cycle: 18 relations
Sat Jan 27 01:15:22 2007  matrix is 62353 x 62806 with weight 3655627 (avg 58.21/col)
Sat Jan 27 01:15:22 2007  filtering completed in 4 passes
Sat Jan 27 01:15:22 2007  matrix is 60789 x 60853 with weight 3464835 (avg 56.94/col)
Sat Jan 27 01:15:23 2007  saving the first 48 matrix rows for later
Sat Jan 27 01:15:23 2007  matrix is 60741 x 60853 with weight 2679405 (avg 44.03/col)
Sat Jan 27 01:15:23 2007  matrix includes 32 packed rows
Sat Jan 27 01:17:20 2007  lanczos halted after 962 iterations
Sat Jan 27 01:17:20 2007  recovered 17 nontrivial dependencies
Sat Jan 27 01:17:23 2007  prp44 factor: 38745744185364135989275373176013064492968519
Sat Jan 27 01:17:23 2007  prp47 factor: 42287395639301185430766513250585783292869637311
Sat Jan 27 01:17:23 2007  elapsed time 02:50:09

(7·10¹⁸⁵-61)/9 = (7)₁₈₄1_<185> = 15869070719_<11> · 221773283827_<12> · 277298503527337722497_<21> · 6105120015064145026321_<22> · 148620272450318305620892247_<27> · C95

C95 = P45 · P51

P45 = 224862363761607190215772027417022972537690791_<45>

P51 = 390623396058772295453140324659480039189781576841383_<51>

Sat Jan 27 01:39:07 2007  
Sat Jan 27 01:39:07 2007  
Sat Jan 27 01:39:07 2007  Msieve v. 1.16
Sat Jan 27 01:39:07 2007  random seeds: 423f607f 2ef68dad
Sat Jan 27 01:39:07 2007  factoring 87836500178362012339391534087557870391705073829131196795608369383843280519245566419346506803953 (95 digits)
Sat Jan 27 01:39:07 2007  using multiplier of 33
Sat Jan 27 01:39:07 2007  sieve interval: 9 blocks of size 65536
Sat Jan 27 01:39:07 2007  processing polynomials in batches of 6
Sat Jan 27 01:39:07 2007  using a sieve bound of 2190817 (81176 primes)
Sat Jan 27 01:39:07 2007  using large prime bound of 328622550 (28 bits)
Sat Jan 27 01:39:07 2007  using double large prime bound of 2138233886692800 (43-51 bits)
Sat Jan 27 01:39:07 2007  using trial factoring cutoff of 55 bits
Sat Jan 27 01:39:07 2007  polynomial 'A' values have 12 factors
Sat Jan 27 08:17:49 2007  81535 relations (20590 full + 60945 combined from 1191119 partial), need 81272
Sat Jan 27 08:17:51 2007  begin with 1211709 relations
Sat Jan 27 08:17:53 2007  reduce to 208204 relations in 10 passes
Sat Jan 27 08:17:53 2007  attempting to read 208204 relations
Sat Jan 27 08:17:56 2007  recovered 208204 relations
Sat Jan 27 08:17:56 2007  recovered 193380 polynomials
Sat Jan 27 08:17:57 2007  attempting to build 81535 cycles
Sat Jan 27 08:17:57 2007  found 81535 cycles in 6 passes
Sat Jan 27 08:17:57 2007  distribution of cycle lengths:
Sat Jan 27 08:17:57 2007     length 1 : 20590
Sat Jan 27 08:17:57 2007     length 2 : 14946
Sat Jan 27 08:17:57 2007     length 3 : 14053
Sat Jan 27 08:17:57 2007     length 4 : 10885
Sat Jan 27 08:17:57 2007     length 5 : 8137
Sat Jan 27 08:17:57 2007     length 6 : 5231
Sat Jan 27 08:17:57 2007     length 7 : 3252
Sat Jan 27 08:17:57 2007     length 9+: 4441
Sat Jan 27 08:17:57 2007  largest cycle: 18 relations
Sat Jan 27 08:17:58 2007  matrix is 81176 x 81535 with weight 5530736 (avg 67.83/col)
Sat Jan 27 08:17:59 2007  filtering completed in 3 passes
Sat Jan 27 08:17:59 2007  matrix is 79614 x 79678 with weight 5312625 (avg 66.68/col)
Sat Jan 27 08:18:00 2007  saving the first 48 matrix rows for later
Sat Jan 27 08:18:00 2007  matrix is 79566 x 79678 with weight 4464667 (avg 56.03/col)
Sat Jan 27 08:18:00 2007  matrix includes 32 packed rows
Sat Jan 27 08:21:49 2007  lanczos halted after 1260 iterations
Sat Jan 27 08:21:49 2007  recovered 17 nontrivial dependencies
Sat Jan 27 08:21:50 2007  prp45 factor: 224862363761607190215772027417022972537690791
Sat Jan 27 08:21:50 2007  prp51 factor: 390623396058772295453140324659480039189781576841383
Sat Jan 27 08:21:50 2007  elapsed time 06:42:43

Jan 27, 2007 (2nd)

By anonymous / GMP-ECM B1=1000000

3·10¹⁸⁷-1 = 2(9)₁₈₇_<188> = 337638313967807182936900258849_<30> · 99433004049017708218656527004744377_<35> · C123

C123 = P38 · P86

P38 = 47527930809248160978423930812756482163_<38>

P86 = 18801394593718690635972065355070083787495002798358052698294076860191499763907183853901_<86>

Jan 27, 2007

By anonymous / GMP-ECM B1=250000, MSieve v1.16

(88·10¹⁹⁴-7)/9 = 9(7)₁₉₄_<195> = 43 · 23003 · 634535111927_<12> · 1951393022626261924751_<22> · 547570844499373857530554471573_<30> · C127

