By Yousuke Koide / GMP-ECM
(10621-1)/9 = (1)621<621> = 33 · 37 · 277 · 757 · 333667 · 11055043 · 1970554717<10> · 109908191603107<15> · 203864078068831<15> · 440334654777631<15> · 11111111111111111111111<23> · 1595352086329224644348978893<28> · 30483187506704565749803762042596649<35> · 823799348530495507269035013254489287846904557<45> · 11033517351146841676953477818524172302174982813132058195800613488154982399<74> · C346
C346 = P40 · C306
P40 = 3343594428384401477244840930119560710799<40>
C306 = [450377923741970808148950296226613032400566155131568499041822243047158328146539757935075382025095148527133551625501785016893572159399932122711365422556992408548848991871421391458636588324840594526713717497745060394412424048730385747613423456947185389836707759125364034009038282054167764539431128404447755521<306>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
(2·10157-11)/9 = (2)1561<157> = 1307 · 227076523 · 41803616430887<14> · C132
C132 = P57 · P76
P57 = 133550863188163178037852511255596245705285448630017952863<57>
P76 = 1341155421012836738800447933210092150861764010961882722169751753291060047181<76>
Number: trial N=179112464145748746805374846504014682308278110369127593030548399981364056346062044214134328695106803134333980305291396012181814029203 ( 132 digits) SNFS difficulty: 157 digits. Divisors found: r1=133550863188163178037852511255596245705285448630017952863 (pp57) r2=1341155421012836738800447933210092150861764010961882722169751753291060047181 (pp76) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 73.93 hours. Scaled time: 38.15 units (timescale=0.516). Factorization parameters were as follows: n: 179112464145748746805374846504014682308278110369127593030548399981364056346062044214134328695106803134333980305291396012181814029203 m: 10000000000000000000000000000000 c5: 200 c0: -11 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3000001) Primes: RFBsize:216816, AFBsize:217237, largePrimes:5721932 encountered Relations: rels:5704445, finalFF:502337 Max relations in full relation-set: 0 Initial matrix: 434118 x 502337 with sparse part having weight 34615373. Pruned matrix : 404026 x 406260 with weight 25796728. Total sieving time: 58.92 hours. Total relation processing time: 0.72 hours. Matrix solve time: 13.86 hours. Time per square root: 0.43 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: 73.93 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
(10591-1)/9 = (1)591<591> = 3 · 37 · 52009 · 2316842929<10> · 3707079392784283<16> · 79040479805615687465683<23> · 7478417919783613513048627<25> · 3599474961483053310878605135585111374469138078226023233589649293<64> · 750914105302558436752000930239222531800507092216032215426336586609291356367521996611125219417012181327241<105> · C343
C343 = P47 · P296
P47 = 14969825042462452779165494832955385273042368237<47>
P296 = 93696223430042503515209992685260973400653568450838728238629096649817396148168839486303968426912972256207993383920531938149701226310489022341502001395015749564990023360486520540430751646613322259497452737670770634148247428397820336451859675947344796100737871536080988501102119909768537672914822587<296>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
10173+9 = 1(0)1729<174> = 72 · 132 · 2515573 · 501355609 · 980959509182183<15> · C139
C139 = P56 · P84
P56 = 43621013613880185555572860857609538355052262229723114093<56>
P84 = 223762640416341510155833285985486831687028975194572884766702131594185801601877826383<84>
Number: 10009_173 N=9760753183879009646135889360607373608838812644875806219835912669099476964166309210938898210949322811535458367356231635756270419228754515619 ( 139 digits) SNFS difficulty: 173 digits. Divisors found: r1=43621013613880185555572860857609538355052262229723114093 (pp56) r2=223762640416341510155833285985486831687028975194572884766702131594185801601877826383 (pp84) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 366.05 hours. Scaled time: 245.99 units (timescale=0.672). Factorization parameters were as follows: name: 10009_173 n: 9760753183879009646135889360607373608838812644875806219835912669099476964166309210938898210949322811535458367356231635756270419228754515619 m: 10000000000000000000000000000000000 c5: 1000 c0: 9 skew: 4 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 10800001) Primes: RFBsize:501962, AFBsize:500591, largePrimes:6442805 encountered Relations: rels:6897642, finalFF:1125193 Max relations in full relation-set: 0 Initial matrix: 1002620 x 1125193 with sparse part having weight 66333627. Pruned matrix : 895561 x 900638 with weight 50940551. Total sieving time: 312.96 hours. Total relation processing time: 1.54 hours. Matrix solve time: 51.22 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: snfs,173,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 366.05 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(22·10186-1)/3 = 7(3)186<187> = 7 · 67 · 331 · C182
C182 = P31 · C151
P31 = 5679860644357315055141531091607<31>
C151 = [8316927375912425675232689124341181802299980314993069805942537621415770313404508190180998100214135140699510365051647362171567079564114595515698728073621<151>]
By Alexander Mkrtychyan / ggnfs-0.77.1-20060513-win32 snfs
(79·10200-7)/9 = 8(7)200<201> = C201
C201 = P77 · P125
P77 = 12552959240238880156671133611977244215193772311428177779302543233603334526387<77>
P125 = 69925964147484466181286398935166368644230263837598388909290350401694329924977506307770282327347615709798206665285899283888971<125>
r1 = 69925964147484466181286398935166368644230263837598388909290350401694329924977506307770282327347615709798206665285899283888971 (p125) r2 = 12552959240238880156671133611977244215193772311428177779302543233603334526387 (p77) n: 877777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777 m: 10000000000000000000000000000000000000000 c5: 79 c0: -7 skew: 1 type: snfs rlim: 30000000 alim: 30000000 lbpr: 30 lbpa: 30 mfbr: 54 mfba: 54 rlambda: 2.2 alambda: 2.2 sieved special-q: [13m;200m) processed with different FBs: lbpr/lbpa(m): 30/30, 40/40, 25/28, 10/30, 8/25 with 30m/30m largePrimes: 5432730 , relations: 9596734, finalFF:4164004 Pruning matrix with wt=0.400 Initial matrix is 3717752 x 4164004 with sparse part having weight 98074369. (total weight is 260467550) Matrix pruned to 3156845 x 3175497 with weight 74485702. Solved successfully. Factorization found on 0,1,2,3,5,6,7,8,12,15 dependencies. --- with 8m/25m relations: 9337677 Matrix loaded: it is 1956035 x 1966635. Original matrix had 2259738 columns. Matrix difficulty is about 6309811.90 --- with 10m/30m rels:8711565, initialFF:0, finalFF:2623788 Pruning matrix with wt=0.300 Initial matrix is 2524472 x 2634693 with sparse part having weight 187685347. (total weight is 319960393) Matrix pruned to 2459960 x 2472646 with weight 173289624. Total elapsed time: 4296.44 seconds. Solved: 715000 seconds. Found only trivial dependencies --- CPU RAM* Process: (GHz days**)(Max RSS) ----------------- ---------- --------- gnfs-lasieve4I14e 2590 135MB procrels 0.04 ??MB matbuild 0.51 711MB matsolve 59.80 393MB sqrt 0.10 ??MB ---------- total 2650.45 * data for successful factorization, w/o unsuccessful time **1GHz day ~= 1 day on P3 1GHz
It's the largest number factored by GGNFS in our tables so far. Congratulations!
See also Records.
By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
(29·10151+7)/9 = 3(2)1503<152> = 32 · 11 · 28597727 · 11536947310113791<17> · C126
C126 = P57 · P70
P57 = 270934293156900183594932829079733518732282549735324741973<57>
P70 = 3641110758838558932109472437657733441598489296771623913270689827230257<70>
Number: trial N=986501769751909411961170002152524580143175098932585822837399053431527946681209013531212654513345836260634733596897677783477061 ( 126 digits) SNFS difficulty: 152 digits. Divisors found: r1=270934293156900183594932829079733518732282549735324741973 (pp57) r2=3641110758838558932109472437657733441598489296771623913270689827230257 (pp70) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 44.89 hours. Scaled time: 24.11 units (timescale=0.537). Factorization parameters were as follows: n: 986501769751909411961170002152524580143175098932585822837399053431527946681209013531212654513345836260634733596897677783477061 m: 1000000000000000000000000000000 c5: 290 c0: 7 skew: 1 type: snfsFactor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2000001) Primes: RFBsize:176302, AFBsize:176383, largePrimes:5285780 encountered Relations: rels:5059326, finalFF:406032 Max relations in full relation-set: 0 Initial matrix: 352752 x 406032 with sparse part having weight 40051505. Pruned matrix : 328838 x 330665 with weight 26384199. Total sieving time: 34.60 hours. Total relation processing time: 0.42 hours. Matrix solve time: 9.43 hours. Time per square root: 0.44 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: 44.89 hours. --------- CPU info (if available) ----------
By Bruce Dodson / GMP-ECM
(10329-1)/9 = (1)329<329> = 239 · 4649 · 35121409 · 1964089881669809395643<22> · 316362908763458525001406154038726382279<39> · C255
C255 = P44 · P212
P44 = 37633698993045258670863410188544865190871951<44>
P212 = 12175990136267618100062412451321121844977125961935799309046323782610299025911626168118737338968216243867796848803259561923384268932593679164283019843448278074106680143267046033732670400418363798167958964008153787<212>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 gnfs
(8·10189-71)/9 = (8)1881<189> = 17 · 521 · 30259 · 1773229 · 625516159 · 74065325249<11> · 345781643941<12> · 292088948280678446566609<24> · C120
C120 = P57 · P64
P57 = 222819387861185833526742714383975148891821116287140753681<57>
P64 = 1793981384058924893821212283538113799870047038762128239533917597<64>
Number: trial N=399733833830372570282527388178208665038615477184692436745428272043328591004926149531322290011212791187921050965128424557 ( 120 digits) Divisors found: r1=222819387861185833526742714383975148891821116287140753681 (pp57) r2=1793981384058924893821212283538113799870047038762128239533917597 (pp64) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 137.34 hours. Scaled time: 70.59 units (timescale=0.514). Factorization parameters were as follows: name: trial n: 399733833830372570282527388178208665038615477184692436745428272043328591004926149531322290011212791187921050965128424557 skew: 103810.45 # norm 3.61e+16 c5: 24480 c4: -297199816 c3: -1382502805553921 c2: 583359676691979072 c1: 4891292481911117734813456 c0: -805602083914226446018861456 # alpha -5.79 Y1: 1319152663103 Y0: -110304165081665752089315 # Murphy_E 2.71e-10 # M 677867400259774854722433970520922671737645589615500042774504931605111288385311259262026269508935052221438696083141795 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, 1 ) Primes: RFBsize:315948, AFBsize:315861, largePrimes:7647100 encountered Relations: rels:7663422, finalFF:728749 Max relations in full relation-set: 0 Initial matrix: 631890 x 728749 with sparse part having weight 70820634. Pruned matrix : 559071 x 562294 with weight 47741797. Total sieving time: 115.87 hours. Total relation processing time: 1.98 hours. Matrix solve time: 18.16 hours. Time per square root: 1.33 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: 137.34 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
(10519-1)/9 = (1)519<519> = 3 · 37 · 347 · 1039 · 14533 · 21528169344472027<17> · 46194618816084982100679234312974236345786346173<47> · 32198046775720891593420454244946597764673353202694265726843479376953223792923910764829129134957786957553803<107> · C337
C337 = P41 · C297
P41 = 27556151204359553942685920311502726470093<41>
C297 = [216514826332371848322762555578613448056021292727337050311807751933401214900332242367650030603068301186552949610544037767579778110246878949700183394024838083707712222016266792473767108010610363941458066189164465028096213015007237587114703846104214458455026790737791798829124341877208532765964548801<297>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(4·10195-1)/3 = 1(3)195<196> = 919 · 2815092622300365139319<22> · C171
C171 = P37 · C135
P37 = 1616772208578912506305058572743036521<37>
C135 = [318773126025054291670957797550571273589430793561728712537650216394184484148701462662385921621852455278537160766090492754352887897550493<135>]
By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 gnfs
(22·10189-1)/3 = 7(3)189<190> = 11419757 · 211184184100965653310251<24> · 5247840149796055570797016942289983138483<40> · C120
C120 = P58 · P63
P58 = 1826310899844750455890038379870677364429281210698126055419<58>
P63 = 317269164063171180914353224226880162452791136883719201604270747<63>
Number: test N=579432132513201923188799315527338302692526852393619136492994578653670372434846049946697734504501561737781423227202527993 ( 120 digits) Divisors found: r1=1826310899844750455890038379870677364429281210698126055419 (pp58) r2=317269164063171180914353224226880162452791136883719201604270747 (pp63) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 168.31 hours. Scaled time: 86.51 units (timescale=0.514). Factorization parameters were as follows: name: test n: 579432132513201923188799315527338302692526852393619136492994578653670372434846049946697734504501561737781423227202527993 skew: 139462.11 # norm 3.25e+16 c5: 11580 c4: 229069215 c3: -1035517698637270 c2: -4821042319501375108 c1: 5743668297144006940945468 c0: 55004793579072396798085029760 # alpha -5.73 Y1: 318511853737 Y0: -137993553767881193160243 # Murphy_E 2.72e-10 # M 554922421292239917976551006198690292058518776280396076817314663820096833353889847215255004097124190281310884136455988765 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, 1 ) Primes: RFBsize:315948, AFBsize:315877, largePrimes:7704379 encountered Relations: rels:7756750, finalFF:729214 Max relations in full relation-set: 0 Initial matrix: 631903 x 729214 with sparse part having weight 72647660. Pruned matrix : 559034 x 562257 with weight 50370839. Total sieving time: 127.06 hours. Total relation processing time: 2.11 hours. Matrix solve time: 37.62 hours. Time per square root: 1.52 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: 168.31 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
(10525-1)/9 = (1)525<525> = 3 · 31 · 37 · 41 · 43 · 71 · 151 · 239 · 271 · 1933 · 4201 · 4649 · 21401 · 25601 · 79801 · 123551 · 2906161 · 10838689 · 35120401 · 435288001 · 30703738801<11> · 182521213001<12> · 625437743071<12> · 102598800232111471<18> · 18525843918490695886751<23> · 57802050308786191965409441<26> · 991474271662986957800680951<27> · 15763985553739191709164170940063151<35> · 54442267778748734853078961420361450411594669214709944589849727424959801<71> · C219
C219 = P43 · P177
P43 = 4401268665169140025731821222935000987130551<43>
P177 = 186243861617073980885505452610064684612129749201325732764290050555482397120222194754557152744180256772035732524938930620412706217059111157975741996041453725977078102648969888751<177>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Yousuke Koide / GMP-ECM
101570+1 = 1(0)15691<1571> = 101 · 3541 · 27961 · 94201 · 207241 · 364241 · 725341 · 3868481 · 5925181 · 7136984465461<13> · 9897542032658521861<19> · 3299894113715127521683201<25> · 28415783195151364586816438858689<32> · [34843277171045295933029273038354723106623942274167877028468403719880416626983967470194597426602476866146739051545997293765790832960699270182751148635492102757666140991780660761728507665838983382655047656132036840522542926670514159867455052679491682106619196393145144395922810075309<281>] · [22454709964066403559107101299163638986979610188692082356449728640968571102518022328651101898576409756577035423368397079217553950196221899081834254023564051072964208366536065240044733114930488490539175912345498307317005607293206687629316616437519512562887849697996400007055383520476112350625041785437433893185759269495528644287257542976626237862359274712053307068223025288940257963206877937004269547005395381663694800169300862181761155654556259088046735158689970456248973987896515914817649250776568167679167984601501635401188978971528638514795642673555900381<557>] · C601
C601 = C38 · C563
P38 = 29761675926781160150142940130769922081<38>
C563 = [54841596780936737488692802484103764893199543412517314910884339498475336340544513602803847141138049993277365711938350078305449521112799665314971784100223901313322213997598891691233982281136056563235763737920054337537589252252790187317793498535722907064286141023558151521345566500495986225152292478101551514112242118800165474543307117844620528591910013208031795692971895367931479213070339699089203649858831044946218140074943673591335814874740780675614559538251147498039991524177044527768326798950790851469961736228988133391948595383324310690985581463715403740244041<563>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By JMB / GGNFS-0.77.1-20060513-pentium4 gnfs
(52·10162-7)/9 = 5(7)162<163> = 103 · 381011 · 946681999961618639<18> · 1221459109676013540068392985396141510503<40> · C99
C99 = P49 · P50
P49 = 8438134055835129687391374189732897448405262542547<49>
P50 = 15088866711043141207643579503789954343073186607831<50>
Number: N N=127321880058410134937874685456288398513745339782992258022290739921523427135877001437678981240885557 ( 99 digits) Divisors found: r1=8438134055835129687391374189732897448405262542547 (pp49) r2=15088866711043141207643579503789954343073186607831 (pp50) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 10.37 hours. Scaled time: 12.47 units (timescale=1.202). Factorization parameters were as follows: name: N n: 127321880058410134937874685456288398513745339782992258022290739921523427135877001437678981240885557 skew: 9643.08 # norm 6.38e+13 c5: 21120 c4: 311152786 c3: -7904505190150 c2: -20055983778161829 c1: 316396256294438203240 c0: 657038077305820350429725 # alpha -5.88 Y1: 6126630781 Y0: -5702173808368634646 # Murphy_E 3.90e-09 # M 48616991791541821940847763123385691274109460482888757071970272973892514502053664826490013542985493 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 25000 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, 1325001) Primes: RFBsize:135072, AFBsize:134685, largePrimes:3786279 encountered Relations: rels:3726881, finalFF:343538 Max relations in full relation-set: 28 Initial matrix: 269840 x 343538 with sparse part having weight 23488350. Pruned matrix : 210003 x 211416 with weight 11580736. Total sieving time: 9.46 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.60 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: gnfs,98,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 10.37 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
101275+1 = 1(0)12741<1276> = 7 · 11 · 13 · 103 · 211 · 241 · 251 · 2161 · 4013 · 5051 · 9091 · 87211 · 102001 · 2254201 · 787223761 · 21993833369<11> · 291078844423<12> · 5516286288241<13> · 78875943472201<14> · 377526955309799110357<21> · 4270914986978327797975291<25> · 165564988462016408581266824201<30> · 201069283252703294533187911388251<33> · 216219010761333454086082249502131<33> · 10000099999999989999899999000000000100001<41> · 73610520788177438692703784333146668068451<41> · 160220794821014452066741918303580917664386555934641<51> · 175137725562337579790651749196120587807233668420015131<54> · 18103293041473682932576480240232418518560200896635102620265398137792101055968813301676929657920974523594103092467214576079129177678145686917465120573429118444647478671055435116260002205526892422444318067914692401<212> · C640
C640 = P31 · C610
P31 = 3228529113769803189332045176651<31>
C610 = [3097354754631152192863055596837469549881472079730729195187714434409989364909503064765447683515430510986536639597179836264932430193956149762360195438774298995821874636636744698536172506813008082807457406388860537959687636020341319784853558770432005208387396767738134036084111618022251571529736556157719626027902604153147271712627114289805521341260481893644390068847368181889709948803734022640623304583086765402879268652929209712202498645521483975053530060875008047953984644164792100095547532556321890446631612021472043959384922289262541118564945552603412445599209736618237653298506605224325056728379017839070851<610>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Chris Monico / GGNFS-0.80.1
(8·10166-71)/9 = (8)1651<166> = 383 · 2887 · 55815703 · C153
C153 = P66 · P88
P66 = 141560894710474867768362601769154727182998709670386480583402999463<66>
P88 = 1017424571164532619839800754370275756667350476653199232325748520042742652983871482885049<88>
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(52·10162-7)/9 = 5(7)162<163> = 103 · 381011 · 946681999961618639<18> · C138
C138 = P40 · C99
P40 = 1221459109676013540068392985396141510503<40>
C99 = [127321880058410134937874685456288398513745339782992258022290739921523427135877001437678981240885557<99>]
By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 gnfs
(2·10197+7)/9 = (2)1963<197> = 1621 · 141974874916545385999<21> · 2232227063658151482511<22> · 43577960060843625073819999006811<32> · C120
C120 = P54 · P67
P54 = 451432857691895875961752904940309204980009605290656993<54>
P67 = 2198844637377041314605159450464334723319742368211499399632756249129<67>
Number: test N=992630718271618283341033880453341958342128797919820395767331503484855179680778194512437518931403483604755119718794009097 ( 120 digits) Divisors found: r1=451432857691895875961752904940309204980009605290656993 (pp54) r2=2198844637377041314605159450464334723319742368211499399632756249129 (pp67) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 129.21 hours. Scaled time: 116.03 units (timescale=0.898). Factorization parameters were as follows: name: test n: 992630718271618283341033880453341958342128797919820395767331503484855179680778194512437518931403483604755119718794009097 skew: 62269.20 # norm 1.52e+16 c5: 49140 c4: 7968213204 c3: -633335444221141 c2: -28081596552590686164 c1: 1107218209111382214603576 c0: 3534481494395924396324930335 # alpha -5.71 Y1: 2082926580031 Y0: -115098657175494752776662 # Murphy_E 2.89e-10 # M 504697680091632283507625193131377291428449168427719895603688346894281193132345617680896109259306414785276999124103053047 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, 1 ) Primes: RFBsize:315948, AFBsize:316002, largePrimes:7651339 encountered Relations: rels:7660346, finalFF:709798 Max relations in full relation-set: 0 Initial matrix: 632033 x 709798 with sparse part having weight 68225438. Pruned matrix : 571453 x 574677 with weight 49175844. Total sieving time: 117.39 hours. Total relation processing time: 2.46 hours. Matrix solve time: 8.63 hours. Time per square root: 0.73 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: 129.21 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
10167+9 = 1(0)1669<168> = 7 · 13 · 53 · 877 · 107171 · C156
C156 = P63 · P93
P63 = 578285490464535003292508528455551062720454372885574351763458327<63>
P93 = 381472790189423991118742839850166453080558585132743676617075753578582424625410729307533832287<93>
Number: 10009_167 N=220600179573565709368504340113503800147035985155837573658020885780015632167763060253476327002737780573173682022539160307617346454159538787082518830731603849 ( 156 digits) SNFS difficulty: 167 digits. Divisors found: r1=578285490464535003292508528455551062720454372885574351763458327 (pp63) r2=381472790189423991118742839850166453080558585132743676617075753578582424625410729307533832287 (pp93) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 178.55 hours. Scaled time: 109.27 units (timescale=0.612). Factorization parameters were as follows: name: 10009_167 n: 220600179573565709368504340113503800147035985155837573658020885780015632167763060253476327002737780573173682022539160307617346454159538787082518830731603849 m: 1000000000000000000000000000000000 c5: 100 c0: 9 skew: 3 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:348501, largePrimes:5953601 encountered Relations: rels:6095608, finalFF:780802 Max relations in full relation-set: 0 Initial matrix: 697078 x 780802 with sparse part having weight 58659671. Pruned matrix : 635534 x 639083 with weight 45096830. Total sieving time: 153.34 hours. Total relation processing time: 0.72 hours. Matrix solve time: 24.20 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 178.55 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
10693+1 = 1(0)6921<694> = 72 · 112 · 13 · 19 · 23 · 127 · 463 · 2689 · 4093 · 8317 · 8779 · 24179 · 52579 · 459691 · 590437 · 648649 · 909091 · 5274739 · 7444361 · 599144041 · 7093127053<10> · 183411838171<12> · 167940794674423<15> · 4539402627853030477<19> · 4924630160315726207887<22> · 136094982876222218559943<24> · 189772422673235585874485732659<30> · 141122524877886182282233539317796144938305111168717<51> · 803956626149925031112757148192164970057208483589704631288984124647169634536861236854805849361<93> · C340
C340 = P37 · C304
P37 = 1992239470584165788605948879953926371<37>
C304 = [4603184964734402473011132054574871768101384322818910046547748531884259027958267080342140972683398434286257762067178960349541200528618030240830132851782792895996117549551271815944610220256799485207702831103176523404549814416087930733678705878813258634914133639328074562923421485980890386223188429086045853<304>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Wataru Sakai / GMP-ECM 6.1
10181+9 = 1(0)1809<182> = 192 · 663883229598790612639169<24> · C155
C155 = P34 · P122
P34 = 1972852879967879178904902617372213<34>
P122 = 21149806574944880773112316633222849030124545193584976920415264370446417132428148912879467226040854694780865097353747249277<122>
(25·10153-1)/3 = 8(3)153<154> = 13 · 135197 · 2146571139152631849772721<25> · C124
C124 = P37 · P87
P37 = 5393541826404464811149133316798078361<37>
P87 = 409533101044409088462546935359683563035408954430106138774390557254932874425892524573013<87>
Number: test N=2208833909780146430450526784619613274824795703886149452683911106599445833442442008509253921427912994781563034774490439871693 ( 124 digits) SNFS difficulty: 154 digits. Divisors found: r1=5393541826404464811149133316798078361 (pp37) r2=409533101044409088462546935359683563035408954430106138774390557254932874425892524573013 (pp87) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 45.70 hours. Scaled time: 20.70 units (timescale=0.453). Factorization parameters were as follows: n: 2208833909780146430450526784619613274824795703886149452683911106599445833442442008509253921427912994781563034774490439871693 m: 5000000000000000000000000000000 c5: 8 c0: -1 skew: 1 type: snfsFactor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 1 ) Primes: RFBsize:176302, AFBsize:176058, largePrimes:5486213 encountered Relations: rels:5409505, finalFF:403557 Max relations in full relation-set: 0 Initial matrix: 352425 x 403557 with sparse part having weight 25966191. Pruned matrix : 321474 x 323300 with weight 19571072. Total sieving time: 40.29 hours. Total relation processing time: 0.39 hours. Matrix solve time: 4.61 hours. Time per square root: 0.41 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 45.70 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
10948+1 = 1(0)9471<949> = 73 · 137 · 170641 · 259121 · 73921249 · 99990001 · 57340465299866278297<20> · 52201702278536187174995982385190339542840861545149808159731432186088602525064098418072959548867561425890781539716300154490510721563835995312133388810104710726015330140180100712831208243369704593632493581391545465384002703669518350982143743148868128174561205103289746036643410805299221918913812703969<299> · C600
C600 = P34 · C566
P34 = 7766457159337484152304096869413649<34>
C566 = [13160605651726332711824188828231198974781817449170107220843017244925292787555978722379682670875489051063645457879559843216704892378318231053991874231132340342953316014469870226734932565533810812418846304981368619810054475856949401252258566231884568535957089879450035409745536613986710956990658406048668451352905354578528814334680077095374009876604796822907072341585310879826779147173972597386594702857046340165047037357564066043359340376061087990248909603666034420683949986454993266279058626732208248361954284400688841746207803537487889583649311294163392186504195737<566>]
10951+1 = 1(0)9501<952> = 7 · 11 · 13 · 3536453 · 12361733 · 23801700277<11> · 38405613853<11> · 68009240067498931554643059611689714176253<41> · [3057680777939340873709128976697248022108596412174873961787759431938025628869678008257542334571156935185136195428088353104791656344052255750374564165542466009514157472101863859769365418973638732536985785497459589011510554591776547201190016880328515272743477435703<262>] · C612
C612 = P33 · C580
P33 = 102570756454098763233742574501743<33>
C580 = [1172012803769621719252365058938965506852034255538255007373757985097563509193496805313736730077703309259876626566612185446011310800300769994399386653021937694266520577838243385384774401385492842581044381509749875841324524047036304574190605332513109880751219408698204055258625861509987926962423351385639646591127710298342927544330033130259244488289180348708388102537736901822082292342772957838450752598706597561798689276191118701886297433227752846591987632088979079350694789923207263820430089623986825840706751833030361951318310171887323357204388747832176545729713142420913287917917<580>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 gnfs
(8·10190-71)/9 = (8)1891<190> = 31 · 130631 · 1819798107166331261<19> · 79551780549152904467<20> · 516691240715476214463353437<27> · C119
C119 = P53 · P67
P53 = 13300943125012238261994582238288397549590803371621527<53>
P67 = 2206240654687068048051269685385242576181184555049501743077860013517<67>
Number: test N=29345081468082457331289864149984090927414031492921287709615885718403229306209097275348874449736436951154902266428180459 ( 119 digits) Divisors found: r1=13300943125012238261994582238288397549590803371621527 (pp53) r2=2206240654687068048051269685385242576181184555049501743077860013517 (pp67) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 115.85 hours. Scaled time: 102.41 units (timescale=0.884). Factorization parameters were as follows: name: test n: 29345081468082457331289864149984090927414031492921287709615885718403229306209097275348874449736436951154902266428180459 skew: 165490.48 # norm 8.52e+16 c5: 23520 c4: 4956381832 c3: -2588841180336804 c2: -98228419725155829003 c1: 24426972850082958580741534 c0: 329035407253681913013070439181 # alpha -6.99 Y1: 6596018737759 Y0: -65950451013578676648460 # Murphy_E 3.21e-10 # M 10717586801923053861335544256814480236621499124251542442465227226576716907432907631440614918980170118495814277857599813 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, 1 ) Primes: RFBsize:315948, AFBsize:315630, largePrimes:7562889 encountered Relations: rels:7550887, finalFF:707603 Max relations in full relation-set: 0 Initial matrix: 631657 x 707603 with sparse part having weight 58660544. Pruned matrix : 568239 x 571461 with weight 40931424. Total sieving time: 99.73 hours. Total relation processing time: 2.04 hours. Matrix solve time: 13.35 hours. Time per square root: 0.72 hours. Prototype def-par.txt line would be: gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 115.85 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
10165+9 = 1(0)1649<166> = 1117 · 29009 · 658851377041905167825719734691<30> · C128
C128 = P45 · P84
P45 = 405476469408529846096552458965513686928349281<45>
P84 = 115521003954448422975067155610313660368992451637991336302242072977588854951379884143<84>
Number: 10009_165 N=46841048825978561356978747541657395628214092574365582530196085768744223145586011443337758767687268157082158826887686500017351183 ( 128 digits) SNFS difficulty: 165 digits. Divisors found: r1=405476469408529846096552458965513686928349281 (pp45) r2=115521003954448422975067155610313660368992451637991336302242072977588854951379884143 (pp84) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 109.42 hours. Scaled time: 66.75 units (timescale=0.610). Factorization parameters were as follows: name: 10009_165 n: 46841048825978561356978747541657395628214092574365582530196085768744223145586011443337758767687268157082158826887686500017351183 m: 1000000000000000000000000000000000 c5: 1 c0: 9 skew: 2 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 4800001) Primes: RFBsize:348513, AFBsize:348501, largePrimes:5792990 encountered Relations: rels:5968131, finalFF:784837 Max relations in full relation-set: 0 Initial matrix: 697078 x 784837 with sparse part having weight 37403878. Pruned matrix : 623951 x 627500 with weight 27859202. Total sieving time: 92.53 hours. Total relation processing time: 0.64 hours. Matrix solve time: 15.99 hours. Time per square root: 0.26 hours. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 109.42 hours. --------- CPU info (if available) ----------
GGNFS, ECM
10164+7 = 1(0)1637<165> = 23 · 379 · 7309 · 12698886469366937367312361817<29> · C129
C129 = P59 · P70
P59 = 89521774571891440725766027916492942543621141376778475868817<59>
P70 = 1380640691183467041940805484295021196494682231216695693196237567677271<70>
Number: N N=123597404720906723070603691171193332824198996716018877260358883611797898401587603600800822151252138669606949349037994378388558407 ( 129 digits) SNFS difficulty: 164 digits. Divisors found: r1=89521774571891440725766027916492942543621141376778475868817 (pp59) r2=1380640691183467041940805484295021196494682231216695693196237567677271 (pp70) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 108.96 hours. Scaled time: 196.45 units (timescale=1.803). Factorization parameters were as follows: name: 10^164+7 n: 123597404720906723070603691171193332824198996716018877260358883611797898401587603600800822151252138669606949349037994378388558407 skew: 1 c5: 10000 c4: 0 c3: 0 c2: 0 c1: 0 c0: 7 m: 100000000000000000000000000000000 type: snfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 47 mfba: 47 rlambda: 2.4 alambda: 2.4 qintsize: 10000Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 47/47 Sieved algebraic special-q in [2000000, 3440001) Primes: RFBsize:283146, AFBsize:283882, largePrimes:5478274 encountered Relations: rels:5452413, finalFF:639994 Max relations in full relation-set: 28 Initial matrix: 567092 x 639993 with sparse part having weight 49903993. Pruned matrix : 517836 x 520735 with weight 38625421. Total sieving time: 102.91 hours. Total relation processing time: 0.28 hours. Matrix solve time: 5.64 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,47,47,2.4,2.4,100000 total time: 108.96 hours. --------- CPU info (if available) ----------
10189+7 = 1(0)1887<190> = 59 · 2131 · C184
C184 = P37 · C148
P37 = 3159054500600988812343025556881597237<37>
C148 = [2517719943928015933161812602621927145881018065738612169370878161327571268215304182048198373665295635371013719764424373030947660451097961657183402859<148>]
ECM, GGNFS gnfs, GGNFS snfs
10198+7 = 1(0)1977<199> = 53 · 571 · 2311139052889<13> · C182
C182 = P40 · C142
P40 = 8981676309068044990065102914772467010071<40>
C142 = [1591858814267617896078250031041439073424924024742250415820682638458770032616911002606947871751429467343698998106474368448419328480312019748431<142>]
10167+7 = 1(0)1667<168> = 383 · 829 · 11591207077<11> · 73347288818135303<17> · 141440849542595046487975537469003983<36> · C100
C100 = P43 · P57
P43 = 2767384195308432800998826640296194868680403<43>
P57 = 946432516737087044441832532380571281421477140914013266779<57>
Number: Job N=2619142388744198489221178578867314405367094314526442514421260482505307467083353062573172058928231937 ( 100 digits) Divisors found: r1=2767384195308432800998826640296194868680403 (pp43) r2=946432516737087044441832532380571281421477140914013266779 (pp57) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 8.60 hours. Scaled time: 15.90 units (timescale=1.850). Factorization parameters were as follows: name: Job n: 2619142388744198489221178578867314405367094314526442514421260482505307467083353062573172058928231937 skew: 8767.84 # norm 1.44e+14 c5: 39960 c4: 10073859 c3: -20284580639278 c2: -124696502742194 c1: 640938381477089277548 c0: -70909371893625224570160 # alpha -6.23 Y1: 8282152207 Y0: -9189813678694628131 # Murphy_E 3.31e-09 # M 1501514031735999265463075416290939630348073546891187053019114908450105058567508383777968256834056499 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 10000 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, 1000001) Primes: RFBsize:135072, AFBsize:135190, largePrimes:3875502 encountered Relations: rels:3862298, finalFF:368646 Max relations in full relation-set: 28 Initial matrix: 270344 x 368646 with sparse part having weight 27249881. Pruned matrix : 197174 x 198589 with weight 13002163. Total sieving time: 7.84 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.56 hours. Time per square root: 0.10 hours. 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: 8.60 hours. --------- CPU info (if available) ----------
10162+7 = 1(0)1617<163> = 373 · 2897560744807<13> · 284650192636237<15> · C133
C133 = P53 · P81
P53 = 10547001703389742749894012224851142970616143003250831<53>
P81 = 308189700406341423181147659113543127355444178794088410677400174480962049420222271<81>
Number: N N=3250477295152857483616387321204676144778298388584513349964512256612201623520987517912245791751948647147902352423129220799543585457201 ( 133 digits) SNFS difficulty: 162 digits. Divisors found: r1=10547001703389742749894012224851142970616143003250831 (pp53) r2=308189700406341423181147659113543127355444178794088410677400174480962049420222271 (pp81) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 79.92 hours. Scaled time: 146.58 units (timescale=1.834). Factorization parameters were as follows: name: 10^162+7 n: 3250477295152857483616387321204676144778298388584513349964512256612201623520987517912245791751948647147902352423129220799543585457201 skew: 1 c5: 100 c4: 0 c3: 0 c2: 0 c1: 0 c0: 7 m: 100000000000000000000000000000000 type: snfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 47 mfba: 47 rlambda: 2.4 alambda: 2.4 qintsize: 10000Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 47/47 Sieved algebraic special-q in [2000000, 3100001) Primes: RFBsize:283146, AFBsize:283097, largePrimes:5323478 encountered Relations: rels:5295599, finalFF:640531 Max relations in full relation-set: 28 Initial matrix: 566309 x 640530 with sparse part having weight 39852777. Pruned matrix : 512205 x 515100 with weight 29578204. Total sieving time: 75.32 hours. Total relation processing time: 0.27 hours. Matrix solve time: 4.22 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,47,47,2.4,2.4,100000 total time: 79.92 hours. --------- CPU info (if available) ----------
ECM, GGNFS snfs
10184+7 = 1(0)1837<185> = 3623 · 14947 · 87049 · 81831577 · 27032969027<11> · 82572781465758823<17> · C137
C137 = P41 · P96
P41 = 13812625427379003182132914528083742520447<41>
P96 = 840787078677037174391304726181032112104649288083138093961703021109819735570348848562966541610497<96>
10178+7 = 1(0)1777<179> = 9779956187<10> · 15061360829503<14> · C155
C155 = P32 · C124
P32 = 28611712108180931576351076849383<32>
C124 = [2372766658386071479394164140981662985967236676580748175830928608025753371979903404338599883260199063087303313743132894406989<124>]
10159+7 = 1(0)1587<160> = 53 · 112071623517499016299<21> · 742724173649744073677<21> · C117
C117 = P57 · P60
P57 = 354663760028666201445811359498151123731853622090995334671<57>
P60 = 639122480641374580716319914410982978520319328839614482642443<60>
Number: N N=226673582103118334143885828835544134495812108823761215777923161449519382625786039701855765820567862409213621214041253 ( 117 digits) SNFS difficulty: 159 digits. Divisors found: r1=354663760028666201445811359498151123731853622090995334671 (pp57) r2=639122480641374580716319914410982978520319328839614482642443 (pp60) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 79.32 hours. Scaled time: 144.21 units (timescale=1.818). Factorization parameters were as follows: name: 10^159+7 n: 226673582103118334143885828835544134495812108823761215777923161449519382625786039701855765820567862409213621214041253 skew: 1 c5: 10000 c4: 0 c3: 0 c2: 0 c1: 0 c0: 7 m: 10000000000000000000000000000000 type: snfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 47 mfba: 47 rlambda: 2.4 alambda: 2.4 qintsize: 10000Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 47/47 Sieved algebraic special-q in [2000000, 3010001) Primes: RFBsize:283146, AFBsize:283882, largePrimes:5284168 encountered Relations: rels:5264200, finalFF:647445 Max relations in full relation-set: 28 Initial matrix: 567093 x 647445 with sparse part having weight 36687284. Pruned matrix : 507077 x 509976 with weight 26304945. Total sieving time: 75.21 hours. Total relation processing time: 0.24 hours. Matrix solve time: 3.76 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,47,47,2.4,2.4,100000 total time: 79.32 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
10163+9 = 1(0)1629<164> = 19 · 223 · 5851 · 88411 · 2701583 · 341165536047659<15> · C130
C130 = P62 · P69
P62 = 21282218145805492933175466817926209552898014184560253546079961<62>
P69 = 232597357666536071396985516556630866129009673684071188821993975702361<69>
Number: 10009_163 N=4950187705997164365857621953071374136800891903657774027127968403552641352310285897052129258301158018266953244295705051113242487921 ( 130 digits) SNFS difficulty: 163 digits. Divisors found: r1=21282218145805492933175466817926209552898014184560253546079961 (pp62) r2=232597357666536071396985516556630866129009673684071188821993975702361 (pp69) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 108.09 hours. Scaled time: 72.85 units (timescale=0.674). Factorization parameters were as follows: name: 10009_163 n: 4950187705997164365857621953071374136800891903657774027127968403552641352310285897052129258301158018266953244295705051113242487921 m: 100000000000000000000000000000000 c5: 1000 c0: 9 skew: 2 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, 4650001) Primes: RFBsize:315948, AFBsize:315061, largePrimes:5821181 encountered Relations: rels:5959009, finalFF:712522 Max relations in full relation-set: 0 Initial matrix: 631076 x 712522 with sparse part having weight 38928691. Pruned matrix : 568676 x 571895 with weight 30046734. Total sieving time: 93.04 hours. Total relation processing time: 0.55 hours. Matrix solve time: 14.28 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: 108.09 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
10198+9 = 1(0)1979<199> = 225961 · 124678768297051697<18> · C176
C176 = P40 · C136
P40 = 9690036302476528221435163969533038158217<40>
C136 = [3663098565111345395412929971728350097530716199796536338138921821753864966157300030614431362264492489238686784881314038315456171995557481<136>]
ECM, GGNFS gnfs
10167+7 = 1(0)1667<168> = 383 · 829 · 11591207077<11> · 73347288818135303<17> · C135
C135 = P36 · C100
P36 = 141440849542595046487975537469003983<36>
C100 = [2619142388744198489221178578867314405367094314526442514421260482505307467083353062573172058928231937<100>]
10172+7 = 1(0)1717<173> = 53 · 191938429 · 331415043556425612418268467<27> · 29849566288772955116003809849<29> · C107
C107 = P36 · P72
P36 = 519653203407133915489828689837558457<36>
P72 = 191222214126927932611849860371304656786463312566330254859420091542285581<72>
Number: Job N=99369236133662997498046538437800014670090090351377956564066351892312953445624960793469992991788770475708517 ( 107 digits) Divisors found: r1=519653203407133915489828689837558457 (pp36) r2=191222214126927932611849860371304656786463312566330254859420091542285581 (pp72) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 42.52 hours. Scaled time: 77.09 units (timescale=1.813). Factorization parameters were as follows: name: Job n: 99369236133662997498046538437800014670090090351377956564066351892312953445624960793469992991788770475708517 skew: 32421.20 # norm 1.79e+14 c5: 4320 c4: -163080001 c3: -12032430761768 c2: 161855080600218078 c1: 6064058439032775643530 c0: -35072402530886590558603860 # alpha -5.01 Y1: 3652301983 Y0: -470276921272562053703 # Murphy_E 1.43e-09 # M 87827777070393059920832879408730568231186274136573932948700867604413699478459017235755435042804514255498026 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, 2600001) Primes: RFBsize:183072, AFBsize:183374, largePrimes:4651120 encountered Relations: rels:4941887, finalFF:559453 Max relations in full relation-set: 28 Initial matrix: 366521 x 559453 with sparse part having weight 52068998. Pruned matrix : 243802 x 245698 with weight 30090006. Total sieving time: 39.81 hours. Total relation processing time: 0.20 hours. Matrix solve time: 2.37 hours. Time per square root: 0.14 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: 42.52 hours. --------- CPU info (if available) ----------
By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 snfs, gnfs
(4·10179-1)/3 = 1(3)179<180> = 1997 · C176
C176 = P48 · P56 · P73
P48 = 253295417124993861031296281669624054174266850009<48>
P56 = 81068109172017008610971560943119572493804243852629380849<56>
P73 = 3251496537693114498458159549987550518732739228349528825468592962030431329<73>
I had to do 2 runs of ggnfs. the first time with snfs crashed but gave me the factor (no output info): r1 = 81068109172017008610971560943119572493804243852629380849 the second run gave: Number: test N=823589171795450761291859546035443959370517761467932302810461890880519047747545879286033387788030175748017974504417531961 ( 120 digits) Divisors found: r1=253295417124993861031296281669624054174266850009 (pp48) r2=3251496537693114498458159549987550518732739228349528825468592962030431329 (pp73) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 165.08 hours. Scaled time: 79.07 units (timescale=0.479). Factorization parameters were as follows: name: test n: 823589171795450761291859546035443959370517761467932302810461890880519047747545879286033387788030175748017974504417531961 skew: 46590.16 # norm 3.33e+16 c5: 84360 c4: -8202502714 c3: -1387888129134160 c2: 11428243751837448755 c1: 653112455495502668312670 c0: -1357104695023944835862993736 # alpha -5.75 Y1: 1171896562859 Y0: -99521041163549129211445 # Murphy_E 2.83e-10 # M 548991466575707693749971971104244681063225514790280051859897817838862609292117688812115775794054142884095234452671759882 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, 4530001) Primes: RFBsize:315948, AFBsize:315899, largePrimes:7613366 encountered Relations: rels:7587614, finalFF:708900 Max relations in full relation-set: 0 Initial matrix: 631935 x 708900 with sparse part having weight 75263515. Pruned matrix : 573365 x 576588 with weight 52935839. Total sieving time: 116.62 hours. Total relation processing time: 2.12 hours. Matrix solve time: 44.85 hours. Time per square root: 1.49 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: 165.08 hours. --------- CPU info (if available) ----------
ECM, GGNFS
10172+7 = 1(0)1717<173> = 53 · 191938429 · 29849566288772955116003809849<29> · C134
C134 = P27 · C107
P27 = 331415043556425612418268467<27>
C107 = [99369236133662997498046538437800014670090090351377956564066351892312953445624960793469992991788770475708517<107>]
10160+7 = 1(0)1597<161> = 5189 · 13931 · C153
C153 = P39 · P115
P39 = 122227155285903457182666321837042118481<39>
P115 = 1131791252435748089591200016536616025548232549159948520144370768984943188816711312258317968241365841533122026175233<115>
Number: N N=138335625162691341167897685422270671661929201791407611881807314548748014866486962233917823022226979738077817358213143076843544579810311147393164053781073 ( 153 digits) SNFS difficulty: 160 digits. Divisors found: r1=122227155285903457182666321837042118481 (pp39) r2=1131791252435748089591200016536616025548232549159948520144370768984943188816711312258317968241365841533122026175233 (pp115) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 56.43 hours. Scaled time: 102.87 units (timescale=1.823). Factorization parameters were as follows: name: 10^160+7 n: 138335625162691341167897685422270671661929201791407611881807314548748014866486962233917823022226979738077817358213143076843544579810311147393164053781073 skew: 1 c5: 1 c4: 0 c3: 0 c2: 0 c1: 0 c0: 7 m: 100000000000000000000000000000000 type: snfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 47 mfba: 47 rlambda: 2.4 alambda: 2.4 qintsize: 10000Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 47/47 Sieved algebraic special-q in [2000000, 2670001) Primes: RFBsize:283146, AFBsize:283082, largePrimes:5150741 encountered Relations: rels:5142908, finalFF:651842 Max relations in full relation-set: 28 Initial matrix: 566294 x 651842 with sparse part having weight 31982635. Pruned matrix : 495098 x 497993 with weight 21734435. Total sieving time: 53.34 hours. Total relation processing time: 0.18 hours. Matrix solve time: 2.81 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,47,47,2.4,2.4,100000 total time: 56.43 hours. --------- CPU info (if available) ----------
10163+7 = 1(0)1627<164> = 751 · 65793577 · 27552936913<11> · C142
C142 = P29 · P114
P29 = 41544031117073918433594752857<29>
P114 = 176807234786569338582523829881595287129675124275481575083841952162459544421538630230247564397123546438974833341401<114>
10190+7 = 1(0)1897<191> = 197 · 8317 · 127747 · 2829317 · 72279887 · 142368179 · 32918013164986911675034336901<29> · C128
C128 = P33 · P40 · P56
P33 = 539949550351081895686956255135631<33>
P40 = 1228769056329366897148936730013579567923<40>
P56 = 75135865542155053300373496564980174488903912122130011293<56>
Number: Job N=92324626598724059947748948540572122551209847634089980073675521676448234822325379449790050554439 ( 95 digits) Divisors found: r1=1228769056329366897148936730013579567923 (pp40) r2=75135865542155053300373496564980174488903912122130011293 (pp56) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 7.99 hours. Scaled time: 14.24 units (timescale=1.783). Factorization parameters were as follows: name: Job n: 92324626598724059947748948540572122551209847634089980073675521676448234822325379449790050554439 m: 6052030409229541070633 deg: 4 c4: 68819760 c3: 523795266544 c2: 139484912789525633 c1: -2180424713438310492 c0: -186745021330265119032750 skew: 1635.250 type: gnfs # adj. I(F,S) = 54.627 # E(F1,F2) = 3.776995e-05 # GGNFS version 0.77.1-20060513-athlon-xp polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1163561373. # 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: 10000 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, 710001) Primes: RFBsize:92938, AFBsize:92932, largePrimes:1912725 encountered Relations: rels:2016957, finalFF:253729 Max relations in full relation-set: 28 Initial matrix: 185949 x 253729 with sparse part having weight 21506926. Pruned matrix : 157656 x 158649 with weight 11234793. Total sieving time: 7.51 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.37 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 7.99 hours. --------- CPU info (if available) ----------
Table 10n+7 was extended up to 200. Remaining 27 composite numbers passed GMP-ECM 5e4, 200 times.
