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
By Sinkiti Sibata / PFGW
(2·102442+7)/9 is prime.
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).
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>
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).
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) ----------
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).
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+
By Sinkiti Sibata / PFGW
7·1012755-9 and 7·1015142-9 are PRPs.
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)
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>
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>
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) ----------
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) ----------
By Sinkiti Sibata / PRIMO
(2·102978-17)/3 is prime.
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) ----------
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>
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.
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+
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)
By Bruce Dodson
(10301-1)/9 is divisible by 1141240390081433457327371568501745249133720840602413587<55>, cofactor is prime.
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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)
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+
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) ----------
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).
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.
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+
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.
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) ----------
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).
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>
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)
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+
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)
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
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+
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) ----------
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+
By Yousuke Koide
(101249-1)/9 is divisible by 3859327619352771895471324837<28>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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>
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.
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) ----------
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+
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>]
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) ----------
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+
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)
By Yousuke Koide
(101509-1)/9 is divisible by 276617318087890951973712854116609<33>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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) ----------
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).
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) ----------
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>
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).
By Sinkiti Sibata / PRIMO
(2·102403+1)/3 is prime.
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.
By Yousuke Koide
(101375-1)/9 is divisible by 584213416911071661540509773751<30>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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.
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)
By Yousuke Koide
(101315-1)/9 is divisible by 155872807295141767753013971998423271<36>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / PRIMO
(2·102362+43)/9 is prime.
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+
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>
By Sinkiti Sibata / PRIMO
(2·102175-17)/3 is prime.
By Sinkiti Sibata / PFGW
2·1012984-7 and 2·1013614-7 are PRP.
By Yousuke Koide
101121+1 is divisible by 69849282640264627005884025897913761023<38>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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+
By Sinkiti Sibata / PFGW
(8·1010717-11)/3, (8·1014673-11)/3, (8·1016754-11)/3 and (8·1017606-11)/3 are PRP.
By suberi / GMP-ECM
(16·10176-61)/9 = 1(7)1751<177> = 3 · 5261 · C173
C173 = P36 · C137
P36 = 817155339792930387676948727914630841<36>
C137 = [13784254841763201401763506838527012403768451779816402753683122065119425484587917320413953839479488490114718629521019279324075409499402757<137>]
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).
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) ----------
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+
By Yousuke Koide
(101177-1)/9 is divisible by 15112598396753272691345143612337643317<38>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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).
By matsui / GMP-ECM
(37·10178-1)/9 = 4(1)178<179> = 7 · 137 · C176
C176 = P33 · C144
P33 = 256606801414902925624321820940911<33>
C144 = [167059987357085613333034797110824057589025658340318711449285988164500386196628719375549643795216399404461119111310119558935462349796606422281239<144>]
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).
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>
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).
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).
By Sinkiti Sibata / PFGW
5·1010820-9 and 5·1014592-9 are PRP.
By Yousuke Koide
(101093-1)/9 is divisible by 199506195135220536755902065305293<33>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Jo Yeong Uk / GMP-ECM
5·10199-9 = 4(9)1981<200> = C200
C200 = P34 · P167
P34 = 1224112416041742410052808832168959<34>
P167 = 40845921783620723265274965609618243098936302659169196754666765677273901878095642440080026040452661066087357309697423682859960350348666458327845592281510888305426519049<167>
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+
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) ----------
By Sinkiti Sibata / PFGW
(22·1011431-7)/3 and (22·1012927-7)/3 are PRP.
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+
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>
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+
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) ----------
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).
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>
By matsui / GMP-ECM
(4·10185-13)/9 = (4)1843<185> = 7 · 1451 · C181
C181 = P33 · C149
P33 = 164277524510786827843488693745099<33>
C149 = [26636298892028694012587941153238062628591187075841112023861911522751253412947765247273184353075516238787560153594780836262462832930974948643067577301<149>]
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+
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.
By Yousuke Koide
(101019-1)/9 is divisible by 1164875952920329463736875905335015089<37>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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>
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!
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.
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+
By Yousuke Koide
101497+1 is divisible by 7016092401376747085885131800303253<34>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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+
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
By Sinitiki Sibata / PFGW
4·1019679-9 is PRP.
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)
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>
By Bruce Dodson
10242+1 is divisible by 209363088773816814667969748813613304559806235889961<51> and cofactor is prime.
Reference: Factoring and Prime Identification (Torbjörn Granlund)
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>
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+
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>
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+
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) ----------
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) ----------
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+
By Sinkiti Sibata / PRIMO
(102153+53)/9 is prime.
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
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+
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).
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+
By Sinkiti Sibata / PRIMO
(22·102159-31)/9 is prime.
By matsui / GMP-ECM
(5·10187-23)/9 = (5)1863<187> = 3 · C187
C187 = P34 · C154
P34 = 1249569676018218532056891295863517<34>
C154 = [1481991670726852801036337564124989580909663768841067210637083024250974479404992726846367777814579781927851301822010278319654383652691909116064846052888903<154>]
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.