C127 = P32 · P95

P32 = 48107124890599585578495748781261_<32>

P95 = 30306592044099494833296625144191873374602388878007797681916634756640525090115817870813053056673_<95>

(2·10¹⁹¹-17)/3 = (6)₁₉₀1_<191> = 7 · 173 · 971 · 2927 · 14214359 · 100193434669659501271_<21> · 1602281856559924955652817548643_<31> · C124

C124 = P31 · P94

P31 = 1644531636700037764624359507241_<31>

P94 = 5161488372639752825103822995595924817290232477476092481206743069772069525520002906576390320729_<94>

(37·10¹⁹⁵-1)/9 = 4(1)₁₉₅_<196> = 71 · 113 · 46807 · 3384119 · 486904141 · 417295439123_<12> · 4293419064773_<13> · 97703178491495521151_<20> · C128

C128 = P27 · P31 · P35 · P37

P27 = 196191505225250176990551527_<27>

P31 = 1761861763144099356621413608877_<31>

P35 = 20971151211185507399381645857980401_<35>

P37 = 5235915257838810422327427243635140559_<37>

Jan 26, 2007 (2nd)

By Yousuke Koide / GMP-ECM

10¹¹²²+1 = 1(0)₁₁₂₁1_<1123> = 89 · 101 · 409 · 3061 · 7481 · 9901 · 1867009 · 5969449 · 28559389 · 134703241 · 259377229 · 330669109 · 1052788969_<10> · 1056689261_<10> · 1491383821_<10> · 5419170769_<10> · 155623169021_<12> · 225974065503889_<15> · 789390798020221_<15> · 2324557465671829_<16> · 2361000305507449_<16> · 44398000479007997569751764249_<29> · [86753591722429179196277499864388589956480152295384249796160875422130713714757701234774165691602257489604032643162429671366217011869609438248577758376700876992475958101904038555335751011999472619586747569193118442466419043654128126430212767873933904801118916504403436000264521920016711367535910291073154001_<305>] · C617

C617 = P34 · C584

P34 = 1626069667027811730097890497028709_<34>

C584 = [38024895493148854800653422613283099215921829542069685361376149530438607273756761856080690798460858306013738403327210096775753858364955072111700913685550086323551314496528572109201746210331371495892159739537730861707388507713450420982812460820500955660272354154047565719880526386831017892454808856584932783761589855269118267078394398844310325020537409424027865400201612007047186241443549154632450444461827579970147399485860432046334343781990972197401352137429710056905803889915605437642224194276297147589246706218777067781645257302547483648186681711700509728333708023948604899809154361_<584>]

10¹¹³⁴+1 = 1(0)₁₁₃₃1_<1135> = 29 · 101 · 109 · 281 · 1009 · 2269 · 9901 · 138349 · 153469 · 226549 · 2925721 · 121499449 · 605070649 · 43266855241_<11> · 999999000001_<12> · 4458192223320340849_<19> · 59779577156334533866654838281_<29> · 165358820733883770736233015527320175869593121_<45> · 22906246896437231227899575633620139766044690040039603689929_<59> · 341796090604674881849636380229010216626944264336893367139245334739710314141368913850637159182300704681_<102> · [6047454835259897495291763612688187307633783265817592232229921776128879618476797113843402906053007327639026397234531321020396264462376520701053491628306270734047741866573281_<172>] · C631

C631 = P31 · C600

P31 = 9391041808951630899634282002781_<31>

C600 = [560621332357238934616966299475879185594948023213484989719849902347321607522840870868240982017830818609496576717751001846384992466019177575772113466002928362881638102389245311752023261289995871190888731510926552515187860263342389008022937210983038113151859183801393207845341298386085668783815342356365241094283815795715052041003342637144443511871673205339970315039695946256107631941004511626733919690430244484123521955214196537703861419349594802139614911527667460644786375501470464939842659073308365090467618293426438485316382071831630280526263470317231189296842007453423797425254132235918123995126309_<600>]

10¹¹⁷⁶+1 = 1(0)₁₁₇₅1_<1177> = 17 · 113 · 337 · 54881 · 5882353 · 90982417 · 9999999900000001_<16> · 243827582384762881_<18> · 73765755896403138401_<20> · 403539336813078648113_<21> · 119968369144846370226083377_<27> · 2070270028985341766616009080161_<31> · 5649333362757164788488040397332687608183771313_<46> · 1433319827159466789806966856379479179916136529424792832495021393_<64> · [7992725630817993387509447658266753245639852185667964923325577122343436495149387850592327530913518038942862729080180818453049855292323904941844008543186707256609661088744711417696766636212293916732420331335060909121431187023889518420170993615058113539941380716719809_<265>] · C647

C647 = P31 · P616

P31 = 6026493503971642113374043042529_<31>

P616 = 7479886445735310298212281574509336546511732856430925087547061188016676845865995264958848117161322132078362683907579847337705836608461661471467610052096672642482112477495893044762678819315272269257998380984735846571207890240541285222802753354488658169465262832949126119749586317994111722121309522760462519340189609610673636927758365329167905230525383356760951540829820516095240537115382434110142048426496301179744763138100240260075123226913663798333509484702964612409358454187157356940022441684271671949641382237872243785316464905028255039958968839518027891677204894071733245344036271799385225297918407032044365486097_<616>

10¹¹⁹⁷+1 = 1(0)₁₁₉₆1_<1198> = 7² · 11 · 13 · 19² · 127 · 2053 · 2689 · 52579 · 459691 · 909091 · 1458973 · 3014047 · 5274739 · 4410785971_<10> · 2911579215499_<13> · 425991366045253_<15> · 909090909090909091_<18> · 247025236977306025681323889_<27> · 307010852070382484317401373_<27> · 1512142910568778709935813681_<28> · 189772422673235585874485732659_<30> · 753201806271328462547977919407_<30> · 61828645758322140842666144519962696417487_<41> · 72021403933746126426491665754465510017877_<41> · 17499101101496101893247811440257935152097401_<44> · 9284668536078237580134472469990637899155265743957_<49> · 6508684267533856834852965580950145565983063793936631379_<55> · 13147963643704652632557279758698587212033283223333451187877069162714784603584406816150353817835190742091970171_<110> · C615