By Yousuke Koide / GMP-ECM
10833+1 = 1(0)8321<834> = 11 · 103 · 197 · 4013 · 609757 · 909091 · 1868879293<10> · 21993833369<11> · 548804832033845773<18> · 5673320472670315859129<22> · 5076141624365532994918781726395939035533<40> · 103746647830421551242486430622636901002236971549990724717454338463<66> · C649
C649 = P33 · C616
P33 = 319824888758480762691339433102367<33>
C616 = [9343574757071792228077434930303221486762476778121423097668652970221821077208958882520710694973513468637733064223309368796024481695602816312019386654632567213658969755944051068351580955006486536290343866440351081883829574626125117079334890962510199844585257226508476000771679651748353042521718234285875124709637675154006541487681538322505116765623644263842843482492186160214527982947155983758385307885977270250086778447914204388035736686604684225936655586388904938583434467168465052464330580158448779970125201984020099036622848607669011680030732134695357973131485493571097432551074841523783382709012137194976990504023<616>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
10159+9 = 1(0)1589<160> = 499 · C157
C157 = P41 · P116
P41 = 25186187487813621841913773118823816536903<41>
P116 = 79567739936888292295596294112639084452134355303693380058498429690502044773614914416009946349393011410085895946365397<116>
Number: 10009_159 N=2004008016032064128256513026052104208416833667334669338677354709418837675350701402805611222444889779559118236472945891783567134268537074148296593186372745491 ( 157 digits) SNFS difficulty: 160 digits. Divisors found: r1=25186187487813621841913773118823816536903 (pp41) r2=79567739936888292295596294112639084452134355303693380058498429690502044773614914416009946349393011410085895946365397 (pp116) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 76.30 hours. Scaled time: 51.50 units (timescale=0.675). Factorization parameters were as follows: name: 10009_159 n: 2004008016032064128256513026052104208416833667334669338677354709418837675350701402805611222444889779559118236472945891783567134268537074148296593186372745491 m: 100000000000000000000000000000000 c5: 1 c0: 90 skew: 2.46 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:283222, largePrimes:5625429 encountered Relations: rels:5626182, finalFF:634517 Max relations in full relation-set: 0 Initial matrix: 566432 x 634517 with sparse part having weight 41516401. Pruned matrix : 514796 x 517692 with weight 29630223. Total sieving time: 63.99 hours. Total relation processing time: 0.41 hours. Matrix solve time: 11.68 hours. Time per square root: 0.21 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: 76.30 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
10196+9 = 1(0)1959<197> = 409 · 24509 · 24568382659368173<17> · C173
C173 = P47 · C126
P47 = 44401499461295046411183451748843306897700065477<47>
C126 = [914485651586525533357484598772878668557145673386605657821723195587345693907083602731033750236232276619318600012074196323998309<126>]
By JMB / GGNFS-0.77.1-20060513-athlon-xp
10164+3 = 1(0)1633<165> = 31 · 72661 · 34398655802053<14> · C145
C145 = P37 · P108
P37 = 4075389007177818510425958607451799493<37>
P108 = 316684198450990245853796446126980851388377309015444532754266605694332398770449162432993865124395996668140177<108>
Number: Job N=1290611301114084388660783119477994372937028016800687221470364447812500253084007981362043316535746405003945717855762764937726394301548860221530261 ( 145 digits) SNFS difficulty: 164 digits. Divisors found: r1=4075389007177818510425958607451799493 (pp37) r2=316684198450990245853796446126980851388377309015444532754266605694332398770449162432993865124395996668140177 (pp108) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 100.00 hours. Scaled time: 183.40 units (timescale=1.834). Factorization parameters were as follows: name: 10164+3 n: 1290611301114084388660783119477994372937028016800687221470364447812500253084007981362043316535746405003945717855762764937726394301548860221530261 skew: 2 c5: 10000 c4: 0 c3: 0 c2: 0 c1: 0 c0: 3 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 qintsize: 20000 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, 3560001) Primes: RFBsize:216816, AFBsize:215581, largePrimes:6043156 encountered Relations: rels:6143733, finalFF:509004 Max relations in full relation-set: 28 Initial matrix: 432461 x 509004 with sparse part having weight 61390523. Pruned matrix : 403943 x 406169 with weight 47820336. Total sieving time: 95.02 hours. Total relation processing time: 0.31 hours. Matrix solve time: 4.55 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 100.00 hours. --------- CPU info (if available) ----------
By JMB / GMP-ECM 6.1.1 B1=11000000
10185+9 = 1(0)1849<186> = 7 · 13 · 229846571 · 1275374768743384691<19> · 2601396325020582930122538337721<31> · C127
C127 = P34 · P93
P34 = 4277579851308146456603644470753277<34>
P93 = 336882235159639253303716540858681759020527027546821580356810549616254660757873213006852842127<93>
By JMB / GGNFS-0.77.1-20060513-athlon-xp
10161+3 = 1(0)1603<162> = 13384170461<11> · 821803718884451141<18> · C133
C133 = P35 · P38 · P61
P35 = 55689458843269071823219640216823151<35>
P38 = 31215643436669954814773315727432097321<38>
P61 = 5229921251194894076800387430777663894801697083886414650870293<61>
Number: Job N=9091602483434276582331722452653348048116352758006019425620053354886938383960657549356599224903299469115788497391900843527220038162003 ( 133 digits) SNFS difficulty: 161 digits. Divisors found: r1=55689458843269071823219640216823151 (pp35) r2=31215643436669954814773315727432097321 (pp38) r3=5229921251194894076800387430777663894801697083886414650870293 (pp61) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 72.01 hours. Scaled time: 131.70 units (timescale=1.829). Factorization parameters were as follows: name: 10^161+3 n: 9091602483434276582331722452653348048116352758006019425620053354886938383960657549356599224903299469115788497391900843527220038162003 skew: 1 c5: 10 c4: 0 c3: 0 c2: 0 c1: 0 c0: 3 m: 100000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 qintsize: 20000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [1250000, 2670001) Primes: RFBsize:183072, AFBsize:183096, largePrimes:3724852 encountered Relations: rels:3939067, finalFF:424694 Max relations in full relation-set: 28 Initial matrix: 366234 x 424694 with sparse part having weight 49131957. Pruned matrix : 345897 x 347792 with weight 38131203. Total sieving time: 68.36 hours. Total relation processing time: 0.16 hours. Matrix solve time: 3.38 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,2500000,2500000,26,26,47,47,2.3,2.3,100000 total time: 72.01 hours. --------- CPU info (if available) ----------
10163+3 = 1(0)1623<164> = 13 · 17 · 23 · 1249 · C157
C157 = P48 · P110
P48 = 117231589899843222398103253015079733333423108013<48>
P110 = 13436086681281923664269307468592392032596002915199098937195994818328776362541162076537167449224244474925441693<110>
Number: Job N=1575133803678788003843956534497714244580791526788221842474963641973976584375901271873292456510949463879582910869321071651734135685491143258891984726872586009 ( 157 digits) SNFS difficulty: 163 digits. Divisors found: r1=117231589899843222398103253015079733333423108013 (pp48) r2=13436086681281923664269307468592392032596002915199098937195994818328776362541162076537167449224244474925441693 (pp110) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 82.88 hours. Scaled time: 151.59 units (timescale=1.829). Factorization parameters were as follows: name: 10^163+3 n: 1575133803678788003843956534497714244580791526788221842474963641973976584375901271873292456510949463879582910869321071651734135685491143258891984726872586009 skew: 2 c5: 1000 c4: 0 c3: 0 c2: 0 c1: 0 c0: 3 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 qintsize: 20000 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, 3140001) Primes: RFBsize:216816, AFBsize:216791, largePrimes:5926753 encountered Relations: rels:5958971, finalFF:493581 Max relations in full relation-set: 28 Initial matrix: 433673 x 493581 with sparse part having weight 56882975. Pruned matrix : 410829 x 413061 with weight 45472614. Total sieving time: 78.17 hours. Total relation processing time: 0.24 hours. Matrix solve time: 4.35 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 82.88 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
10156+9 = 1(0)1559<157> = 149 · 12577 · 17257 · C146
C146 = P42 · P46 · P59
P42 = 383981700070505184610830877165967851949977<42>
P46 = 1245447807805174631186627010827838254868677573<46>
P59 = 64659942178328230286420137484904735606524156752097366805889<59>
Number: 10009_156 N=30922270259706918541273994104183262432014945588155444494107881550493940763192232543551971147645731712248062829627325026727144031780555472245719869 ( 146 digits) SNFS difficulty: 156 digits. Divisors found: r1=383981700070505184610830877165967851949977 (pp42) r2=1245447807805174631186627010827838254868677573 (pp46) r3=64659942178328230286420137484904735606524156752097366805889 (pp59) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 51.11 hours. Scaled time: 31.23 units (timescale=0.611). Factorization parameters were as follows: name: 10009_156 n: 30922270259706918541273994104183262432014945588155444494107881550493940763192232543551971147645731712248062829627325026727144031780555472245719869 m: 10000000000000000000000000000000 c5: 10 c0: 9 skew: 2 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:216791, largePrimes:5577567 encountered Relations: rels:5506820, finalFF:485813 Max relations in full relation-set: 0 Initial matrix: 433674 x 485813 with sparse part having weight 32645438. Pruned matrix : 399323 x 401555 with weight 25027274. Total sieving time: 43.95 hours. Total relation processing time: 0.31 hours. Matrix solve time: 6.64 hours. Time per square root: 0.21 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: 51.11 hours. --------- CPU info (if available) ----------
By JMB / GGNFS-0.77.1-20060513-athlon-xp
10158+3 = 1(0)1573<159> = 19 · 181 · 42367021 · C147
C147 = P41 · P107
P41 = 56562887171939352687533078968873450917397<41>
P107 = 12134121153120891677860517234609605899226468109948574988494138769478971577913168918124640360449818429183421<107>
Number: Job N=686340925714619629813773407842849504154136513898346137695447647130283089746715169548133228993215230649747386989970687059844292811941864550032875137 ( 147 digits) SNFS difficulty: 158 digits. Divisors found: r1=56562887171939352687533078968873450917397 (pp41) r2=12134121153120891677860517234609605899226468109948574988494138769478971577913168918124640360449818429183421 (pp107) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 73.73 hours. Scaled time: 136.77 units (timescale=1.855). Factorization parameters were as follows: name: 10^158+3 n: 686340925714619629813773407842849504154136513898346137695447647130283089746715169548133228993215230649747386989970687059844292811941864550032875137 skew: 1 c5: 1000 c4: 0 c3: 0 c2: 0 c1: 0 c0: 3 m: 10000000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 qintsize: 20000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [1000000, 2480001) Primes: RFBsize:148933, AFBsize:149150, largePrimes:2286233 encountered Relations: rels:2556588, finalFF:336729 Max relations in full relation-set: 28 Initial matrix: 298149 x 336729 with sparse part having weight 39120057. Pruned matrix : 285932 x 287486 with weight 31441874. Total sieving time: 71.27 hours. Total relation processing time: 0.11 hours. Matrix solve time: 2.27 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,2000000,2000000,25,25,46,46,2.3,2.3,100000 total time: 73.73 hours. --------- CPU info (if available) ----------
10159+3 = 1(0)1583<160> = 27481 · 21857807 · 50342736358471<14> · C134
C134 = P57 · P77
P57 = 365088561996659184739622906690610283957025786636979183011<57>
P77 = 90578648466036397927895461652215642063389691714124448760625362551232618315489<77>
Number: Job N=33069228516066127828095467188710501944989981714508049208067552235661273476089033705608855208287520512577078328935684044968578266957379 ( 134 digits) SNFS difficulty: 159 digits. Divisors found: r1=365088561996659184739622906690610283957025786636979183011 (pp57) r2=90578648466036397927895461652215642063389691714124448760625362551232618315489 (pp77) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 67.02 hours. Scaled time: 123.99 units (timescale=1.850). Factorization parameters were as follows: name: 10^159+3 n: 33069228516066127828095467188710501944989981714508049208067552235661273476089033705608855208287520512577078328935684044968578266957379 skew: 1 c5: 10000 c4: 0 c3: 0 c2: 0 c1: 0 c0: 3 m: 10000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 qintsize: 20000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [1250000, 2510001) Primes: RFBsize:183072, AFBsize:182136, largePrimes:3638522 encountered Relations: rels:3804343, finalFF:422771 Max relations in full relation-set: 28 Initial matrix: 365272 x 422771 with sparse part having weight 42045423. Pruned matrix : 343496 x 345386 with weight 31618122. Total sieving time: 63.83 hours. Total relation processing time: 0.16 hours. Matrix solve time: 2.94 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,2500000,2500000,26,26,47,47,2.3,2.3,100000 total time: 67.02 hours. --------- CPU info (if available) ----------
By JMB / GGNFS-0.77.1-20060513-athlon-xp
10154+3 = 1(0)1533<155> = 7 · 3963860422906687<16> · C138
C138 = P69 · P70
P69 = 149423443005462551721301379502643750647745574130417390277014997318813<69>
P70 = 2411930932482573111391518332280642017351271749416029057705410264299159<70>
Number: Job N=360399024222921909270235911303974311261988445519545605666583983972180980784491046755349332963748845118776491140122019197845700079530778267 ( 138 digits) SNFS difficulty: 154 digits. Divisors found: r1=149423443005462551721301379502643750647745574130417390277014997318813 (pp69) r2=2411930932482573111391518332280642017351271749416029057705410264299159 (pp70) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 45.44 hours. Scaled time: 79.88 units (timescale=1.758). Factorization parameters were as follows: name: 10^154+3 n: 360399024222921909270235911303974311261988445519545605666583983972180980784491046755349332963748845118776491140122019197845700079530778267 skew: 1 c5: 10000 c4: 0 c3: 0 c2: 0 c1: 0 c0: 3 m: 1000000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 qintsize: 20000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [1000000, 1860001) Primes: RFBsize:148933, AFBsize:148285, largePrimes:2191969 encountered Relations: rels:2400183, finalFF:341909 Max relations in full relation-set: 28 Initial matrix: 297282 x 341909 with sparse part having weight 30111148. Pruned matrix : 280747 x 282297 with weight 22030937. Total sieving time: 43.61 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.66 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2000000,2000000,25,25,46,46,2.3,2.3,100000 total time: 45.44 hours. --------- CPU info (if available) ----------
By JMB / GGNFS-0.77.1-20060513-pentium4
10153+3 = 1(0)1523<154> = 29 · 67 · C150
C150 = P42 · P109
P42 = 376761827601512787036094285501223811506077<42>
P109 = 1366030211688845889671647585845412059913391266235993559996651995578056259930708624299661596143715652351500473<109>
Number: N N=514668039114770972722593926917138445702521873391662377766340710241893978383942357179619145651055069480185280494081317550180133813690169840452907874421 ( 150 digits) SNFS difficulty: 153 digits. Divisors found: r1=376761827601512787036094285501223811506077 (pp42) r2=1366030211688845889671647585845412059913391266235993559996651995578056259930708624299661596143715652351500473 (pp109) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 43.84 hours. Scaled time: 39.81 units (timescale=0.908). Factorization parameters were as follows: name: 10^153+3 n: 514668039114770972722593926917138445702521873391662377766340710241893978383942357179619145651055069480185280494081317550180133813690169840452907874421 skew: 1 c5: 1000 c4: 0 c3: 0 c2: 0 c1: 0 c0: 3 m: 1000000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 qintsize: 20000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [1000000, 1840001) Primes: RFBsize:148933, AFBsize:149150, largePrimes:2192600 encountered Relations: rels:2396730, finalFF:336011 Max relations in full relation-set: 28 Initial matrix: 298149 x 336011 with sparse part having weight 30541850. Pruned matrix : 283874 x 285428 with weight 23315534. Total sieving time: 40.28 hours. Total relation processing time: 0.28 hours. Matrix solve time: 3.09 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2000000,2000000,25,25,46,46,2.3,2.3,100000 total time: 43.84 hours. --------- CPU info (if available) ----------
By JMB / GGNFS-0.77.1-20060513-pentium4
10148+3 = 1(0)1473<149> = 7 · 5107 · 2157481 · 330473699221<12> · C126
C126 = P44 · P83
P44 = 10179078449976201273125762528418361136218099<44>
P83 = 38542844162420837355114416087578812267010926136810640691082927212474664077128617153<83>
Number: N N=392330634414488974731222398448381945764017396400978605812774161961346108149639752235416711259679426819944874434795840080452147 ( 126 digits) SNFS difficulty: 148 digits. Divisors found: r1=10179078449976201273125762528418361136218099 (pp44) r2=38542844162420837355114416087578812267010926136810640691082927212474664077128617153 (pp83) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 57.98 hours. Scaled time: 52.13 units (timescale=0.899). Factorization parameters were as follows: name: 10^148+3 n: 392330634414488974731222398448381945764017396400978605812774161961346108149639752235416711259679426819944874434795840080452147 skew: 1 c5: 1000 c4: 0 c3: 0 c2: 0 c1: 0 c0: 3 m: 100000000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 qintsize: 25000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [750000, 3225001) Primes: RFBsize:114155, AFBsize:114347, largePrimes:2340638 encountered Relations: rels:2602625, finalFF:264638 Max relations in full relation-set: 28 Initial matrix: 228568 x 264638 with sparse part having weight 32674494. Pruned matrix : 218631 x 219837 with weight 25690126. Total sieving time: 55.13 hours. Total relation processing time: 0.47 hours. Matrix solve time: 2.20 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,25,25,46,46,2.3,2.3,100000 total time: 57.98 hours. --------- CPU info (if available) ----------
10150+3 = 1(0)1493<151> = 4993 · 909599715918703<15> · C132
C132 = P58 · P75
P58 = 1312781142610220555791731442886796814088531285959604282653<58>
P75 = 167724222837335381788066096688395065923446964535816909617221682818743071569<75>
Number: N N=220185196899808391220278424731994458406334096942740234561275226231125986856866486145907394280837878238350277133007976381084084192557 ( 132 digits) SNFS difficulty: 150 digits. Divisors found: r1=1312781142610220555791731442886796814088531285959604282653 (pp58) r2=167724222837335381788066096688395065923446964535816909617221682818743071569 (pp75) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 48.22 hours. Scaled time: 44.70 units (timescale=0.927). Factorization parameters were as follows: name: 10^148+3 n: 220185196899808391220278424731994458406334096942740234561275226231125986856866486145907394280837878238350277133007976381084084192557 skew: 1 c5: 1 c4: 0 c3: 0 c2: 0 c1: 0 c0: 3 m: 1000000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [1000000, 2050001) Primes: RFBsize:148933, AFBsize:148825, largePrimes:2182381 encountered Relations: rels:2406623, finalFF:361245 Max relations in full relation-set: 28 Initial matrix: 297822 x 361245 with sparse part having weight 30716807. Pruned matrix : 259122 x 260675 with weight 20259735. Total sieving time: 45.43 hours. Total relation processing time: 0.40 hours. Matrix solve time: 2.21 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2000000,2000000,25,25,46,46,2.3,2.3,100000 total time: 48.22 hours. --------- CPU info (if available) ----------
By Hoogendoorn / GNFS
10372+1 = 1(0)3711<373> = 73 · 137 · 1489 · 700849 · 11110153 · 99990001 · 5419392721<10> · 640543322297<12> · 1220725699657<13> · 27908132670449<14> · 42367299139993<14> · 384705444182230291105649<24> · 16584440161215846282167330487128069170776821649169<50> · 97645954668018846467287180866355758374263120864803042536883990817097<68> · C143
C143 = P68 · P76
P68 = 23140616853203983900922551785166946660605063239337678349130406077337<68>
P76 = 1194053240550935343606131291791034479414833114386116350011658511441777011841<76>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
10154+9 = 1(0)1539<155> = 532 · 173 · C149
C149 = P56 · P93
P56 = 61663679403222757509249170662209857982446222255631728629<56>
P93 = 333712690670157588584103442128065072187953963434123029832366265075137324719065556444993079553<93>
Number: 10009_154 N=20577952370271443769716250614766327061859382620272987116144020973049055780655490094802626569840541447082766582228468773986175731597651644075504622837 ( 149 digits) SNFS difficulty: 155 digits. Divisors found: r1=61663679403222757509249170662209857982446222255631728629 (pp56) r2=333712690670157588584103442128065072187953963434123029832366265075137324719065556444993079553 (pp93) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 46.83 hours. Scaled time: 31.57 units (timescale=0.674). Factorization parameters were as follows: name: 10009_154 n: 20577952370271443769716250614766327061859382620272987116144020973049055780655490094802626569840541447082766582228468773986175731597651644075504622837 m: 10000000000000000000000000000000 c5: 1 c0: 90 skew: 2.46 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:216791, largePrimes:5594606 encountered Relations: rels:5553568, finalFF:488763 Max relations in full relation-set: 0 Initial matrix: 433671 x 488763 with sparse part having weight 29962612. Pruned matrix : 393661 x 395893 with weight 22762725. Total sieving time: 40.33 hours. Total relation processing time: 0.39 hours. Matrix solve time: 5.95 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 46.83 hours. --------- CPU info (if available) ----------
By JMB / GMP-ECM 6.0.1 B1=11000000
10149+3 = 1(0)1483<150> = 31 · 409 · 36299 · 68161 · 15786109931<11> · C126
C126 = P39 · P87
P39 = 384564861922004165543203544546821681061<39>
P87 = 525097150223725778038006971456374587050144448028021793732567240767742167666853365031593<87>
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(4·10163-1)/3 = 1(3)163<164> = 13 · 1617029653<10> · 4089127132463729329999260241<28> · C126
C126 = P44 · P82
P44 = 28707745798935503163763288419355671086157031<44>
P82 = 5403158344513526647772426770905270937762013647747568800406619329811247104567363907<82>
(22·10164-1)/3 = 7(3)164<165> = 302310500269409<15> · 5356131642213641307217<22> · C129
C129 = P38 · P92
P38 = 19880083080642109940248774655855594509<38>
P92 = 22781313294600518394371135010929040796865768981345365259606629590515987330582853978145551929<92>
By JMB / GGNFS-0.77.1-20060513-pentium4
10147+3 = 1(0)1463<148> = 17 · 2797246489<10> · C137
C137 = P56 · P81
P56 = 33108811339229359436324412647303299386888839796775859569<56>
P81 = 635150657593861735194302722673849771111790656208078860699275923576820452341058299<81>
Number: N N=21029083294262633671806153503575132464951006198960260283809320282565328457608252837898295818594576069027076635542747249450985536866013131 ( 137 digits) SNFS difficulty: 147 digits. Divisors found: r1=33108811339229359436324412647303299386888839796775859569 (pp56) r2=635150657593861735194302722673849771111790656208078860699275923576820452341058299 (pp81) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 49.41 hours. Scaled time: 41.85 units (timescale=0.847). Factorization parameters were as follows: name: 10^147+3 n: 21029083294262633671806153503575132464951006198960260283809320282565328457608252837898295818594576069027076635542747249450985536866013131 skew: 3 c5: 100 c4: 0 c3: 0 c2: 0 c1: 0 c0: 3 m: 100000000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 qintsize: 25000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [750000, 750000) Primes: RFBsize:114155, AFBsize:114062, largePrimes:2364569 encountered Relations: rels:2647538, finalFF:270674 Max relations in full relation-set: 28 Initial matrix: 228281 x 270674 with sparse part having weight 33459960. Pruned matrix : 216513 x 217718 with weight 25537184. Total sieving time: 46.63 hours. Total relation processing time: 0.32 hours. Matrix solve time: 2.27 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,25,25,46,46,2.3,2.3,100000 total time: 49.41 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
10153+9 = 1(0)1529<154> = 89 · C152
C152 = P63 · P89
P63 = 952968475741213558173290137369408967511606469763002925432064241<63>
P89 = 11790479267890275373671218734902940171749839873008160665577378805343748249303568644645441<89>
Number: 10009_153 N=11235955056179775280898876404494382022471910112359550561797752808988764044943820224719101123595505617977528089887640449438202247191011235955056179775281 ( 152 digits) SNFS difficulty: 153 digits. Divisors found: r1=952968475741213558173290137369408967511606469763002925432064241 (pp63) r2=11790479267890275373671218734902940171749839873008160665577378805343748249303568644645441 (pp89) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 37.55 hours. Scaled time: 22.98 units (timescale=0.612). Factorization parameters were as follows: name: 10009_153 n: 11235955056179775280898876404494382022471910112359550561797752808988764044943820224719101123595505617977528089887640449438202247191011235955056179775281 m: 1000000000000000000000000000000 c5: 1000 c0: 9 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:175423, largePrimes:5312210 encountered Relations: rels:5104149, finalFF:395224 Max relations in full relation-set: 0 Initial matrix: 351792 x 395224 with sparse part having weight 34367720. Pruned matrix : 330997 x 332819 with weight 25228972. Total sieving time: 32.45 hours. Total relation processing time: 0.29 hours. Matrix solve time: 4.65 hours. Time per square root: 0.16 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: 37.55 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
10697+1 = 1(0)6961<698> = 11 · 103 · 4013 · 21993833369<11> · 184952466900411703<18> · 2670502781396266997<19> · 3404193829806058997303<22> · C623
C623 = P36 · C588
P36 = 165525666279467793827703089744624213<36>
C588 = [359308269096977993468093022170028740789105888937019217440271136286307204483028607858609615266113376516383023083848873449534549812651676704385372391699541362333520709239824241861826048462909768049054998600630004856083526307688205397516081320883180154956234677233733708022746446335764039000144525507020153228092177960020254012635565656955544446401735609511013569408383142528271068437721625972496891588748833444695155776023844893509719346662131705237949421619292292987308359772640486630794121781644687628562377035413028618766356654036959027614880581534111595840593306457044705296820387620249<588>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Chris Monico / GGNFS-08
(8·10161-71)/9 = (8)1601<161> = 3 · 13 · 532 · 180073 · 209738761 · C143
C143 = P50 · P93
P50 = 51115477509159931763794507652915563600336098152047<50>
P93 = 420292278186894375636799893551544441041889854586442640683219972715067693082843449444417750241<93>
By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
10150+9 = 1(0)1499<151> = 322132274449397<15> · C136
C136 = P43 · P93
P43 = 6485315883937021911089291466838963163589677<43>
P93 = 478668255410426241114341996907533012450905011400520344471359974267559844215862172691771363961<93>
Number: 10009_150 N=3104314839949660628761284448066712660067595495580808482022733961156681326684053029198082216491817414591705050127114942813910431229430597 ( 136 digits) SNFS difficulty: 150 digits. Divisors found: r1=6485315883937021911089291466838963163589677 (pp43) r2=478668255410426241114341996907533012450905011400520344471359974267559844215862172691771363961 (pp93) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 30.86 hours. Scaled time: 20.83 units (timescale=0.675). Factorization parameters were as follows: name: 10009_150 n: 3104314839949660628761284448066712660067595495580808482022733961156681326684053029198082216491817414591705050127114942813910431229430597 m: 1000000000000000000000000000000 c5: 1 c0: 9 skew: 1.55 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, 1650001) Primes: RFBsize:114155, AFBsize:114062, largePrimes:2660088 encountered Relations: rels:2608863, finalFF:256764 Max relations in full relation-set: 0 Initial matrix: 228281 x 256764 with sparse part having weight 19959461. Pruned matrix : 219518 x 220723 with weight 14982825. Total sieving time: 29.28 hours. Total relation processing time: 0.18 hours. Matrix solve time: 1.31 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 30.86 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1
10144+9 = 1(0)1439<145> = 3510171520019041<16> · C129
C129 = P45 · P84
P45 = 343319428714803493135074217320184461540413041<45>
P84 = 829799713580309012101243243527869721960794456291028171104017893615600289042582210489<84>
Number: 10009_144 N=284886363614099255967532873170574356025189075001931636327243695405714234954473049582554837281255866762695290468589842291862587049 ( 129 digits) SNFS difficulty: 145 digits. Divisors found: r1=343319428714803493135074217320184461540413041 (pp45) r2=829799713580309012101243243527869721960794456291028171104017893615600289042582210489 (pp84) Version: GGNFS-0.77.1 Total time: 20.78 hours. Scaled time: 12.41 units (timescale=0.597). Factorization parameters were as follows: name: 10009_144 n: 284886363614099255967532873170574356025189075001931636327243695405714234954473049582554837281255866762695290468589842291862587049 m: 100000000000000000000000000000 c5: 1 c0: 90 skew: 2.46 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 2550001) Relations: rels:2850045, finalFF:254863 Initial matrix: 200113 x 254863 with sparse part having weight 28420798. Pruned matrix : 194157 x 195221 with weight 17535297. Total sieving time: 18.93 hours. Total relation processing time: 0.27 hours. Matrix solve time: 1.49 hours. Time per square root: 0.09 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: 20.78 hours. --------- CPU info (if available) ----------
By Chris Monico / GGNFS-08
(8·10158-71)/9 = (8)1571<158> = 3 · 19 · C158
C158 = P34 · P47 · P77
P34 = 9664697394220315840642753734651277<34>
P47 = 14494535430151793717771340261148093622724469909<47>
P77 = 11132175926860369123565167768321340729065242118076195884675837389472472816681<77>
SNFS difficulty: 158 digits. Divisors found: r1=9664697394220315840642753734651277 (pp34) r2=14494535430151793717771340261148093622724469909 (pp47) r3=11132175926860369123565167768321340729065242118076195884675837389472472816681 (pp77) Version: GGNFS-08 Total time: 49.61 hours.