By matsui / GMP-ECM
(2·10189+61)/9 = (2)1889<189> = 31 · 107 · C185
C185 = P36 · C149
P36 = 927349548463379812942637190276565777<36>
C149 = [72243462018069324109887983093635000589160560432323063168326829250562665832911989665414796383191130798805708121654081515508917870686847094978760612881<149>]
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) ----------
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+
By Yousuke Koide
101749+1 is divisible by 1107787169378395599401257233239538397<37>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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+
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).
By Yousuke Koide
101079+1 is divisible by 12872791513686398145408033283561<32>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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+
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) ----------
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+
By matsui / GMP-ECM
(2·10186-17)/3 = (6)1851<186> = 577 · C184
C184 = P35 · C149
P35 = 56045655546039900196398563598407527<35>
C149 = [20615362435591879186624607699826768353984778680961983009624827499187120028491903918962048793936194257434728540858949740169821440639266289814167775059<149>]
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>
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+
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).
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+
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).
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) ----------
By Yousuke Koide
(101683-1)/9 is divisible by 2597072697640403933361917807092159369<37>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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+
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).
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+
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) ----------
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.
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>]
By Sinkiti Sibata / GGNFS
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) ----------
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+
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) ----------
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+
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).
By JMB / GMP-ECM
9·10178+7 = 9(0)1777<179> = 149 · C177
C177 = P35 · C143
P35 = 34477381911603229695013790339605181<35>
C143 = [17519510245477803843772234672206519263441432562534062592219996721821259842723144120268391140425192935308257597913633559158414046764815248848903<143>]
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
By matsuix / GMP-ECM
(79·10188-7)/9 = 8(7)188<189> = 17 · 293 · C186
C186 = P32 · C154
P32 = 21765125120660595551469602307679<32>
C154 = [8096678074753473185944039706917079992623437626274897607442886516416138091715794569583278042469134900566577085836441842147205791368296429713363394770501523<154>]
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) ----------
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>
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
By matsuix / GMP-ECM
2·10177+3 = 2(0)1763<178> = 19 · 23 · 107 · C173
C173 = P30 · C144
P30 = 221303620588838744540899263379<30>
C144 = [193275258075082552732257542798544930147975742565477273667881259410088142299640908729176984976444019569373369657540183408799360677960504958362823<144>]
By JMB / GMP-ECM
9·10179+7 = 9(0)1787<180> = 367699 · 313009111137872717<18> · C157
C157 = P34 · P124
P34 = 1707358559977705545311234918697001<34>
P124 = 4580030236511827524816894288626065240922568714998170751384355667293248449614016116415020750898340461128531874477462326513929<124>
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.
By Yousuke Koide
(101309-1)/9 is divisible by 1163807225003295831984120638730881<34>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By matsuix / GMP-ECM
6·10194-1 = 5(9)194<195> = 19 · C194
C194 = P30 · P164
P30 = 552558220648518327302187386107<30>
P164 = 57150443497805430547760194830899991379283534240795388543593799035627131426642721828037543684764910233345763252213386580962086660768427630404724977220097501462854303<164>
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).
By Robert Backstrom / GMP-ECM
2·10165+3 = 2(0)1643<166> = 94136405394950299<17> · C149
C149 = P36 · P113
P36 = 838305023383274289860418539450587157<36>
P113 = 25343717347214324824522098723663613215893017202640604427624247481323908812513490062007103784101162836271292998421<113>
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>
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+
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>]
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+
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>
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).
By matsuix / GMP-ECM
6·10166-1 = 5(9)166<167> = 1415744095201<13> · C155
C155 = P26 · C130
P26 = 12712979409464320156621733<26>
C130 = [3333643448967159954626524687734330724615407100378702091659234658746271899362005594705868470962976554854259399799326518042378430003<130>]
By matsuix / GMP-ECM
(55·10180-1)/9 = 6(1)180<181> = 3 · 23 · C179
C179 = P30 · P150
P30 = 101498619902504222710961733499<30>
P150 = 872591447867335155263871338215982008049920291961559255672354899684344056901549523294371067281499223907198249217989811855244487724718971598186664829281<150>
By matsuix / GMP-ECM
(8·10174-53)/9 = (8)1733<174> = 2309 · C171
C171 = P29 · C143
P29 = 28200513448768426338019164149<29>
C143 = [13651064825355236966422593727849148145450828300351719858603135500864608496173059635187685618753649483887590160393912399962653031892990513454363<143>]
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>
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).
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).
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) ----------
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+
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>
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>
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>
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>
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) ----------
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>
By Torbjörn Granlund
(10843-1)/9 is divisible by 769166959867961874063651865987632601<36>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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>
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) ----------
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>
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).
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.
By Sinkiti Sibata / PFGW
9·1010855-7 is PRP. It is the only PRP of the form 9·10n-7 (10001≤n≤20000).
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).
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) ----------
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) ----------
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).