C615 = P30 · C585

P30 = 237496748126669166794404728277_<30>

C585 = [922922847813274238465132665036974822845258340644871405049259288157037278960832039185277361106989442033855182445021438441460557399754790305129137620361964345260321681895127537725577401157304125322364765852776880361958443014430688589178204497272072060536416186604376537044072702325440583554858414064745202261449782554748371997504328009626327185383358681482752898447663266556749331693716692867547107530177574318083085484173010253581739509297324615785328784094793245470981713427472307156882602024997235453435574170873703830526131287425439986638786476519308647363490124573515449894635706459_<585>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 26, 2007

By anonymous / GMP-ECM

2·10¹⁷⁹-9 = 1(9)₁₇₈1_<180> = 11 · 109 · 1531 · 197084090167072070444501_<24> · 30192185167289557139962813541_<29> · C122

C122 = P32 · C91

P32 = 11175180923359872868625684424731_<32>

C91 = [1638456613705646625512724389739829497429579295062517050049568260367385691018719269270812409_<91>]

(7·10¹⁸⁵-61)/9 = (7)₁₈₄1_<185> = 15869070719_<11> · 221773283827_<12> · 277298503527337722497_<21> · 6105120015064145026321_<22> · C122

C122 = P27 · C95

P27 = 148620272450318305620892247_<27>

C95 = [87836500178362012339391534087557870391705073829131196795608369383843280519245566419346506803953_<95>]

(46·10¹⁸⁵-1)/9 = 5(1)₁₈₅_<186> = 408259642487330101945035612397_<30> · 3203645235931038405785927946751_<31> · C126

C126 = P29 · P97

P29 = 42225614244343951163609141599_<29>

P97 = 9254617593308380520522644377019828568736648765423288773779267862870153521377141934322650187063587_<97>

Jan 25, 2007

By Bruce Dodson / GMP-ECM

10³¹⁹+1 = 1(0)₃₁₈1_<320> = 11² · 23 · 59 · 1277 · 4093 · 8779 · 357281 · 49561573447_<11> · 154083204930662557781201849_<27> · C261

C261 = P48 · P213

P48 = 776277205967881079419436133930781972785940099183_<48>

P213 = 626657074575157591670286302317367581085608444623672462325497948095754924038193523465028605939320242167544103268138744951272220715162590347092606720139597682209974278152746342271155492839334102785932336774383913103_<213>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 24, 2007

By suberi / GGNFS-0.77.1-20060513-pentium4

(65·10¹⁵²+43)/9 = 7(2)₁₅₁7_<153> = C153

C153 = P67 · P87

P67 = 6550213397685364775986550762989701971314721157128662740183066777671_<67>

P87 = 110259342463168051908664963775205452537386095869746869361395515038990560570276567780437_<87>

Number: 72227_152
N=722222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227
  ( 153 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=6550213397685364775986550762989701971314721157128662740183066777671 (pp67)
 r2=110259342463168051908664963775205452537386095869746869361395515038990560570276567780437 (pp87)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 43.65 hours.
Scaled time: 28.11 units (timescale=0.644).
Factorization parameters were as follows:
n: 722222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227
m: 1000000000000000000000000000000
c5: 6500
c0: 43
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 100000
)
Primes: RFBsize:176302, AFBsize:176528, largePrimes:5513675 encountered
Relations: rels:5400593, finalFF:452520
Max relations in full relation-set: 28
Initial matrix: 352897 x 452520 with sparse part having weight 40973848.
Pruned matrix : 314268 x 316096 with weight 25151271.
Total sieving time: 38.70 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 4.53 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 43.65 hours.
 --------- CPU info (if available) ----------

Jan 22, 2007

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(64·10¹⁹⁹-1)/9 = 7(1)₁₉₉_<200> = 213858623010582669308138843_<27> · C174

C174 = P37 · P138

P37 = 1077191248228337884969877852893668437_<37>

P138 = 308686674498773596485102045607380792674577494444212073502216332070219814475881776793364497854287456457170773816915942831194015229438823921_<138>

Jan 22, 2007 (2nd)

By anonymous / GGNFS-0.77.1-20060513-athlon-xp

(88·10¹⁹⁹-7)/9 = 9(7)₁₉₉_<200> = 4519 · 896656869650457347_<18> · 8483312795598774487816778893_<28> · 1543835570469777214012062083587_<31> · C121

C121 = P48 · P73

P48 = 914873563129692842500063828197206474139300829067_<48>

P73 = 2013927998159455384275057837246928675939493887607041425750660883017786337_<73>

Jan 22, 2007

By suberi / GGNFS-0.77.1-20060513-pentium4

(46·10¹⁵⁶-1)/9 = 5(1)₁₅₆_<157> = C157

C157 = P71 · P86

P71 = 67019244981090782189600282925830264926764069416668648055858406658449659_<71>

P86 = 76263334696670950528282975338822886018690472664746650628843107889406583521316114469029_<86>

Number: 51111_156
N=5111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
  ( 157 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=67019244981090782189600282925830264926764069416668648055858406658449659 (pp71)
 r2=76263334696670950528282975338822886018690472664746650628843107889406583521316114469029 (pp86)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 51.94 hours.
Scaled time: 32.88 units (timescale=0.633).
Factorization parameters were as follows:
n: 5111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
m: 10000000000000000000000000000000
c5: 460
c0: -1
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:216621, largePrimes:5675467 encountered
Relations: rels:5682667, finalFF:589446
Max relations in full relation-set: 28
Initial matrix: 433504 x 589446 with sparse part having weight 47631889.
Pruned matrix : 344252 x 346483 with weight 29516259.
Total sieving time: 45.09 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 6.28 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 51.94 hours.
 --------- CPU info (if available) ----------