By Sinkiti Sibata / GGNFS-0.77.1
10143+9 = 1(0)1429<144> = 7 · 13 · C142
C142 = P59 · P83
P59 = 14123789326633390707175391575607972980529708650840213007567<59>
P83 = 77804976659407440945486259813469379792634366567097067716248415916074333006508991397<83>
Number: 10009_143 N=1098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901099 ( 142 digits) SNFS difficulty: 143 digits. Divisors found: r1=14123789326633390707175391575607972980529708650840213007567 (pp59) r2=77804976659407440945486259813469379792634366567097067716248415916074333006508991397 (pp83) Version: GGNFS-0.77.1 Total time: 14.91 hours. Scaled time: 8.92 units (timescale=0.598). Factorization parameters were as follows: name: 10009_143 n: 1098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901099 m: 10000000000000000000000000000 c5: 1000 c0: 9 skew: 1 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [650000, 1950001) Relations: rels:2708264, finalFF:268021 Initial matrix: 199881 x 268021 with sparse part having weight 25165854. Pruned matrix : 191247 x 192310 with weight 13144682. Total sieving time: 13.45 hours. Total relation processing time: 0.22 hours. Matrix solve time: 1.15 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 14.91 hours. --------- CPU info (if available) ----------
By Chris Monico / GGNFS-08
(8·10154-71)/9 = (8)1531<154> = 66931 · 582031 · 174515111 · 69342185953<11> · C125
C125 = P38 · P87
P38 = 31716109421076795373899516364671743827<38>
P87 = 594516036272926696957983957018200081631523371414648045151308665913465157064353040222081<87>
Number: c125 N=18855735659017004221926364859533618632308778279455693268834359906070907088429160187428975507074831009421689650151349620843987 ( 125 digits) SNFS difficulty: 155 digits. Divisors found: r1=31716109421076795373899516364671743827 (pp38) r2=594516036272926696957983957018200081631523371414648045151308665913465157064353040222081 (pp87) Version: GGNFS-08 Total time: 35.90 hours. Scaled time: 59.48 units (timescale=1.657).
By JMB / GGNFS-0.77.1-20060513-athlon-xp gnfs
(4·10181-13)/9 = (4)1803<181> = 3 · 827188008473580331<18> · 10341603447151033621<20> · 1860973789180998551990153<25> · C119
C119 = P48 · P72
P48 = 726067165586600200426994691694728588706768743169<48>
P72 = 128170200259701857704179587352956111803036733849614320791625723061356983<72>
Number: Job N=93060174015228656729616238454217002066624174075285843608385241945839383503618594794008152364953724591856137946551699127 ( 119 digits) Divisors found: r1=726067165586600200426994691694728588706768743169 (pp48) r2=128170200259701857704179587352956111803036733849614320791625723061356983 (pp72) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 109.54 hours. Scaled time: 200.90 units (timescale=1.834). Factorization parameters were as follows: name: (4*10^181-13)/9 n: 93060174015228656729616238454217002066624174075285843608385241945839383503618594794008152364953724591856137946551699127 skew: 35804.230469 # norm 1.52E+016 c5: 22320 c4: -269603043 c3: -52175301422496 c2: -15944797089324958901 c1: -131609207918808280745515 c0: 7642729809721080297442975 #alpha -5.140000 Y1: 1270960327241 Y0: -83948695108610829227264 # Murphy_E 3.07E-010 # M 90961936046725712570246445405155753284738409683224429212522550955092555241968797291283361669678102998864944648970158616 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 10000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1750000, 3130001) Primes: RFBsize:250150, AFBsize:250327, largePrimes:5911345 encountered Relations: rels:5922142, finalFF:563897 Max relations in full relation-set: 28 Initial matrix: 500555 x 563897 with sparse part having weight 60164839. Pruned matrix : 453510 x 456076 with weight 46325804. Total sieving time: 103.43 hours. Total relation processing time: 0.52 hours. Matrix solve time: 5.35 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,48,48,2.5,2.5,60000 total time: 109.54 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1
(43·10154-7)/9 = 4(7)154<155> = 19 · C154
C154 = P66 · P88
P66 = 698263010678625674370967526486806265752943801620969881754577082577<66>
P88 = 3601250309102059914245749920964728989234812179604000200365723315889504010401022986601979<88>
Number: 47777_154 N=2514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883 ( 154 digits) SNFS difficulty: 156 digits. Divisors found: r1=698263010678625674370967526486806265752943801620969881754577082577 (pp66) r2=3601250309102059914245749920964728989234812179604000200365723315889504010401022986601979 (pp88) Version: GGNFS-0.77.1 Total time: 68.58 hours. Scaled time: 40.26 units (timescale=0.587). Factorization parameters were as follows: name: 47777_154 n: 2514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883 m: 10000000000000000000000000000000 c5: 43 c0: -70 skew: 1.1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 3200001) Relations: rels:5765318, finalFF:550075 Initial matrix: 432277 x 550075 with sparse part having weight 49724344. Pruned matrix : 410491 x 412716 with weight 27468631. Total sieving time: 61.33 hours. Total relation processing time: 0.45 hours. Matrix solve time: 6.59 hours. Time per square root: 0.21 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: 68.58 hours. --------- CPU info (if available) ----------
By JMB / GGNFS-0.77.1-20060513-athlon-xp gnfs
(16·10191-7)/9 = 1(7)191<192> = 3 · 629989 · 25671759360749<14> · 11323837291914005426115767<26> · 3902932380637696095354177901<28> · C119
C119 = P58 · P62
P58 = 3313559207083922318452043728233410351643032203699722342601<58>
P62 = 25020053629257740914748280168854757559710770983903542575058857<62>
Number: Job N=82905429064960492892446546401102851207709716257923855791406358121027685128379036667899534988442001145414894295493467057 ( 119 digits) Divisors found: r1=3313559207083922318452043728233410351643032203699722342601 (pp58) r2=25020053629257740914748280168854757559710770983903542575058857 (pp62) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 86.96 hours. Scaled time: 159.05 units (timescale=1.829). Factorization parameters were as follows: name: (16*10^191-7)/9 n: 82905429064960492892446546401102851207709716257923855791406358121027685128379036667899534988442001145414894295493467057 skew: 64828.738281 # norm 7.74E+016 c5: 17280 c4: 23663102248 c3: 1216620397219238 c2: -64977991546399907181 c1: 801562380717716146640790 c0: -7074472263971952664800082359 #alpha -6.600000 Y1: 4367385213937 Y0: -86337969377655390346892 # Murphy_E 3.08E-010 # M 25944347532134769767907568398236224281537579246278114917804371101060475961289806978069322558141325860930682671642234443 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 10000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1750000, 3040001) Primes: RFBsize:250150, AFBsize:251085, largePrimes:5868461 encountered Relations: rels:5909219, finalFF:607135 Max relations in full relation-set: 28 Initial matrix: 501314 x 607135 with sparse part having weight 61027499. Pruned matrix : 421447 x 424017 with weight 42368054. Total sieving time: 82.18 hours. Total relation processing time: 0.58 hours. Matrix solve time: 3.97 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,48,48,2.5,2.5,60000 total time: 86.96 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1
(43·10152-7)/9 = 4(7)152<153> = 3 · 8629 · 879522223 · C140
C140 = P31 · P37 · P73
P31 = 1430176486021512778804762093129<31>
P37 = 2634124550304617716630218784122614557<37>
P73 = 5570208680054061570851852839330927864723474994741869020269931636097026509<73>
Number: 47777_152 N=20984441024199006214282702098464189974691210272294309386562281479507447360215780310022944469827007599041064432596741706279115742469976314177 ( 140 digits) SNFS difficulty: 153 digits. Divisors found: r1=1430176486021512778804762093129 (pp31) r2=2634124550304617716630218784122614557 (pp37) r3=5570208680054061570851852839330927864723474994741869020269931636097026509 (pp73) Version: GGNFS-0.77.1 Total time: 55.54 hours. Scaled time: 33.10 units (timescale=0.596). Factorization parameters were as follows: name: 47777_152 n: 20984441024199006214282702098464189974691210272294309386562281479507447360215780310022944469827007599041064432596741706279115742469976314177 m: 1000000000000000000000000000000 c5: 4300 c0: -7 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2600001) Relations: rels:5441857, finalFF:403012 Initial matrix: 352762 x 403012 with sparse part having weight 38799169. Pruned matrix : 345979 x 347806 with weight 27944683. Total sieving time: 49.59 hours. Total relation processing time: 0.40 hours. Matrix solve time: 5.37 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 55.54 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
10656+1 = 1(0)6551<657> = 353 · 449 · 641 · 1409 · 69857 · 100903134230125793<18> · C623
C623 = P34 · C590
P34 = 1949975276463991211904463972906337<34>
C590 = [50823695292702772906341828639455475186647084238747143611310950107698664508702621537825683410277773548418553874833180885510941098608107516138705610549253764670513600487368737266381728491047492823332668468416979823751543426920331292534858116250899476667931096593493578610079917954613498853005960271246538325723981011978624099775752021245226369977923645972435305810863664445813538162336277625018754170859794869301439617688692791374520418480663972891570617818368839585655305169743630905264600480140364320122421217972550689446678530923120039113856690785669930590009751858140096880310930568743361<590>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By JMB / GGNFS-0.77.1-20060513-pentium4 gnfs
(5·10185-17)/3 = 1(6)1841<186> = 11 · 29 · 593 · 1033 · 1499 · 2882608259<10> · 3543071821004207029<19> · 1137427574791532814978635687<28> · C119
C119 = P57 · P63
P57 = 416163504929315546190282656125579228074066057762843035549<57>
P63 = 117692311104550786192947019689157514283557182010799089717768293<63>
Number: N N=48979244692501259904533934318356529766121780019559339790576785973107299044147705538529594775240417601599059313944047857 ( 119 digits) Divisors found: r1=416163504929315546190282656125579228074066057762843035549 (pp57) r2=117692311104550786192947019689157514283557182010799089717768293 (pp63) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 115.79 hours. Scaled time: 158.99 units (timescale=1.373). Factorization parameters were as follows: name: (5*10^185-17)/3 n: 48979244692501259904533934318356529766121780019559339790576785973107299044147705538529594775240417601599059313944047857 skew: 122278.929688 # norm 1.29E+017 c5: 9600 c4: 6283065260 c3: 2000094815017190 c2: -67480579476213504922 c1: -847972170400202950243923 c0: -45718757145201865256163772173 #alpha -6.430000 Y1: 3832867280899 Y0: -87406891867936911620456 # Murphy_E 2.76E-010 # M 7581874911340103816943540432161851288274241187794851548422255318280451895893905204460717843344170291847154658792726238 type: gnfs rlim: 3000000 alim: 3000000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 10000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2620001) Primes: RFBsize:216816, AFBsize:216487, largePrimes:4292994 encountered Relations: rels:4649215, finalFF:507934 Max relations in full relation-set: 28 Initial matrix: 433379 x 507934 with sparse part having weight 60887804. Pruned matrix : 383677 x 385907 with weight 46743624. Total sieving time: 106.56 hours. Total relation processing time: 0.46 hours. Matrix solve time: 8.46 hours. Time per square root: 0.31 hours. Prototype def-par.txt line would be: gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,26,26,48,48,2.5,2.5,10000 total time: 115.79 hours. --------- CPU info (if available) ----------
By Dirk Augustin / Oct 14, 2006
1031810+9 = 1(0)318099<31811> is PRP. This is the only PRP for 10n+9 with 4562 < n < 39254.
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(52·10192-7)/9 = 5(7)192<193> = 292 · 124121 · C185
C185 = P32 · C154
P32 = 18595565132796813986844950129137<32>
C154 = [2976529499611077203351314293501630935725085943516388594718960226957377562030460064235579076244868260455936858563466712545309238934826051949497196929491361<154>]
By JMB / GGNFS-0.77.1-20060513-pentium4 gnfs
(4·10183-31)/9 = (4)1821<183> = 33 · 7 · 101450189547527<15> · 5144414891929831963<19> · 1494159724423093628331262781519<31> · C118
C118 = P46 · P73
P46 = 1766892702122215773694321824469898688927028541<46>
P73 = 1706709577193253910450975857316609717444200221315333520908743744458950411<73>
Number: N N=3015572696584852809456973175599019254442494069685606449037092916837733527003570743285631033556963439554618401900680351 ( 118 digits) Divisors found: r1=1766892702122215773694321824469898688927028541 (pp46) r2=1706709577193253910450975857316609717444200221315333520908743744458950411 (pp73) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 7.89 hours. Scaled time: 10.99 units (timescale=1.394). Factorization parameters were as follows: name: (4*10^183-31)/9 n: 3015572696584852809456973175599019254442494069685606449037092916837733527003570743285631033556963439554618401900680351 skew: 80655.687500 # norm 2.93E+016 c5: 44160 c4: 75823687 c3: -1227681520676813 c2: 1934855151663165448 c1: 2180936122400030909134833 c0: 8766828659110871169453784725 #alpha -6.110000 Y1: 249093839953 Y0: -36886559257510036546034 # Murphy_E 3.58E-010 # M 1645930614903737644997169554295783841518726258894790408243495281749846408113031966724666382214204881428543513397336941 type: gnfs rlim: 3000000 alim: 3000000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 10000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 5585000 ) Primes: RFBsize:216816, AFBsize:216353, largePrimes:4290124 encountered Relations: rels:4641865, finalFF:510826 Max relations in full relation-set: 28 Initial matrix: 433255 x 510826 with sparse part having weight 62444546. Pruned matrix : 380371 x 382601 with weight 47424543. Total sieving time: 0.00 hours. Total relation processing time: 0.59 hours. Matrix solve time: 6.64 hours. Time per square root: 0.66 hours. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,26,26,48,48,2.5,2.5,10000 total time: 7.89 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(52·10193-7)/9 = 5(7)193<194> = 3 · 1517945766670785449<19> · 7229865440639606423<19> · C157
C157 = P29 · C128
P29 = 36201349029514598526708460117<29>
C128 = [48476176164638862053734691122979671227372039614455965680139465155443601982618066197127877857347079214807473440402864044309127201<128>]
(22·10189-1)/3 = 7(3)189<190> = 11419757 · 211184184100965653310251<24> · C160
C160 = P40 · C120
P40 = 5247840149796055570797016942289983138483<40>
C120 = [579432132513201923188799315527338302692526852393619136492994578653670372434846049946697734504501561737781423227202527993<120>]
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(2·10163+43)/9 = (2)1627<163> = 7 · 665141705436521827<18> · 16929455156593115948878553<26> · C118
C118 = P43 · P76
P43 = 6031404599401018735875679381997121151338791<43>
P76 = 4674270295113837822854436114846620958627275146480609988485697911563517332841<76>
Number: 22227_163 N=28192415356793158638192183338666628496972623324831542589743436403638771282467070408328673563565546545108383620701535231 ( 119 digits) SNFS difficulty: 163 digits. Divisors found: r1=6031404599401018735875679381997121151338791 (pp43) r2=4674270295113837822854436114846620958627275146480609988485697911563517332841 (pp76) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 123.25 hours. Scaled time: 75.30 units (timescale=0.611). Factorization parameters were as follows: name: 22227_163 n: 28192415356793158638192183338666628496972623324831542589743436403638771282467070408328673563565546545108383620701535231 m: 200000000000000000000000000000000 c5: 125 c0: 86 skew: 3 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, 5050001) Primes: RFBsize:315948, AFBsize:316481, largePrimes:5868108 encountered Relations: rels:5997608, finalFF:752496 Max relations in full relation-set: 28 Initial matrix: 632494 x 752496 with sparse part having weight 52357200. Pruned matrix : 542953 x 546179 with weight 37194109. Total sieving time: 107.20 hours. Total relation processing time: 0.55 hours. Matrix solve time: 15.26 hours. Time per square root: 0.24 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: 123.25 hours. --------- CPU info (if available) ----------
By JMB / GGNFS-0.77.1-20060513-pentium4 gnfs
(43·10175-7)/9 = 4(7)175<176> = 14939 · 4317097 · 1960212386193323<16> · 127940434931842043369211386141447<33> · C118
C118 = P39 · P79
P39 = 763897337718851240158040328891174998761<39>
P79 = 3866933145518429531145860572794691424526989665039376693712221630894313776948959<79>
Number: N N=2953939934998311490528636347565898394866912376577013806908991905371744510519282906721459264905889799112985767185239799 ( 118 digits) Divisors found: r1=763897337718851240158040328891174998761 (pp39) r2=3866933145518429531145860572794691424526989665039376693712221630894313776948959 (pp79) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 54.19 hours. Scaled time: 75.38 units (timescale=1.391). Factorization parameters were as follows: name: (43*10^175-7)/9 n: 2953939934998311490528636347565898394866912376577013806908991905371744510519282906721459264905889799112985767185239799 skew: 27933.439453 # norm 2.76E+016 c5: 46440 c4: 15919347198 c3: 794873662952672 c2: -16331705097650427727 c1: 72617376145568288769948 c0: -3166591147057956099235500 #alpha -6.130000 Y1: 2146726319689 Y0: -36366385004763909404629 # Murphy_E 4.21E-010 # M 1451513041968703703828818440282867894869931362701179822260165269419519531044952989144692605747778864404447562205796047 type: gnfs rlim: 3000000 alim: 3000000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 1500000) Primes: RFBsize:216816, AFBsize:216593, largePrimes:4196009 encountered Relations: rels:4469126, finalFF:496294 Max relations in full relation-set: 28 Initial matrix: 433493 x 496294 with sparse part having weight 55279533. Pruned matrix : .Bye386919 x 389150 with weight 41507429. Total sieving time: 41.95 hours. Total relation processing time: 0.49 hours. Matrix solve time: 4.16 hours. Time per square root: 7.59 hours. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,26,26,48,48,2.5,2.5,10000 total time: 54.19 hours. --------- CPU info (if available) ----------
Note: Stage-1 was run on a half dozen various Win 2K/XP systems under a Win32 Service which did sieving and then reported the results via TCP to the server. The server was a Win XP system using the standard (unchanged factLat Perl script under Cygwin. After finishing enough sieving, the server then ran stage-2 to combine the relationships into a solution. The distributed solution is nearly ready for release and is undergoing final testing. This allows the usage of widely seperated sieving boxes connected via the Internet with no real limit to the number of boxes doing the sieving. The only real limit remains the ability of GGNFS running stage-2 on a single computer. (JMB)
By JMB / GGNFS-0.77.1-20060513-pentium4 gnfs, GMP-ECM
(28·10173-1)/9 = 3(1)173<174> = 53 · 103612676339<12> · 9737493193419986671<19> · 4029058309486985448887299<25> · C118
C118 = P46 · P72
P46 = 8534554809469539304814207677240295290372836899<46>
P72 = 169197978104796095779666677633728972685095582295334772633741546037171823<72>
Number: (28*10^173-1)/9 N=1444029417786809326216074338636756742582966400392870610411306174183091069957309374175846325040369985779578551217496877 ( 118 digits) Divisors found: r1=8534554809469539304814207677240295290372836899 (pp46) r2=169197978104796095779666677633728972685095582295334772633741546037171823 (pp72) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 5.55 hours. Scaled time: 7.57 units (timescale=1.362). Factorization parameters were as follows: name: (28*10^173-1) / 9 n: 1444029417786809326216074338636756742582966400392870610411306174183091069957309374175846325040369985779578551217496877 skew: 194611.937500 # norm 2.85E+016 c5: 1680 c4: 1335413090 c3: 321482727796697 c2: -68089523444144920932 c1: -2302372693675166477282388 c0: 251690766419023337740020717303 #alpha -6.140000 Y1: 3444533872571 Y0: -61213817829518135028194 # Murphy_E 3.67E-010 # M 239252686453123260267081379725652920492612042247994112100599700325613153692251770206633906010643691349709478943063231 type: gnfs rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 10000 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, 480000 ) Primes: RFBsize:216816, AFBsize:216947, largePrimes:4950686 encountered Relations: rels:5036597, finalFF:488485 Max relations in full relation-set: 28 Initial matrix: 433843 x 488485 with sparse part having weight 51885627. Pruned matrix : 394594 x 396827 with weight 39632489. Total sieving time: 0.00 hours. Total relation processing time: 0.97 hours. Matrix solve time: 4.29 hours. Time per square root: 0.29 hours. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,48,48,2.5,2.5,10000 total time: 5.55 hours. --------- CPU info (if available) ----------
(5·10199-23)/9 = (5)1983<199> = 3 · 31277 · 34583 · 36830777 · 6174445327<10> · 6305736184704221383<19> · 724344547984221899382886622270430893<36> · C118
C118 = P41 · P78
P41 = 15858988068329679345878746056908033966491<41>
P78 = 103932934578622459308779680198050058529802658072383622797509303406164951216671<78>
By Yousuke Koide / GMP-ECM
(10999-1)/9 = (1)999<999> = 33 · 372 · 757 · 1999 · 333667 · 2028119 · 96455449 · 247629013 · 427437692443<12> · 440334654777631<15> · 30557051518647307<17> · 2212394296770203368013<22> · 8845981170865629119271997<25> · 90077814396055017938257237117<29> · 2503678796850536532770633167883644999<37> · [4136757950500351829215273898264330779279657730180289971062696133525101971148657576622167629405278071146511535383508907868849825502655065801803508961793912566261290961976951<172>] · C634
C634 = P35 · P599
P35 = 68885090548207172944216819625900521<35>
P599 = 16989834767951509031938751456470779957376208624594709376211656213370064684984633304388134960508271034832056618519143241563631532588441360500147367129958133789914094159571288306035042403779689292340510647516223418462257058336779201137214951212266048958064627771176958757849988307147846164903913010604988764934222058919014664774137590031035792137818601922602807016038065261064197179079525701612553643232430118896932477008910217562927802867516220097438300248900772708069422161298115050068864917478406641492193973323261629305188343912545008348449403435869162536203715623201231362280817617231040081308533<599>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(52·10189-7)/9 = 5(7)189<190> = 193 · 936953 · 4752323308811190522323273<25> · C157
C157 = P33 · P125
P33 = 221420394725445605000799427000151<33>
P125 = 30364219319826735248650667358804337247970993171027903229829909448703653062603642525176895821064372165356594333176821379499831<125>
(52·10172-7)/9 = 5(7)172<173> = 3 · 53 · 229 · 331 · 17419 · 7794933312767<13> · 574391550268011338538164911<27> · C122
C122 = P32 · P91
P32 = 14367225085697915795287524745117<32>
P91 = 4278422527553913505771834755528035916005882974401794090104527392050825146837825931010046247<91>
By Yousuke Koide / GMP-ECM
(10933-1)/9 = (1)933<933> = 3 · 37 · 1867 · 3733 · 339613 · 4344673058714954477761314793437392900672885445361103905548950933<64> · 2557410180456133012695296509537372979376491356924379552525114935669331084986752230647446546259197479934221837065635648510025350381215759674118823641087628274237766333894639357732286152115312924645292259846495854098673368096039697255340580355564267<247> · C608
C608 = P36 · C572
P36 = 481990095942746727246571539537397351<36>
C572 = [78968209816937478263795842683215577016210668185929748401436435310861329800142492283086732016766909763162151381418413878504379769468460785295342817558185727530083174996166240797880342488083669178503520526523380736471188636753000749537543105862022786061825823041600010019846303925381814720695174047893552825653768463736056901073303302448320439833336792060480962786440653551493748044022646053792698490482715162079526964365506374555421425625940882637068430487326265191809589604211734852371071652770674214608049631562009647437331939060116244949916713624889373626257566587128587<572>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Bruce Dodson / GMP-ECM
(10393-1)/9 = (1)393<393> = 3 · 37 · 787 · 80173 · 109517 · 141811693 · 446790173 · 7370364319027<13> · 15594845538029429933<20> · 7317723970031057677693<22> · 131758351065116151205213<24> · 180222062287834025451247081<27> · 11983466231266295686798098306470812807267<41> · C217
C217 = P49 · P169
P49 = 1100517845115354201024243897527295703743726722437<49>
P169 = 8680060322508824594393450058221938248644256663178820249090487083301292519777205595423409349376525925423911644010932939670160279114134954869470847308423421566533831579067<169>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Wataru Sakai / GGNFS-0.77.1-20060513-pentium4
10183-9 = (9)1821<183> = C183
C183 = P59 · P62 · P63
P59 = 49314675241585004778040302476198275634070752715382741171333<59>
P62 = 27179661213248372553517898319953454110361829996769269348594493<62>
P63 = 746070354608195431221196594309881696831382401936346066887929639<63>
Number: test N=999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 ( 183 digits) SNFS difficulty: 183 digits. Divisors found: r1=49314675241585004778040302476198275634070752715382741171333 (pp59) r2=27179661213248372553517898319953454110361829996769269348594493 (pp62) r3=746070354608195431221196594309881696831382401936346066887929639 (pp63) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 693.77 hours. Scaled time: 870.68 units (timescale=1.255). Factorization parameters were as follows: n: 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 m: 1000000000000000000000000000000000000 c5: 1000 c0: -9 skew: 1 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 10400001) Primes: RFBsize:501962, AFBsize:500591, largePrimes:6582409 encountered Relations: rels:7042426, finalFF:1138240 Max relations in full relation-set: 28 Initial matrix: 1002620 x 1138240 with sparse part having weight 77666909. Pruned matrix : 890943 x 896020 with weight 60231765. Total sieving time: 658.07 hours. Total relation processing time: 1.06 hours. Matrix solve time: 34.33 hours. Time per square root: 0.32 hours. Prototype def-par.txt line would be: snfs,183,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 693.77 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 gnfs
(2·10163+61)/9 = (2)1629<163> = 32 · 139 · 1210801 · 1115069503<10> · 725285628261153897132220859<27> · C118
C118 = P42 · P76
P42 = 761860097003061775609574934943524755379623<42>
P76 = 2381064543231869191934548798422487616615874054481195444767670889236963622749<76>
Number: 22229_163 N=1814038063877182841401857985549425415789637699634763116341145011895306527483066218905233296189598338648966492853843627 ( 118 digits) Divisors found: r1=761860097003061775609574934943524755379623 (pp42) r2=2381064543231869191934548798422487616615874054481195444767670889236963622749 (pp76) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 95.14 hours. Scaled time: 58.23 units (timescale=0.612). Factorization parameters were as follows: name: 22229_163 n: 1814038063877182841401857985549425415789637699634763116341145011895306527483066218905233296189598338648966492853843627 skew: 54556.16 # norm 5.22e+15 c5: 35760 c4: 824980868 c3: -243975418425104 c2: 1210152699479810801 c1: 365768834554650299254910 c0: -4225460881627121993335122775 # alpha -5.23 Y1: 1134037947163 Y0: -34757594460612935108244 # Murphy_E 3.82e-10 # M 145070186104097092653043400977547244110897557992933454442252958316216359431500264754146837604667943660512937007560201 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, 3990001) Primes: RFBsize:315948, AFBsize:315208, largePrimes:7659692 encountered Relations: rels:7760879, finalFF:780547 Max relations in full relation-set: 28 Initial matrix: 631240 x 780547 with sparse part having weight 65108804. Pruned matrix : 504499 x 507719 with weight 38951632. Polynomial selection time: 4.43 hours. Total sieving time: 75.34 hours. Total relation processing time: 0.92 hours. Matrix solve time: 13.94 hours. Time per square root: 0.53 hours. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 95.14 hours. --------- CPU info (if available) ----------
By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
(14·10153-41)/9 = 1(5)1521<154> = 3 · 11 · 88256925209<11> · 9297581956571547150667<22> · C119
C119 = P37 · P38 · P45
P37 = 5869281371990934517896039538832558131<37>
P38 = 24106869046755270050566332204861288659<38>
P45 = 406000940317690411891991058441288457615883581<45>
Number: test N=57445072003404701363203335515060261736047876565777623202277926783180283144761034643442564878604284961558202284453114149 ( 119 digits) SNFS difficulty: 154 digits. Divisors found: r1=5869281371990934517896039538832558131 (pp37) r2=24106869046755270050566332204861288659 (pp38) r3=406000940317690411891991058441288457615883581 (pp45) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 34.66 hours. Scaled time: 29.67 units (timescale=0.856). Factorization parameters were as follows: n: 57445072003404701363203335515060261736047876565777623202277926783180283144761034643442564878604284961558202284453114149 m: 2000000000000000000000000000000 c5: 875 c0: -82 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2200001) Primes: RFBsize:176302, AFBsize:176584, largePrimes:5473280 encountered Relations: rels:5306437, finalFF:400078 Max relations in full relation-set: 0 Initial matrix: 352952 x 400078 with sparse part having weight 33257430. Pruned matrix : 331945 x 333773 with weight 24776358. Total sieving time: 29.50 hours. Total relation processing time: 0.46 hours. Matrix solve time: 4.46 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 34.66 hours. --------- CPU info (if available) ----------
By JMB / GGNFS-0.77.1-20060513-pentium4 gnfs
10180+9 = 1(0)1799<181> = 29 · 53 · 67033 · 2271206017<10> · 5186257364017<13> · 23670431279329<14> · 1153178324949098471581835646098710369<37> · C101
C101 = P36 · P66
P36 = 280771938914481207966046774999018277<36>
P66 = 107515366282598987181603343567825994793954957702377171456669085293<66>
Number: Job N=30187297854265955340839026475771432703339043701378522512760624169899371628725359916608624530578900161 ( 101 digits) Divisors found: r1=280771938914481207966046774999018277 (pp36) r2=107515366282598987181603343567825994793954957702377171456669085293 (pp66) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 1.51 hours. Scaled time: 1.99 units (timescale=1.320). Factorization parameters were as follows: name: Job n: 30187297854265955340839026475771432703339043701378522512760624169899371628725359916608624530578900161 skew: 14419.32 # norm 2.67e+014 c5: 30000 c4: -200576340 c3: -19944828508384 c2: -76423963274765993 c1: 1256607135224133054124 c0: -2933090521390132407939712 # alpha -6.51 Y1: 23452030007 Y0: -15868703858252830905 # Murphy_E 2.94e-009 # M 26243756146532592332210597896072185256913651889324693570901958506917004720982464758064521831519658178 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 10000 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, 1440001) Primes: RFBsize:135072, AFBsize:133877, largePrimes:3811261 encountered Relations: rels:3721649, finalFF:307182 Max relations in full relation-set: 28 Initial matrix: 269029 x 307182 with sparse part having weight 22082602. Pruned matrix : 240697 x 242106 with weight 14550235. Total sieving time: 0.00 hours. Total relation processing time: 0.27 hours. Matrix solve time: 1.08 hours. Time per square root: 0.16 hours. 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: 1.51 hours. --------- CPU info (if available) ----------
Note: A mix of 4 systems (XP & 2K) with an experimental network version of GGNFS. One system local, the other 3 systems remote over the Internet. Actual real time, exactly 4.5 hours. (JMB)
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
10180+9 = 1(0)1799<181> = 29 · 53 · 67033 · 2271206017<10> · 5186257364017<13> · 23670431279329<14> · C137
C137 = P37 · C101
P37 = 1153178324949098471581835646098710369<37>
C101 = [30187297854265955340839026475771432703339043701378522512760624169899371628725359916608624530578900161<101>]
(4·10183-1)/3 = 1(3)183<184> = 31 · 191 · 1441447205041<13> · C168
C168 = P34 · P134
P34 = 6072305590934333145116691628161281<34>
P134 = 25727128498375098828468605178370279518924233409783280779712479401958175869912315139968289557372463400226652457116345975767906836633413<134>
By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 gnfs
10187+9 = 1(0)1869<188> = 131 · 889796277314453<15> · 257182844103564007<18> · 534221796617984999646462038876207<33> · C120
C120 = P38 · P83
P38 = 46380071957938637799624457780838279939<38>
P83 = 13463038988859045230601743027672415432613633469191464238601408561268969782958135733<83>
Number: test N=624416717075815956418387439219885297129632171625703612920258713290457714163614874975484756782174120692018842001812960287 ( 120 digits) Divisors found: r1=46380071957938637799624457780838279939 (pp38) r2=13463038988859045230601743027672415432613633469191464238601408561268969782958135733 (pp83) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 108.78 hours. Scaled time: 95.62 units (timescale=0.879). Factorization parameters were as follows: name: test n: 624416717075815956418387439219885297129632171625703612920258713290457714163614874975484756782174120692018842001812960287 skew: 82032.68 # norm 1.58e+16 c5: 26640 c4: -1892851050 c3: -665282759993338 c2: 21579123426525373733 c1: 1604607886731191767427182 c0: 12012190188221992101476024128 # alpha -5.34 Y1: 1507813949081 Y0: -118573636331197106730999 # Murphy_E 2.79e-10 # M 194582865165137178428195865785239108272202113357042784592412946166876127374665336547701087884574524171915983078141962741 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, 4710001) Primes: RFBsize:315948, AFBsize:316939, largePrimes:7679259 encountered Relations: rels:7699054, finalFF:710267 Max relations in full relation-set: 0 Initial matrix: 632966 x 710267 with sparse part having weight 73630538. Pruned matrix : 573734 x 576962 with weight 53605846. Total sieving time: 83.27 hours. Total relation processing time: 1.75 hours. Matrix solve time: 22.99 hours. Time per square root: 0.77 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: 108.78 hours. --------- CPU info (if available) ----------
By JMB / GGNFS-0.77.1-20060513-athlon-xp gnfs
(5·10162-17)/3 = 1(6)1611<163> = 164076642253592773<18> · 3467585771022759954025112257<28> · C118
C118 = P50 · P69
P50 = 13087620058046631959993084591838258467056180917457<50>
P69 = 223827837558522390339892066815882054959737192972738012418729835888593<69>
Number: Job N=2929373696380120915420844504125371244948839260830283456490946306945700548601185908936173210016579452797771199580868001 ( 118 digits) Divisors found: r1=13087620058046631959993084591838258467056180917457 (pp50) r2=223827837558522390339892066815882054959737192972738012418729835888593 (pp69) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 47.15 hours. Scaled time: 86.94 units (timescale=1.844). Factorization parameters were as follows: name: (5*10^162-17)/3 (C118) n: 2929373696380120915420844504125371244948839260830283456490946306945700548601185908936173210016579452797771199580868001 skew: 42442.109375 # norm 1.58E+016 c5: 113220 c4: -13331106708 c3: -598331550851393 c2: 14672009091871272899 c1: 638442542548238304495483 c0: -1094640139667582557540540821 #alpha -6.560000 Y1: 2615262625259 Y0: -30378841351670209238248 # Murphy_E 4.03E-010 # M 945153404266162509028427668802199907711894421324314351187289110756934010427599444509716626073746157422304913109119527 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 3750001) Primes: RFBsize:250150, AFBsize:249604, largePrimes:7791659 encountered Relations: rels:7812331, finalFF:624982 Max relations in full relation-set: 28 Initial matrix: 499838 x 624982 with sparse part having weight 63103867. Pruned matrix : 408269 x 410832 with weight 41941917. Total sieving time: 42.72 hours. Total relation processing time: 0.32 hours. Matrix solve time: 3.87 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.5,2.5,60000 total time: 47.15 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10171-7)/9 = 9(7)171<172> = 32 · 19 · 1811 · 11839 · 824679440616849163<18> · 75641005071705113898148003<26> · C119
C119 = P50 · P70
P50 = 14605153717126806279150957554605672217739146622139<50>
P70 = 2927264666988950529424877716042538664876915437450385858565497463678093<70>
Number: 97777_171 N=42753150432087633563269806313292842264358298521714558766823452062563630797240050069307805296959170412010015283803100927 ( 119 digits) SNFS difficulty: 173 digits. Divisors found: r1=14605153717126806279150957554605672217739146622139 (pp50) r2=2927264666988950529424877716042538664876915437450385858565497463678093 (pp70) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 385.43 hours. Scaled time: 235.50 units (timescale=0.611). Factorization parameters were as follows: name: 97777_171 n: 42753150432087633563269806313292842264358298521714558766823452062563630797240050069307805296959170412010015283803100927 m: 20000000000000000000000000000000000 c5: 55 c0: -14 skew: 3 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 11300001) Primes: RFBsize:501962, AFBsize:502197, largePrimes:6536889 encountered Relations: rels:7002442, finalFF:1146396 Max relations in full relation-set: 28 Initial matrix: 1004225 x 1146396 with sparse part having weight 71985085. Pruned matrix : 881319 x 886404 with weight 54141652. Total sieving time: 331.63 hours. Total relation processing time: 1.33 hours. Matrix solve time: 52.03 hours. Time per square root: 0.43 hours. Prototype def-par.txt line would be: snfs,173,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 385.43 hours. --------- CPU info (if available) ----------
By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
(10160+71)/9 = (1)1599<160> = 3 · 6781 · 935971 · 10662763 · 54488692536470399<17> · C126
C126 = P34 · P92
P34 = 7705207815128361758535915747767663<34>
P92 = 13035257023255755892253709177324288688206891999314832662653855898078395052424282312810258233<92>
Number: test N=100439364287797115559198333140766663985000303404901034584222277865427662296609088955539445318007939959959632657299956316919479 ( 126 digits) SNFS difficulty: 160 digits. Divisors found: r1=7705207815128361758535915747767663 (pp34) r2=13035257023255755892253709177324288688206891999314832662653855898078395052424282312810258233 (pp92) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 64.35 hours. Scaled time: 56.11 units (timescale=0.872). Factorization parameters were as follows: n: 100439364287797115559198333140766663985000303404901034584222277865427662296609088955539445318007939959959632657299956316919479 m: 100000000000000000000000000000000 c5: 1 c0: 71 skew: 2.35 type: snfsFactor 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:283453, largePrimes:5686050 encountered Relations: rels:5720090, finalFF:636577 Max relations in full relation-set: 0 Initial matrix: 566663 x 636577 with sparse part having weight 38066033. Pruned matrix : 514471 x 517368 with weight 28552678. Total sieving time: 51.02 hours. Total relation processing time: 0.42 hours. Matrix solve time: 12.62 hours. Time per square root: 0.30 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: 64.35 hours. --------- CPU info (if available) ----------
By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
10173-9 = (9)1721<173> = 401 · 2528185841<10> · C161
C161 = P45 · P117
P45 = 938580727415304869460365420846237262713037883<45>
P117 = 105093292974603519781220816145515742537483095614362298755215504949519619870717052285912811121252640366779911913175797<117>
Number: 99991_173 N=98638539366573120452994767723440582424050055416812167532315793178419311373542771635535734084350490583679502593832805512478586901259119729035900095445164099717751 ( 161 digits) SNFS difficulty: 173 digits. Divisors found: r1=938580727415304869460365420846237262713037883 (pp45) r2=105093292974603519781220816145515742537483095614362298755215504949519619870717052285912811121252640366779911913175797 (pp117) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 255.28 hours. Scaled time: 222.86 units (timescale=0.873). Factorization parameters were as follows: n: 98638539366573120452994767723440582424050055416812167532315793178419311373542771635535734084350490583679502593832805512478586901259119729035900095445164099717751 m: 10000000000000000000000000000000000 c5: 1000 c0: -9 skew: 1 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 9700001) Primes: RFBsize:501962, AFBsize:500591, largePrimes:6358041 encountered Relations: rels:6796903, finalFF:1124380 Max relations in full relation-set: 0 Initial matrix: 1002620 x 1124380 with sparse part having weight 61398959. Pruned matrix : 897151 x 902228 with weight 46452392. Total sieving time: 207.68 hours. Total relation processing time: 1.52 hours. Matrix solve time: 45.57 hours. Time per square root: 0.50 hours. Prototype def-par.txt line would be: snfs,173,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 255.28 hours. --------- CPU info (if available) ----------
By CWI / gnfs
10396+1 = 1(0)3951<397> = 73 · 137 · 617 · 2377 · 3169 · 16369 · 98641 · 432961 · 761113 · 99990001 · 6796152793<10> · 24387741577<11> · 99677548081<11> · 440718109921<12> · 3199044596370769<16> · 126197002179733470481<21> · 283830826522232279893972777<27> · 4987445373502665124237014313<28> · 16205834846012967584927082656402106953<38> · 7408727338313716781446937691661250885891761<43> · C141
C141 = P69 · P73
P69 = 246288943607463575049631057704872789315648893038409344335438892115177<69>
P73 = 3286441734725167632640591449151190304019453738946987847768004461574472857<73>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Yousuke Koide / GMP-ECM
(10617-1)/9 = (1)617<617> = C617
C617 = P31 · C586
P31 = 4830562365700424178611903148293<31>
C586 = [2300169270146668925037321150876838558648667950628240672650039331746387974782871253313969194853396587686058063292655000320957266896220069555631724155204278453926330052442955420796251175701773298213899837780766062880369630179988196955676879181343546242395734859492490033529658820766340472502868595502146307641275074456945435446896412683895393487125218380817138534097945963671721164306273869369942045979928375831793037151313223825888601824572075094230007167441099574805037126062025169064291518766436994915997184460232574847196621162803220266629118550960504767813084206134721484308826030427<586>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By JMB / GGNFS-0.77.1 gnfs
(8·10156-71)/9 = (8)1551<156> = 7 · 47 · 131 · 248692069 · 9944396663<10> · 9275005532447911<16> · C117
C117 = P31 · P37 · P50
P31 = 2997698735605426418767872380233<31>
P37 = 9764529913019020615309018869039972997<37>
P50 = 30717538201460534340297361939081901505386210927107<50>
Number: Job N=899136715284523369077591605553594215443688063801386230671576796657095902988937771674709332494070529673951870737835207 ( 117 digits) Divisors found: r1=2997698735605426418767872380233 (pp31) r2=9764529913019020615309018869039972997 (pp37) r3=30717538201460534340297361939081901505386210927107 (pp50) Version: GGNFS-0.77.1 Total time: 41.67 hours. Scaled time: 77.09 units (timescale=1.850). Factorization parameters were as follows: name: (8*10^156-71)/9 n: 899136715284523369077591605553594215443688063801386230671576796657095902988937771674709332494070529673951870737835207 skew: 26671.449219 # norm 2.20E+016 c5: 475200 c4: 25292363578 c3: -734548944339791 c2: -19516094989828822425 c1: -162675718473930164799925 c0: 455080907979280906821907451 #alpha -6.580000 Y1: 343208536379 Y0: -18004860957275713061334 # Murphy_E 4.14E-010 # M 739616504969869649068527192358617520744048083453378070391281540997102668229365593228562839239521216353745679411815636 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 3550001) Relations: rels:6527129, finalFF:568546 Initial matrix: 500690 x 568546 with sparse part having weight 49461972. Pruned matrix : 475185 x 477752 with weight 34016748. Total sieving time: 37.60 hours. Total relation processing time: 0.22 hours. Matrix solve time: 3.61 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,49,49,2.4,2.4,100000 total time: 41.67 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
101070+1 = 1(0)10691<1071> = 101 · 2141 · 3541 · 6421 · 27961 · 40882343106721<14> · 10719760477926601<17> · 96252210267521261<17> · 1044374808061138338437701<25> · 2421825498886875706568085804897442030525256100180294305383840413574930314582991559155197335837338973747281007884658776715423100656032123324942160620509168628560523446063044557248001192491268292405581<199> · C381 · [45694159383400420895364062596466617852011611775786881006869558599910610477217486868157712852442098496522223654849953527635815397518621032760219197455320181715888758085627187505475337742196481586876017626037509524302125956337784834421608468635159467331874295244291090287619654281670689896547808944858108979299754064139473542218852080477844583741540567121079524887709382309414572330079377484133964448440781<404>]
C381 = P40 · C341
P40 = 2663175124735692788546303920893311173981<40>
C341 = [56025976983785216427301670566879779317040561350457827417120594801025302395071738849640118305957601394748668668688506204426236050310120629885748911472915942193623343473886452313329016411247009778894661048613349991077945420288986786603484482370957104815945360455226140581889842852067952305461502335440826258942522067467072165653391816299579621<341>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 gnfs
5·10160-1 = 4(9)160<161> = 19 · 436091 · 2329189 · 1033904918067164428884577564259<31> · C118
C118 = P49 · P69
P49 = 6893933938446466919399636517410130127156761488611<49>
P69 = 363485282102468445025331961873781689545727542437808306501301663929371<69>
Number: 49999_160 N=2505843522411995360881620202892235691372910031817756477061988171397055319833605473171594643548876245306856441524893681 ( 118 digits) Divisors found: r1=6893933938446466919399636517410130127156761488611 (pp49) r2=363485282102468445025331961873781689545727542437808306501301663929371 (pp69) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 101.60 hours. Scaled time: 68.58 units (timescale=0.675). Factorization parameters were as follows: name: 49999_160 n: 2505843522411995360881620202892235691372910031817756477061988171397055319833605473171594643548876245306856441524893681 skew: 67698.81 # norm 1.66e+16 c5: 43680 c4: 2257503728 c3: -777745474760110 c2: -6995506859892789237 c1: 1061094916189007052816270 c0: 6870339507820636323602079525 # alpha -6.12 Y1: 1479919241581 Y0: -35623294165211846579056 # Murphy_E 3.92e-10 # M 2441904005236875944325738509808338119467647459205288901605343286851365346903917443586164924402372617797036892016430170 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 4170001) Primes: RFBsize:315948, AFBsize:315757, largePrimes:7681791 encountered Relations: rels:7773988, finalFF:761206 Max relations in full relation-set: 28 Initial matrix: 631791 x 761206 with sparse part having weight 66536489. Pruned matrix : 524261 x 527483 with weight 42459606. Total sieving time: 84.05 hours. Total relation processing time: 0.97 hours. Matrix solve time: 16.09 hours. Time per square root: 0.49 hours. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 101.60 hours. --------- CPU info (if available) ----------
By JMB / GGNFS-0.77.1 gnfs
(82·10163+71)/9 = 9(1)1629<164> = 32 · 112 · 395287 · 2377426606649<13> · 150235770371064075681776231<27> · C117
C117 = P46 · P72
P46 = 1380055841093701458474306253109586399637999751<46>
P72 = 429391857648325781478819024438910645718621748253085861588269453741208257<72>
Number: Job N=592584741265647161919373632559337423859197124960778106705162031198827682993772730378812360822463487801493429405144007 ( 117 digits) Divisors found: r1=1380055841093701458474306253109586399637999751 (pp46) r2=429391857648325781478819024438910645718621748253085861588269453741208257 (pp72) Version: GGNFS-0.77.1 Total time: 44.05 hours. Scaled time: 81.27 units (timescale=1.845). Factorization parameters were as follows: name: (82*10^163+71)/9 n: 592584741265647161919373632559337423859197124960778106705162031198827682993772730378812360822463487801493429405144007 skew: 18073.009766 # norm 4.72E+015 c5: 310800 c4: 16468673320 c3: -198783222359184 c2: -4542315464963551881 c1: 32947377273969925276064 c0: -76038780804607144144203495 #alpha -5.490000 Y1: 19557325663 Y0: -18032414674158987800432 # Murphy_E 4.32E-010 # M 462678572950758850991351445594612693415045523695436613693612378778682584519992700519503425655894148746364718950202916 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 3650001) Relations: rels:6680093, finalFF:602897 Initial matrix: 500010 x 602897 with sparse part having weight 56108267. Pruned matrix : 465300 x 467864 with weight 33835212. Total sieving time: 40.09 hours. Total relation processing time: 0.23 hours. Matrix solve time: 3.48 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,49,49,2.4,2.4,100000 total time: 44.05 hours. --------- CPU info (if available) ----------
Tyler Cadigan certified 239 prime numbers by using PRIMO 2.2.0 beta 6. All the prime numbers under 2000 digits in our tables had been completely certified.