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) ----------
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+
By matsui / GMP-ECM
(5·10166+7)/3 = 1(6)1659<167> = 38609 · 75787 · C157
C157 = P36 · C122
P36 = 156630091583671031730558418871436461<36>
C122 = [36365559895016016644306948036519971789440001831406469011965021801985852343260659678682774063764231328439857717070493184563<122>]
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>
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+
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>
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>
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+
By Sinkiti Sibata / PRIMO
(85·102960-31)/9 is prime.
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) ----------
By Yousuke Koide
(101265-1)/9 is divisible by 7973059286225484515918622191263721<34>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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+
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
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) ----------
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>]
By Womack
(10309-1)/9 is divisible by 5294796903161592416528456780680376286484870226446771978908657527791<67> and the cofactor is prime.
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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
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) ----------
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).
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+
By matsui / GMP-ECM
(5·10181+7)/3 = 1(6)1809<182> = 19 · 167393 · C175
C175 = P38 · P138
P38 = 15723245803923831841763637804116393807<38>
P138 = 333284910953414496865344254925662573105861000375900329621890909608385992777196180707248922993978075855583628204941899412869920935091825201<138>
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>
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>]
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) ----------
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>
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>
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) ----------
By Sinkiti Sibata / PRIMO
(5·102847+1)/3 is prime.
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.
By Yousuke Koide
101121+1 is divisible by 162578197086018239450239785966343<33>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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) ----------
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).
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+
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+
By Sinkiti Sibata / PRIMO
(26·102688-11)/3 is prime.
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>]
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+
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>
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) ----------
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+
By Kurt Beschorner
10753+1 is divisible by 1756473376297178637489284481878718601<37>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Yousuke Koide
101371+1 is divisible by 127539278618607069275328998039143<33>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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) ----------
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).
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+
By Sinkiti Sibata / PRIMO
(85·102580-13)/9 is prime.
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).
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) ----------
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>
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+
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>
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) ----------
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).
By Yousuke Koide
101073+1 is divisible by 588831771788611721102815421599303<33>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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).
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) ----------
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).
By Sinkiti Sibata / PRIMO
(19·102450-1)/9 is prime.
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.
By anonymous / GMP-ECM
(5·10197+7)/3 = 1(6)1969<198> = 83 · C196
C196 = P32 · P165
P32 = 15064399083367851403807447165139<32>
P165 = 133296530276542123994572514856391958946944378887295148756651456417065116602615650106241786028692598529148978098311741021285646641176103363192439421156437978817430437<165>
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+
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) ----------
By Yousuke Koide
101240+1 is divisible by 15595203791066837732161767737921<32>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By suberi / PRIMO
(49·102340+23)/9 is prime.
(49·102454+23)/9 is prime.
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).
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+
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) ----------
By Sinkiti Sibata / PRIMO
(8·102308+7)/3 is prime.
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!
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+
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) ----------
By Sinkiti Sibata / PRIMO
(13·102215+23)/9 is prime.
By suberi / PRIMO
(32·102488-41)/9 is prime.
6·102749+7 is prime.
(55·102684+17)/9 is prime.
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) ----------
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) ----------
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+
By Sinkiti Sibata / PRIMO
(86·102107+13)/9 is prime.
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) ----------
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>
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>
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) ----------
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+
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) ----------
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.
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+
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) ----------
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>
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).
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+
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) ----------
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
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+
By Yousuke Koide
101009+1 is divisible by 873234964696345278371172272680705837<36>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
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.
By Sinkiti Sibata / PRIMO
(28·102207+53)/9 is prime.
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).
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) ----------
By Sinkiti Sibata / PRIMO
(8·102073-11)/3 is prime.
By suberi / PRIMO
5·102733+9 is prime.
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).
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+
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>
By Sinkiti Sibata / PRIMO
(31·102177+23)/9 is prime.
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+
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) ----------
By Sinkiti Sibata / PRIMO
(17·102068-53)/9 is prime.
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)
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) ----------
By Jo Yeong Uk / GMP-ECM
10192+9 = 1(0)1919<193> = C193
C193 = P48 · P145
P48 = 325208379747671632800443572929049811907718391209<48>
P145 = 3074951515012920315894112276452006313835272802228418099697777887803931547784516799444634005241238767287033369894773351997005678938044816110863201<145>
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.
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) ----------
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+
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) ----------
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) ----------
By Jo Yeong Uk / PRIMO
(55·102015+17)/9 is prime.
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+
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).
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) ----------
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).
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+
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) ----------
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>]
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) ----------
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+
By Jo Yeong Uk / PRIMO
(38·102043+61)/9 is prime.
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>
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) ----------
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+
By suberi / PRIMO
(13·102563+41)/9 is prime.
(13·102641+41)/9 is prime.
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
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) ----------
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).
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.
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).
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) ----------
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+
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).
By Jo Yeong Uk / PRIMO
4·102038+9 is prime!
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) ----------
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).
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) ----------
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+
By Bruce Dodson
(10339-1)/9 is divisible by 777734075184513369134763199249605543798943174359980119<54>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Yousuke Koide
101075+1 is divisible by 17749774754658825560922224895404476651<38>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By suberi / PRIMO
6·102593+7 is prime!
(55·102969+71)/9 is prime!
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+
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