Jan 20, 2007 (3rd)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(32·10¹⁵²-23)/9 = 3(5)₁₅₁3_<153> = 166436508169_<12> · C142

C142 = P56 · P86

P56 = 24983431076103788248780535505480205082016621953205041909_<56>

P86 = 85508008469422781728401987797180068200107544091935710529435160405484716934720561999893_<86>

Number: trial
N=2136283436050723047271475802452405123406573092123782739942106166426777071226645962304450583198389424242352782711578731736541539865039918515737
  ( 142 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=24983431076103788248780535505480205082016621953205041909 (pp56)
 r2=85508008469422781728401987797180068200107544091935710529435160405484716934720561999893 (pp86)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 48.45 hours.
Scaled time: 26.60 units (timescale=0.549).
Factorization parameters were as follows:
n: 2136283436050723047271475802452405123406573092123782739942106166426777071226645962304450583198389424242352782711578731736541539865039918515737
m: 2000000000000000000000000000000
c5: 100
c0: -23
skew: 1
type: snfsFactor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176568, largePrimes:5365061 encountered
Relations: rels:5173821, finalFF:395912
Max relations in full relation-set: 0
Initial matrix: 352934 x 395912 with sparse part having weight 33592138.
Pruned matrix : 332328 x 334156 with weight 25008927.
Total sieving time: 38.94 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 8.79 hours.
Time per square root: 0.36 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 48.45 hours.
 --------- CPU info (if available) ----------

Jan 20, 2007 (2nd)

By anonymous / GMP-ECM 6.0.1 B1=250000

(14·10¹⁵²-41)/9 = 1(5)₁₅₁1_<153> = 151 · 973057 · C145

C145 = P33 · C112

P33 = 847196941648551132106333324010269_<33>

C112 = [1249642878021033284825168208794036075612473963907528490275936932677995158635356633750195668907903252864903462797_<112>]

Jan 20, 2007

By Philippe Strohl / GMP-ECM 6.1.1, Msieve v. 1.15

(7·10¹⁶⁶-43)/9 = (7)₁₆₅3_<166> = 3 · 7481 · 13757 · 148473482141539_<15> · 853488537369761_<15> · C129

C129 = P32 · P98

P32 = 14538253415215247868020585242079_<32>

P98 = 13673889379613398816674163054944244938766219062696794576223016527492008237104180821858195847688303_<98>

(7·10¹⁶⁷-43)/9 = (7)₁₆₆3_<167> = 53 · 229 · 3067 · 2967427 · 50588827 · C146

C146 = P38 · P108

P38 = 47278220151991681544364704654234008633_<38>

P108 = 294397847651944968902502340312163444716371421074662099661707779901800819546932063167621491168426789665148391_<108>

(7·10¹⁶⁹-43)/9 = (7)₁₆₈3_<169> = 3² · 113 · 49991 · C162

C162 = P31 · C131

P31 = 5632442647674936588605121832519_<31>

C131 = [27161013734198267779787441623856865261526769714349621384721227945530504045181223735394220143911476359430775105460879711466662180261_<131>]

(7·10¹⁷⁴-43)/9 = (7)₁₇₃3_<174> = 2763763 · 684763151954031346584259_<24> · C144

C144 = P40 · P41 · P64

P40 = 2473302413612770799643152842693818608929_<40>

P41 = 48717161252159813125322496014384853177479_<41>

P64 = 3410791362646423058561965131274823744860566964407906465017976259_<64>

Msieve v. 1.15
Thu Jan 18 12:37:58 2007  random seeds: 1cc05034 008c3284
Thu Jan 18 12:37:58 2007  factoring 166164072811519690832461794293729536181397138309018877229323442903299839132241567459806526348130335471061 (105 digits)
Thu Jan 18 12:37:59 2007  using multiplier of 5
Thu Jan 18 12:37:59 2007  sieve interval: 9 blocks of size 65536
Thu Jan 18 12:37:59 2007  processing polynomials in batches of 6
Thu Jan 18 12:37:59 2007  using a sieve bound of 3877483 (137335 primes)
Thu Jan 18 12:37:59 2007  using large prime bound of 581622450 (29 bits)
Thu Jan 18 12:37:59 2007  using double large prime bound of 5975222047534050 (44-53 bits)
Thu Jan 18 12:37:59 2007  using trial factoring cutoff of 60 bits
Thu Jan 18 12:37:59 2007  polynomial 'A' values have 14 factors
Thu Jan 18 12:38:05 2007  restarting with 28567 full and 1880708 partial relations
Thu Jan 18 17:57:13 2007  137489 relations (31331 full + 106158 combined from 2063696 partial), need 137431
Thu Jan 18 17:58:20 2007  begin with 2095027 relations
Thu Jan 18 17:58:39 2007  reduce to 368362 relations in 12 passes
Thu Jan 18 17:58:39 2007  attempting to read 368362 relations
Thu Jan 18 17:59:35 2007  recovered 368362 relations
Thu Jan 18 17:59:36 2007  recovered 362031 polynomials
Thu Jan 18 17:59:36 2007  attempting to build 137489 cycles
Thu Jan 18 17:59:36 2007  found 137489 cycles in 6 passes
Thu Jan 18 17:59:36 2007  distribution of cycle lengths:
Thu Jan 18 17:59:36 2007     length 1 : 31331
Thu Jan 18 17:59:36 2007     length 2 : 22747
Thu Jan 18 17:59:36 2007     length 3 : 22468
Thu Jan 18 17:59:36 2007     length 4 : 19018
Thu Jan 18 17:59:36 2007     length 5 : 14682
Thu Jan 18 17:59:36 2007     length 6 : 10283
Thu Jan 18 17:59:36 2007     length 7 : 6972
Thu Jan 18 17:59:36 2007     length 9+: 9988
Thu Jan 18 17:59:36 2007  largest cycle: 25 relations
Thu Jan 18 17:59:38 2007  matrix is 137335 x 137489 with weight 9928481 (avg 72.21/col)
Thu Jan 18 17:59:39 2007  filtering completed in 3 passes
Thu Jan 18 17:59:39 2007  matrix is 135618 x 135682 with weight 9726461 (avg 71.69/col)
Thu Jan 18 17:59:40 2007  saving the first 48 matrix rows for later
Thu Jan 18 17:59:41 2007  matrix is 135570 x 135682 with weight 7744943 (avg 57.08/col)
Thu Jan 18 17:59:41 2007  matrix includes 32 packed rows
Thu Jan 18 18:14:22 2007  lanczos halted after 2145 iterations
Thu Jan 18 18:14:24 2007  recovered 16 nontrivial dependencies
Thu Jan 18 18:14:25 2007  prp41 factor: 48717161252159813125322496014384853177479
Thu Jan 18 18:14:25 2007  prp64 factor: 3410791362646423058561965131274823744860566964407906465017976259