Newly certified prime numbers are: 101383+7, (101452+71)/9, (101679+71)/9, (11·101179+7)/9, (11·101596+7)/9, (11·101084+43)/9, (4·101205+17)/3, (4·101835+17)/3, (13·101443+23)/9, (13·101111+41)/9, (14·101323+31)/9, (5·101083-11)/3, (5·101296+1)/3, (5·101356+1)/3, (5·101398+7)/3, (16·101756-7)/9, 2·101370-3, 2·101488+3, 2·101819+3, (19·101344+17)/9, (19·101573+17)/9, (2·101011+7)/9, (2·101178+7)/9, (2·101217+7)/9, (2·101168+43)/9, (2·101695+43)/9, (7·101049-1)/3, (7·101006+17)/3, (22·101801-13)/9, (22·101941+23)/9, (23·101746-41)/9, (23·101277+13)/9, (23·101665+13)/9, (23·101979+13)/9, (8·101190+7)/3, (25·101241-7)/9, (25·101417+11)/9, (26·101307-71)/9, (26·101237+1)/9, 3·101137+7, (28·101505-1)/9, (28·101805+53)/9, (29·101005-11)/9, (101732-7)/3, (101918-7)/3, (31·101334+23)/9, (31·101482+41)/9, (32·101965+13)/9, (32·101052+31)/9, (32·101163+31)/9, (32·101485+31)/9, (32·101731+31)/9, (32·101970+31)/9, (11·101088-17)/3, (11·101219-17)/3, (11·101656-17)/3, (34·101185+11)/9, (35·101609-71)/9, (35·101668-71)/9, (35·101674-71)/9, (35·101127+1)/9, (35·101518+1)/9, (35·101761+1)/9, 4·101609-9, 4·101737+3, (37·101871+71)/9, (13·101040-7)/3, (13·101887-7)/3, (13·101246-1)/3, (13·101752-1)/3, (13·101860+11)/3, (4·101310+23)/9, (4·101044+41)/9, (41·101456-23)/9, (41·101217+13)/9, (41·101640+13)/9, (41·101450+31)/9, (14·101063-17)/3, (14·101509-11)/3, (14·101608+1)/3, (14·101904+1)/3, (43·101041-7)/9, (43·101089-7)/9, (43·101093-7)/9, (43·101297-7)/9, (43·101271+11)/9, (43·101412+11)/9, (44·101706-17)/9, (44·101090+1)/9, 5·101091-3, 5·101366-3, 5·101714-3, 5·101774-3, 5·101077+3, 5·101177+3, 5·101552+3, 5·101199+9, (46·101235-1)/9, (46·101727-1)/9, (46·101812-1)/9, (46·101048+17)/9, (47·101641-11)/9, (47·101646-11)/9, (47·101304+43)/9, (47·101644+43)/9, (16·101705-1)/3, (49·101799-31)/9, (49·101782+23)/9, (49·101077+41)/9, (49·101383+41)/9, (49·101566+41)/9, (49·101960+41)/9, (5·101002+31)/9, (17·101777-11)/3, (17·101252+7)/3, (17·101893+7)/3, (52·101097-61)/9, (52·101226-7)/9, (52·101324+11)/9, (52·101600+11)/9, (53·101115-71)/9, (53·101419-71)/9, (53·101689-71)/9, (53·101201+1)/9, 6·101022-7, (55·101195+53)/9, (19·101272-7)/3, (19·101008+11)/3, (19·101517+11)/3, (58·101340-31)/9, (58·101575-13)/9, (58·101234+23)/9, (58·101538+23)/9, (59·101363-41)/9, (59·101876-41)/9, (59·101332-23)/9, (59·101395-23)/9, (59·101811-23)/9, (59·101489+13)/9, (59·101488+31)/9, (2·101600-17)/3, (61·101055-43)/9, (61·101997-43)/9, (61·101193-7)/9, (61·101730-7)/9, (61·101811-7)/9, (61·101871-7)/9, (62·101027-71)/9, (62·101605-53)/9, (62·101362-17)/9, 7·101255-9, 7·101259-9, 7·101384-3, 7·101594-3, 7·101048+3, 7·101974+3, 7·101058+9, 7·101563+9, 7·101695+9, 7·101816+9, 7·101937+9, (64·101724+71)/9, (65·101132-11)/9, (65·101570-11)/9, (65·101851+61)/9, (22·101089-7)/3, (22·101607-7)/3, (22·101079-1)/3, (22·101595+17)/3, (67·101315-31)/9, (68·101346-41)/9, (68·101843+31)/9, (23·101157-11)/3, (23·101344+7)/3, (7·101067-61)/9, (71·101314-53)/9, (71·101728-53)/9, (71·101728+1)/9, (71·101876+1)/9, (71·101884+1)/9, 8·101157-9, 8·101427-9, 8·101876-7, 8·101359+3, (73·101746-1)/9, (73·101461+53)/9, (73·101614+71)/9, (74·101154+7)/9, (74·101246+7)/9, (74·101874+43)/9, (74·101067+61)/9, (25·101925-1)/3, (25·101420+17)/3, (25·101462+17)/3, (76·101614-31)/9, (76·101339-13)/9, (76·101797-13)/9, (77·101074-41)/9, (77·101211-23)/9, (77·101056+13)/9, (77·101856+31)/9, (26·101176-11)/3, (26·101473+7)/3, (79·101319-61)/9, (79·101227-43)/9, (8·101096-71)/9, (8·101419-71)/9, 9·101061-7, 9·101186-7, 9·101853-7, 9·101350+7, 9·101736+7, (82·101909+53)/9, (83·101810-11)/9, (83·101373+7)/9, (28·101025+11)/3, (28·101172+11)/3, (28·101353+11)/3, (85·101290-13)/9, (85·101915+23)/9, (86·101416-41)/9, (86·101450-41)/9, (86·101442-23)/9, (86·101721-23)/9, (29·101131-17)/3, (29·101198-17)/3, (29·101743-17)/3, (29·101872-17)/3, (29·101408+1)/3, (29·101486+1)/3, (29·101712+1)/3, (88·101031-43)/9, (88·101239-43)/9, (88·101891-7)/9, (89·101192-71)/9, (89·101260-71)/9, (89·101392-53)/9, 101107-9 and 101887-3.
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(4·10181-1)/3 = 1(3)181<182> = 13 · 208003 · 947369 · 6213997 · C162
C162 = P30 · C133
P30 = 422657489810930235663875844391<30>
C133 = [1981741514598812229481879734997465766050310558827137636411795585696942843981824920305180687606156525827556280138909164422933883661169<133>]
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 gnfs
(19·10156-1)/9 = 2(1)156<157> = 71 · 6632063 · 36137897 · 72099682374588477659537<23> · C118
C118 = P43 · P75
P43 = 4636228306457607462635241942913928692255657<43>
P75 = 371144524930028738274438333409653087743425848528036989882492056181504067359<75>
Number: 21111_156 N=1720710752267360410105609345232545624387885928118481566071559188882648454506534550677196332416770769659285549776799863 ( 118 digits) Divisors found: r1=4636228306457607462635241942913928692255657 (pp43) r2=371144524930028738274438333409653087743425848528036989882492056181504067359 (pp75) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 95.69 hours. Scaled time: 58.56 units (timescale=0.612). Factorization parameters were as follows: name: 21111_156 n: 1720710752267360410105609345232545624387885928118481566071559188882648454506534550677196332416770769659285549776799863 skew: 67470.35 # norm 7.69e+15 c5: 8340 c4: 2693958160 c3: -247736409110981 c2: -9971288712667080996 c1: 310344041495595923871180 c0: 5692810027268370676923538416 # alpha -5.31 Y1: 297831307213 Y0: -46015927782010312498585 # Murphy_E 3.88e-10 # M 22695345206128828176637561883451475757938048504662292121030122801492708956969441634842119491414876978104227342224742 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, 3990001) Primes: RFBsize:315948, AFBsize:316687, largePrimes:7668538 encountered Relations: rels:7774387, finalFF:785989 Max relations in full relation-set: 28 Initial matrix: 632712 x 785989 with sparse part having weight 63385380. Pruned matrix : 502602 x 505829 with weight 37903759. Total sieving time: 80.36 hours. Total relation processing time: 1.43 hours. Matrix solve time: 13.36 hours. Time per square root: 0.54 hours. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 95.69 hours. --------- CPU info (if available) ----------
By JMB / GGNFS-0.77.1 gnfs
(79·10182-7)/9 = 8(7)182<183> = 115987387 · 125687914650272813477483495359<30> · 277453739305469829129656557217<30> · C117
C117 = P48 · P70
P48 = 162056010817029360137027687776827583842235554323<48>
P70 = 1339135644904339985823718669445723597191456382468572443486293907060559<70>
Number: Job N=217014980556087308878927231813617367028075041392377799114208275145971398575415608280897569212675022064944352895246557 ( 117 digits) Divisors found: r1=162056010817029360137027687776827583842235554323 (pp48) r2=1339135644904339985823718669445723597191456382468572443486293907060559 (pp70) Version: GGNFS-0.77.1 Total time: 42.65 hours. Scaled time: 79.12 units (timescale=1.855). Factorization parameters were as follows: name: (79*10^182-7)/9 n: 217014980556087308878927231813617367028075041392377799114208275145971398575415608280897569212675022064944352895246557 skew: 61590.828125 # norm 2.24E+016 c5: 20880 c4: -12338727134 c3: -419279908850309 c2: 33963095371967508346 c1: 681561752337410900249080 c0: -23423277003549404626500902592 #alpha -6.490000 Y1: 2658245483993 Y0: -25313793572045121558227 # Murphy_E 4.27E-010 # M 102689576836686222011314360928127318722076257797759486725450542555420135684534362258338233999715520749962921487761097 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 3600001) Relations: rels:6609022, finalFF:597261 Initial matrix: 500200 x 597261 with sparse part having weight 53144885. Pruned matrix : 466084 x 468649 with weight 32422170. Total sieving time: 38.83 hours. Total relation processing time: 0.22 hours. Matrix solve time: 3.36 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,49,49,2.4,2.4,100000 total time: 42.65 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 gnfs
8·10167-1 = 7(9)167<168> = 9439 · 6271129 · 106683139 · 4006996902901<13> · 288689376711364702949<21> · C117
C117 = P46 · P71
P46 = 6699442777335423652252069571185108736736497909<46>
P71 = 16346846671469550453943562736383940599589650231774542042153858211713471<71>
Number: 79999_167 N=109514763865386290777458175990679805223116309295754300737131171375962407278963151743982808794463348440192106698632139 ( 117 digits) Divisors found: r1=6699442777335423652252069571185108736736497909 (pp46) r2=16346846671469550453943562736383940599589650231774542042153858211713471 (pp71) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 84.68 hours. Scaled time: 56.99 units (timescale=0.673). Factorization parameters were as follows: name: 79999_167 n: 109514763865386290777458175990679805223116309295754300737131171375962407278963151743982808794463348440192106698632139 skew: 36968.17 # norm 4.75e+15 c5: 30660 c4: -6699269768 c3: -93580883140749 c2: 8089962192932196080 c1: 67664030510233170685222 c0: -1238997054605988332371740160 # alpha -5.37 Y1: 1305639979501 Y0: -20444727018117514523559 # Murphy_E 4.51e-10 # M 39792006408851603576345681438263979568746439464916972834789019409408685336844465229572147209599156983171569402045178 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 3870001) Primes: RFBsize:315948, AFBsize:315999, largePrimes:7638500 encountered Relations: rels:7740528, finalFF:787770 Max relations in full relation-set: 28 Initial matrix: 632032 x 787770 with sparse part having weight 65396655. Pruned matrix : 497525 x 500749 with weight 38439370. Total sieving time: 69.89 hours. Total relation processing time: 1.17 hours. Matrix solve time: 13.17 hours. Time per square root: 0.45 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 84.68 hours. --------- CPU info (if available) ----------
By JMB / GGNFS-0.77.1 gnfs
(73·10152-1)/9 = 8(1)152<153> = 5231 · 1054888361<10> · 183000140980702502916941<24> · C117
C117 = P47 · P71
P47 = 24501822758582821147734188172261373770858670363<47>
P71 = 32782291808142593311323070496639770907390327179373591214478907883163487<71>
Number: Job N=803225903503251375441492928863425757906879320546286373789569303265743856991535394189124497517331138811415542970635781 ( 117 digits) Divisors found: r1=24501822758582821147734188172261373770858670363 (pp47) r2=32782291808142593311323070496639770907390327179373591214478907883163487 (pp71) Version: GGNFS-0.77.1 Total time: 48.48 hours. Scaled time: 89.70 units (timescale=1.850). Factorization parameters were as follows: name: (73*10^152-1)/9 n: 803225903503251375441492928863425757906879320546286373789569303265743856991535394189124497517331138811415542970635781 skew: 23007.630859 # norm 3.68E+015 c5: 84780 c4: -9423911058 c3: -132469474889920 c2: 4155757346501018329 c1: 27456603732540635947216 c0: -406511063813649227120699245 #alpha -5.050000 Y1: 231241072423 Y0: -24849001857844668661608 # Murphy_E 4.22E-010 # M 187023802232222326968134068717950088092301513770255333477897951266691344534879367302085971353460158407144614502961620 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 3550001) Relations: rels:6514381, finalFF:562397 Initial matrix: 500042 x 562397 with sparse part having weight 49028961. Pruned matrix : 475951 x 478515 with weight 34662345. Total sieving time: 44.20 hours. Total relation processing time: 0.25 hours. Matrix solve time: 3.79 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,49,49,2.4,2.4,100000 total time: 48.48 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
101365+1 = 1(0)13641<1366> = 72 · 11 · 132 · 127 · 131 · 157 · 211 · 241 · 859 · 2161 · 2689 · 2731 · 6397 · 9091 · 15601 · 102103 · 216451 · 459691 · 909091 · 925081 · 4147571 · 5528251 · 21705503 · 1058313049<10> · 6097697971<10> · 29970369241<11> · 388847808493<12> · 2475034612051<13> · 1081846114760321<16> · 1661378260814161<16> · 46205575684179731<17> · 265212793249617641<18> · 18276168846821336356291<23> · 8396862596258693901610602298557167100076327481<46> · 50678387411703889101759125785290439894389920385627096501794498837<65> · 63054129911571801941639263405768461425999152026392552531582926655481271974023945336611<86> · 8912569571903773640423787742857701624820835919699625957033503601168338923351027082278688276455237261214743926133405384757726021771250608797<139> · [7348023713666465741898930375855789029789464909885364967534063144593321690065366703003692450137448338937174103088086714517623508982957303799165476749049702132200218043013256379700020843782902271375636103812410575633147508310537651713291289362891<244>] · C557
C557 = P34 · C523
P34 = 5953395590224596670581957589121611<34>
C523 = [2004998801509816834528353258112094373105529161478551283683705464440700442984709214710195875363759710481731526743624317554533712190365917140323245459612168736799912101299519392426066712075092932531520557875236443696387407579531930581235067950866698744918032256986617935009109949405241428228768640408192661482239626787198518652265480559638316410906287531592065772701689250814432033269924896413227127820439562911129321577880582441778297527405930723705963499683331617178413325297388589135242867960612562900048832019334801463851<523>]
101490+1 = 1(0)14891<1491> = 101 · 3541 · 8941 · 10729 · 27961 · 62581 · 607921 · 14118155281<11> · 4672884738461<13> · 72286688991301<14> · 171815892427926701<18> · 136916416686052955621<21> · 2336398996447692315465181<25> · 43449727365272099794386367962241<32> · [110870679844269144354635709949582391774770890704083103791132633566371413253392265378550591815806580691669808595307539634355488864836833845471616794677024940025967620229919340559408262151273358247434378152195260280636870443948931086228877135378433246056449430881437009<267>] · [1605214440709619357797351581919800889833597416421394148739815672950024771161380823847360755208273655227157019000219766490046550207325155036864476602837123952047383195091299758360303040822482624716944164463773873136231905729534814986307576307291846151794615420341552185181793289760376366513402259834628028778708825939521820938434639815230158850634413284564675945198522078882483236008364966125191436705573836033815481341830782769681163394145324260216840198126909976526595416165428782222227927578041059481<502>] · C565
C565 = P33 · C532
P33 = 288402714464678603661515072629901<33>
C532 = [4687503701333508851256425417962904885375200005043201496848030933628747825778284688210275818169480640608168077056902317515395120792907032865219785785076968504013049506348485769792263508395503545914909970684711332090901533468360290476533363489724126165274721454889372181951580540850435434732716298746125463875071075773117230503169402354871600441390151925280448418028302390337639009056554495130407551605694121397154681442893998340626858000137971953882007629207560203701156525511475684644675528789377433417628326649954345383225734414041<532>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Larry Soule found the new record of near-repdigit prime. Congratulations!