Jan 19, 2007

By suberi / GGNFS-0.77.1-20060513-pentium4

(82·10¹⁵²-1)/9 = 9(1)₁₅₂_<153> = 62011 · 1325918057_<10> · C140

C140 = P50 · P90

P50 = 22550069509713664559026749569442993274151819905367_<50>

P90 = 491403265370574320319518339345132528573678706318350804575322001861825388135684665475793579_<90>

Number: 91111_152
N=11081177791406720661140565361292085684700961206642439012506081693013377229211683049809107096356752560306216353598571706777675679193006238493
  ( 140 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=22550069509713664559026749569442993274151819905367 (pp50)
 r2=491403265370574320319518339345132528573678706318350804575322001861825388135684665475793579 (pp90)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 50.37 hours.
Scaled time: 31.94 units (timescale=0.634).
Factorization parameters were as follows:
n: 11081177791406720661140565361292085684700961206642439012506081693013377229211683049809107096356752560306216353598571706777675679193006238493
m: 1000000000000000000000000000000
c5: 8200
c0: -1
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2700001)
Primes: RFBsize:176302, AFBsize:176209, largePrimes:5716740 encountered
Relations: rels:5645464, finalFF:433017
Max relations in full relation-set: 28
Initial matrix: 352578 x 433017 with sparse part having weight 45882923.
Pruned matrix : 324886 x 326712 with weight 31719937.
Total sieving time: 43.89 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 5.88 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 50.37 hours.
 --------- CPU info (if available) ----------

Jan 18, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

5·10¹⁵²-1 = 4(9)₁₅₂_<153> = 6855481 · 2245341102733892629_<19> · C128

C128 = P54 · P74

P54 = 744672514925099317753393598897750509322858911004792161_<54>

P74 = 43619875480449736340301463870436173570992711432762799275899219166322466491_<74>

Number: trial
N=32482522374746180058621483531208610399036688675149812231189223879705895716746882551984274642698225023160685803137554338341977051
  ( 128 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=744672514925099317753393598897750509322858911004792161 (pp54)
 r2=43619875480449736340301463870436173570992711432762799275899219166322466491 (pp74)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 47.42 hours.
Scaled time: 24.85 units (timescale=0.524).
Factorization parameters were as follows:
n: 32482522374746180058621483531208610399036688675149812231189223879705895716746882551984274642698225023160685803137554338341977051
m: 1000000000000000000000000000000
c5: 500
c0: -1
skew: 1
type: snfsFactor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:175758, largePrimes:5321331 encountered
Relations: rels:5123801, finalFF:397027
Max relations in full relation-set: 0
Initial matrix: 352126 x 397027 with sparse part having weight 34163740.
Pruned matrix : 330330 x 332154 with weight 25010739.
Total sieving time: 37.60 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 9.06 hours.
Time per square root: 0.40 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 47.42 hours.
 --------- CPU info (if available) ----------

Jan 15, 2007 (2nd)

By Yousuke Koide / GMP-ECM

(10¹⁰⁸³-1)/9 = (1)₁₀₈₃_<1083> = 3 · 37 · 21319 · 10749631 · 81671197 · 14830831597_<11> · 100110048074161_<15> · 1111111111111111111_<19> · 88231338953639484307_<20> · 103143975536225777711_<21> · 1290118416840734700343441_<25> · 2747268108721464854672161_<25> · 3931123022305129377976519_<25> · 4604283618329785428488803_<25> · 11614395396735967816534625117_<29> · 220706363362058009698248377980921202870796191_<45> · [191052108988079642161639478453077817431939492714409561224107609992762821015057864360563144173296784309543301342314616278756836677316469309622645791578584595972760708661277734651667182128879712026387_<198>] · C612

C612 = P33 · C579

P33 = 281997552115245416778864294482683_<33>

C579 = [402086827149525774203662574494762629781977575683448426528585129955793038573903462046000944607841346127321128768455654455924188986573902734362553095147618565475236745929228030480592036362734811733853089917782754468236923798842212827701672228437829439017037811329791783886407486347321166723616477001381322703982864461430430770579143530473025432640645589916634282025494866497100131324334144862038619504404398219865858608567272827886724898522016094545757984781148617753287717459033960492246352633577245622244313202654308552812851000246392034695534030715521754959243493574827942501717_<579>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 15, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(7·10¹⁵²-1)/3 = 2(3)₁₅₂_<153> = 83 · 113 · 727 · 2451016031350978753621_<22> · C125

C125 = P44 · P81

P44 = 26409294675329952520047051769456344988144483_<44>

P81 = 528667830402888076655586260487501175538292363907075027865455219436299973499985007_<81>

Number: trial
N=13961744518477230470350606331141294339438120672030969453053758445119353748825714158062698843568975300693893288090793249766381
  ( 125 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=26409294675329952520047051769456344988144483 (pp44)
 r2=528667830402888076655586260487501175538292363907075027865455219436299973499985007 (pp81)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 43.19 hours.
Scaled time: 22.16 units (timescale=0.513).
Factorization parameters were as follows:
n: 13961744518477230470350606331141294339438120672030969453053758445119353748825714158062698843568975300693893288090793249766381
m: 1000000000000000000000000000000
c5: 700
c0: -1
skew: 1
type: snfsFactor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:176098, largePrimes:5270546 encountered
Relations: rels:5044165, finalFF:395396
Max relations in full relation-set: 0
Initial matrix: 352467 x 395396 with sparse part having weight 33232459.
Pruned matrix : 329623 x 331449 with weight 23770136.
Total sieving time: 33.68 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 8.80 hours.
Time per square root: 0.39 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 43.19 hours.
 --------- CPU info (if available) ----------

Jan 14, 2007

By suberi / GGNFS-0.77.1-20060513-pentium4

(89·10¹⁵²+1)/9 = 9(8)₁₅₁9_<153> = C153

C153 = P44 · P110

P44 = 10190419905946011268576405253557768498330481_<44>

P110 = 97041034424094909444203541070911753967506741360316917336324363078053621728588507016698294822884773453384829769_<110>

Number: 98889_152
N=988888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
  ( 153 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=10190419905946011268576405253557768498330481 (pp44)
 r2=97041034424094909444203541070911753967506741360316917336324363078053621728588507016698294822884773453384829769 (pp110)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 43.91 hours.
Scaled time: 25.77 units (timescale=0.587).
Factorization parameters were as follows:
n: 988888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889
m: 1000000000000000000000000000000
c5: 8900
c0: 1
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2300001)
Primes: RFBsize:176302, AFBsize:176708, largePrimes:5432566 encountered
Relations: rels:5283059, finalFF:427140
Max relations in full relation-set: 28
Initial matrix: 353077 x 427140 with sparse part having weight 38289802.
Pruned matrix : 323868 x 325697 with weight 25340331.
Total sieving time: 38.58 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 4.83 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 43.91 hours.
 --------- CPU info (if available) ----------

Jan 13, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(82·10¹⁵¹+71)/9 = 9(1)₁₅₀9_<152> = 3 · 11 · C151

C151 = P44 · P107

P44 = 35069973450053660193547829746422455292614743_<44>

P107 = 78726685233305657195869491293886236269349095897975770932964245045062337031935266807921069259133902472143401_<107>

Number: trial
N=2760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760943
  ( 151 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=35069973450053660193547829746422455292614743 (pp44)
 r2=78726685233305657195869491293886236269349095897975770932964245045062337031935266807921069259133902472143401 (pp107)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 48.94 hours.
Scaled time: 26.53 units (timescale=0.542).
Factorization parameters were as follows:
n: 2760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760943
m: 1000000000000000000000000000000
c5: 820
c0: 71
skew: 1
type: snfsFactor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:177415, largePrimes:5450553 encountered
Relations: rels:5305620, finalFF:400263
Max relations in full relation-set: 0
Initial matrix: 353784 x 400263 with sparse part having weight 29574952.
Pruned matrix : 328941 x 330773 with weight 22211379.
Total sieving time: 39.83 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 8.35 hours.
Time per square root: 0.39 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 48.94 hours.
 --------- CPU info (if available) ----------

Jan 12, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

10¹⁷⁴+9 = 1(0)₁₇₃9_<175> = 17 · 61 · 1549 · 2389 · 100193 · 322986173 · 6165013601203081_<16> · C136

C136 = P60 · P76

P60 = 208421712381864306682687832510484289595729702062678553885057_<60>

P76 = 6266937537962105847323092604694692272408337913842644374735743827566692617849_<76>

Number: 10009_174
N=1306165853052246849781899785761522612064909196147670902104619894369304705937455838360831479554162941730696135578839680075251560772582393
  ( 136 digits)
SNFS difficulty: 175 digits.
Divisors found:
 r1=208421712381864306682687832510484289595729702062678553885057 (pp60)
 r2=6266937537962105847323092604694692272408337913842644374735743827566692617849 (pp76)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 377.97 hours.
Scaled time: 255.13 units (timescale=0.675).
Factorization parameters were as follows:
name: 10009_174
n: 1306165853052246849781899785761522612064909196147670902104619894369304705937455838360831479554162941730696135578839680075251560772582393
m: 100000000000000000000000000000000000
c5: 1
c0: 90
skew: 4
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 11100001)
Primes: RFBsize:501962, AFBsize:502106, largePrimes:6479175 encountered
Relations: rels:6943230, finalFF:1125572
Max relations in full relation-set: 0
Initial matrix: 1004132 x 1125572 with sparse part having weight 67043105.
Pruned matrix : 899940 x 905024 with weight 52364715.
Total sieving time: 323.38 hours.
Total relation processing time: 1.57 hours.
Matrix solve time: 52.66 hours.
Time per square root: 0.36 hours.
Prototype def-par.txt line would be:
snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 377.97 hours.
 --------- CPU info (if available) ----------

Jan 11, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(71·10¹⁵¹-17)/9 = 7(8)₁₅₀7_<152> = 7 · 11 · C151

C151 = P31 · P120

P31 = 2205331001349523573387368105769_<31>

P120 = 464570181938256034584375771245098460597040578279992603056301171490975801434203173520421749936099623719003021600191268699_<120>