The Top Twenty: Near-repdigit (Chris Caldwell)
The Prime Database: 99*10^139670-1 (Chris Caldwell)
By JMB / GGNFS-0.77.1 gnfs
(25·10165-1)/3 = 8(3)165<166> = 13 · 83 · 4639 · 32467 · 51827 · 4107116293025635448404972857043840170431<40> · C111
C111 = P49 · P62
P49 = 5999449387037714495954196079889132518450585874639<49>
P62 = 40153768547251570734358449133185923567697636094197901682467253<62>
Number: Job N=240900502098062695718454982659129074938309425445966501601113646284209039650805899058746429435186090844480696667 ( 111 digits) Divisors found: r1=5999449387037714495954196079889132518450585874639 (pp49) r2=40153768547251570734358449133185923567697636094197901682467253 (pp62) Version: GGNFS-0.77.1 Total time: 20.41 hours. Scaled time: 37.59 units (timescale=1.842). Factorization parameters were as follows: name: (25*10^165-1)/3 n: 240900502098062695718454982659129074938309425445966501601113646284209039650805899058746429435186090844480696667 skew: 25466.730469 # norm 3.39E+015 c5: 27120 c4: -5390987914 c3: 8497381520849 c2: 1595269104010676103 c1: 24596920797753575326655 c0: 132349367513539707807132675 #alpha -6.330000 Y1: 314787248407 Y0: -1547793846076789196966 # Murphy_E 9.05E-010 # M 14119416429294653906379593036307881965427918338110091922459921111477241917334756269198169367046346216231247206 type: gnfs rlim: 1500000 alim: 1500000 lpbr: 27 lpba: 27 mfbr: 48 mfba: 48 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [750000, 1750001) Relations: rels:5560796, finalFF:280603 Initial matrix: 228357 x 280603 with sparse part having weight 33124374. Pruned matrix : 219090 x 220295 with weight 21292064. Total sieving time: 19.29 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.84 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,27,27,48,48,2.4,2.4,50000 total time: 20.41 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GMP-ECM 6.1
(4·10157-31)/9 = (4)1561<157> = 29 · 412 · 229 · 1029337 · C144
C144 = P41 · P104
P41 = 11185420019696678677811865661633748545271<41>
P104 = 34578520511371229487723717650783373547939991261364004863630803290628246801392406565091826983685186774023<104>
By JMB / GGNFS-0.77.1 gnfs
(5·10170-41)/9 = (5)1691<170> = 37 · 313 · 908057 · 3670254134669<13> · 24536274467882790513965408261<29> · C117
C117 = P45 · P73
P45 = 153844545425862687340722165776442412015106329<45>
P73 = 6451109343674756752111870167141420157744082464822706132191420041611257973<73>
Number: Job N=992467984470178341940502766726206764199893272446874595614385542559268311663027354996771104251058134036124229044011117 ( 117 digits) Divisors found: r1=153844545425862687340722165776442412015106329 (pp45) r2=6451109343674756752111870167141420157744082464822706132191420041611257973 (pp73) Version: GGNFS-0.77.1 Total time: 39.49 hours. Scaled time: 71.48 units (timescale=1.810). Factorization parameters were as follows: name: (5*10^170-41)/9 n: 992467984470178341940502766726206764199893272446874595614385542559268311663027354996771104251058134036124229044011117 skew: 21869.570313 # norm 7.97E+015 c5: 279420 c4: 24104791726 c3: -411335644337987 c2: -11129444714046459234 c1: 94497930495376867528312 c0: 473069290404730440743411628 #alpha -6.040000 Y1: 2040608782597 Y0: -20421660632318944258709 # Murphy_E 4.31E-010 # M 600250544765919998160706580103596564837744526025385686492718238874592079176948007294093484952357404053668839267024766 type: gnfs rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 3200001) Relations: rels:6636270, finalFF:511212 Initial matrix: 434513 x 511212 with sparse part having weight 51974095. Pruned matrix : 411595 x 413831 with weight 34111046. Total sieving time: 36.03 hours. Total relation processing time: 0.22 hours. Matrix solve time: 3.02 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,49,49,2.4,2.4,100000 total time: 39.49 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(4·10177-1)/3 = 1(3)177<178> = 4409 · 22961 · 43665368763292497076610163467<29> · C141
C141 = P36 · P105
P36 = 629137278840301384011004218471056683<36>
P105 = 479430089604487894618926344059780662233800055303705449563176659285817775888589892056977346367120055373397<105>
(25·10165-1)/3 = 8(3)165<166> = 13 · 83 · 4639 · 32467 · 51827 · C150
C150 = P40 · C111
P40 = 4107116293025635448404972857043840170431<40>
C111 = [240900502098062695718454982659129074938309425445966501601113646284209039650805899058746429435186090844480696667<111>]
By JMB / GGNFS-0.77.1 gnfs
(29·10157+7)/9 = 3(2)1563<158> = 3 · 11 · 10067 · 854403763 · 975070907 · 1066205252151981181<19> · C117
C117 = P58 · P59
P58 = 9862368846537342478020282947582970294867350950735042705057<58>
P59 = 11071846866820804070085218362918235577295451087767095667769<59>
Number: Job N=109194637612965582757157054678170405369236672431925016095884673701161331105134448751110568439919685652183431528207833 ( 117 digits) Divisors found: r1=9862368846537342478020282947582970294867350950735042705057 (pp58) r2=11071846866820804070085218362918235577295451087767095667769 (pp59) Version: GGNFS-0.77.1 Total time: 39.11 hours. Scaled time: 70.76 units (timescale=1.809). Factorization parameters were as follows: name: (29*10^157+7)/9 n: 109194637612965582757157054678170405369236672431925016095884673701161331105134448751110568439919685652183431528207833 skew: 68782.632813 # norm 1.60E+016 c5: 37440 c4: -7349052604 c3: -559191156216077 c2: 28413876272894978735 c1: 1584022261071821381770041 c0: 4521208474751966537468523345 #alpha -6.460000 Y1: 1266860677159 Y0: -19632436184550177958918 # Murphy_E 4.58E-010 # M 38032488552444801230624772198371492566513504629713595090916085391814893942557929506764709525238802175151229697766689 type: gnfs rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 3200001) Relations: rels:6627335, finalFF:516251 Initial matrix: 433511 x 516251 with sparse part having weight 51455107. Pruned matrix : 408909 x 411140 with weight 32653240. Total sieving time: 35.77 hours. Total relation processing time: 0.22 hours. Matrix solve time: 2.90 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,49,49,2.4,2.4,100000 total time: 39.11 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
10749+1 = 1(0)7481<750> = 11 · 1499 · 28463 · 32957 · 74687 · 392263 · 795653 · 909091 · 280267614929<12> · 194749234429526109677<21> · 75477148962003664034473049<26> · 628293465283949443537007319053023<33> · 9140689231828972552925524522037823147045937571379494322686226282352288670801988451<82> · C542
C542 = P35 · C507
P35 = 56551536406585191369576818265496921<35>
C507 = [228020479574439748034731153191840116996782247349077540725301759571900604992195906919299727529964169457434823051161598425307013757847295654890840215377471075792693206151779377142860486225077961374792309623921202576927179385859455798305838359439471140797559276496307070424120514928275979572460313570875861453835674283860562132374210839334869812450578929519584579066252591802632127979694097389410891779196128461569361161421596684619548820343893072038813674553976083993845844401013665766500188220965881996874493<507>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(8·10163+1)/9 = (8)1629<163> = 32 · 23 · 47 · 16210981 · 14927571306573495683<20> · C133
C133 = P36 · P98
P36 = 371170022616402508958072914658993689<36>
P98 = 10172036962400690910532121592646379027538365586549967767020563977473616469588683434425556511531503<98>
(25·10183-1)/3 = 8(3)183<184> = 13 · 264283155301751969<18> · C166
C166 = P34 · C132
P34 = 3549264066261561396021839666828027<34>
C132 = [683388405517072877233927862242245555525777832139299820368098214942685744600601296640806157169483609696082817414193194488909381546507<132>]
By JMB / GGNFS-0.77.1 gnfs
(28·10168+17)/9 = 3(1)1673<169> = 666228053 · 12470878883<11> · 33138415031<11> · 32490475068028908608957<23> · C117
C117 = P53 · P65
P53 = 16385707085601640431344222972305731862833563422720619<53>
P65 = 21224749018633649910137929505034946199285667288473150875648596319<65>
Number: Job N=347782520384741861506700307174557396694002746074477872300429362821720689080996955971489594953074389906021259448801461 ( 117 digits) Divisors found: r1=16385707085601640431344222972305731862833563422720619 (pp53) r2=21224749018633649910137929505034946199285667288473150875648596319 (pp65) Version: GGNFS-0.77.1 Total time: 40.43 hours. Scaled time: 73.50 units (timescale=1.818). Factorization parameters were as follows: name: (28*10^168+17)/9 n: 347782520384741861506700307174557396694002746074477872300429362821720689080996955971489594953074389906021259448801461 skew: 26425.080078 # norm 8.62E+015 c5: 182280 c4: -2058113582 c3: 164545497386647 c2: 5984825622362747370 c1: -183822693896929580967684 c0: -46177562120726179069454520 #alpha -6.580000 Y1: 322427535091 Y0: -18034901040942785950027 # Murphy_E 4.68E-010 # M 75060498289421360939860192635877806438078360018099897025350154299777835814830611224896812915499159086862264755479752 type: gnfs rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 3200001) Relations: rels:6864582, finalFF:591946 Initial matrix: 433812 x 591946 with sparse part having weight 63602478. Pruned matrix : 388948 x 391181 with weight 31094194. Total sieving time: 37.23 hours. Total relation processing time: 0.23 hours. Matrix solve time: 2.78 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,49,49,2.4,2.4,100000 total time: 40.43 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GMP-ECM 6.1, GGNFS-0.77.1-20060513-pentium4 gnfs
(22·10184-1)/3 = 7(3)184<185> = 13 · 613 · 2281 · 14868970103047296245613937657<29> · C150
C150 = P40 · P44 · P67
P40 = 2031080946385714878679659203604090401921<40>
P44 = 21945234169387169334196823964344482962911429<44>
P67 = 6087289750244991176881048532900144215876009240110234950082092759569<67>
-------------------------------------------------------------------------------- Input number is 271326008406630128238872515463149625877354734768189047779930524749980293347074947943662398980732616918692654155507590620036804998472605855111160688021 (150 digits) Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1650881922 Step 1 took 349291ms Step 2 took 112389ms ********** Factor found in step 2: 21945234169387169334196823964344482962911429 Found probable prime factor of 44 digits: 21945234169387169334196823964344482962911429 Composite cofactor 12363778226851658638804893129335340162753617078451260421665895618168765300291081742463569950579841228732049 has 107 digits -------------------------------------------------------------------------------- Number: template N=12363778226851658638804893129335340162753617078451260421665895618168765300291081742463569950579841228732049 ( 107 digits) Divisors found: r1=2031080946385714878679659203604090401921 (pp40) r2=6087289750244991176881048532900144215876009240110234950082092759569 (pp67) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 18.29 hours. Scaled time: 22.99 units (timescale=1.257). Factorization parameters were as follows: name: template n: 12363778226851658638804893129335340162753617078451260421665895618168765300291081742463569950579841228732049 skew: 22789.77 # norm 3.10e+014 c5: 2340 c4: -398302965 c3: -10216058861434 c2: -13884546662538244 c1: 2027046464299948407818 c0: -2007001082567218081705635 # alpha -5.19 Y1: 154384318913 Y0: -350423791053635097226 # Murphy_E 1.50e-009 # M 10817716021220227761602447619130818932091000933110480399993043144783173863818229918415548312281906103274965 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, 2450001) Primes: RFBsize:183072, AFBsize:183087, largePrimes:4569109 encountered Relations: rels:4788587, finalFF:554889 Max relations in full relation-set: 28 Initial matrix: 366236 x 554889 with sparse part having weight 43558978. Pruned matrix : 242243 x 244138 with weight 23035380. Polynomial selection time: 1.08 hours. Total sieving time: 15.61 hours. Total relation processing time: 0.23 hours. Matrix solve time: 1.16 hours. Time per square root: 0.20 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: 18.29 hours. --------- CPU info (if available) ---------- --------------------------------------------------------------------------------
By JMB / GGNFS-0.77.1 gnfs
(2·10180+43)/9 = (2)1797<180> = 17 · 239 · 113177 · 15272032201952205157<20> · 136224300968205436467179879754395287<36> · C117
C117 = P40 · P77
P40 = 5558661540664315482839927301493931936647<40>
P77 = 41788890014541574244523074808400148246998304107338687225849783582778228178449<77>
Number: Job N=232290295750883296131439774105626527875056675632797772800763276168416357472031357205659940208252291417037581678720503 ( 117 digits) Divisors found: r1=5558661540664315482839927301493931936647 (pp40) r2=41788890014541574244523074808400148246998304107338687225849783582778228178449 (pp77) Version: GGNFS-0.77.1 Total time: 39.38 hours. Scaled time: 59.14 units (timescale=1.502). Factorization parameters were as follows: name: (2*10^180+43)/9 n: 232290295750883296131439774105626527875056675632797772800763276168416357472031357205659940208252291417037581678720503 skew: 9349.429688 # norm 1.71E+015 c5: 264720 c4: -9523916494 c3: -61337468606242 c2: 22676187366698402 c1: -269265682539014474973 c0: 5121980116927843701921948 #alpha -4.640000 Y1: 318706942937 Y0: -15440057987372811183991 # Murphy_E 4.66E-010 # M 69253233117561781989395062316267320386824023092863487817179644402226643072076701551648395600868986918207942320169534 type: gnfs rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 3200001) Relations: rels:6790880, finalFF:559535 Initial matrix: 433737 x 559535 with sparse part having weight 57653840. Pruned matrix : 397949 x 400181 with weight 31074701. Total sieving time: 35.94 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.00 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,49,49,2.4,2.4,100000 total time: 39.38 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10169-7)/9 = 9(7)169<170> = 379 · 1277 · 4273 · 475167601 · C152
C152 = P35 · P46 · P72
P35 = 37350460755027633587644875964382999<35>
P46 = 4409353470751458981059214537553493540306417779<46>
P72 = 604170426485645551645435173395485943426251747190098266896590237901019043<72>
Number: 97777_169 N=99501663567416802757943949514997808834996790510533353884050335532583489142338088177622578683020941966164588894667452416472305275977351140857946300585503 ( 152 digits) SNFS difficulty: 171 digits. Divisors found: r1=37350460755027633587644875964382999 (pp35) r2=4409353470751458981059214537553493540306417779 (pp46) r3=604170426485645551645435173395485943426251747190098266896590237901019043 (pp72) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 320.06 hours. Scaled time: 215.08 units (timescale=0.672). Factorization parameters were as follows: name: 97777_169 n: 99501663567416802757943949514997808834996790510533353884050335532583489142338088177622578683020941966164588894667452416472305275977351140857946300585503 m: 10000000000000000000000000000000000 c5: 44 c0: -35 skew: 4 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, 9800001) Primes: RFBsize:412849, AFBsize:412837, largePrimes:6333893 encountered Relations: rels:6634339, finalFF:947650 Max relations in full relation-set: 28 Initial matrix: 825752 x 947650 with sparse part having weight 76425953. Pruned matrix : 730966 x 735158 with weight 59238469. Total sieving time: 278.68 hours. Total relation processing time: 1.49 hours. Matrix solve time: 39.52 hours. Time per square root: 0.36 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: 320.06 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GMP-ECM 6.1, GGNFS-0.77.1-20060513-pentium4 gnfs
(4·10165-1)/3 = 1(3)165<166> = 157 · 83297702222519<14> · 31498475790963799<17> · C133
C133 = P38 · P39 · P56
P38 = 73734584147276662658901916882345178111<38>
P39 = 763162496562153777788361534760296511667<39>
P56 = 57521243829208317483878443841979756256108901163271675277<56>
Input number is 3236804907430004528606917948362126891424658553679801203805105246107656670221796513073490090353393840110682144058628658834319679302249 (133 digits) Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=93173744 Step 1 took 279290ms Step 2 took 96017ms ********** Factor found in step 2: 73734584147276662658901916882345178111 Found probable prime factor of 38 digits: 73734584147276662658901916882345178111 Composite cofactor 43898056046059001796632047622934408387778458962541754944675353574964831022429528052130265956759 has 95 digits --------------------------------------------------------------- Number: template N=43898056046059001796632047622934408387778458962541754944675353574964831022429528052130265956759 ( 95 digits) Divisors found: r1=763162496562153777788361534760296511667 (pp39) r2=57521243829208317483878443841979756256108901163271675277 (pp56) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 8.83 hours. Scaled time: 11.17 units (timescale=1.265). Factorization parameters were as follows: name: template n: 43898056046059001796632047622934408387778458962541754944675353574964831022429528052130265956759 m: 5555252496116222501049 deg: 4 c4: 46092480 c3: -97993599572 c2: 595858358302098957 c1: -165953902866421130 c0: -851764011351318078373880 skew: 1635.250 type: gnfs # adj. I(F,S) = 55.637 # E(F1,F2) = 3.551640e-005 # GGNFS version 0.77.1-20060513-pentium4 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1156655070. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [600000, 1440001) Primes: RFBsize:92938, AFBsize:93056, largePrimes:1920708 encountered Relations: rels:2025755, finalFF:251251 Max relations in full relation-set: 28 Initial matrix: 186075 x 251251 with sparse part having weight 22285816. Pruned matrix : 159264 x 160258 with weight 11995849. Total sieving time: 8.34 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.32 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 8.83 hours. --------- CPU info (if available) ----------
By JMB / GGNFS-0.77.1 gnfs, GGNFS-0.77.1-20050930-prescott gnfs
(19·10152-1)/9 = 2(1)152<153> = 59 · 67 · 179 · 211 · 209919090707<12> · 23255047412505613<17> · C117
C117 = P45 · P73
P45 = 103466483476477569371883659837304092315490593<45>
P73 = 2799496547093994558129967204266584630456496784372432258039009023750741721<73>
Number: N N=289654063232356797575174326723012494182204658797247957617870812204664068855517973508513921321914344063894921748130553 ( 117 digits) Divisors found: r1=103466483476477569371883659837304092315490593 (pp45) r2=2799496547093994558129967204266584630456496784372432258039009023750741721 (pp73) Version: GGNFS-0.77.1 Total time: 39.11 hours. Scaled time: 71.29 units (timescale=1.823). Factorization parameters were as follows: name: (19*10^152-1)/9 n: 289654063232356797575174326723012494182204658797247957617870812204664068855517973508513921321914344063894921748130553 skew: 33281.148438 # norm 1.31E+016 c5: 146760 c4: 8776090268 c3: -378888624324306 c2: 2008532010338895485 c1: 181500397538308165856108 c0: -9512360289270801960444615 #alpha -6.180000 Y1: 1353449699413 Y0: -18157414057605125091206 # Murphy_E 4.39E-010 # M 57804010562778641285000682977123609322272133912438546446115654711394932009165525472078479225981090915205914161475441 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [2000000, 3600001) Relations: rels:6482955, finalFF:650007 Initial matrix: 566651 x 650007 with sparse part having weight 48490135. Pruned matrix : 527816 x 530713 with weight 30728326. Total sieving time: 35.03 hours. Total relation processing time: 0.19 hours. Matrix solve time: 3.65 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 39.11 hours. --------- CPU info (if available) ----------
(16·10167-7)/9 = 1(7)167<168> = 32 · 401 · 1129 · 731121689659444742569<21> · 288186292597430549439121<24> · C117
C117 = P54 · P63
P54 = 466603873318081534951944598024969453319073680131135729<54>
P63 = 443797980480291249951903306203053836868259406908879789548246217<63>
Number: N N=207077856662846240235313334079932768382063026764942737221802202305784699021628764915860564562697346780044408337787193 ( 117 digits) Divisors found: r1=466603873318081534951944598024969453319073680131135729 (pp54) r2=443797980480291249951903306203053836868259406908879789548246217 (pp63) Version: GGNFS-0.77.1-20050930-prescott Total time: 61.26 hours. Scaled time: 34.73 units (timescale=0.567). Factorization parameters were as follows: name: (16*10^167-7)/9 n: 207077856662846240235313334079932768382063026764942737221802202305784699021628764915860564562697346780044408337787193 skew: 15523.200195 # norm 3.87E+015 c5: 95760 c4: -22188300468 c3: -68028203400212 c2: 5340600972906269443 c1: 8989035250724614085172 c0: -50635669207311551042279145 #alpha -5.510000 Y1: 660506461483 Y0: -18492286938618375162754 # Murphy_E 4.50E-010 # M 181309531116944392876346575739884961409984050243104986523315894074131008584101572192481570234445987008852354289724910 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [2000000, 3450001) Primes: RFBsize:283146, AFBsize:283160, largePrimes:6597661 encountered Relations: rels:6649891, finalFF:727592 Max relations in full relation-set: 40 Initial matrix: 566388 x 727592 with sparse part having weight 60993166. Pruned matrix : 431545 x 434440 with weight 33848319. Total sieving time: 55.21 hours. Total relation processing time: 0.47 hours. Matrix solve time: 4.84 hours. Time per square root: 0.74 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 61.26 hours. --------- CPU info (if available) ----------
By Bruce Dodson / GMP-ECM
10381+1 = 1(0)3801<382> = 7 · 11 · 13 · 2287 · 3557 · 857772733 · 1094479651<10> · 1125629957<10> · 451897625287<12> · 616896149073719728613<21> · 10860110813777339731289<23> · 1053449334720579590200819<25> · 36099531273603138218699301565567581705151216702113889<53> · C214
C214 = P67 · P147
P67 = 4444349792156709907895752551798631908946180608768737946280238078881<67>
P147 = 227106988265159616528571981140572415396122551755756282296008613353922816015404819504625289055134338407924996143023758066472872886277706507970899321<147>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By JMB / GGNFS-0.77.1-20050930-prescott gnfs
(85·10152+41)/9 = 9(4)1519<153> = 13 · 197 · 647467307 · 47985896085289799139356507<26> · C116
C116 = P45 · P71
P45 = 170725642594225454451474174348792505239958339<45>
P71 = 69524300558461150094284117980194046531241851609895069471577519549231219<71>
Number: N N=11869580888757347476677473220519036107142951936630492926951713697053493324085561964441889112990282999987147038185241 ( 116 digits) Divisors found: r1=170725642594225454451474174348792505239958339 (pp45) r2=69524300558461150094284117980194046531241851609895069471577519549231219 (pp71) Version: GGNFS-0.77.1-20050930-prescott Total time: 57.90 hours. Scaled time: 37.86 units (timescale=0.654). Factorization parameters were as follows: name: N n: 11869580888757347476677473220519036107142951936630492926951713697053493324085561964441889112990282999987147038185241 skew: 77179.72 # norm 1.06e+16 c5: 28500 c4: -1605905960 c3: -548908396432052 c2: 7781721018062958274 c1: 1362966716976629355637771 c0: 710581451553397893524894505 # alpha -6.08 Y1: 652928892803 Y0: -13302042930398130801026 # Murphy_E 4.80e-10 # M 8449198108053675294351358438215934681689131985295566294009697841106082365994216984520945583606473255174825235480823 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [2000000, 3500001) Primes: RFBsize:283146, AFBsize:283339, largePrimes:6781742 encountered Relations: rels:7035319, finalFF:894776 Max relations in full relation-set: 40 Initial matrix: 566568 x 894776 with sparse part having weight 74170174. Pruned matrix : 326506 x 329402 with weight 45123261. Total sieving time: 53.51 hours. Total relation processing time: 0.41 hours. Matrix solve time: 3.47 hours. Time per square root: 0.50 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 57.90 hours. --------- CPU info (if available) ----------
By JMB / GGNFS-0.77.1-20050930-prescott gnfs
(82·10173-1)/9 = 9(1)173<174> = 17 · 31 · 19429 · 19681 · 446657 · 2013294557<10> · 78950206397<11> · 1126772355818365857299<22> · C116
C116 = P49 · P68
P49 = 1571702898001461970102304550267406109116965542297<49>
P68 = 35960170890831727400644102888162433825269692846803398137464594472023<68>
Number: N N=56518704801748040280654501946968595175553050255691308769059931493973136174743292493725036143767525833564358589656831 ( 116 digits) Divisors found: r1=1571702898001461970102304550267406109116965542297 (pp49) r2=35960170890831727400644102888162433825269692846803398137464594472023 (pp68) Version: GGNFS-0.77.1-20050930-prescott Total time: 62.22 hours. Scaled time: 40.32 units (timescale=0.648). Factorization parameters were as follows: name: N n: 56518704801748040280654501946968595175553050255691308769059931493973136174743292493725036143767525833564358589656831 skew: 50027.61 # norm 2.07e+16 c5: 31200 c4: -147363988 c3: -781844286702183 c2: 2754728581108013796 c1: 352679167912523767114844 c0: -2293971195865843122762610752 # alpha -5.89 Y1: 1067130078613 Y0: -17848739285818037536723 # Murphy_E 4.47e-10 # M 48101014183249661044274227258519366403604948342237387695100379056370372856318552282656444115075891531416884556421210 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [2000000, 3450001) Primes: RFBsize:283146, AFBsize:282427, largePrimes:6542520 encountered Relations: rels:6563316, finalFF:702600 Max relations in full relation-set: 40 Initial matrix: 565654 x 702600 with sparse part having weight 57603385. Pruned matrix : 450451 x 453343 with weight 32528559. Total sieving time: 56.51 hours. Total relation processing time: 0.52 hours. Matrix solve time: 4.62 hours. Time per square root: 0.57 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 62.22 hours. --------- CPU info (if available) ----------
By JMB / GGNFS-0.77.1-20050930-prescott gnfs
(64·10164+53)/9 = 7(1)1637<165> = 3 · 53503 · 940054483999<12> · 48314243429010383503977289365067<32> · C116
C116 = P43 · P74
P43 = 1236425327944059453891143340199750359794291<43>
P74 = 78893636386011202413634291580709861715696520613238084327309376292733676671<74>
Number: N N=97546090241273282452005139478114991165570138671605243661933236313861034028750412443788439979037553951353899665685261 ( 116 digits) Divisors found: r1=1236425327944059453891143340199750359794291 (pp43) r2=78893636386011202413634291580709861715696520613238084327309376292733676671 (pp74) Version: GGNFS-0.77.1-20050930-prescott Total time: 70.33 hours. Scaled time: 45.79 units (timescale=0.651). Factorization parameters were as follows: name: N n: 97546090241273282452005139478114991165570138671605243661933236313861034028750412443788439979037553951353899665685261 skew: 80764.59 # norm 5.65e+15 c5: 8340 c4: -2213261435 c3: -160091135790358 c2: 12519422774154137710 c1: 589488626580099139001148 c0: -2075649157121883264460470960 # alpha -5.35 Y1: 329529074237 Y0: -25918451818514317799591 # Murphy_E 4.36e-10 # M 27211831738470055975133877654146693096996886542471751876593738751162646426142430179529429567875903904370129517859170 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [2000000, 3750001) Primes: RFBsize:283146, AFBsize:284148, largePrimes:6627799 encountered Relations: rels:6697658, finalFF:733495 Max relations in full relation-set: 40 Initial matrix: 567373 x 733495 with sparse part having weight 64372911. Pruned matrix : 434499 x 437399 with weight 36901761. Total sieving time: 64.04 hours. Total relation processing time: 0.42 hours. Matrix solve time: 4.65 hours. Time per square root: 1.22 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 70.33 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
10749+1 = 1(0)7481<750> = 11 · 1499 · 28463 · 32957 · 74687 · 392263 · 795653 · 909091 · 280267614929<12> · 194749234429526109677<21> · 75477148962003664034473049<26> · 9140689231828972552925524522037823147045937571379494322686226282352288670801988451<82> · C574
C574 = P33 · C542
P33 = 628293465283949443537007319053023<33>
C542 = [12894908452100944414773295073237073300097153241069055774583676737987242414978167908170745727915227967124884330106729412910004744110688873186180052252315852704258881528632513902371451144536293287065361925405261134609289404751378279953125297836822595137476253746855502501879820915343255108864259910503445366286746174398958106605930707640542374737365384945958881525381230321897275240619255078705928789062325522127169718285243629639148526956551496372360311580957215245892505084246451683751602241720569665488251213588481612988433384522783514936053<542>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By JMB / GGNFS-0.77.1 gnfs
(68·10176+13)/9 = 7(5)1757<177> = 16223 · 17119019860271735061587461<26> · 619193651836871434301224119229241<33> · C115
C115 = P57 · P58
P57 = 548948053972127355988942710985004349672426023173799306821<57>
P58 = 8003843611567193197494230112384504996406675622815584431179<58>
Number: N N=4393694374867054312301107826304771911374972036279600016021736599645847049491465120275629018011759197571909779771959 ( 115 digits) Divisors found: r1=548948053972127355988942710985004349672426023173799306821 (pp57) r2=8003843611567193197494230112384504996406675622815584431179 (pp58) Version: GGNFS-0.77.1 Total time: 32.28 hours. Scaled time: 58.21 units (timescale=1.803). Factorization parameters were as follows: name: N n: 4393694374867054312301107826304771911374972036279600016021736599645847049491465120275629018011759197571909779771959 skew: 53771.14 # norm 3.67e+15 c5: 14820 c4: 2364063772 c3: -125507969059803 c2: -6212088143643651894 c1: 142181987154929592317020 c0: 4332116672479151476518939000 # alpha -6.03 Y1: 1352439577637 Y0: -12427816160811681721229 # Murphy_E 6.10e-10 # M 1802485709720975932650912060256348315066217203872719209037178881701464471070355288236397841569812479480893529323810 type: gnfs rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 48 mfba: 48 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 2800001) Relations: rels:5518218, finalFF:548008 Initial matrix: 434577 x 548008 with sparse part having weight 43296502. Pruned matrix : 392771 x 395007 with weight 22476050. Total sieving time: 30.00 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.94 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,48,48,2.6,2.6,100000 total time: 32.28 hours. --------- CPU info (if available) ----------
By JMB / GGNFS-0.77.1-20050930-prescott gnfs, GGNFS-0.77.1 gnfs
(5·10175-41)/9 = (5)1741<175> = 489133 · 1403517697<10> · 2435964161<10> · 64249247182044594022865768916254657<35> · C116
C116 = P53 · P64
P53 = 11432280413830847705222617918639919503658191618454389<53>
P64 = 4522835909054636966935411318813189352741986783000127616479400367<64>
Number: N N=51706328378056163380057929616176601960754010322432217032605771561958673172388892161904595921026362579749982059360763 ( 116 digits) Divisors found: r1=11432280413830847705222617918639919503658191618454389 (pp53) r2=4522835909054636966935411318813189352741986783000127616479400367 (pp64) Version: GGNFS-0.77.1-20050930-prescott Total time: 67.22 hours. Scaled time: 43.82 units (timescale=0.652). Factorization parameters were as follows: name: N n: 51706328378056163380057929616176601960754010322432217032605771561958673172388892161904595921026362579749982059360763 skew: 48471.32 # norm 3.13e+16 c5: 62640 c4: -25535682078 c3: -506576515487491 c2: 39285307741783792721 c1: 883264678769304412824603 c0: -5539902059876483682909070875 # alpha -7.01 Y1: 1235812731637 Y0: -15252507920133843820594 # Murphy_E 4.57e-10 # M 29043992165356704836730301334734947366103788037605666308576012135096877153525389509722854916494244119203075603669450 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [2000000, 3450001) Primes: RFBsize:283146, AFBsize:284128, largePrimes:6820518 encountered Relations: rels:7099104, finalFF:911668 Max relations in full relation-set: 40 Initial matrix: 567353 x 911668 with sparse part having weight 77857218. Pruned matrix : 328657 x 331557 with weight 50217778. Total sieving time: 62.74 hours. Total relation processing time: 0.48 hours. Matrix solve time: 3.46 hours. Time per square root: 0.54 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 67.22 hours. --------- CPU info (if available) ----------
(5·10171-41)/9 = (5)1701<171> = 29 · 31 · 720497 · 1160893 · 1389257819416175659<19> · 30759678135525993098827<23> · C116
C116 = P49 · P68
P49 = 1136655398395752973921842937526529232079565032873<49>
P68 = 15210727229336895157226227619434966245190813056156538561963023879721<68>
Number: N N=17289355218751056377545280878875714628143017402531836624568896246743444355039258118995609342080638646672485363068433 ( 116 digits) Divisors found: r1=1136655398395752973921842937526529232079565032873 (pp49) r2=15210727229336895157226227619434966245190813056156538561963023879721 (pp68) Version: GGNFS-0.77.1 Total time: 34.84 hours. Scaled time: 63.17 units (timescale=1.813). Factorization parameters were as follows: name: N n: 17289355218751056377545280878875714628143017402531836624568896246743444355039258118995609342080638646672485363068433 skew: 41329.98 # norm 1.43e+16 c5: 45360 c4: 17199219306 c3: -361286661039353 c2: -30330523569186455797 c1: 147135491563252297346847 c0: 2812009785225248206216779777 # alpha -6.81 Y1: 3459577597769 Y0: -13068099480518898224536 # Murphy_E 5.16e-10 # M 2825033727445633616920687394495604557664583264776442097248695246583418859121758722048738749391100367416691389534089 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [2000000, 3400001) Relations: rels:6519610, finalFF:684370 Initial matrix: 566316 x 684370 with sparse part having weight 52581928. Pruned matrix : 512474 x 515369 with weight 28888924. Total sieving time: 31.34 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.08 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 34.84 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10168-7)/9 = 9(7)168<169> = 3 · 3047423 · 16256750647861<14> · C149
C149 = P55 · P95
P55 = 1161650092196977606911825290197250998288654336989039493<55>
P95 = 56633981075298388052167979569831042502150003956481301205335843212489749948759816365886195227421<95>
Number: 97777_168 N=65788869337602257470354512709932976498964658419801366922367938905952098946499946563937605731014460005019249788707206813716626708384762770883485537553 ( 149 digits) SNFS difficulty: 169 digits. Divisors found: r1=1161650092196977606911825290197250998288654336989039493 (pp55) r2=56633981075298388052167979569831042502150003956481301205335843212489749948759816365886195227421 (pp95) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 307.87 hours. Scaled time: 207.19 units (timescale=0.673). Factorization parameters were as follows: name: 97777_168 n: 65788869337602257470354512709932976498964658419801366922367938905952098946499946563937605731014460005019249788707206813716626708384762770883485537553 m: 2000000000000000000000000000000000 c5: 2750 c0: -7 skew: 3 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, 9400001) Primes: RFBsize:412849, AFBsize:412242, largePrimes:6265476 encountered Relations: rels:6545172, finalFF:932138 Max relations in full relation-set: 28 Initial matrix: 825158 x 932138 with sparse part having weight 72124302. Pruned matrix : 741740 x 745929 with weight 55940787. Total sieving time: 267.84 hours. Total relation processing time: 1.59 hours. Matrix solve time: 38.06 hours. Time per square root: 0.38 hours. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 307.87 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GGNFS-0.77.1-20060513-pentium4
(2·10158+7)/9 = (2)1573<158> = 191 · C156
C156 = P36 · P120
P36 = 131762990689564553924901894505812253<36>
P120 = 882999942521541802647808796269686171357208978670046129416456874646530567606892048042407142275493669636303904492109195301<120>
Number: test N=116346713205351948807446189645142524723676556137289121582315299592786503781268179173938336242001163467132053519488074461896451425247236765561372891215823153 ( 156 digits) SNFS difficulty: 158 digits. Divisors found: r1=131762990689564553924901894505812253 (pp36) r2=882999942521541802647808796269686171357208978670046129416456874646530567606892048042407142275493669636303904492109195301 (pp120) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 60.11 hours. Scaled time: 76.03 units (timescale=1.265). Factorization parameters were as follows: n: 116346713205351948807446189645142524723676556137289121582315299592786503781268179173938336242001163467132053519488074461896451425247236765561372891215823153 m: 20000000000000000000000000000000 c5: 125 c0: 14 skew: 1 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3800001) Primes: RFBsize:283146, AFBsize:283727, largePrimes:5772505 encountered Relations: rels:5857015, finalFF:699322 Max relations in full relation-set: 28 Initial matrix: 566938 x 699322 with sparse part having weight 46601840. Pruned matrix : 465701 x 468599 with weight 31108907. Total sieving time: 54.10 hours. Total relation processing time: 0.29 hours. Matrix solve time: 5.54 hours. Time per square root: 0.18 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: 60.11 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(4·10163-1)/3 = 1(3)163<164> = 13 · 1617029653<10> · C153
C153 = P28 · C126
P28 = 4089127132463729329999260241<28>
C126 = [155112496265691502702356326760306526844120861180050281869646762856380657373483770708019727853353298989247112858037210723680117<126>]
By Bruce Dodson / GMP-ECM
10328+1 = 1(0)3271<329> = 17 · 5882353 · 6051298241<10> · 48656086054529<14> · 669995415570582921859463287135169<33> · C264
C264 = P56 · C209
P56 = 18798124481332409484502894235050519095834690259132073729<56>
C209 = [26966706888061228309314861584452783093449979584971248841728716375604431259788120714089993744450304753814274573818260830964443146927438209553380971499989034253234857050497492661619432197590261828134053458180609<209>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By JMB / GGNFS-0.77.1-20050930-prescott gnfs
(10172+71)/9 = (1)1719<172> = 32 · 4391 · 4919 · 6337 · 503573969713352179<18> · 4894102405193232341523799<25> · C117
C117 = P50 · P68
P50 = 15441280903831977725272445863464931495519706268391<50>
P68 = 23701256234827907885716605563878213283252164799721868829312661738797<68>
Number: N N=365977755295676774775510425752865543407563187811110276370278426136480960683749215044820881215418051861192830419465627 ( 117 digits) Divisors found: r1=15441280903831977725272445863464931495519706268391 (pp50) r2=23701256234827907885716605563878213283252164799721868829312661738797 (pp68) Version: GGNFS-0.77.1-20050930-prescott Total time: 63.00 hours. Scaled time: 40.44 units (timescale=0.642). Factorization parameters were as follows: name: N n: 365977755295676774775510425752865543407563187811110276370278426136480960683749215044820881215418051861192830419465627 skew: 46221.68 # norm 2.11e+15 c5: 8880 c4: 800381912 c3: 48637968167417 c2: -2591345113024835856 c1: -66628290509630989647114 c0: 676846138220199379674969111 # alpha -4.77 Y1: 3658631464037 Y0: -33343215984948588542900 # Murphy_E 4.21e-10 # M 132425972767365485666788243273465066850953504834744825058251254902605105935877722859492830520304156857092881157938327 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [2000000, 3550001) Primes: RFBsize:283146, AFBsize:282237, largePrimes:6531912 encountered Relations: rels:6522365, finalFF:676176 Max relations in full relation-set: 40 Initial matrix: 565464 x 676176 with sparse part having weight 55755486. Pruned matrix : 474048 x 476939 with weight 33468131. Total sieving time: 57.16 hours. Total relation processing time: 0.41 hours. Matrix solve time: 4.88 hours. Time per square root: 0.55 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000 total time: 63.00 hours. --------- CPU info (if available) ----------
By JMB / GGNFS-0.77.1 gnfs
(5·10158-17)/3 = 1(6)1571<159> = 72 · 227 · 587117 · 28302487 · 4405758911640887447737379<25> · C117
C117 = P50 · P67
P50 = 67621902109110330371869937121494348175237496572533<50>
P67 = 3026700483864348901223166729369813676797114347757361309491810095819<67>
Number: N N=204671243833471872423458363170935132549848443077825215001952886645519860774092659259664652641538107318116138813539527 ( 117 digits) Divisors found: r1=67621902109110330371869937121494348175237496572533 (pp50) r2=3026700483864348901223166729369813676797114347757361309491810095819 (pp67) Version: GGNFS-0.77.1 Total time: 41.48 hours. Scaled time: 75.41 units (timescale=1.818). Factorization parameters were as follows: name: N n: 204671243833471872423458363170935132549848443077825215001952886645519860774092659259664652641538107318116138813539527 skew: 40873.77 # norm 5.27e+15 c5: 29340 c4: 1476685827 c3: -284808719427086 c2: -1625016887507574014 c1: 139298769983634584929104 c0: -300252010840174442528395056 # alpha -5.13 Y1: 456887006213 Y0: -23373258294493079571857 # Murphy_E 4.33e-10 # M 69218691873820054618000039397568631155747605271065307352011942265970179923676763177576565812296351208189263969084310 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [2000000, 3680001) Relations: rels:6458002, finalFF:634911 Initial matrix: 565919 x 634911 with sparse part having weight 48642764. Pruned matrix : 533302 x 536195 with weight 32985209. Total sieving time: 37.05 hours. Total relation processing time: 0.19 hours. Matrix solve time: 3.99 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,60000 total time: 41.48 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(4·10177-1)/3 = 1(3)177<178> = 4409 · 22961 · C170
C170 = P29 · C141
P29 = 43665368763292497076610163467<29>
C141 = [301627341967929378435673111291397900932534777570343251996445617288863617272291852009571123885313428683074596057961228788786605535514717262151<141>]
By JMB / Msieve v. 2.04
(34·10155-43)/9 = 3(7)1543<156> = 11 · 520702915570613<15> · 5555018987718121828955407<25> · 4441619662273433601989908731614767<34> · C82
C82 = P35 · P47
P35 = 35949300598985833824141852183554201<35>
P47 = 74359481489915926639112034917743709079659453219<47>
Msieve v. 2.04 Fri Aug 11 07:21:22 2006 random seeds: 16034e40 0065c729 factoring 2673171352465710644495563497271882852656939209210070623777550975107357 875710423019 (82 digits) using multiplier of 1 using sieve block of 65536 using a sieve bound of 1508867 (57131 primes) using large prime bound of 15088670 (23 bits) prp35 factor: 35949300598985833824141852183554201 prp47 factor: 74359481489915926639112034917743709079659453219 elapsed time 01:12:29
By JMB / GMP-ECM 6.0.1 B1=11000000
(34·10155-43)/9 = 3(7)1543<156> = 11 · 520702915570613<15> · 5555018987718121828955407<25> · C116
C116 = P34 · C82
P34 = 4441619662273433601989908731614767<34>
C82 = [2673171352465710644495563497271882852656939209210070623777550975107357875710423019<82>]
By JMB / GMP-ECM 6.0.1 B1=11000000
10171+9 = 1(0)1709<172> = 114870713498291<15> · 152103797335211<15> · 1077903296318851813591058561693<31> · C113
C113 = P39 · P75
P39 = 119386461467535400538961423925754434819<39>
P75 = 444749782753570053864318452769186104647351235367140088183461389738755377327<75>
By JMB / GMP-ECM 6.0.1 B1=11000000
(28·10162+17)/9 = 3(1)1613<163> = 196961 · 76407693552855061<17> · 615007859440361597069371583<27> · C114
C114 = P35 · P80
P35 = 14985999353401319166603348866934571<35>
P80 = 22430131294455821462057713883010980947736349572806097941827659523032229508329521<80>
By Wataru Sakai / GMP-ECM 6.1 B1=11000000, GGNFS-0.77.1-20060513-pentium4 gnfs
10162+9 = 1(0)1619<163> = 5573 · 735595652772776933<18> · C141
C141 = P32 · P47 · P63
P32 = 44574910306875039119713293503029<32>
P47 = 15796214831501458885442791692067196909108663273<47>
P63 = 346440210180306140299079585071546545979928246632083029744358053<63>
Number: template N=5472443986278634559182270530295372853227297441893538310967286061401558754596631170156064966170636476322887469 ( 109 digits) Divisors found: r1=15796214831501458885442791692067196909108663273 (pp47) r2=346440210180306140299079585071546545979928246632083029744358053 (pp63) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 23.20 hours. Scaled time: 29.24 units (timescale=1.260). Factorization parameters were as follows: name: template n: 5472443986278634559182270530295372853227297441893538310967286061401558754596631170156064966170636476322887469 skew: 11018.09 # norm 3.20e+014 c5: 15000 c4: 2049539905 c3: -16085797091712 c2: -213274340734910712 c1: 131380839582017791300 c0: -170902177794463511226600 # alpha -4.86 Y1: 62487254993 Y0: -817367011602365383949 # Murphy_E 1.12e-009 # M 5004784583434845831078841956713121671236324974689500294609609848605805097246009678817654938417451410693748427 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2900001) Primes: RFBsize:230209, AFBsize:230832, largePrimes:7319197 encountered Relations: rels:7139177, finalFF:579821 Max relations in full relation-set: 28 Initial matrix: 461116 x 579821 with sparse part having weight 43420824. Pruned matrix : 363223 x 365592 with weight 24332046. Polynomial selection time: 1.35 hours. Total sieving time: 18.27 hours. Total relation processing time: 0.42 hours. Matrix solve time: 2.90 hours. Time per square root: 0.27 hours. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 23.20 hours. --------- CPU info (if available) ----------
By JMB / GGNFS-0.77.1-20050930-prescott gnfs
(4·10166-31)/9 = (4)1651<166> = 43 · 421 · 11489 · 13063 · 219281 · 2114323 · 1401498638512800602338683574933<31> · C112
C112 = P44 · P68
P44 = 73852723653066632145630012304772718105985831<44>
P68 = 34088684369438135938395966419974474187769342866960086047456527452129<68>
Number: (4ﾂｷ10166-31)/9 C112 N=2517542186432726614519045066152878943434736864305600228130570201750511709672675584135765717546155715010204784199 ( 112 digits) Divisors found: r1=73852723653066632145630012304772718105985831 (pp44) r2=34088684369438135938395966419974474187769342866960086047456527452129 (pp68) Version: GGNFS-0.77.1-20050930-prescott Total time: 32.53 hours. Scaled time: 19.81 units (timescale=0.609). Factorization parameters were as follows: name: (4ﾂｷ10166-31)/9 C112 n: 2517542186432726614519045066152878943434736864305600228130570201750511709672675584135765717546155715010204784199 skew: 20807.37 # norm 5.54e+15 c5: 38400 c4: -5696422944 c3: -270524084185390 c2: 2834749926957496277 c1: 13883696403005631212110 c0: -33266943953232428779977728 # alpha -6.34 Y1: 673389653299 Y0: -2308515873579294509673 # Murphy_E 8.40e-10 # M 1689938327551674534910204802217113629727040156762154475652360671688288051808192850060885510573294732167029196891 type: gnfs rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 48 mfba: 48 rlambda: 2.6 alambda: 2.6 qintsize: 50000 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, 2450001) Primes: RFBsize:216816, AFBsize:216527, largePrimes:5456723 encountered Relations: rels:5350941, finalFF:537741 Max relations in full relation-set: 40 Initial matrix: 433419 x 537741 with sparse part having weight 40511458. Pruned matrix : 345227 x 347458 with weight 21610858. Total sieving time: 28.65 hours. Total relation processing time: 0.48 hours. Matrix solve time: 3.03 hours. Time per square root: 0.38 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,48,48,2.6,2.6,100000 total time: 32.53 hours. --------- CPU info (if available) ---------- 3.2ghz P4, 2gb DDR, 7200 RPM IDE
Daniel Heuer found the largest known near-repdigit prime number 3·10119292-1 = 2(9)119292<119293>. Congratulations!