Number: trial
N=1024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531
  ( 151 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=2205331001349523573387368105769 (pp31)
 r2=464570181938256034584375771245098460597040578279992603056301171490975801434203173520421749936099623719003021600191268699 (pp120)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 56.86 hours.
Scaled time: 27.41 units (timescale=0.482).
Factorization parameters were as follows:
n: 1024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531
m: 1000000000000000000000000000000
c5: 710
c0: -17
skew: 1
type: snfsFactor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2300001)
Primes: RFBsize:176302, AFBsize:176394, largePrimes:5541572 encountered
Relations: rels:5380892, finalFF:396083
Max relations in full relation-set: 0
Initial matrix: 352763 x 396083 with sparse part having weight 35361529.
Pruned matrix : 336068 x 337895 with weight 27207539.
Total sieving time: 46.19 hours.
Total relation processing time: 0.48 hours.
Matrix solve time: 9.73 hours.
Time per square root: 0.47 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 56.86 hours.
 --------- CPU info (if available) ----------

Jan 9, 2007

By Alexander Mkrtychyan / ECM 6.1.1 B1=250000, GGNFS gnfs

(13·10¹⁵²-31)/9 = 1(4)₁₅₁1_<153>= 3 · 19 · 13897843 · 1472439017099_<13> · C132

C132 = P29 · P36 · P67

P29 = 69203916985256093273443311767_<29>

P36 = 348036351261652831474816398956189791_<36>

P67 = 5141454366009327072515341569204717595183088932017476504080654912297_<67>

Jan 8, 2007 (2nd)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(32·10¹⁵¹-23)/9 = 3(5)₁₅₀3_<152> = 3³ · 11 · 751 · C147

C147 = P35 · P49 · P63

P35 = 29704376250087176089384555018418717_<35>

P49 = 7329957724845526430867535194461391003844188206139_<49>

P63 = 732131639319491982759033718127556933102481696860560835703262873_<63>

Number: trial
N=159408355887124935800775422021168433359585896943494221198023535647444509702240135736215037886882834360271851024921005687391247385329350117040603799
  ( 147 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=29704376250087176089384555018418717 (pp35)
 r2=7329957724845526430867535194461391003844188206139 (pp49)
 r3=732131639319491982759033718127556933102481696860560835703262873 (pp63)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 42.66 hours.
Scaled time: 23.16 units (timescale=0.543).
Factorization parameters were as follows:
n: 159408355887124935800775422021168433359585896943494221198023535647444509702240135736215037886882834360271851024921005687391247385329350117040603799
m: 2000000000000000000000000000000
c5: 10
c0: -23
skew: 1.18
type: snfsFactor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:176848, largePrimes:5314675 encountered
Relations: rels:5109303, finalFF:397925
Max relations in full relation-set: 0
Initial matrix: 353216 x 397925 with sparse part having weight 34108941.
Pruned matrix : 329641 x 331471 with weight 24727169.
Total sieving time: 33.39 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 8.56 hours.
Time per square root: 0.40 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 42.66 hours.
 --------- CPU info (if available) ----------

Jan 8, 2007

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(22·10¹⁹⁹-1)/3 = 7(3)₁₉₉_<200> = C200

C200 = P37 · C164

P37 = 3916191119470963292419684811737586897_<37>

C164 = [18725677857938635102800293854827076679431418635663009851050014378555511187283752984298513248021481688538630054612852943075905187223262519297988713024848150252683589_<164>]

Jan 6, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(68·10¹⁵¹+13)/9 = 7(5)₁₅₀7_<152> = 7 · 11² · 47419 · 12673998341_<11> · C135

C135 = P65 · P70

P65 = 49485565672041586998733670851755250709829332943434100817742227397_<65>

P70 = 2999427830798455535060535857115593476513217672800509841431136058898137_<70>

Number: trial
N=148428382899526212777811198132944467792004330764376905321699883663179315020730966778383238234201544317147463027711347263226731913659389
  ( 135 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=49485565672041586998733670851755250709829332943434100817742227397 (pp65)
 r2=2999427830798455535060535857115593476513217672800509841431136058898137 (pp70)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 49.49 hours.
Scaled time: 26.87 units (timescale=0.543).
Factorization parameters were as follows:
n: 148428382899526212777811198132944467792004330764376905321699883663179315020730966778383238234201544317147463027711347263226731913659389
m: 1000000000000000000000000000000
c5: 680
c0: 13
skew: 1
type: snfsFactor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1
)
Primes: RFBsize:176302, AFBsize:176093, largePrimes:5609088 encountered
Relations: rels:5535765, finalFF:399520
Max relations in full relation-set: 0
Initial matrix: 352462 x 399520 with sparse part having weight 27003417.
Pruned matrix : 328388 x 330214 with weight 20757565.
Total sieving time: 44.17 hours.
Total relation processing time: 0.46 hours.
Matrix solve time: 4.47 hours.
Time per square root: 0.39 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 49.49 hours.
 --------- CPU info (if available) ----------

Jan 5, 2007

By Alexander Mkrtychyan / GMP-ECM 6.1.1

2·10¹⁵⁴-1 = 1(9)₁₅₄_<155> = 7 · 47 · 6473 · 60889 · 820757286744157311721_<21> · C123

C123 = P30 · P93

P30 = 709409658839905576587856324121_<30>

P93 = 264897466561486457459040040838987171311953866242931984277806029435709662518462889628767297703_<93>

(8·10¹⁵⁷-17)/9 = (8)₁₅₆7_<157> = 7 · C157

C157 = P28 · C129

P28 = 8739994595235952825155053837_<28>

C129 = [145290852986733231960131889761460491703794538807068334652232282714626655166495302127159129035785015114582751752183571455452299093_<129>]

Jan 4, 2007 (3rd)

By Yousuke Koide / GMP-ECM

(10⁷⁶⁷-1)/9 = (1)₇₆₇_<767> = 53 · 79 · 305267 · 52306333 · 265371653 · 22214840363_<11> · 2559647034361_<13> · 4340876285657460212144534289928559826755746751_<46> · C673