References:
By suberi / GGNFS-0.77.1-20060513-pentium4
(19·10167-1)/9 = 2(1)167<168> = 48761 · 7783163 · C156
C156 = P52 · P104
P52 = 9213779069369765001437791549262278092034656923926957<52>
P104 = 60373251713664375579895563454106435402505689903757733131520095501842512209171123875885660397963312420961<104>
Number: 21111_167 N=556265802989153120515703738711098287930938971259492519112654427574545887025752040989524841887031236074654193034645440519108902890194259867325067154799745677 ( 156 digits) SNFS difficulty: 168 digits. Divisors found: r1=9213779069369765001437791549262278092034656923926957 (pp52) r2=60373251713664375579895563454106435402505689903757733131520095501842512209171123875885660397963312420961 (pp104) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 247.08 hours. Scaled time: 150.72 units (timescale=0.610). Factorization parameters were as follows: n: 556265802989153120515703738711098287930938971259492519112654427574545887025752040989524841887031236074654193034645440519108902890194259867325067154799745677 m: 1000000000000000000000000000000000 c5: 1900 c0: -1 skew: 1 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, 7850001) Primes: RFBsize:380800, AFBsize:380927, largePrimes:6183340 encountered Relations: rels:6431532, finalFF:886589 Max relations in full relation-set: 28 Initial matrix: 761794 x 886589 with sparse part having weight 68124049. Pruned matrix : 666101 x 669973 with weight 51560289. Total sieving time: 209.69 hours. Total relation processing time: 3.21 hours. Matrix solve time: 33.74 hours. Time per square root: 0.44 hours. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000 total time: 247.08 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(22·10163-1)/3 = 7(3)163<164> = 197 · 84948082135073744830961689889<29> · C133
C133 = P31 · P102
P31 = 5766978834890632029154858016207<31>
P102 = 759859441556857392031887053491686419668387447209216643623736091892709102130571496823704046528074412543<102>
By Wataru Sakai / GMP-ECM 6.1 B1=11000000, Msieve v. 1.07, GGNFS-0.77.1-20060513-pentium4 gnfs
(8·10181+1)/9 = (8)1809<181> = 32 · 162703 · 436529 · 198685966079416987465648073668331204609<39> · C131
C131 = P33 · P39 · P60
P33 = 542441679016241624644644490188229<33>
P39 = 496477762884048622818601277837137881409<39>
P60 = 259882036616767224751131892084058161800893633111811279277667<60>
Wed Aug 02 23:25:50 2006 Msieve v. 1.07 Wed Aug 02 23:25:50 2006 random seeds: e7b26820 9874fbc3 Wed Aug 02 23:25:50 2006 factoring 129025652153242999985739343146124661528545137305441516429669637230365891830754470129895176228192803 (99 digits) Wed Aug 02 23:25:51 2006 using multiplier of 35 Wed Aug 02 23:25:51 2006 sieve interval: 9 blocks of size 65536 Wed Aug 02 23:25:51 2006 processing polynomials in batches of 6 Wed Aug 02 23:25:51 2006 using a sieve bound of 2542933 (92576 primes) Wed Aug 02 23:25:51 2006 using large prime bound of 381439950 (28 bits) Wed Aug 02 23:25:51 2006 using double large prime bound of 2796192470588850 (43-52 bits) Wed Aug 02 23:25:51 2006 using trial factoring cutoff of 57 bits Wed Aug 02 23:25:51 2006 polynomial 'A' values have 13 factors Thu Aug 03 10:52:49 2006 93021 relations (22595 full + 70426 combined from 1375827 partial), need 92672 Thu Aug 03 10:52:51 2006 begin with 1375827 relations Thu Aug 03 10:52:52 2006 reduce to 219529 relations in 11 passes Thu Aug 03 10:52:52 2006 attempting to read 22595 full and 219529 partial relations Thu Aug 03 10:52:57 2006 recovered 22595 full and 219529 partial relations Thu Aug 03 10:52:57 2006 recovered 231943 polynomials Thu Aug 03 10:52:57 2006 attempting to build 70426 cycles Thu Aug 03 10:52:57 2006 found 70426 cycles in 5 passes Thu Aug 03 10:52:58 2006 distribution of cycle lengths: Thu Aug 03 10:52:58 2006 length 2 : 16312 Thu Aug 03 10:52:58 2006 length 3 : 15721 Thu Aug 03 10:52:58 2006 length 4 : 12700 Thu Aug 03 10:52:58 2006 length 5 : 9570 Thu Aug 03 10:52:58 2006 length 6 : 6390 Thu Aug 03 10:52:58 2006 length 7 : 3981 Thu Aug 03 10:52:58 2006 length 8 : 2563 Thu Aug 03 10:52:58 2006 length 9+: 3189 Thu Aug 03 10:52:58 2006 largest cycle: 21 relations Thu Aug 03 10:52:58 2006 92576 x 92640 system, weight 5982638 (avg 64.58/col) Thu Aug 03 10:52:58 2006 reduce to 91077 x 91141 in 3 passes Thu Aug 03 10:55:46 2006 lanczos halted after 1442 iterations Thu Aug 03 10:55:46 2006 recovered 63 nontrivial dependencies Thu Aug 03 10:56:18 2006 prp39 factor: 496477762884048622818601277837137881409 Thu Aug 03 10:56:18 2006 prp60 factor: 259882036616767224751131892084058161800893633111811279277667 Thu Aug 03 10:56:18 2006 elapsed time 11:30:28
Number: template N=129025652153242999985739343146124661528545137305441516429669637230365891830754470129895176228192803 ( 99 digits) Divisors found: r1=496477762884048622818601277837137881409 (pp39) r2=259882036616767224751131892084058161800893633111811279277667 (pp60) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 6.16 hours. Scaled time: 7.73 units (timescale=1.254). Factorization parameters were as follows: name: template n: 129025652153242999985739343146124661528545137305441516429669637230365891830754470129895176228192803 skew: 9546.64 # norm 5.82e+013 c5: 25440 c4: 327356204 c3: -2756380090446 c2: -26695770066661670 c1: 13726476804124437779 c0: 730114543638448319289596 # alpha -6.09 Y1: 10835548823 Y0: -5508452295331048625 # Murphy_E 4.07e-009 # M 43647947722120531491045537206099770873096300206510332994071869368876871426009741108841708977697337 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 [900000, 1300001) Primes: RFBsize:135072, AFBsize:135627, largePrimes:3897401 encountered Relations: rels:3987587, finalFF:468705 Max relations in full relation-set: 28 Initial matrix: 270777 x 468705 with sparse part having weight 31420460. Pruned matrix : 135986 x 137403 with weight 11779890. Polynomial selection time: 0.45 hours. Total sieving time: 5.17 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.27 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: gnfs,98,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 6.16 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
10631+1 = 1(0)6301<632> = 11 · 111478771 · 7144726022423651<16> · 25275592878679576093<20> · 324340568278356513982411<24> · C564
C564 = P33 · C531
P33 = 215007779702918011813855565694983<33>
C531 = [647549189090766885539933216048953381766282962756191273299208190433157850091993991879210354251404437260181512652894093774881642980661569572938361554582904065808145062221178935594264088903446558313933923951452627617040506754385034509397492029650065938555770272362685341300381208344171606718543565358130740121026865773917747329408645838090080628394617515583502194446165611330220785781361533250749575952629581355453371379965611509754045286244674853219793092966102089424772461223062153805403748147135382956547785370167119053568537747219<531>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By JMB / GGNFS-0.77.1-20050930-prescott gnfs, GMP-ECM 6.0.1
(61·10170-7)/9 = 6(7)170<171> = 89 · 59149 · 73106034559740600637<20> · 455443373077175325700179430733987<33> · C112
C112 = P54 · P59
P54 = 259634246889555898861112235610888816344185272851756101<54>
P59 = 14893621763832231129772178482053300115800386287663092493903<59>
Number: N N=3866894270110480495299331929349939555976910470220605286134629327779460046947883016645268141896942460825185552203 ( 112 digits) Divisors found: r1=259634246889555898861112235610888816344185272851756101 (pp54) r2=14893621763832231129772178482053300115800386287663092493903 (pp59) Version: GGNFS-0.77.1-20050930-prescott Total time: 38.99 hours. Scaled time: 25.62 units (timescale=0.657). Factorization parameters were as follows: name: N n: 3866894270110480495299331929349939555976910470220605286134629327779460046947883016645268141896942460825185552203 skew: 40962.73 # norm 5.21e+15 c5: 17400 c4: -239661230 c3: -193594578520121 c2: 459645264047848230 c1: 12630770380130446786544 c0: -185397841779260423540488128 # alpha -6.15 Y1: 526615703819 Y0: -2946882526904680098125 # Murphy_E 7.99e-10 # M 906621222046150642737111880646727832873613351095034764872743174328229588823611973950586077300151454670273150662 type: gnfs rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 48 mfba: 48 rlambda: 2.6 alambda: 2.6 qintsize: 50000 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:216754, largePrimes:5420312 encountered Relations: rels:5291749, finalFF:520517 Max relations in full relation-set: 40 Initial matrix: 433648 x 520517 with sparse part having weight 36906463. Pruned matrix : 359939 x 362171 with weight 20487459. Total sieving time: 36.43 hours. Total relation processing time: 0.27 hours. Matrix solve time: 1.93 hours. Time per square root: 0.36 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,48,48,2.6,2.6,100000 total time: 38.99 hours. --------- CPU info (if available) ----------
(86·10192+31)/9 = 9(5)1919<193> = 13 · 79801 · 113754799183<12> · 1840989671002883<16> · 64478288440428854599<20> · 477664605616311721510870585903<30> · C112
C112 = P48 · P64
P48 = 544743413352596587064461975415669241172263459607<48>
P64 = 2621528754462436339398526557224274787788408344875291572559019753<64>
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10167-7)/9 = 9(7)167<168> = 547 · 255917 · 62987719 · 168095479 · C144
C144 = P36 · P109
P36 = 173057865665730828088779240795479581<36>
P109 = 3811978501475933954155211857611104093457904408402378553499026213538586627283954077584331779888287710077425683<109>
Number: 97777_167 N=659692863429076083431306133363648261064622208616886952777689858266262337273979785875087842161434570070362767114570543284589051713060979871478823 ( 144 digits) SNFS difficulty: 168 digits. Divisors found: r1=173057865665730828088779240795479581 (pp36) r2=3811978501475933954155211857611104093457904408402378553499026213538586627283954077584331779888287710077425683 (pp109) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 237.31 hours. Scaled time: 144.52 units (timescale=0.609). Factorization parameters were as follows: name: 97777_167 n: 659692863429076083431306133363648261064622208616886952777689858266262337273979785875087842161434570070362767114570543284589051713060979871478823 m: 2000000000000000000000000000000000 c5: 275 c0: -7 skew: 3 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, 7750001) Primes: RFBsize:380800, AFBsize:381318, largePrimes:6147199 encountered Relations: rels:6384742, finalFF:880495 Max relations in full relation-set: 28 Initial matrix: 762184 x 880495 with sparse part having weight 65754152. Pruned matrix : 670303 x 674177 with weight 49760472. Total sieving time: 206.57 hours. Total relation processing time: 1.11 hours. Matrix solve time: 29.28 hours. Time per square root: 0.34 hours. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000 total time: 237.31 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(4·10181-31)/9 = (4)1801<181> = 691 · C178
C178 = P35 · C144
P35 = 18341311570927686739221204596281603<35>
C144 = [350678423961842493729246583229724423685615232184993031214145040572519155068819591779849294477911743031232439012498194912517275810305005552598017<144>]
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(8·10194+1)/9 = (8)1939<194> = 7129 · 7193 · 490057 · 13676537335459<14> · 59621355333702961<17> · C151
C151 = P35 · P117
P35 = 12622486933254640856936731027878923<35>
P117 = 343668142793819369342868699647116068318546166592509493762943274316967670246952436452566986782105405574673788064694033<117>
By Wataru Sakai / GMP-ECM 6.1 B1=11000000, GGNFS-0.77.1-20060513-pentium4 gnfs
(8·10184+1)/9 = (8)1839<184> = 3 · 19603 · 172173708801163613627<21> · C159
C159 = P29 · C131
P29 = 27179099398845119796776615939<29>
C131 = [32299945255435921563264500910223759473383544543244622969530356135443820563047187110300569176110925997216606362828072402522777701457<131>]
(8·10181+1)/9 = (8)1809<181> = 32 · 162703 · 436529 · C170
C170 = P39 · C131
P39 = 198685966079416987465648073668331204609<39>
C131 = [69988891390170684419064864292472492567266787296607386124102937093503944074615798168449992226257202972265875496995584237861973115887<131>]
(8·10175+1)/9 = (8)1749<175> = 3 · 103 · 270950423 · 24229424690721201848947<23> · C142
C142 = P37 · P43 · P64
P37 = 1187459593948663942345533369324773863<37>
P43 = 1621372469742717880365943926655152482024861<43>
P64 = 2275906557941688510267400481774821829901703819890554273677954787<64>
Number: template N=3690092236753563552546589205826588094126097050469521337750003386324822725505644653827392179184738967959607 ( 106 digits) Divisors found: r1=1621372469742717880365943926655152482024861 (pp43) r2=2275906557941688510267400481774821829901703819890554273677954787 (pp64) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 13.34 hours. Scaled time: 16.68 units (timescale=1.250). Factorization parameters were as follows: name: template n: 3690092236753563552546589205826588094126097050469521337750003386324822725505644653827392179184738967959607 skew: 17540.76 # norm 2.22e+014 c5: 18540 c4: 445661492 c3: -20154034773225 c2: -117243062043128466 c1: 2055231393406905905146 c0: 6780112294565646891804960 # alpha -5.98 Y1: 90312434587 Y0: -181879797367810544261 # Murphy_E 1.89e-009 # M 559630045337832813518883705861953988295828468353446159222632565406767852774425818137205583461403479764802 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, 2150001) Primes: RFBsize:183072, AFBsize:182547, largePrimes:4443465 encountered Relations: rels:4565926, finalFF:502025 Max relations in full relation-set: 28 Initial matrix: 365702 x 502025 with sparse part having weight 36650530. Pruned matrix : 257832 x 259724 with weight 17722141. Total sieving time: 11.85 hours. Total relation processing time: 0.19 hours. Matrix solve time: 1.12 hours. Time per square root: 0.18 hours. 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: 13.34 hours. --------- CPU info (if available) ----------
(8·10187+1)/9 = (8)1869<187> = 3 · 263 · 26821 · 88883 · 1119746363<10> · 918134378332008821<18> · C148
C148 = P33 · P36 · P80
P33 = 165805694449843257500642766390827<33>
P36 = 934070656153121251699814499393013861<36>
P80 = 29680534863754695395148746244944140636632693438105910924697912984920615447644347<80>
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10166-7)/9 = 9(7)166<167> = 107 · 22585789 · 644297617169<12> · 4056411030394169<16> · C131
C131 = P60 · P71
P60 = 795997355428448940999990564851890555756567795185419778731011<60>
P71 = 19448271711557563851095010492190619092216476162100540985170829304296669<71>
Number: 97777_166 N=15480772850053735174812154400698448628670785732665450293762375478799791273005124409888204255075924043017964918964150912682694302359 ( 131 digits) SNFS difficulty: 168 digits. Divisors found: r1=795997355428448940999990564851890555756567795185419778731011 (pp60) r2=19448271711557563851095010492190619092216476162100540985170829304296669 (pp71) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 211.66 hours. Scaled time: 142.23 units (timescale=0.672). Factorization parameters were as follows: name: 97777_166 n: 15480772850053735174812154400698448628670785732665450293762375478799791273005124409888204255075924043017964918964150912682694302359 m: 2000000000000000000000000000000000 c5: 55 c0: -14 skew: 2 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, 7150001) Primes: RFBsize:380800, AFBsize:380438, largePrimes:6071781 encountered Relations: rels:6279833, finalFF:858677 Max relations in full relation-set: 28 Initial matrix: 761304 x 858677 with sparse part having weight 61581012. Pruned matrix : 685817 x 689687 with weight 47025780. Total sieving time: 181.11 hours. Total relation processing time: 0.93 hours. Matrix solve time: 29.30 hours. Time per square root: 0.31 hours. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000 total time: 211.66 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
10190+9 = 1(0)1899<191> = 17 · 661 · 3617 · 9255737 · C176
C176 = P38 · C138
P38 = 58578835214747005278058475891560020601<38>
C138 = [453784202451725518980480133089420040136273460591104916659256777047754295589507064687162836139574199000297912034696834143699088261379945733<138>]
10171+9 = 1(0)1709<172> = 114870713498291<15> · 152103797335211<15> · C176
C143 = P31 · C113
P31 = 1077903296318851813591058561693<31>
C113 = [53097102801403831665746807018118510756849451124526459253855124796660194850247112567565191453771626718853971948813<113>]
By Alfred Reich / Msieve V 1.06
(10161+71)/9 = (1)1609<161> = 23327 · 321131832988051<15> · 1191317231086892298689<22> · C121
C121 = P39 · P82
P39 = 157827640943815926474954927538137344371<39>
P82 = 7888687536686028472531832671390978588451330433797341725738861291549234482598071113<82>
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(22·10161-1)/3 = 7(3)161<162> = 73 · 34653533 · C153
C153 = P32 · C122
P32 = 22935196665910109914667553700279<32>
C122 = [12639461723608598020994817140915197006312553495483248231488432539680347420405192366902367090348663282604229103442194528503<122>]
(25·10197-1)/3 = 8(3)197<198> = 656603 · 170454115654360806479399<24> · C169
C169 = P33 · P137
P33 = 165593497569484456997057320046729<33>
P137 = 44964018754490646891491038249988341848259629720873308924575013742259137181650315743036690343984815431548345392057804704806670264403772241<137>
(22·10152-1)/3 = 7(3)152<153> = 417587987 · 10350831019<11> · C135
C135 = P35 · P100
P35 = 17497935690527231337957237637215421<35>
P100 = 9695972941720835118569525522840796078591641123474745316988805837411044124787063482971552015328045641<100>
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10165-7)/9 = 9(7)165<166> = 3 · C166
C166 = P77 · P89
P77 = 45346200595934146934131296942427106498745059419385026179154277004358396423331<77>
P89 = 71875024068752797477559446177335736254751869797365522711198282153882911150417196506178889<89>
Number: 97777_165 N=3259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259 ( 166 digits) SNFS difficulty: 166 digits. Divisors found: r1=45346200595934146934131296942427106498745059419385026179154277004358396423331 (pp77) r2=71875024068752797477559446177335736254751869797365522711198282153882911150417196506178889 (pp89) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 178.89 hours. Scaled time: 120.39 units (timescale=0.673). Factorization parameters were as follows: name: 97777_165 n: 3259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259 m: 1000000000000000000000000000000000 c5: 88 c0: -7 skew: 2 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, ) Primes: RFBsize:348513, AFBsize:348862, largePrimes:6048552 encountered Relations: rels:6244545, finalFF:823730 Max relations in full relation-set: 28 Initial matrix: 697441 x 823730 with sparse part having weight 63288732. Pruned matrix : 602166 x 605717 with weight 47023567. Total sieving time: 158.14 hours. Total relation processing time: 0.93 hours. Matrix solve time: 19.53 hours. Time per square root: 0.29 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: 178.89 hours. --------- CPU info (if available) ----------
By suberi / GGNFS-0.77.1-20060513-pentium4
(7·10154-61)/9 = (7)1531<154> = 59040511 · 30846605261<11> · C136
C136 = P36 · P41 · P60
P36 = 169750613328204889527307493147334971<36>
P41 = 70847408418392222124674327036637004102729<41>
P60 = 355109856140986847622896672372910163920648639023544483933139<60>
Number: 77771_154 N=4270689989174991981377200663819930402301374317453540384390776208047194568640332560832240274686466139739702588331996549083657274648231401 ( 136 digits) SNFS difficulty: 155 digits. Divisors found: r1=169750613328204889527307493147334971 (pp36) r2=70847408418392222124674327036637004102729 (pp41) r3=355109856140986847622896672372910163920648639023544483933139 (pp60) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 55.96 hours. Scaled time: 35.92 units (timescale=0.642). Factorization parameters were as follows: n: 4270689989174991981377200663819930402301374317453540384390776208047194568640332560832240274686466139739702588331996549083657274648231401 m: 10000000000000000000000000000000 c5: 7 c0: -610 skew: 2.44 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3000001) Primes: RFBsize:216816, AFBsize:217162, largePrimes:5654054 encountered Relations: rels:5570235, finalFF:503190 Max relations in full relation-set: 28 Initial matrix: 434043 x 503190 with sparse part having weight 42264052. Pruned matrix : 404056 x 406290 with weight 30433715. Total sieving time: 46.92 hours. Total relation processing time: 0.38 hours. Matrix solve time: 8.44 hours. Time per square root: 0.22 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: 55.96 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GGNFS-0.77.1-20060513-pentium4
10139+9 = 1(0)1389<140> = 23 · 881 · 2143 · C132
C132 = P41 · P43 · P49
P41 = 24164159986601181377625015589587447765463<41>
P43 = 2160786218367515171952203262064220489890903<43>
P49 = 4410527972854632022342616725553254342960601726209<49>
Number: 132 N=230289472254597723556326237185858964417259744578116480369008481077655245099503360027030457095355662400147348415927381807440279779601 ( 132 digits) SNFS difficulty: 140 digits. Divisors found: r1=24164159986601181377625015589587447765463 (pp41) r2=2160786218367515171952203262064220489890903 (pp43) r3=4410527972854632022342616725553254342960601726209 (pp49) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 11.71 hours. Scaled time: 14.75 units (timescale=1.260). Factorization parameters were as follows: n: 230289472254597723556326237185858964417259744578116480369008481077655245099503360027030457095355662400147348415927381807440279779601 m: 10000000000000000000000000000 c5: 1 c0: 90 skew: 2.46 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, 1900001) Primes: RFBsize:78498, AFBsize:64158, largePrimes:1620854 encountered Relations: rels:1636099, finalFF:171123 Max relations in full relation-set: 28 Initial matrix: 142720 x 171123 with sparse part having weight 17573423. Pruned matrix : 135646 x 136423 with weight 12496049. Total sieving time: 11.31 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.25 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 11.71 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GGNFS-0.77.1-20060513-pentium4, GMP-ECM 6.1 B1=11000000
10132+9 = 1(0)1319<133> = 17401 · C128
C128 = P51 · P78
P51 = 411766421379824555923211974201163701971862160573257<51>
P78 = 139564468173065601765541228336856563574840263361218702800225268893329303849737<78>
Number: 132 N=57467961611401643583702086087006493879662088385724958335727831733808401815987586920291937244985920349405206597321992988908683409 ( 128 digits) SNFS difficulty: 132 digits. Divisors found: r1=411766421379824555923211974201163701971862160573257 (pp51) r2=139564468173065601765541228336856563574840263361218702800225268893329303849737 (pp78) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 6.31 hours. Scaled time: 7.55 units (timescale=1.196). Factorization parameters were as follows: n: 57467961611401643583702086087006493879662088385724958335727831733808401815987586920291937244985920349405206597321992988908683409 m: 100000000000000000000000000 c5: 100 c0: 9 skew: 1 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1100001) Primes: RFBsize:63951, AFBsize:63918, largePrimes:1507019 encountered Relations: rels:1497774, finalFF:158693 Max relations in full relation-set: 28 Initial matrix: 127933 x 158693 with sparse part having weight 12991852. Pruned matrix : 119793 x 120496 with weight 8138677. Total sieving time: 6.03 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.16 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 6.31 hours. --------- CPU info (if available) ----------
10200+9 = 1(0)1999<201> = 27793 · 1619861 · 67747437129266000269703021<26> · C164
C164 = P39 · P125
P39 = 400259908045666561971192213216134042261<39>
P125 = 81912816932939583803515921686223425749837243002793830987141671128762200181930502382006509105387526239568992549021452850921893<125>
By Wataru Sakai / GMP-ECM 6.1 B1=11000000, GGNFS-0.77.1-20060513-pentium4 gnfs
10160+9 = 1(0)1599<161> = 14215681 · 3834622668996503113<19> · C135
C135 = P32 · P37 · P67
P32 = 49511107570580443175710053727301<32>
P37 = 1308389305580216069241507311202182597<37>
P67 = 2831848842389382643911352301752663424041355458316158491328312822249<67>
Number: template N=3705160740401983100863517084343862366824251826484260212973356231617143408125614337889537228469702200653 ( 103 digits) Divisors found: r1=1308389305580216069241507311202182597 (pp37) r2=2831848842389382643911352301752663424041355458316158491328312822249 (pp67) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 12.29 hours. Scaled time: 15.45 units (timescale=1.257). Factorization parameters were as follows: name: template n: 3705160740401983100863517084343862366824251826484260212973356231617143408125614337889537228469702200653 skew: 4201.71 # norm 7.68e+013 c5: 90300 c4: -2164338660 c3: -1124179346981 c2: 42838024495449134 c1: 61102231652332890264 c0: -405169698669360292416 # alpha -5.23 Y1: 24804153473 Y0: -33313894859610357733 # Murphy_E 2.50e-009 # M 409331033215913408196436280112604987913307780173380076602933295804435792192031068107187579200174582780 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1950001) Primes: RFBsize:169511, AFBsize:168711, largePrimes:4431119 encountered Relations: rels:4528620, finalFF:477444 Max relations in full relation-set: 28 Initial matrix: 338303 x 477444 with sparse part having weight 35664560. Pruned matrix : 232265 x 234020 with weight 17071067. Polynomial selection time: 0.70 hours. Total sieving time: 10.32 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.90 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 12.29 hours. --------- CPU info (if available) ----------
10187+9 = 1(0)1869<188> = 131 · 889796277314453<15> · 257182844103564007<18> · C153
C153 = P33 · C120
P33 = 534221796617984999646462038876207<33>
C120 = [624416717075815956418387439219885297129632171625703612920258713290457714163614874975484756782174120692018842001812960287<120>]
(22·10182-1)/3 = 7(3)182<183> = 89 · 30881 · 50951 · C172
C172 = P30 · P143
P30 = 211784225570152472986757190977<30>
P143 = 24727131741565022058499972481875489125584547784555429383313765026067944643006887924236480665366530944658610666404211729996682943925108626752731<143>
(4·10168-31)/9 = (4)1671<168> = 3 · 31583582440048607<17> · 1950453510567170479421<22> · C130
C130 = P26 · P51 · P53
P26 = 40723997197061580454452377<26>
P51 = 619122012365504891624162034727407775467907313977069<51>
P53 = 95383354177663653668796178560357826807941934754091677<53>
Number: template N=59053934184646809250152288479730635440029899839203450505619529839464005477473756144806045588979501754713 ( 104 digits) Divisors found: r1=619122012365504891624162034727407775467907313977069 (pp51) r2=95383354177663653668796178560357826807941934754091677 (pp53) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 12.42 hours. Scaled time: 15.68 units (timescale=1.262). Factorization parameters were as follows: name: template n: 59053934184646809250152288479730635440029899839203450505619529839464005477473756144806045588979501754713 skew: 1584.29 # norm 7.76e+013 c5: 71820 c4: -1805456645 c3: 11521704364278 c2: 6361480388015250 c1: -933919547984490022 c0: -275396482201632940785 # alpha -4.41 Y1: 35687964367 Y0: -60673908364196146748 # Murphy_E 2.20e-009 # M 49808284345992182295493254281137799247143107035608798248782164222227195480358896851882845839564880622878 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1950001) Primes: RFBsize:169511, AFBsize:170363, largePrimes:4462254 encountered Relations: rels:4584204, finalFF:495463 Max relations in full relation-set: 28 Initial matrix: 339955 x 495463 with sparse part having weight 37585090. Pruned matrix : 225047 x 226810 with weight 17772037. Polynomial selection time: 0.79 hours. Total sieving time: 10.47 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.80 hours. Time per square root: 0.17 hours. 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: 12.42 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
(10909-1)/9 = (1)909<909> = 32 · 37 · 3637 · 139987 · 333667 · 2096761 · 85556852551<11> · 272295362253883<15> · 4531530181816613234555190841<28> · 759144383635787638836170905729<30> · 129063282232848961951985354966759<33> · 18998088572819375252842078421374368604969<41> · 157793041231623437279937408119546555586267712054762280488959320521697937521092276297325262649574267470228259745983773969571127099146658127611270714291518805884658999061123143366757<180> · C551
C551 = P34 · C518
P34 = 1612816483312672025726565521114761<34>
C518 = [18731404609543283232112940354795529905218765028242063904196821320680480327243060323107781513864932349843045574631527371074296472799300221176307921568568002896760698073729122374916147359104494785465229670909538835427313759161196304769503931083522392265590989266657153680618595864394113036876314100827462251460591513613066058256339288827531526049865833183556781227354644105909808435821244299021369213150268134537877336607415598924249317297200399350701289053180044523558985734207417941440449142445239590201068779937245641<518>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10161-7)/9 = 9(7)161<162> = 6445832807<10> · 876136231807637<15> · C138
C138 = P42 · P96
P42 = 326386964613543818430660282822859481650049<42>
P96 = 530464933735084358644926407333310225908640242061529220050842604319203486402399066374016158839947<96>
Number: 97777_161 N=173136839555718845089395520437996758583369835563867385590113997400708115694647626459437368550520023989996609780014966931069180525255707403 ( 138 digits) SNFS difficulty: 163 digits. Divisors found: r1=326386964613543818430660282822859481650049 (pp42) r2=530464933735084358644926407333310225908640242061529220050842604319203486402399066374016158839947 (pp96) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 120.62 hours. Scaled time: 81.06 units (timescale=0.672). Factorization parameters were as follows: name: 97777_161 n: 173136839555718845089395520437996758583369835563867385590113997400708115694647626459437368550520023989996609780014966931069180525255707403 m: 200000000000000000000000000000000 c5: 55 c0: -14 skew: 2 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:315472, largePrimes:5815005 encountered Relations: rels:5892056, finalFF:708237 Max relations in full relation-set: 28 Initial matrix: 631486 x 708237 with sparse part having weight 49942408. Pruned matrix : 576793 x 580014 with weight 37827629. Total sieving time: 102.75 hours. Total relation processing time: 0.72 hours. Matrix solve time: 16.87 hours. Time per square root: 0.28 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: 120.62 hours. --------- CPU info (if available) ----------
By suberi / GGNFS-0.77.1-20060513-pentium4
8·10151-3 = 7(9)1507<152> = 7 · 11 · 547 · 773187643 · C139
C139 = P35 · P36 · P69
P35 = 14629262442055574950399532444482723<35>
P36 = 196829145630461974806359025749407327<36>
P69 = 853129957804341508281677086652220527996609373987586466237769116989621<69>
Number: 79997_151 N=2456558048184250863322473394420778738862152389300191605362777223146582956017106437011501898864484201066970818565473010790375814652861561441 ( 139 digits) SNFS difficulty: 152 digits. Divisors found: r1=14629262442055574950399532444482723 (pp35) r2=196829145630461974806359025749407327 (pp36) r3=853129957804341508281677086652220527996609373987586466237769116989621 (pp69) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 27.22 hours. Scaled time: 16.96 units (timescale=0.623). Factorization parameters were as follows: n: 2456558048184250863322473394420778738862152389300191605362777223146582956017106437011501898864484201066970818565473010790375814652861561441 m: 2000000000000000000000000000000 c5: 5 c0: -6 skew: 1.04 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, 1200000 ) Primes: RFBsize:176302, AFBsize:176493, largePrimes:5630517 encountered Relations: rels:5727860, finalFF:651263 Max relations in full relation-set: 28 Initial matrix: 352860 x 651263 with sparse part having weight 54729852. Pruned matrix : 233396 x 235224 with weight 23367511. Total sieving time: 24.99 hours. Total relation processing time: 0.27 hours. Matrix solve time: 1.83 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: 27.22 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
10910+1 = 1(0)9091<911> = 29 · 101 · 281 · 421 · 521 · 3541 · 27961 · 2311921 · 3471301 · 13489841 · 121499449 · 13159402621<11> · 60368344121<11> · 173827038841<12> · 654721485601<12> · 8886004303541<13> · 19721126575796101<17> · 131454539198398781<18> · 527145878168855401<18> · 1031498834064949381<19> · 12763852652999774041<20> · 643852143556794829021<21> · 848654483879497562821<21> · 1900381976777332243781<22> · 12119730504567977254081<23> · 2737820036624672031089487008281<31> · 3571618567996393297210217238290456648947344377957590363519828421<64> · 431916413820617754546053476804635449461410533962843828981966782964481<69> · 4767139238062537528030092551972140250033930916026378932262992171010636949541765875548467191896982395151649733315765032710728474425304027277684227427428124448895116793267389997296790711552867188304460393677245196360641469741<223> · C248
C248 = P48 · P200
P48 = 191616955559592384669436097618582851538253404221<48>
P200 = 60604177158952949654034234379162779182404932436722562911710488710546750366134190897463822800510718962616059662401246546056631138751315004311007246335189571430318613812710829402180309391025505571625641<200>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By suberi / GGNFS-0.77.1-20060513-pentium4
(28·10168-1)/9 = 3(1)168<169> = 32 · 12377 · 41984093 · C156
C156 = P39 · P118
P39 = 149519217696375701284876859610392404589<39>
P118 = 4449137523398654304792825589316222412507885968946755039869777257202378161648912566744773192577933233445826406381882751<118>
Number: 31111_168 N=665231561922157233475900748929464114477514261952773705464562504266252579976754133622808054623764706488624353353542718704652248879655622068869216787952344339 ( 156 digits) SNFS difficulty: 169 digits. Divisors found: r1=149519217696375701284876859610392404589 (pp39) r2=4449137523398654304792825589316222412507885968946755039869777257202378161648912566744773192577933233445826406381882751 (pp118) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 197.02 hours. Scaled time: 119.59 units (timescale=0.607). Factorization parameters were as follows: n: 665231561922157233475900748929464114477514261952773705464562504266252579976754133622808054623764706488624353353542718704652248879655622068869216787952344339 m: 2000000000000000000000000000000000 c5: 875 c0: -1 skew: 1 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3000000, 6800001) Primes: RFBsize:412849, AFBsize:412326, largePrimes:5990289 encountered Relations: rels:6246818, finalFF:925072 Max relations in full relation-set: 28 Initial matrix: 825241 x 925072 with sparse part having weight 51654832. Pruned matrix : 740939 x 745129 with weight 38208626. Total sieving time: 163.63 hours. Total relation processing time: 2.39 hours. Matrix solve time: 30.57 hours. Time per square root: 0.42 hours. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 197.02 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(4·10154-31)/9 = (4)1531<154> = 193 · C152
C152 = P33 · P120
P33 = 226956410701884405296554862880163<33>
P120 = 101465340791608510434494867505301603408393063217871447504733527448696165828183418411522030373903962435273708671186630099<120>
(4·10189-31)/9 = (4)1881<189> = 3 · 7 · 59 · 11766674917381365427<20> · 899820802396378955324797<24> · C143
C143 = P33 · P111
P33 = 151931647080061133943087045931571<33>
P111 = 222991415928408701409099236295630310191601638543825165330887266241674230685086304307031418000582086049995350531<111>
By Yousuke Koide / GMP-ECM
(10831-1)/9 = (1)831<831> = 3 · 37 · 1016157022810759<16> · 102092644289739525085919338335107091799<39> · [10710314284791727138118967000605618050187771277688525854207599641117948350932588043961150274118997769379253719854788136101522618592904749621229242261158372761237323432155862577154173589241914856373487807099618367356448232871<224>] · C552
C552 = P32 · C521
P32 = 14583704002876908994687648285921<32>
C521 = [61774491632796531682229129873134854879188889606538991865332732378489613917642712894011233667125452960677817718645793548343784265838763017108563978280693473570714461360003441670259367095714791812784790366631151371036353906505354116538073913505900343716004543484940400938476020223329814783335017162164415847386994139858278658122209555752018698663655721317115426995955226660305071601616168697847105681145122778246346351136132821871465226031104186177624186006825691556823580704133107006746051978806489360025005083661153378671<521>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Wataru Sakai / GMP-ECM 6.1, Msieve v. 1.06, GGNFS-0.77.1-20060513-pentium4 gnfs
(4·10161-31)/9 = (4)1601<161> = 131 · 883 · 2208991 · 797310706397702315094462679<27> · C123
C123 = P30 · P36 · P58
P30 = 153277297944560404960341396997<30>
P36 = 193655081371246644974840248683617429<36>
P58 = 7349490069689279731072870885529978893158946134836342940881<58>
(4·10166-31)/9 = (4)1651<166> = 43 · 421 · 11489 · 13063 · 219281 · 2114323 · C142
C142 = P31 · C112
P31 = 1401498638512800602338683574933<31>
C112 = [2517542186432726614519045066152878943434736864305600228130570201750511709672675584135765717546155715010204784199<112>]
(4·10171-31)/9 = (4)1701<171> = 3 · 72 · 8461 · C165
C165 = P35 · P130
P35 = 75940027078135399879289466595503179<35>
P130 = 4705520875214939206494061499478771720307848518422079127300817212971538067413967160505918436922055101273111247866701496915002960237<130>
(4·10174-31)/9 = (4)1731<174> = 32 · 1511 · C170
C170 = P33 · C137
P33 = 598391798346729415087360619163761<33>
C137 = [54616627017681544743986838092415411816852954873128335763888764844274262889698533737577934396314791125895856004100260211391989572520846519<137>]
(4·10176-31)/9 = (4)1751<176> = C176
C176 = P35 · C142
P35 = 11555355372315498456034551118161869<35>
C142 = [3846220476345118832108998656213957231199997566866995772725881777424686109863785283056075100863623068462636649438105703704881296092597727524989<142>]
(4·10183-31)/9 = (4)1821<183> = 33 · 7 · 101450189547527<15> · 5144414891929831963<19> · C148
C148 = P31 · C118
P31 = 1494159724423093628331262781519<31>
C118 = [3015572696584852809456973175599019254442494069685606449037092916837733527003570743285631033556963439554618401900680351<118>]
(4·10191-31)/9 = (4)1901<191> = 17 · 79 · 12641819 · C181
C181 = P29 · P37 · P55 · P61
P29 = 46245390417253053507069198277<29>
P37 = 3288698610155369685906033017650636339<37>
P55 = 6012569771633282473568788226836503805781988591612498859<55>
P61 = 2862722471577172119621072059567891400550774220987060325119249<61>
Number: template N=17212318597180223748039000448764292888344649921197914387046064123268426383453754767791117982035636735387868051436891 ( 116 digits) Divisors found: r1=6012569771633282473568788226836503805781988591612498859 (pp55) r2=2862722471577172119621072059567891400550774220987060325119249 (pp61) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 58.42 hours. Scaled time: 74.02 units (timescale=1.267). Factorization parameters were as follows: name: template n: 17212318597180223748039000448764292888344649921197914387046064123268426383453754767791117982035636735387868051436891 skew: 91533.13 # norm 1.54e+016 c5: 7980 c4: 4784704672 c3: -222715949872387 c2: -28504304548550969888 c1: 807182662022460227434248 c0: 37026508934687569946500720770 # alpha -6.60 Y1: 284642025107 Y0: -18482745986698681165733 # Murphy_E 5.10e-010 # M 796204495222869985094069394924151158413871914738322193795127044010427633415413290021916171230526019932611113948771 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, 3570001) Primes: RFBsize:315948, AFBsize:316377, largePrimes:7496042 encountered Relations: rels:7514280, finalFF:746705 Max relations in full relation-set: 28 Initial matrix: 632408 x 746705 with sparse part having weight 56823289. Pruned matrix : 530076 x 533302 with weight 34084002. Polynomial selection time: 3.19 hours. Total sieving time: 46.55 hours. Total relation processing time: 0.52 hours. Matrix solve time: 7.77 hours. Time per square root: 0.38 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 58.42 hours. --------- CPU info (if available) ----------
(4·10194-31)/9 = (4)1931<194> = 157 · 983 · 107612863 · 18342123221<11> · 6108145067228494618057<22> · 12278415751815556076259294677<29> · C121
C121 = P39 · P41 · P42
P39 = 101989504789797446295973287236116553803<39>
P41 = 41521142648191624706188680775787708523349<41>
P42 = 459382092743332026030965233512572367869779<42>
(4·10196-31)/9 = (4)1951<196> = 173 · 8951 · 406573 · C184
C184 = P29 · C156
P29 = 18872789591510503930184653933<29>
C156 = [374046150228173323380807595022805382554654053940337044029074580835216463679660422954179214722659465000076502672706389982552032900972277554928993940469580563<156>]
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10159-7)/9 = 9(7)159<160> = 3 · 103 · 5775893 · C151
C151 = P34 · P117
P34 = 5975646174723226470913875531969593<34>
P117 = 916806470240261764242266409467665050319996173440276451312922130501690767888779961598648122293529899763384835078305697<117>
Number: 97777_159 N=5478511076852723780235660847157060648052640735371009236667389281655145464018197502578354313971024281791862019220095682055259107438013227824279762671321 ( 151 digits) SNFS difficulty: 161 digits. Divisors found: r1=5975646174723226470913875531969593 (pp34) r2=916806470240261764242266409467665050319996173440276451312922130501690767888779961598648122293529899763384835078305697 (pp117) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 102.43 hours. Scaled time: 68.83 units (timescale=0.672). Factorization parameters were as follows: name: 97777_159 n: 5478511076852723780235660847157060648052640735371009236667389281655145464018197502578354313971024281791862019220095682055259107438013227824279762671321 m: 100000000000000000000000000000000 c5: 44 c0: -35 skew: 2 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:316147, largePrimes:5850617 encountered Relations: rels:5997354, finalFF:772910 Max relations in full relation-set: 28 Initial matrix: 632161 x 772910 with sparse part having weight 47864839. Pruned matrix : 522860 x 526084 with weight 32637755. Total sieving time: 88.02 hours. Total relation processing time: 0.71 hours. Matrix solve time: 13.48 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: 102.43 hours. --------- CPU info (if available) ----------
By Wojciech Florek / GMP-ECM 6.1
10200+3 = 1(0)1993<201> = C201
C201 = P29 · C172
P29 = 16892897616604738393032473779<29>
C172 = [5919647550678682918318585392550030687321219331802429980672060525048639901448866420111089641083403610030206379807979210510870824800479444820240779860283084327969945191577457<172>]
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(22·10172-1)/3 = 7(3)172<173> = 13 · 84201814666201<14> · C158
C158 = P28 · C131
P28 = 1272085084357714677202671397<28>
C131 = [52664802777632128483139943807112499915228136328357345310586727772346381267412255744083863646372276716206868216067462224684412144253<131>]
10189+9 = 1(0)1889<190> = 14929 · 269221423 · C177
C177 = P35 · P143
P35 = 12192227834085072186320734367252819<35>
P143 = 20406879351220085024953499773532182396131297871099978867280706469418636599119483854979393271010719938699602587208502179786539720548754102460333<143>
By suberi / GGNFS-0.77.1-20060513-pentium4
(2·10157+1)/3 = (6)1567<157> = 7 · 23 · 541 · C152
C152 = P27 · P125
P27 = 890782728330524191869166267<27>
P125 = 85923866571843740803540965749926517381370019113790480690155834870443120275131486394405562940747729082323857462899385910744101<125>
Number: 66667_157 N=76539496293574891983635855692433688093898654052957677485524467763477648553594868792168478739241417052234379245550185034232289717301370439681136458440967 ( 152 digits) SNFS difficulty: 157 digits. Divisors found: r1=890782728330524191869166267 (pp27) r2=85923866571843740803540965749926517381370019113790480690155834870443120275131486394405562940747729082323857462899385910744101 (pp125) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 48.81 hours. Scaled time: 31.29 units (timescale=0.641). Factorization parameters were as follows: n: 76539496293574891983635855692433688093898654052957677485524467763477648553594868792168478739241417052234379245550185034232289717301370439681136458440967 m: 10000000000000000000000000000000 c5: 200 c0: 1 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2700001) Primes: RFBsize:216816, AFBsize:216391, largePrimes:5587411 encountered Relations: rels:5531851, finalFF:540104 Max relations in full relation-set: 28 Initial matrix: 433272 x 540104 with sparse part having weight 41840958. Pruned matrix : 367301 x 369531 with weight 26704226. Total sieving time: 41.91 hours. Total relation processing time: 0.34 hours. Matrix solve time: 6.39 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: 48.81 hours. --------- CPU info (if available) ----------
(2·10162-11)/9 = (2)1611<162> = 2999 · 13291 · 737369127871<12> · C142
C142 = P58 · P85
P58 = 3477161523419951142339720131731396316406999807975085010917<58>
P85 = 2174420563538039342235832474859054013840635530546636646389334682567283354466126851267<85>
Number: 22221_162 N=7560811519267597547267443095951233885561978836680096060752707770152009100385863396144664462142405057459157349147876168151822386943389530281839 ( 142 digits) SNFS difficulty: 162 digits. Divisors found: r1=3477161523419951142339720131731396316406999807975085010917 (pp58) r2=2174420563538039342235832474859054013840635530546636646389334682567283354466126851267 (pp85) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 80.13 hours. Scaled time: 50.56 units (timescale=0.631). Factorization parameters were as follows: n: 7560811519267597547267443095951233885561978836680096060752707770152009100385863396144664462142405057459157349147876168151822386943389530281839 m: 100000000000000000000000000000000 c5: 200 c0: -11 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, 4549000 ) Primes: RFBsize:315948, AFBsize:316992, largePrimes:5799465 encountered Relations: rels:5908229, finalFF:740494 Max relations in full relation-set: 28 Initial matrix: 633005 x 740494 with sparse part having weight 45607314. Pruned matrix : 551212 x 554441 with weight 32109977. Total sieving time: 66.12 hours. Total relation processing time: 0.35 hours. Matrix solve time: 13.41 hours. Time per square root: 0.25 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: 80.13 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM / Jun 13, 2006
(10629-1)/9 = (1)629<629> = 52837 · 2028119 · 2071723 · 247629013 · 654756293 · 5363222357<10> · 2212394296770203368013<22> · C563
C563 = P37 · C527
P37 = 1789869609522556717733652117803369849<37>
C527 = [14534606650760746267274530737012122249588886991871533480924248527831473439337496631299129179522033276819164732384678553894131236188994972432041295892899181561322393208614711702308252990527266567131722050002675497142409690259209102269418390421674637868575482378208912819748484996888540615006146463031999507378641474887080601161024829052876998932648990033604585060950024365773053544964048384392311758635258298416485361871913055731243696761053009538099247807223175971678734515859190036820748543634426650689638017502134520137543399<527>]
By Brude Dodson / GMP-ECM / Jun 25, 2006
(10369-1)/9 = (1)369<369> = 32 · 37 · 83 · 1231 · 333667 · 538987 · 1811791 · 626920594693<12> · 9425856976319889649<19> · 1900016393894413508477719<25> · 201763709900322803748657942361<30> · 3151445759294008336434146467746716852125711<43> · 8414640003465161203119978906558054839526493<43> · C174
C174 = P52 · P122
P52 = 4624740815741021164555032450406356165555243059597323<52>
P122 = 36075379229129405137442680972370788324414060277012433191198831287911648192680373281921936535843435181632954359677168188643<122>
By Yousuke Koide / GMP-ECM / Jun 28, 2006
(10791-1)/9 = (1)791<791> = 227 · 239 · 4649 · 123397 · 1177009 · 142101569 · 908191467191<12> · 1793584572599<13> · 5325832146769<13> · 827436967363609<15> · 609308862837834547266089<24> · 53895712312217719065267103426685397298498705173449226555003346881878523705781079015749721646701723<98> · C589
C589 = P38 · C552
P38 = 17268952016347267202474461693447627333<38>
C552 = [524338276467821469306866110640693273267456771354911491249811039886750737206459012463989313027609454624719205006551535049494191144723719815372375176302554242015920402149910500053458715224907875055739914800002691751396537788564528624249078377798631613710343087407520477946788491848531530083964817956899222619192798538490548065449464266022982267809530617447686365811014092939620045876935557367216873409267163582736418854782229284649982294276357936431663242770726403360599987506648872509414316421874236089815724432810048030031264456545314684078313249739241<552>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10154-7)/9 = 9(7)154<155> = 739 · 1409 · 89561 · 9944520990408625844894246647<28> · C117
C117 = P40 · P77
P40 = 5837116682833462849392995823393826958467<40>
P77 = 18062736791772976438494600135843067934866747134653325808014080402535275160343<77>
Number: 97777_154 N=105434302264887821200236582241715413873905252645232754612561173722931173696896607522883110803817912699363819426474181 ( 117 digits) SNFS difficulty: 156 digits. Divisors found: r1=5837116682833462849392995823393826958467 (pp40) r2=18062736791772976438494600135843067934866747134653325808014080402535275160343 (pp77) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 61.01 hours. Scaled time: 37.15 units (timescale=0.609). Factorization parameters were as follows: name: 97777_154 n: 105434302264887821200236582241715413873905252645232754612561173722931173696896607522883110803817912699363819426474181 m: 10000000000000000000000000000000 c5: 44 c0: -35 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3000001) Primes: RFBsize:216816, AFBsize:216382, largePrimes:5730781 encountered Relations: rels:5731090, finalFF:574418 Max relations in full relation-set: 28 Initial matrix: 433264 x 574418 with sparse part having weight 48987164. Pruned matrix : 363853 x 366083 with weight 31040164. Total sieving time: 53.51 hours. Total relation processing time: 0.53 hours. Matrix solve time: 6.76 hours. Time per square root: 0.21 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: 61.01 hours. --------- CPU info (if available) ----------
By suberi / GGNFS-0.77.1-20060513-pentium4
(2·10156+7)/9 = (2)1553<156> = 23 · 3499 · 23646641 · C144
C144 = P61 · P83
P61 = 6926356052576897781946985964283783248377448772933915690211713<61>
P83 = 16859373684167425982860874223536195143299267692900426968939447864947450149457709003<83>
Number: 22223_156 N=116774024959988722821062037579716837704602479668438645177019103488857401948400666554562683576727032687209786010840712519018713258848097016152139 ( 144 digits) SNFS difficulty: 156 digits. Divisors found: r1=6926356052576897781946985964283783248377448772933915690211713 (pp61) r2=16859373684167425982860874223536195143299267692900426968939447864947450149457709003 (pp83) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 44.21 hours. Scaled time: 26.92 units (timescale=0.609). Factorization parameters were as follows: n: 116774024959988722821062037579716837704602479668438645177019103488857401948400666554562683576727032687209786010840712519018713258848097016152139 m: 10000000000000000000000000000000 c5: 20 c0: 7 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2500001) Primes: RFBsize:216816, AFBsize:215976, largePrimes:5576703 encountered Relations: rels:5572542, finalFF:588575 Max relations in full relation-set: 28 Initial matrix: 432858 x 588575 with sparse part having weight 43819791. Pruned matrix : 321876 x 324104 with weight 27043784. Total sieving time: 37.95 hours. Total relation processing time: 0.73 hours. Matrix solve time: 5.26 hours. Time per square root: 0.26 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 44.21 hours. --------- CPU info (if available) ----------
10154-3 = (9)1537<154> = 13 · 11243 · 6067869097<10> · C140
C140 = P37 · P48 · P56
P37 = 1640121535660974334937516641312705897<37>
P48 = 632474589733957453044658343116704489644784209341<48>
P56 = 10869739116142629212501414649177235931983515829671794207<56>
Number: 99997_154 N=11275562949784345252112605626469572573490020234580540167103938207368024209876467537743006522462110907256030913689041774978331494305994400539 ( 140 digits) SNFS difficulty: 155 digits. Divisors found: r1=1640121535660974334937516641312705897 (pp37) r2=632474589733957453044658343116704489644784209341 (pp48) r3=10869739116142629212501414649177235931983515829671794207 (pp56) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 37.22 hours. Scaled time: 23.49 units (timescale=0.631). Factorization parameters were as follows: n: 11275562949784345252112605626469572573490020234580540167103938207368024209876467537743006522462110907256030913689041774978331494305994400539 m: 10000000000000000000000000000000 c5: 1 c0: -30 skew: 1.97 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, 2400001) Primes: RFBsize:216816, AFBsize:215581, largePrimes:5481373 encountered Relations: rels:5403721, finalFF:528307 Max relations in full relation-set: 28 Initial matrix: 432461 x 528307 with sparse part having weight 37745359. Pruned matrix : 360063 x 362289 with weight 23851643. Total sieving time: 30.84 hours. Total relation processing time: 0.27 hours. Matrix solve time: 5.94 hours. Time per square root: 0.18 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: 37.22 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GMP-ECM 6.1 B1=11000000
10152+9 = 1(0)1519<153> = 29 · 293 · 1640081714429881<16> · C133
C133 = P33 · P101
P33 = 269884379947565697172496988236741<33>
P101 = 26588335208574136942682656526949478340363566869268859697120096025992721634714319195150472641068851757<101>
10157+9 = 1(0)1569<158> = 103 · 379 · 11025855177473150881<20> · C134
C134 = P30 · P104
P30 = 489153471136315018633879719917<30>
P104 = 47496995862766072526492146025536044546152041717277054294283602053960385357153879208150508927116593915441<104>
10194+9 = 1(0)1939<195> = 601 · 1669 · 4157 · 102873857153<12> · C174
C174 = P30 · P144
P30 = 779377879409212880284613409841<30>
P144 = 299113536682015207303470362477684416309447351856104432130038973632908830947016400385722023444292682919977688505297634840607839940972350056603601<144>
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10153-7)/9 = 9(7)153<154> = 33 · 19 · 71 · 3260123 · C143
C143 = P38 · P43 · P63
P38 = 99116919537660717344019019386864967843<38>
P43 = 1546063793752448861604594357599366716472771<43>
P63 = 537347530384367705748566479582863469498681675372594701184956221<63>
Number: 97777_153 N=82343716238265332733845578767001197316759534003740090541991240208597861404143350691125394255272175363383252368085479900141859271017232097820613 ( 143 digits) SNFS difficulty: 154 digits. Divisors found: r1=99116919537660717344019019386864967843 (pp38) r2=1546063793752448861604594357599366716472771 (pp43) r3=537347530384367705748566479582863469498681675372594701184956221 (pp63) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 50.96 hours. Scaled time: 34.24 units (timescale=0.672). Factorization parameters were as follows: name: 97777_153 n: 82343716238265332733845578767001197316759534003740090541991240208597861404143350691125394255272175363383252368085479900141859271017232097820613 m: 2000000000000000000000000000000 c5: 2750 c0: -7 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2700001) Primes: RFBsize:216816, AFBsize:216172, largePrimes:5588683 encountered Relations: rels:5518212, finalFF:527248 Max relations in full relation-set: 28 Initial matrix: 433055 x 527248 with sparse part having weight 41503672. Pruned matrix : 374357 x 376586 with weight 27113464. Total sieving time: 44.17 hours. Total relation processing time: 0.41 hours. Matrix solve time: 6.18 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 50.96 hours. --------- CPU info (if available) ----------
By suberi / GGNFS-0.77.1-20060513-pentium4
(37·10153-1)/9 = 4(1)153<154> = 19 · 52673 · 6828739 · 53203810549582657<17> · C125
C125 = P58 · P67
P58 = 1449115186608669999968721909978577884920205127608130753117<58>
P67 = 7802457274112608923698648032270060088171243614756391036896564625483<67>
Number: 41111_153 N=11306659328781867934200901863811224235021793204640218687383945073613523898676275009234833635994753050785147831466037839880511 ( 125 digits) SNFS difficulty: 154 digits. Divisors found: r1=1449115186608669999968721909978577884920205127608130753117 (pp58) r2=7802457274112608923698648032270060088171243614756391036896564625483 (pp67) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 53.40 hours. Scaled time: 34.28 units (timescale=0.642). Factorization parameters were as follows: n: 11306659328781867934200901863811224235021793204640218687383945073613523898676275009234833635994753050785147831466037839880511 m: 1000000000000000000000000000000 c5: 37000 c0: -1 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3000001) Primes: RFBsize:216816, AFBsize:217626, largePrimes:5592626 encountered Relations: rels:5485878, finalFF:487203 Max relations in full relation-set: 28 Initial matrix: 434509 x 487203 with sparse part having weight 39884456. Pruned matrix : 411756 x 413992 with weight 30091644. Total sieving time: 44.27 hours. Total relation processing time: 0.40 hours. Matrix solve time: 8.51 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 53.40 hours. --------- CPU info (if available) ----------
8·10152-1 = 7(9)152<153> = 23 · C152
C152 = P40 · P112
P40 = 7901339528982736247439245218030751681423<40>
P112 = 4402115434739492378122395747854232895486096498939727009935645870272775578543880889791663422087920251843606452631<112>
Number: 79999_152 N=34782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913 ( 152 digits) SNFS difficulty: 152 digits. Divisors found: r1=7901339528982736247439245218030751681423 (pp40) r2=4402115434739492378122395747854232895486096498939727009935645870272775578543880889791663422087920251843606452631 (pp112) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 33.81 hours. Scaled time: 20.62 units (timescale=0.610). Factorization parameters were as follows: n: 34782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913 m: 2000000000000000000000000000000 c5: 25 c0: -1 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2000001) Primes: RFBsize:176302, AFBsize:176093, largePrimes:5463800 encountered Relations: rels:5400866, finalFF:508492 Max relations in full relation-set: 28 Initial matrix: 352459 x 508492 with sparse part having weight 43119422. Pruned matrix : 279663 x 281489 with weight 22308678. Total sieving time: 29.53 hours. Total relation processing time: 0.59 hours. Matrix solve time: 3.46 hours. Time per square root: 0.23 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: 33.81 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(88·10152-7)/9 = 9(7)152<153> = 432 · 1699 · 9787 · 26731 · C139
C139 = P36 · P52(1123...) · P52(7199...)
P36 = 147069431940540632633622231942675241<36>
P52(1123...) = 1123545359101834709721738804452009746749923728439347<52>
P52(7199...) = 7199992653826193042600639583180770081495925912971633<52>
Number: 97777_152 N=1189720865726551197046584113282700046958525888139439104529939391718176978625271748994829022891657295537737626613238339384672302925168944891 ( 139 digits) SNFS difficulty: 153 digits. Divisors found: r1=147069431940540632633622231942675241 (pp36) r2=1123545359101834709721738804452009746749923728439347 (pp52) r3=7199992653826193042600639583180770081495925912971633 (pp52) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 44.45 hours. Scaled time: 27.07 units (timescale=0.609). Factorization parameters were as follows: name: 97777_152 n: 1189720865726551197046584113282700046958525888139439104529939391718176978625271748994829022891657295537737626613238339384672302925168944891 m: 2000000000000000000000000000000 c5: 275 c0: -7 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2300001) Primes: RFBsize:176302, AFBsize:176544, largePrimes:5634915 encountered Relations: rels:5575605, finalFF:493838 Max relations in full relation-set: 28 Initial matrix: 352912 x 493838 with sparse part having weight 45407063. Pruned matrix : 299744 x 301572 with weight 25519786. Total sieving time: 39.81 hours. Total relation processing time: 0.32 hours. Matrix solve time: 4.14 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 44.45 hours. --------- CPU info (if available) ----------
By suberi / GGNFS-0.77.1-20060513-pentium4
2·10153-9 = 1(9)1521<154> = 11 · C153
C153 = P41 · P45 · P68
P41 = 14143455769740740001759009960126743688349<41>
P45 = 453912657024767148614711372141519336680287959<45>
P68 = 28321058492200039254937740121739341593546053812714710601460743639391<68>
Number: 19991_153 N=181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181 ( 153 digits) SNFS difficulty: 153 digits. Divisors found: r1=14143455769740740001759009960126743688349 (pp41) r2=453912657024767148614711372141519336680287959 (pp45) r3=28321058492200039254937740121739341593546053812714710601460743639391 (pp68) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 37.97 hours. Scaled time: 23.05 units (timescale=0.607). Factorization parameters were as follows: n: 181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181 m: 2000000000000000000000000000000 c5: 125 c0: -18 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:176188, largePrimes:5665430 encountered Relations: rels:5691661, finalFF:578636 Max relations in full relation-set: 28 Initial matrix: 352556 x 578636 with sparse part having weight 51231586. Pruned matrix : 262318 x 264144 with weight 24854504. Total sieving time: 33.49 hours. Total relation processing time: 0.69 hours. Matrix solve time: 3.55 hours. Time per square root: 0.24 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: 37.97 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
6·10151-1 = 5(9)151<152> = 61 · 129113 · C145
C145 = P33 · P47 · P66
P33 = 836660367018273797355323968615817<33>
P47 = 17524625066162102246330727763070206160904572767<47>
P66 = 519581298814572713681606589033971690588245769057952345724971828437<66>
Number: 59999_151 N=7618183741196077701919007787434389979650561529975077111890677031798171966023408393181573187954686535228449650090472280413154419441706483315606243 ( 145 digits) SNFS difficulty: 151 digits. Divisors found: r1=836660367018273797355323968615817 (pp33) r2=17524625066162102246330727763070206160904572767 (pp47) r3=519581298814572713681606589033971690588245769057952345724971828437 (pp66) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 32.65 hours. Scaled time: 19.88 units (timescale=0.609). Factorization parameters were as follows: name: 59999_151 n: 7618183741196077701919007787434389979650561529975077111890677031798171966023408393181573187954686535228449650090472280413154419441706483315606243 m: 1000000000000000000000000000000 c5: 60 c0: -1 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2000001) Primes: RFBsize:176302, AFBsize:175738, largePrimes:5548666 encountered Relations: rels:5544388, finalFF:557581 Max relations in full relation-set: 28 Initial matrix: 352107 x 557581 with sparse part having weight 49093900. Pruned matrix : 263359 x 265183 with weight 23631186. Total sieving time: 29.11 hours. Total relation processing time: 0.33 hours. Matrix solve time: 3.06 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 32.65 hours. --------- CPU info (if available) ----------
By Wojciech Florek / GMP-ECM 6.0.1 B1=250000
10182+3 = 1(0)1813<183> = C183
C183 = P27 · P156
P27 = 406739627350936953562388377<27>
P156 = 245857529671480737053230473791951684664784508684537281437794354233101717382061812791982857492060102011506560855529194447399887136377222705239997696635282939<156>
By Alfred Reich / Msieve v. 1.06
(2·10157+43)/9 = (2)1567<157> = 7 · 6011267 · 11340661 · 26297446143827679370836289<26> · C117
C117 = P54 · P63
P54 = 297907083346305195502362629714985396531415470201105233<54>
P63 = 594416225273485143935306604924356739743242652295164459113417819<63>
prp54 factor: 297907083346305195502362629714985396531415470201105233 prp63 factor: 594416225273485143935306604924356739743242652295164459113417819 Fri Jun 16 15:30:27 2006 Fri Jun 16 15:30:27 2006 Fri Jun 16 15:30:27 2006 Msieve v. 1.06 Fri Jun 16 15:30:27 2006 random seeds: 6e3be7d0 af211ff4 Fri Jun 16 15:30:27 2006 factoring 177080803964944263576713030557411134623070902269225184654689439234506372676272442327285572763581070913582793916346827 (117 digits) Fri Jun 16 15:30:28 2006 using multiplier of 17 Fri Jun 16 15:30:28 2006 sieve interval: 19 blocks of size 65536 Fri Jun 16 15:30:28 2006 processing polynomials in batches of 3 Fri Jun 16 15:30:28 2006 using a sieve bound of 10566139 (350000 primes) Fri Jun 16 15:30:28 2006 using large prime bound of 1584920850 (30 bits) Fri Jun 16 15:30:28 2006 using double large prime bound of 36308945412966600 (47-56 bits) Fri Jun 16 15:30:28 2006 using trial factoring cutoff of 68 bits Fri Jun 16 15:30:28 2006 polynomial 'A' values have 16 factors Sat Jun 17 14:47:39 2006 5839 relations (5561 full + 278 combined from 322304 partial), need 350096 Sat Jun 17 14:47:39 2006 elapsed time 23:17:12 Sat Jun 17 14:48:21 2006 Sat Jun 17 14:48:21 2006 Sat Jun 17 14:48:21 2006 Msieve v. 1.06 Sat Jun 17 14:48:21 2006 random seeds: a6d38e10 66593cf6 Sat Jun 17 14:48:21 2006 factoring 177080803964944263576713030557411134623070902269225184654689439234506372676272442327285572763581070913582793916346827 (117 digits) Sat Jun 17 14:48:23 2006 using multiplier of 17 Sat Jun 17 14:48:23 2006 sieve interval: 19 blocks of size 65536 Sat Jun 17 14:48:23 2006 processing polynomials in batches of 3 Sat Jun 17 14:48:23 2006 using a sieve bound of 10566139 (350000 primes) Sat Jun 17 14:48:23 2006 using large prime bound of 1584920850 (30 bits) Sat Jun 17 14:48:23 2006 using double large prime bound of 36308945412966600 (47-56 bits) Sat Jun 17 14:48:23 2006 using trial factoring cutoff of 68 bits Sat Jun 17 14:48:23 2006 polynomial 'A' values have 16 factors Sat Jun 17 15:05:03 2006 67 relations (67 full + 0 combined from 3929 partial), need 350096 Sat Jun 17 15:05:03 2006 elapsed time 00:16:42 Sat Jun 17 15:08:44 2006 Sat Jun 17 15:08:44 2006 Sat Jun 17 15:08:44 2006 Msieve v. 1.06 Sat Jun 17 15:08:44 2006 random seeds: 2edef0b0 ff574550 Sat Jun 17 15:08:44 2006 factoring 177080803964944263576713030557411134623070902269225184654689439234506372676272442327285572763581070913582793916346827 (117 digits) Sat Jun 17 15:08:46 2006 using multiplier of 17 Sat Jun 17 15:08:46 2006 sieve interval: 19 blocks of size 65536 Sat Jun 17 15:08:46 2006 processing polynomials in batches of 3 Sat Jun 17 15:08:46 2006 using a sieve bound of 10566139 (350000 primes) Sat Jun 17 15:08:46 2006 using large prime bound of 1584920850 (30 bits) Sat Jun 17 15:08:46 2006 using double large prime bound of 36308945412966600 (47-56 bits) Sat Jun 17 15:08:46 2006 using trial factoring cutoff of 68 bits Sat Jun 17 15:08:46 2006 polynomial 'A' values have 16 factors Sat Jun 17 15:08:52 2006 restarting with 45113 full and 2586148 partial relations Sat Jun 17 15:10:15 2006 79829 relations (45115 full + 34714 combined from 2586446 partial), need 350096 Sat Jun 17 15:10:15 2006 elapsed time 00:01:31 Sat Jun 17 15:11:28 2006 Sat Jun 17 15:11:28 2006 Sat Jun 17 15:11:28 2006 Msieve v. 1.06 Sat Jun 17 15:11:28 2006 random seeds: f0c64d78 a1063e8e Sat Jun 17 15:11:28 2006 factoring 177080803964944263576713030557411134623070902269225184654689439234506372676272442327285572763581070913582793916346827 (117 digits) Sat Jun 17 15:11:29 2006 using multiplier of 17 Sat Jun 17 15:11:29 2006 sieve interval: 19 blocks of size 65536 Sat Jun 17 15:11:29 2006 processing polynomials in batches of 3 Sat Jun 17 15:11:29 2006 using a sieve bound of 10566139 (350000 primes) Sat Jun 17 15:11:29 2006 using large prime bound of 1584920850 (30 bits) Sat Jun 17 15:11:29 2006 using double large prime bound of 36308945412966600 (47-56 bits) Sat Jun 17 15:11:29 2006 using trial factoring cutoff of 68 bits Sat Jun 17 15:11:29 2006 polynomial 'A' values have 16 factors Sun Jun 18 14:02:17 2006 5722 relations (5458 full + 264 combined from 315736 partial), need 350096 Sun Jun 18 14:02:17 2006 elapsed time 22:50:49 Sun Jun 18 14:53:41 2006 Sun Jun 18 14:53:41 2006 Sun Jun 18 14:53:41 2006 Msieve v. 1.06 Sun Jun 18 14:53:41 2006 random seeds: a7040c00 6bf83931 Sun Jun 18 14:53:41 2006 factoring 177080803964944263576713030557411134623070902269225184654689439234506372676272442327285572763581070913582793916346827 (117 digits) Sun Jun 18 14:53:43 2006 using multiplier of 17 Sun Jun 18 14:53:43 2006 sieve interval: 19 blocks of size 65536 Sun Jun 18 14:53:43 2006 processing polynomials in batches of 3 Sun Jun 18 14:53:43 2006 using a sieve bound of 10566139 (350000 primes) Sun Jun 18 14:53:43 2006 using large prime bound of 1584920850 (30 bits) Sun Jun 18 14:53:43 2006 using double large prime bound of 36308945412966600 (47-56 bits) Sun Jun 18 14:53:43 2006 using trial factoring cutoff of 68 bits Sun Jun 18 14:53:43 2006 polynomial 'A' values have 16 factors Sun Jun 18 14:53:58 2006 restarting with 98809 full and 5685171 partial relations Sun Jun 18 14:53:58 2006 489590 relations (98809 full + 390781 combined from 5685171 partial), need 350096 Sun Jun 18 14:54:19 2006 begin with 5685171 relations Sun Jun 18 14:54:35 2006 reduce to 1179398 relations in 14 passes Sun Jun 18 14:54:35 2006 attempting to read 98809 full and 1179398 partial relations Sun Jun 18 14:55:21 2006 recovered 98809 full and 1179398 partial relations Sun Jun 18 14:55:21 2006 recovered 1255866 polynomials Sun Jun 18 14:55:27 2006 attempting to build 390781 cycles Sun Jun 18 14:55:28 2006 found 390781 cycles in 6 passes Sun Jun 18 14:55:30 2006 distribution of cycle lengths: Sun Jun 18 14:55:30 2006 length 2 : 76003 Sun Jun 18 14:55:30 2006 length 3 : 82423 Sun Jun 18 14:55:30 2006 length 4 : 72166 Sun Jun 18 14:55:30 2006 length 5 : 57921 Sun Jun 18 14:55:30 2006 length 6 : 40330 Sun Jun 18 14:55:30 2006 length 7 : 26146 Sun Jun 18 14:55:30 2006 length 8 : 16036 Sun Jun 18 14:55:30 2006 length 9+: 19756 Sun Jun 18 14:55:30 2006 largest cycle: 21 relations Sun Jun 18 14:55:31 2006 350000 x 350064 system, weight 22152847 (avg 63.28/col) Sun Jun 18 14:55:34 2006 reduce to 338708 x 338772 in 4 passes Sun Jun 18 16:11:11 2006 lanczos halted after 5357 iterations Sun Jun 18 16:11:15 2006 recovered 56 nontrivial dependencies Sun Jun 18 16:13:09 2006 prp54 factor: 297907083346305195502362629714985396531415470201105233 Sun Jun 18 16:13:09 2006 prp63 factor: 594416225273485143935306604924356739743242652295164459113417819 Sun Jun 18 16:13:12 2006 elapsed time 01:19:31
By Wataru Sakai / GMP-ECM 6.1
(25·10161-1)/3 = 8(3)161<162> = 71 · 627632323902741384517983871<27> · C134
C134 = P33 · P101
P33 = 402923263960731990459276252411929<33>
P101 = 46412264609376042963875982573595320846726898199501545598399929674110110204265192309020927313561073797<101>
(25·10189-1)/3 = 8(3)189<190> = 13 · 69481 · 14970782913227<14> · 86676545786512496411372249<26> · C145
C145 = P29 · P33 · P85
P29 = 22947665214016491792948713879<29>
P33 = 263220054799792924810769047222031<33>
P85 = 1177079381440907821047749257131763892168650187727161937621530953691546230966643693843<85>
(25·10193-1)/3 = 8(3)193<194> = 2729 · 9431 · 113622631267<12> · C176
C176 = P37 · P140
P37 = 1234673054650272416503200054655444603<37>
P140 = 23080258080801038899595047931573006063528336563000814220369471250323182879121823026175822141456825879452373941615318614152585303505844325067<140>
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(73·10151-1)/9 = 8(1)151<152> = 3 · 29 · 47 · 193 · 457697 · C141
C141 = P33 · P34 · P75
P33 = 528012984669708627919758887087231<33>
P34 = 2640623962369281969675262349483603<34>
P75 = 161055923586852517269688910385341375145213411153442717701673814626750164283<75>
Number: 81111_151 N=224557655449331640744698222153463653716415037742054456753768335971442934095442031868984712643312221148993545757459799412236334041135414093919 ( 141 digits) SNFS difficulty: 152 digits. Divisors found: r1=528012984669708627919758887087231 (pp33) r2=2640623962369281969675262349483603 (pp34) r3=161055923586852517269688910385341375145213411153442717701673814626750164283 (pp75) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 44.55 hours. Scaled time: 29.98 units (timescale=0.673). Factorization parameters were as follows: name: 81111_151 n: 224557655449331640744698222153463653716415037742054456753768335971442934095442031868984712643312221148993545757459799412236334041135414093919 m: 1000000000000000000000000000000 c5: 730 c0: -1 skew: 2 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:176503, largePrimes:5534398 encountered Relations: rels:5399634, finalFF:435070 Max relations in full relation-set: 28 Initial matrix: 352872 x 435070 with sparse part having weight 39896073. Pruned matrix : 320448 x 322276 with weight 25707123. Total sieving time: 39.82 hours. Total relation processing time: 0.36 hours. Matrix solve time: 4.20 hours. Time per square root: 0.17 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: 44.55 hours. --------- CPU info (if available) ----------
By suberi / GGNFS-0.77.1-20060513-pentium4
(8·10153-71)/9 = (8)1521<153> = 8825839534511526662522911<25> · C129
C129 = P46 · P83
P46 = 1296444514871243498998765398449712354381717833<46>
P83 = 77685061845475214425509536216756309596984840086525079446336201532416456388867813687<83>
Number: 88881_153 N=100714372316999662567112812918965620315388389942591227612416816485546219492067911197547793034221068381867775300311816362049380271 ( 129 digits) SNFS difficulty: 153 digits. Divisors found: r1=1296444514871243498998765398449712354381717833 (pp46) r2=77685061845475214425509536216756309596984840086525079446336201532416456388867813687 (pp83) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 60.66 hours. Scaled time: 37.13 units (timescale=0.612). Factorization parameters were as follows: n: 100714372316999662567112812918965620315388389942591227612416816485546219492067911197547793034221068381867775300311816362049380271 m: 2000000000000000000000000000000 c5: 250 c0: -71 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2700001) Primes: RFBsize:176302, AFBsize:175124, largePrimes:5822215 encountered Relations: rels:5825108, finalFF:487746 Max relations in full relation-set: 28 Initial matrix: 351492 x 487746 with sparse part having weight 52251534. Pruned matrix : 305361 x 307182 with weight 32152741. Total sieving time: 53.71 hours. Total relation processing time: 1.08 hours. Matrix solve time: 5.58 hours. Time per square root: 0.29 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: 60.66 hours. --------- CPU info (if available) ----------
By suberi / GGNFS-0.77.1-20060513-pentium4
(4·10153+41)/9 = (4)1529<153> = 23 · 29 · 7877 · 873567461478995351<18> · C128
C128 = P53 · P76
P53 = 10278202000310109853026337644927666384593872391970911<53>
P76 = 9421438220178605267247787803414490154127967731184104140712790580208553504351<76>
Number: 44449_153 N=96835445160437861836793054504352665974763358359367105494199949648027977115227878216143159883536675005810147600085224164703933761 ( 128 digits) SNFS difficulty: 153 digits. Divisors found: r1=10278202000310109853026337644927666384593872391970911 (pp53) r2=9421438220178605267247787803414490154127967731184104140712790580208553504351 (pp76) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 36.61 hours. Scaled time: 23.54 units (timescale=0.643). Factorization parameters were as follows: n: 96835445160437861836793054504352665974763358359367105494199949648027977115227878216143159883536675005810147600085224164703933761 m: 2000000000000000000000000000000 c5: 125 c0: 41 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2300001) Primes: RFBsize:176302, AFBsize:176674, largePrimes:5475359 encountered Relations: rels:5331530, finalFF:432026 Max relations in full relation-set: 28 Initial matrix: 353041 x 432026 with sparse part having weight 38289105. Pruned matrix : 319991 x 321820 with weight 24785869. Total sieving time: 31.58 hours. Total relation processing time: 0.31 hours. Matrix solve time: 4.55 hours. Time per square root: 0.16 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: 36.61 hours. --------- CPU info (if available) ----------
(5·10157-41)/9 = (5)1561<157> = 31638006853<11> · 127308301733038781811409<24> · C124
C124 = P47 · P77
P47 = 62177795589380677359547676171051471759978319277<47>
P77 = 22183309247072798284455041381076813661365827752047238245813949734174421655119<77>
Number: 55551_157 N=1379309267860510631923280660454483985542807005995371878444954987504570972707580675762406732618983047945197528669850163428963 ( 124 digits) SNFS difficulty: 157 digits. Divisors found: r1=62177795589380677359547676171051471759978319277 (pp47) r2=22183309247072798284455041381076813661365827752047238245813949734174421655119 (pp77) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 53.50 hours. Scaled time: 36.75 units (timescale=0.687). Factorization parameters were as follows: n: 1379309267860510631923280660454483985542807005995371878444954987504570972707580675762406732618983047945197528669850163428963 m: 10000000000000000000000000000000 c5: 500 c0: -41 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3300001) Primes: RFBsize:216816, AFBsize:216877, largePrimes:5686463 encountered Relations: rels:5613572, finalFF:490335 Max relations in full relation-set: 28 Initial matrix: 433759 x 490335 with sparse part having weight 45003353. Pruned matrix : 410960 x 413192 with weight 34410874. Total sieving time: 43.92 hours. Total relation processing time: 0.31 hours. Matrix solve time: 9.07 hours. Time per square root: 0.20 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: 53.50 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(28·10151-1)/9 = 3(1)151<152> = 31 · 19843 · 434831 · C141
C141 = P60 · P81
P60 = 974853410034804062561219744184438708636042947181325656020147<60>
P81 = 119312702335017997752212094830142486881715593155366467314651908260291633099814831<81>
Number: 31111_151 N=116312394731759824276532451135704508184575224005721352126402868892503361415954444774635572442848479083945663759064809382402290241666105400157 ( 141 digits) SNFS difficulty: 152 digits. Divisors found: r1=974853410034804062561219744184438708636042947181325656020147 (pp60) r2=119312702335017997752212094830142486881715593155366467314651908260291633099814831 (pp81) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 36.44 hours. Scaled time: 24.31 units (timescale=0.667). Factorization parameters were as follows: name: 31111_151 n: 116312394731759824276532451135704508184575224005721352126402868892503361415954444774635572442848479083945663759064809382402290241666105400157 m: 1000000000000000000000000000000 c5: 280 c0: -1 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:176603, largePrimes:5432957 encountered Relations: rels:5288454, finalFF:437164 Max relations in full relation-set: 28 Initial matrix: 352972 x 437164 with sparse part having weight 38153671. Pruned matrix : 312776 x 314604 with weight 23827219. Total sieving time: 32.14 hours. Total relation processing time: 0.34 hours. Matrix solve time: 3.80 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 36.44 hours. --------- CPU info (if available) ----------
By Alexander Mkrtychyan / ggnfs-0.77.1-20060513-win32
(10186+71)/9 = (1)1859<186> = C186
C186 = P53 · P133
P53 = 21956285956390994430963419957738743694747827961903819<53>
P133 = 5060560394039188481932328242445842739178885005851611298737492037561232350261294769209243502470606386060971130677592702162720129986701<133>
From dependence 1, sqrt obtained: r1=21956285956390994430963419957738743694747827961903819 (p53) r2=5060560394039188481932328242445842739178885005851611298737492037561232350261294769209243502470606386060971130677592702162720129986701 (p133) sieving params: n: 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111119 m: 10000000000000000000000000000000000000 c5: 10 c0: 71 skew: 1.48 type: snfs rlim: 11000000 alim: 11000000 lbpr: 28 lbpa: 28 mfbr: 48 mfba: 48 rlambda: 2.2 alambda: 2.2 CPU RAM Process: (GHz days) (Max RSS) ----------------- ---------- --------- gnfs-lasieve4I14e 562 58MB procrels 0.06 ??MB matbuild 0.06 672MB matsolve 5.17 348MB sqrt 0.08 ??MB ---------- total 567.37 Special-q: ~[6M;51M) Processing with different factor bases (with additional(+1M) special-q sieving): -------- 13M/13M unique relations: 3134973 full relation sets: 1730732 Pruning matrix with wt=0.700 Initial matrix is 1696502 x 1730732 with sparse part having weight 39373085. (total weight is 106462937) Matrix pruned to 1670902 x 1679448 with weight 39534812. matsolve found only trivial dependencies. 6M/6M unique relations: 3362796 full relation sets: 949650 Pruning matrix with wt=0.700 Initial matrix is 825087 x 949650 with sparse part having weight 107831245. (total weight is 172292685) Matrix pruned to 780833 x 785022 with weight 77805320.