C673 = P40 · C633

P40 = 2853501516303948010794020280793592455507_<40>

C633 = [889174648697326939177684178268996371003045246228078861746645062156730400269719384944790989153058757148303931075688667206199979737929977594118405280407892375436810251127379517901088006159225027254825092728128056986443222555451048911731324918821013872861811819723206169438781888017389966772691574054134710717924112989922189761624097116462890343930462811061144042405510972749980054180919764197806156130640326602991234046425531622069602350611573632172807373054802126586780509133235592708043145380986200739118832686526332661035841701755113675284212097858014641864160740582669607631627484363510546376918980352636496474171658410323177124641_<633>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 4, 2007 (2nd)

By Alexander Mkrtychyan / GMP-ECM 6.1.1 B1=250000

(71·10¹⁹⁸-17)/9 = 7(8)₁₉₇7_<199> = 3 · 214174957 · C191

C191 = P31 · C160

P31 = 7028572982139370167790480255649_<31>

C160 = [1746862562467380248119030911967387426321458529683450495371415590591659222234729701631478386438280766700113951265045633708921823699119520795223624506675796515953_<160>]

Jan 4, 2007

By Alexander Mkrtychyan / ggnfs-0.77.1-20060513-win32-athlon-xp gnfs

(71·10¹⁸²-17)/9 = 7(8)₁₈₁7_<183> = 379 · 1021 · 2254085732632417_<16> · 70354500661406300509_<20> · 12897936240962970721879_<23> · C120

C120 = P44 · P77

P44 = 13855196374270107186027526900439874151942013_<44>

P77 = 71937552978293304611770250967086159641208638041183449177873097949335842345303_<77>

r1=13855196374270107186027526900439874151942013 (pp44)                                 
r2=71937552978293304611770250967086159641208638041183449177873097949335842345303 (pp77)

skew: 44899.59
# norm 2.44e+016
c5: 36540
c4: -12653216212
c3: 487308661251077
c2: 24468059663304010833
c1: 43344197537957658137219
c0: -2793341395855198500654392085
# alpha -5.46
Y1: 1416246269647
Y0: -122225074088335592900342
# Murphy_E 2.94e-010
# M 892389320392560569094612128195562317644209955514499986657591571589603307854782580578088218581614492481306060370855465122
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4

special-q: [2000000;2708819)U[3000000;3256093)

maxrelsinff=14
rels:9724854, initialFF:0, finalFF:772267                                 
Pruning matrix with wt=0.700                                              
Initial matrix is 664491 x 772267 with sparse part having weight 50696051.
(total weight is 89193220)                                                
Matrix pruned to 610266 x 613652 with weight 33681497.                    

factors found on 0 dependency

Jan 3, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(64·10¹⁵¹+53)/9 = 7(1)₁₅₀7_<152> = 7 · 11 · 16094242777874151616807_<23> · C128

C128 = P55 · P74

P55 = 1203829898530831982368976018578666612940790262374639019_<55>

P74 = 47666258705407778643846255032921079760125039476078784971539438996875578437_<74>

Number: trial
N=57382067380675432813932087137355619458933771524799307680083423847570082150658194677901984048504274751332116408746591264695233303
  ( 128 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=1203829898530831982368976018578666612940790262374639019 (pp55)
 r2=47666258705407778643846255032921079760125039476078784971539438996875578437 (pp74)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 54.26 hours.
Scaled time: 27.83 units (timescale=0.513).
Factorization parameters were as follows:
n: 57382067380675432813932087137355619458933771524799307680083423847570082150658194677901984048504274751332116408746591264695233303
m: 2000000000000000000000000000000
c5: 20
c0: 53
skew: 1.22
type: snfsFactor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2200001)
Primes: RFBsize:176302, AFBsize:175293, largePrimes:5554678 encountered
Relations: rels:5471328, finalFF:394558
Max relations in full relation-set: 0
Initial matrix: 351661 x 394558 with sparse part having weight 26795082.
Pruned matrix : 329629 x 331451 with weight 20952925.
Total sieving time: 45.59 hours.
Total relation processing time: 0.51 hours.
Matrix solve time: 7.79 hours.
Time per square root: 0.37 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 54.26 hours.
 --------- CPU info (if available) ----------

Jan 1, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(2·10¹⁵⁷+7)/9 = (2)₁₅₆3_<157> = 3² · 109 · 2617 · 532529 · 1600321 · 10276598863_<11> · C128

C128 = P57 · P72

P57 = 275644563889396195991601548242531083466591268839139865547_<57>

P72 = 358563065522327430052239803536935822255232574805406605801612939291916351_<72>

Number: trial
N=98835959822746937698308102564263258552782657865133587909723978877125659006562567345781266447367330423891517396177228162110858997
  ( 128 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=275644563889396195991601548242531083466591268839139865547 (pp57)
 r2=358563065522327430052239803536935822255232574805406605801612939291916351 (pp72)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 71.01 hours.
Scaled time: 31.96 units (timescale=0.450).
Factorization parameters were as follows:
n: 98835959822746937698308102564263258552782657865133587909723978877125659006562567345781266447367330423891517396177228162110858997
m: 10000000000000000000000000000000
c5: 200
c0: 7
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 1
)
Primes: RFBsize:216816, AFBsize:216921, largePrimes:5627776 encountered
Relations: rels:5564900, finalFF:499188
Max relations in full relation-set: 0
Initial matrix: 433802 x 499188 with sparse part having weight 36071355.
Pruned matrix : 403610 x 405843 with weight 26335382.
Total sieving time: 59.98 hours.
Total relation processing time: 0.55 hours.
Matrix solve time: 10.00 hours.
Time per square root: 0.48 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 71.01 hours.
 --------- CPU info (if available) ----------

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