(4·10189-7)/3 = 1(3)1881<190> = 11 · C189
C189 = P77 · P112
P77 = 22727342670242448304921294300019680181558260484479909955238866999770020899617<77>
P112 = 5333316920100283702649243746356914291163645388535270424514041824457524502483749417048804695185211155141229296313<112>
From dependence 0, sqrt obtained: r1=5333316920100283702649243746356914291163645388535270424514041824457524502483749417048804695185211155141229296313 (p112) r2=22727342670242448304921294300019680181558260484479909955238866999770020899617 (p77) sieving params: m: 100000000000000000000000000000000000000 c5: 2 c0: -35 skew: 1.77 type: snfs rlim: 14000000 alim: 14000000 lbpr: 29 lbpa: 29 mfbr: 54 mfba: 54 rlambda: 2.3 alambda: 2.3 Special-q: ~[6M;60M) Processing with different factor bases (with additional(+0.3M) special-q sieving): -------- 8M/8M unique relations: 3691813 full relation sets: 1245850 Pruning matrix with wt=0.700 Initial matrix is 1079262 x 1245850 with sparse part having weight 81530763. (total weight is 145966109) Matrix pruned to 1004047 x 1009507 with weight 56671324. 7M/7M unique relations: 3837154 full relation sets: 1169049 Pruning matrix with wt=0.700 Initial matrix is 952777 x 1169049 with sparse part having weight 105082045. (total weight is 174741652) Matrix pruned to 868214 x 873041 with weight 67229090. !Solved successfully CPU RAM Process: (GHz days) (Max RSS) ----------------- ---------- --------- gnfs-lasieve4I14e 675 62MB procrels 0.06 ??MB matbuild 0.08 765MB matsolve 5.38 300MB sqrt 0.04 132MB ---------- total 680.56
These are the largest number and the second largest number factored by GGNFS in our tables so far. Congratulations!
By Alfred Reich / Msieve v. 1.06
10161+9 = 1(0)1609<162> = 7 · 13 · 23 · 157 · 8059 · 13415957160051517<17> · 33227221889480924019367<23> · C113
C113 = P47 · P67
P47 = 37811313891994346064305264570354822948081755411<47>
P67 = 2240332608851730481538608681856319442213805555106852747449191086419<67>
number: 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) prp47 factor: 37811313891994346064305264570354822948081755411 prp67 factor: 2240332608851730481538608681856319442213805555106852747449191086419 Tue Jun 06 14:10:29 2006 Tue Jun 06 14:10:29 2006 Tue Jun 06 14:10:29 2006 Msieve v. 1.06 Tue Jun 06 14:10:29 2006 random seeds: 82bb10e0 ef1ee166 Tue Jun 06 14:10:29 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Tue Jun 06 14:10:30 2006 using multiplier of 1 Tue Jun 06 14:10:30 2006 sieve interval: 17 blocks of size 65536 Tue Jun 06 14:10:31 2006 processing polynomials in batches of 3 Tue Jun 06 14:10:31 2006 using a sieve bound of 8423407 (282760 primes) Tue Jun 06 14:10:31 2006 using large prime bound of 1263511050 (30 bits) Tue Jun 06 14:10:31 2006 using double large prime bound of 24145837678737600 (47-55 bits) Tue Jun 06 14:10:31 2006 using trial factoring cutoff of 65 bits Tue Jun 06 14:10:31 2006 polynomial 'A' values have 15 factors Tue Jun 06 14:10:31 2006 restarting with 563 full and 34999 partial relations Tue Jun 06 14:26:35 2006 579 relations (576 full + 3 combined from 36265 partial), need 282856 Tue Jun 06 14:26:35 2006 elapsed time 00:16:06 Tue Jun 06 14:27:05 2006 Tue Jun 06 14:27:05 2006 Tue Jun 06 14:27:05 2006 Msieve v. 1.06 Tue Jun 06 14:27:05 2006 random seeds: 14acdaf0 f2db2c6e Tue Jun 06 14:27:05 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Tue Jun 06 14:27:06 2006 using multiplier of 1 Tue Jun 06 14:27:06 2006 sieve interval: 17 blocks of size 65536 Tue Jun 06 14:27:06 2006 processing polynomials in batches of 3 Tue Jun 06 14:27:06 2006 using a sieve bound of 8423407 (282760 primes) Tue Jun 06 14:27:06 2006 using large prime bound of 1263511050 (30 bits) Tue Jun 06 14:27:06 2006 using double large prime bound of 24145837678737600 (47-55 bits) Tue Jun 06 14:27:06 2006 using trial factoring cutoff of 65 bits Tue Jun 06 14:27:06 2006 polynomial 'A' values have 15 factors Wed Jun 07 10:19:26 2006 1110 relations (1097 full + 13 combined from 66807 partial), need 282856 Wed Jun 07 10:19:26 2006 elapsed time 19:52:21 Wed Jun 07 10:23:45 2006 Wed Jun 07 10:23:45 2006 Wed Jun 07 10:23:45 2006 Msieve v. 1.06 Wed Jun 07 10:23:45 2006 random seeds: b353bbc0 876a3e65 Wed Jun 07 10:23:45 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Wed Jun 07 10:23:46 2006 using multiplier of 1 Wed Jun 07 10:23:46 2006 sieve interval: 17 blocks of size 65536 Wed Jun 07 10:23:46 2006 processing polynomials in batches of 3 Wed Jun 07 10:23:46 2006 using a sieve bound of 8423407 (282760 primes) Wed Jun 07 10:23:46 2006 using large prime bound of 1263511050 (30 bits) Wed Jun 07 10:23:46 2006 using double large prime bound of 24145837678737600 (47-55 bits) Wed Jun 07 10:23:46 2006 using trial factoring cutoff of 65 bits Wed Jun 07 10:23:46 2006 polynomial 'A' values have 15 factors Wed Jun 07 12:03:49 2006 5 relations (5 full + 0 combined from 375 partial), need 282856 Wed Jun 07 12:03:49 2006 elapsed time 01:40:04 Wed Jun 07 12:05:32 2006 Wed Jun 07 12:05:32 2006 Wed Jun 07 12:05:32 2006 Msieve v. 1.06 Wed Jun 07 12:05:32 2006 random seeds: d4971db8 71711aba Wed Jun 07 12:05:32 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Wed Jun 07 12:05:34 2006 using multiplier of 1 Wed Jun 07 12:05:34 2006 sieve interval: 17 blocks of size 65536 Wed Jun 07 12:05:34 2006 processing polynomials in batches of 3 Wed Jun 07 12:05:34 2006 using a sieve bound of 8423407 (282760 primes) Wed Jun 07 12:05:34 2006 using large prime bound of 1263511050 (30 bits) Wed Jun 07 12:05:34 2006 using double large prime bound of 24145837678737600 (47-55 bits) Wed Jun 07 12:05:34 2006 using trial factoring cutoff of 65 bits Wed Jun 07 12:05:34 2006 polynomial 'A' values have 15 factors Wed Jun 07 12:05:34 2006 restarting with 251 full and 16479 partial relations Sun Jun 11 18:34:58 2006 2339 relations (2267 full + 72 combined from 140829 partial), need 282856 Sun Jun 11 18:34:58 2006 elapsed time 102:29:26 Sun Jun 11 18:35:59 2006 Sun Jun 11 18:35:59 2006 Sun Jun 11 18:35:59 2006 Msieve v. 1.06 Sun Jun 11 18:35:59 2006 random seeds: cefb7950 3127a798 Sun Jun 11 18:35:59 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Sun Jun 11 18:36:00 2006 using multiplier of 1 Sun Jun 11 18:36:00 2006 sieve interval: 17 blocks of size 65536 Sun Jun 11 18:36:00 2006 processing polynomials in batches of 3 Sun Jun 11 18:36:00 2006 using a sieve bound of 8423407 (282760 primes) Sun Jun 11 18:36:00 2006 using large prime bound of 1263511050 (30 bits) Sun Jun 11 18:36:00 2006 using double large prime bound of 24145837678737600 (47-55 bits) Sun Jun 11 18:36:00 2006 using trial factoring cutoff of 65 bits Sun Jun 11 18:36:00 2006 polynomial 'A' values have 15 factors Mon Jun 12 08:41:31 2006 1024 relations (1015 full + 9 combined from 63554 partial), need 282856 Mon Jun 12 08:41:31 2006 elapsed time 14:05:32 Mon Jun 12 08:42:14 2006 Mon Jun 12 08:42:14 2006 Mon Jun 12 08:42:14 2006 Msieve v. 1.06 Mon Jun 12 08:42:14 2006 random seeds: 79f08e3c 332b9a51 Mon Jun 12 08:42:14 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Mon Jun 12 08:42:16 2006 using multiplier of 1 Mon Jun 12 08:42:16 2006 sieve interval: 17 blocks of size 65536 Mon Jun 12 08:42:16 2006 processing polynomials in batches of 3 Mon Jun 12 08:42:16 2006 using a sieve bound of 8423407 (282760 primes) Mon Jun 12 08:42:16 2006 using large prime bound of 1263511050 (30 bits) Mon Jun 12 08:42:16 2006 using double large prime bound of 24145837678737600 (47-55 bits) Mon Jun 12 08:42:16 2006 using trial factoring cutoff of 65 bits Mon Jun 12 08:42:16 2006 polynomial 'A' values have 15 factors Mon Jun 12 17:08:38 2006 647 relations (645 full + 2 combined from 38538 partial), need 282856 Mon Jun 12 17:08:38 2006 elapsed time 08:26:24 Mon Jun 12 17:09:29 2006 Mon Jun 12 17:09:29 2006 Mon Jun 12 17:09:29 2006 Msieve v. 1.06 Mon Jun 12 17:09:29 2006 random seeds: f3d65b18 0b843bac Mon Jun 12 17:09:29 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Mon Jun 12 17:09:31 2006 using multiplier of 1 Mon Jun 12 17:09:31 2006 sieve interval: 17 blocks of size 65536 Mon Jun 12 17:09:31 2006 processing polynomials in batches of 3 Mon Jun 12 17:09:31 2006 using a sieve bound of 8423407 (282760 primes) Mon Jun 12 17:09:31 2006 using large prime bound of 1263511050 (30 bits) Mon Jun 12 17:09:31 2006 using double large prime bound of 24145837678737600 (47-55 bits) Mon Jun 12 17:09:31 2006 using trial factoring cutoff of 65 bits Mon Jun 12 17:09:31 2006 polynomial 'A' values have 15 factors Mon Jun 12 19:20:38 2006 3 relations (3 full + 0 combined from 307 partial), need 282856 Mon Jun 12 19:20:38 2006 elapsed time 02:11:09 Tue Jun 13 20:38:45 2006 Tue Jun 13 20:38:45 2006 Tue Jun 13 20:38:45 2006 Msieve v. 1.06 Tue Jun 13 20:38:45 2006 random seeds: a273f300 21eb8982 Tue Jun 13 20:38:45 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Tue Jun 13 20:38:46 2006 using multiplier of 1 Tue Jun 13 20:38:46 2006 sieve interval: 17 blocks of size 65536 Tue Jun 13 20:38:46 2006 processing polynomials in batches of 3 Tue Jun 13 20:38:46 2006 using a sieve bound of 8423407 (282760 primes) Tue Jun 13 20:38:46 2006 using large prime bound of 1263511050 (30 bits) Tue Jun 13 20:38:46 2006 using double large prime bound of 24145837678737600 (47-55 bits) Tue Jun 13 20:38:46 2006 using trial factoring cutoff of 65 bits Tue Jun 13 20:38:46 2006 polynomial 'A' values have 15 factors Tue Jun 13 20:39:13 2006 restarting with 65188 full and 4084882 partial relations Tue Jun 13 20:39:13 2006 283482 relations (65188 full + 218294 combined from 4084882 partial), need 282856 Tue Jun 13 20:39:35 2006 begin with 4084882 relations Tue Jun 13 20:41:14 2006 reduce to 682551 relations in 11 passes Tue Jun 13 20:41:14 2006 attempting to read 65188 full and 682551 partial relations Tue Jun 13 20:42:40 2006 Tue Jun 13 20:42:40 2006 Tue Jun 13 20:42:40 2006 Msieve v. 1.06 Tue Jun 13 20:42:40 2006 random seeds: d70a9350 476c372a Tue Jun 13 20:42:40 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Tue Jun 13 20:42:42 2006 using multiplier of 1 Tue Jun 13 20:42:42 2006 sieve interval: 17 blocks of size 65536 Tue Jun 13 20:42:42 2006 processing polynomials in batches of 3 Tue Jun 13 20:42:42 2006 using a sieve bound of 8423407 (282760 primes) Tue Jun 13 20:42:42 2006 using large prime bound of 1263511050 (30 bits) Tue Jun 13 20:42:42 2006 using double large prime bound of 24145837678737600 (47-55 bits) Tue Jun 13 20:42:42 2006 using trial factoring cutoff of 65 bits Tue Jun 13 20:42:42 2006 polynomial 'A' values have 15 factors Tue Jun 13 20:42:42 2006 restarting with 40 full and 2846 partial relations Wed Jun 14 08:18:35 2006 869 relations (861 full + 8 combined from 55706 partial), need 282856 Wed Jun 14 08:18:36 2006 elapsed time 11:35:56 Wed Jun 14 08:35:10 2006 Wed Jun 14 08:35:10 2006 Wed Jun 14 08:35:10 2006 Msieve v. 1.06 Wed Jun 14 08:35:10 2006 random seeds: e8029fd8 a91fd695 Wed Jun 14 08:35:10 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Wed Jun 14 08:35:12 2006 using multiplier of 1 Wed Jun 14 08:35:12 2006 sieve interval: 17 blocks of size 65536 Wed Jun 14 08:35:12 2006 processing polynomials in batches of 3 Wed Jun 14 08:35:12 2006 using a sieve bound of 8423407 (282760 primes) Wed Jun 14 08:35:12 2006 using large prime bound of 1263511050 (30 bits) Wed Jun 14 08:35:12 2006 using double large prime bound of 24145837678737600 (47-55 bits) Wed Jun 14 08:35:12 2006 using trial factoring cutoff of 65 bits Wed Jun 14 08:35:12 2006 polynomial 'A' values have 15 factors Wed Jun 14 08:35:12 2006 restarting with 861 full and 55706 partial relations Wed Jun 14 10:07:52 2006 982 relations (969 full + 13 combined from 62762 partial), need 282856 Wed Jun 14 10:07:52 2006 elapsed time 01:32:42 Wed Jun 14 10:20:08 2006 Wed Jun 14 10:20:08 2006 Wed Jun 14 10:20:08 2006 Msieve v. 1.06 Wed Jun 14 10:20:08 2006 random seeds: 5238bafc 871b85b0 Wed Jun 14 10:20:08 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Wed Jun 14 10:20:09 2006 using multiplier of 1 Wed Jun 14 10:20:10 2006 sieve interval: 17 blocks of size 65536 Wed Jun 14 10:20:10 2006 processing polynomials in batches of 3 Wed Jun 14 10:20:10 2006 using a sieve bound of 8423407 (282760 primes) Wed Jun 14 10:20:10 2006 using large prime bound of 1263511050 (30 bits) Wed Jun 14 10:20:10 2006 using double large prime bound of 24145837678737600 (47-55 bits) Wed Jun 14 10:20:10 2006 using trial factoring cutoff of 65 bits Wed Jun 14 10:20:10 2006 polynomial 'A' values have 15 factors Wed Jun 14 10:20:10 2006 restarting with 969 full and 62762 partial relations Wed Jun 14 13:12:30 2006 1209 relations (1193 full + 16 combined from 75765 partial), need 282856 Wed Jun 14 13:12:30 2006 elapsed time 02:52:22 Wed Jun 14 18:50:58 2006 Wed Jun 14 18:50:58 2006 Wed Jun 14 18:50:58 2006 Msieve v. 1.06 Wed Jun 14 18:50:58 2006 random seeds: 8c3ee704 426cdfd2 Wed Jun 14 18:50:58 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Wed Jun 14 18:50:59 2006 using multiplier of 1 Wed Jun 14 18:50:59 2006 sieve interval: 17 blocks of size 65536 Wed Jun 14 18:50:59 2006 processing polynomials in batches of 3 Wed Jun 14 18:50:59 2006 using a sieve bound of 8423407 (282760 primes) Wed Jun 14 18:50:59 2006 using large prime bound of 1263511050 (30 bits) Wed Jun 14 18:50:59 2006 using double large prime bound of 24145837678737600 (47-55 bits) Wed Jun 14 18:50:59 2006 using trial factoring cutoff of 65 bits Wed Jun 14 18:50:59 2006 polynomial 'A' values have 15 factors Wed Jun 14 18:51:00 2006 restarting with 1193 full and 75765 partial relations Wed Jun 14 19:51:59 2006 1271 relations (1255 full + 16 combined from 80189 partial), need 282856 Wed Jun 14 19:52:00 2006 elapsed time 01:01:02 Wed Jun 14 22:17:46 2006 Wed Jun 14 22:17:46 2006 Wed Jun 14 22:17:46 2006 Msieve v. 1.06 Wed Jun 14 22:17:46 2006 random seeds: 2dad8c00 a44d233d Wed Jun 14 22:17:46 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Wed Jun 14 22:17:48 2006 using multiplier of 1 Wed Jun 14 22:17:48 2006 sieve interval: 17 blocks of size 65536 Wed Jun 14 22:17:48 2006 processing polynomials in batches of 3 Wed Jun 14 22:17:48 2006 using a sieve bound of 8423407 (282760 primes) Wed Jun 14 22:17:48 2006 using large prime bound of 1263511050 (30 bits) Wed Jun 14 22:17:48 2006 using double large prime bound of 24145837678737600 (47-55 bits) Wed Jun 14 22:17:48 2006 using trial factoring cutoff of 65 bits Wed Jun 14 22:17:48 2006 polynomial 'A' values have 15 factors Wed Jun 14 22:17:51 2006 restarting with 1255 full and 80189 partial relations Thu Jun 15 00:50:04 2006 1436 relations (1415 full + 21 combined from 90611 partial), need 282856 Thu Jun 15 00:50:05 2006 elapsed time 02:32:19 Thu Jun 15 11:31:23 2006 Thu Jun 15 11:31:23 2006 Thu Jun 15 11:31:23 2006 Msieve v. 1.06 Thu Jun 15 11:31:23 2006 random seeds: 8e6443e4 c4db7961 Thu Jun 15 11:31:23 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Thu Jun 15 11:31:25 2006 using multiplier of 1 Thu Jun 15 11:31:25 2006 sieve interval: 17 blocks of size 65536 Thu Jun 15 11:31:25 2006 processing polynomials in batches of 3 Thu Jun 15 11:31:25 2006 using a sieve bound of 8423407 (282760 primes) Thu Jun 15 11:31:25 2006 using large prime bound of 1263511050 (30 bits) Thu Jun 15 11:31:25 2006 using double large prime bound of 24145837678737600 (47-55 bits) Thu Jun 15 11:31:25 2006 using trial factoring cutoff of 65 bits Thu Jun 15 11:31:25 2006 polynomial 'A' values have 15 factors Thu Jun 15 11:31:57 2006 restarting with 1684 full and 106708 partial relations Thu Jun 15 11:56:42 2006 1745 relations (1712 full + 33 combined from 108446 partial), need 282856 Thu Jun 15 11:56:42 2006 elapsed time 00:25:19 Thu Jun 15 11:57:29 2006 Thu Jun 15 11:57:29 2006 Thu Jun 15 11:57:29 2006 Msieve v. 1.06 Thu Jun 15 11:57:29 2006 random seeds: 2b5719bc ac70f93d Thu Jun 15 11:57:29 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Thu Jun 15 11:57:30 2006 using multiplier of 1 Thu Jun 15 11:57:30 2006 sieve interval: 17 blocks of size 65536 Thu Jun 15 11:57:30 2006 processing polynomials in batches of 3 Thu Jun 15 11:57:30 2006 using a sieve bound of 8423407 (282760 primes) Thu Jun 15 11:57:30 2006 using large prime bound of 1263511050 (30 bits) Thu Jun 15 11:57:30 2006 using double large prime bound of 24145837678737600 (47-55 bits) Thu Jun 15 11:57:30 2006 using trial factoring cutoff of 65 bits Thu Jun 15 11:57:30 2006 polynomial 'A' values have 15 factors Thu Jun 15 11:57:31 2006 restarting with 1415 full and 90611 partial relations Thu Jun 15 13:24:02 2006 1536 relations (1511 full + 25 combined from 96442 partial), need 282856 Thu Jun 15 13:24:03 2006 elapsed time 01:26:34 Thu Jun 15 14:41:32 2006 Thu Jun 15 14:41:32 2006 Thu Jun 15 14:41:32 2006 Msieve v. 1.06 Thu Jun 15 14:41:32 2006 random seeds: 2bf13d00 55c23d38 Thu Jun 15 14:41:32 2006 factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits) Thu Jun 15 14:41:34 2006 using multiplier of 1 Thu Jun 15 14:41:34 2006 sieve interval: 17 blocks of size 65536 Thu Jun 15 14:41:34 2006 processing polynomials in batches of 3 Thu Jun 15 14:41:34 2006 using a sieve bound of 8423407 (282760 primes) Thu Jun 15 14:41:34 2006 using large prime bound of 1263511050 (30 bits) Thu Jun 15 14:41:34 2006 using double large prime bound of 24145837678737600 (47-55 bits) Thu Jun 15 14:41:34 2006 using trial factoring cutoff of 65 bits Thu Jun 15 14:41:34 2006 polynomial 'A' values have 15 factors Thu Jun 15 14:42:02 2006 restarting with 66448 full and 4166452 partial relations Thu Jun 15 14:42:02 2006 288182 relations (66448 full + 221734 combined from 4166452 partial), need 282856 Thu Jun 15 14:42:24 2006 begin with 4166452 relations Thu Jun 15 14:43:44 2006 reduce to 700937 relations in 11 passes Thu Jun 15 14:43:44 2006 attempting to read 66448 full and 700937 partial relations Thu Jun 15 14:44:56 2006 recovered 66448 full and 700937 partial relations Thu Jun 15 14:44:56 2006 recovered 756557 polynomials Thu Jun 15 14:45:51 2006 attempting to build 221734 cycles Thu Jun 15 14:45:54 2006 found 221734 cycles in 6 passes Thu Jun 15 14:52:54 2006 distribution of cycle lengths: Thu Jun 15 14:52:54 2006 length 2 : 47366 Thu Jun 15 14:52:54 2006 length 3 : 47173 Thu Jun 15 14:52:54 2006 length 4 : 39485 Thu Jun 15 14:52:54 2006 length 5 : 31205 Thu Jun 15 14:52:54 2006 length 6 : 21691 Thu Jun 15 14:52:54 2006 length 7 : 14202 Thu Jun 15 14:52:54 2006 length 8 : 8893 Thu Jun 15 14:52:54 2006 length 9+: 11719 Thu Jun 15 14:52:54 2006 largest cycle: 23 relations Thu Jun 15 14:53:30 2006 282760 x 282824 system, weight 19624908 (avg 69.39/col) Thu Jun 15 14:53:49 2006 reduce to 278846 x 278910 in 3 passes Thu Jun 15 19:56:16 2006 lanczos halted after 4412 iterations Thu Jun 15 19:56:26 2006 recovered 60 nontrivial dependencies Thu Jun 15 20:07:51 2006 prp47 factor: 37811313891994346064305264570354822948081755411 Thu Jun 15 20:07:51 2006 prp67 factor: 2240332608851730481538608681856319442213805555106852747449191086419 Thu Jun 15 20:08:04 2006 elapsed time 05:26:32
By Wojciech Florek / GMP-ECM 6.0.1 B1=50000
10200+9 = 1(0)1999<201> = 27793 · 1619861 · C190
C190 = P26 · C164
P26 = 67747437129266000269703021<26>
C164 = [32786416573339916713456581271610480336366936402832697536081978826368233931128306550623785015488259274779087861845908056248255213200999357697362157495980354472120073<164>]
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
3·10151-1 = 2(9)151<152> = 103 · 15607 · 35159 · 14094323 · C134
C134 = P48 · P86
P48 = 803919452098002873794823857201688324440053056001<48>
P86 = 46845872075351073831628759072931045137614880228706167557837224075618406020863534117667<86>
Number: 29999_151 N=37660307811869368071143626717392891077148245893848443905585408084269631973112722238396669205370621661836143893933492373568490474469667 ( 134 digits) SNFS difficulty: 151 digits. Divisors found: r1=803919452098002873794823857201688324440053056001 (pp48) r2=46845872075351073831628759072931045137614880228706167557837224075618406020863534117667 (pp86) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 32.36 hours. Scaled time: 19.77 units (timescale=0.611). Factorization parameters were as follows: name: 29999_151 n: 37660307811869368071143626717392891077148245893848443905585408084269631973112722238396669205370621661836143893933492373568490474469667 m: 1000000000000000000000000000000 c5: 30 c0: -1 skew: 2 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:175423, largePrimes:5562413 encountered Relations: rels:5551679, finalFF:551257 Max relations in full relation-set: 28 Initial matrix: 351792 x 551257 with sparse part having weight 48702916. Pruned matrix : 264444 x 266266 with weight 23590245. Total sieving time: 28.86 hours. Total relation processing time: 0.28 hours. Matrix solve time: 3.04 hours. Time per square root: 0.17 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: 32.36 hours. --------- CPU info (if available) ----------
By Wojciech Florek / GMP-ECM 6.0.1 B1=50000
10155+9 = 1(0)1549<156> = 7 · 13 · 36819899903<11> · C143
C143 = P26 · P117
P26 = 79017600284684020776597601<26>
P117 = 377704507649203485094138150729343418582135548032657891156331722185962796664870047824029441603130922378771354117137333<117>
10185+9 = 1(0)1849<186> = 7 · 13 · 229846571 · 1275374768743384691<19> · C157
C157 = P31 · C127
P31 = 2601396325020582930122538337721<31>
C127 = [1441040661382525705417821587285663316407691187456963366088056617767879156058816313976715675551433626176389802439909676048900179<127>]
By suberi / GGNFS-0.77.1-20060513-pentium4
(4·10152-13)/9 = (4)1513<152> = 17 · 157 · 6476783 · C142
C142 = P68 · P74
P68 = 70051112394180511931099325798622432992902701888617624858258185590861<68>
P74 = 36702405181637427368617502969073420790220101845842707621638501963536194669<74>
Number: 44443_152 N=2571044310515636631591363642344402560399099518358547822280233718276022116764197533447168630264726143496554443438364403140703983099575283320009 ( 142 digits) SNFS difficulty: 152 digits. Divisors found: r1=70051112394180511931099325798622432992902701888617624858258185590861 (pp68) r2=36702405181637427368617502969073420790220101845842707621638501963536194669 (pp74) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 37.42 hours. Scaled time: 23.50 units (timescale=0.628). Factorization parameters were as follows: n: 2571044310515636631591363642344402560399099518358547822280233718276022116764197533447168630264726143496554443438364403140703983099575283320009 m: 2000000000000000000000000000000 c5: 25 c0: -26 skew: 1.01 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:176748, largePrimes:5547592 encountered Relations: rels:5457284, finalFF:473655 Max relations in full relation-set: 28 Initial matrix: 353114 x 473655 with sparse part having weight 41920058. Pruned matrix : 304103 x 305932 with weight 24002656. Total sieving time: 32.17 hours. Total relation processing time: 0.29 hours. Matrix solve time: 4.80 hours. Time per square root: 0.16 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: 37.42 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(25·10151-1)/3 = 8(3)151<152> = 40213 · 31173893 · 13946968278689<14> · C127
C127 = P46 · P81
P46 = 8173120943122339742908571543763108966367651147<46>
P81 = 583167752877706836532991362620680694133049760946451667127882465043575940344860839<81>
Number: 83333_151 N=4766300574398378856441697253711236415813730164095873758343781948185529731621724242828907536094532267344007114712574137013732333 ( 127 digits) SNFS difficulty: 152 digits. Divisors found: r1=8173120943122339742908571543763108966367651147 (pp46) r2=583167752877706836532991362620680694133049760946451667127882465043575940344860839 (pp81) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 39.49 hours. Scaled time: 26.61 units (timescale=0.674). Factorization parameters were as follows: name: 83333_151 n: 4766300574398378856441697253711236415813730164095873758343781948185529731621724242828907536094532267344007114712574137013732333 m: 1000000000000000000000000000000 c5: 250 c0: -1 skew: 2 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:175838, largePrimes:5676207 encountered Relations: rels:5686431, finalFF:561341 Max relations in full relation-set: 28 Initial matrix: 352206 x 561341 with sparse part having weight 51177717. Pruned matrix : 270625 x 272450 with weight 25638975. Total sieving time: 35.78 hours. Total relation processing time: 0.33 hours. Matrix solve time: 3.24 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 39.49 hours. --------- CPU info (if available) ----------
By Wojciech Florek / GMP-ECM 6.0.1 B1=250000
10171+3 = 1(0)1703<172> = C172
C172 = P26 · C146
P26 = 11766503516695099357653883<26>
C146 = [84987014076113040368276240003085477274619465136310452297603910182168194570059311533447910927491502082842012464686661684313334515329656218133967641<146>]
By Wojciech Florek / GGNFS-0.77.1
10155+3 = 1(0)1543<156> = C156
C156 = P77 · P79
P77 = 82104127886814499369024993996312311665706556142420410416782489897012262753547<77>
P79 = 1217965558782331157844625900310263781587935921261132202891162537797114525084649<79>
Number: 10,310-M N=100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 ( 156 digits) SNFS difficulty: 155 digits. Divisors found: r1=82104127886814499369024993996312311665706556142420410416782489897012262753547 (pp77) r2=1217965558782331157844625900310263781587935921261132202891162537797114525084649 (pp79) Version: GGNFS-0.77.1 Total time: 88.84 hours. Scaled time: 48.68 units (timescale=0.548). Factorization parameters were as follows: name: 10^155+3 10,310-M n: 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 type: snfs m: 10000000000000000000000000000000 skew: 1.2 c5: 1 c4: 0 c3: 0 c2: 0 c1: 0 c0: 3 rlim: 4000000 alim: 3700000 lpbr: 27 lpba: 27 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 qintsize: 50000 Factor base limits: 4000000/3700000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1850000, 2300001) Relations: rels:5171311, finalFF:626344 Initial matrix: 546367 x 626344 with sparse part having weight 32686910. Pruned matrix : 502764 x 505559 with weight 19259495. Total sieving time: 77.41 hours. Total relation processing time: 0.59 hours. Matrix solve time: 10.59 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,4000000,3700000,27,27,48,48,2.3,2.3,100000 total time: 88.84 hours. --------- CPU info (if available) ---------- CPU0: Intel Pentium III (Coppermine) stepping 06 CPU1: Intel Pentium III (Coppermine) stepping 06 Memory: 514812k/524224k available (1676k kernel code, 8652k reserved, 708k data, 180k init, 0k highmem) Calibrating delay loop... 1851.39 BogoMIPS Calibrating delay loop... 1867.77 BogoMIPS Total of 2 processors activated (3719.16 BogoMIPS). x86info v1.12b. Dave Jones 2001-2003 Feedback to <davej@redhat.com>. Found 2 CPUs -------------------------------------------------------------------------- CPU #1 Family: 6 Model: 8 Stepping: 6 Type: 0 Brand: 2 CPU Model: Pentium III-M (Coppermine) [cC0] Original OEM Instruction TLB: 4KB pages, 4-way associative, 32 entries Instruction TLB: 4MB pages, fully associative, 2 entries Data TLB: 4KB pages, 4-way associative, 64 entries L2 unified cache: Size: 256KB 8-way associative. line size=32 bytes. L1 Instruction cache: Size: 16KB 4-way associative. line size=32 bytes. Data TLB: 4MB pages, 4-way associative, 8 entries L1 Data cache: Size: 16KB 4-way associative. line size=32 bytes. 950MHz processor (estimate). -------------------------------------------------------------------------- CPU #2 Family: 6 Model: 8 Stepping: 6 Type: 0 Brand: 2 CPU Model: Pentium III-M (Coppermine) [cC0] Original OEM Instruction TLB: 4KB pages, 4-way associative, 32 entries Instruction TLB: 4MB pages, fully associative, 2 entries Data TLB: 4KB pages, 4-way associative, 64 entries L2 unified cache: Size: 256KB 8-way associative. line size=32 bytes. L1 Instruction cache: Size: 16KB 4-way associative. line size=32 bytes. Data TLB: 4MB pages, 4-way associative, 8 entries L1 Data cache: Size: 16KB 4-way associative. line size=32 bytes. 950MHz processor (estimate). -------------------------------------------------------------------------- WARNING: Detected SMP, but unable to access cpuid driver. Used Uniprocessor CPU routines. Results inaccurate.
P77 is the largest factor found by GGNFS in our tables so far. Congratulations!
By suberi / GGNFS-0.77.1-20060513-pentium4 gnfs
(2·10177+61)/9 = (2)1769<177> = 373 · 52452310739<11> · 122313301254781630237<21> · 698935614467460981599711<24> · C120
C120 = P39 · P82
P39 = 102274804112509011932166621876688728607<39>
P82 = 1299075864221558361306831248327523719975317527188803043876725435794660391001753143<82>
Number: 22229_177 N=132862729540548235885710325806135088341175371249479339168970742759531835213425691441068602652953432293108269044736261801 ( 120 digits) Divisors found: r1=102274804112509011932166621876688728607 (pp39) r2=1299075864221558361306831248327523719975317527188803043876725435794660391001753143 (pp82) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 94.67 hours. Scaled time: 60.78 units (timescale=0.642). Factorization parameters were as follows: name: 22229_177 n: 132862729540548235885710325806135088341175371249479339168970742759531835213425691441068602652953432293108269044736261801 skew: 118264.19 # norm 2.48e+016 c5: 16380 c4: 2906053828 c3: -842318987455755 c2: -31805894219144108025 c1: 3829700256869416762366795 c0: 61382773760292758874608119257 # alpha -6.53 Y1: 11968793848913 Y0: -95899409147692607700800 # Murphy_E 3.46e-010 # M 97739709333115584892434197029876455362571111405703888251707455578910987395730840374213972981668836923260695644624972375 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 4110001) Primes: RFBsize:315948, AFBsize:315964, largePrimes:7684067 encountered Relations: rels:7782590, finalFF:772270 Max relations in full relation-set: 28 Initial matrix: 631997 x 772270 with sparse part having weight 65670693. Pruned matrix : 514290 x 517513 with weight 40913071. Total sieving time: 76.06 hours. Total relation processing time: 1.04 hours. Matrix solve time: 17.06 hours. Time per square root: 0.52 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: 94.67 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4
(16·10151-1)/3 = 5(3)151<152> = 152311 · 715209641 · 313198861778351<15> · C124
C124 = P55 · P69
P55 = 4492114583152676075568292046791383513694243521858826159<55>
P69 = 347987062260942870395968830956400479517277155958985376021550782808187<69>
Number: 53333_151 N=1563197757130839718450150233073190481919155646304989399336964917055382221284358227647965491014654792583752170529025474963733 ( 124 digits) SNFS difficulty: 152 digits. Divisors found: r1=4492114583152676075568292046791383513694243521858826159 (pp55) r2=347987062260942870395968830956400479517277155958985376021550782808187 (pp69) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 33.13 hours. Scaled time: 22.33 units (timescale=0.674). Factorization parameters were as follows: name: 53333_151 n: 1563197757130839718450150233073190481919155646304989399336964917055382221284358227647965491014654792583752170529025474963733 m: 1000000000000000000000000000000 c5: 160 c0: -1 skew: 2 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:176093, largePrimes:5402411 encountered Relations: rels:5275796, finalFF:456173 Max relations in full relation-set: 28 Initial matrix: 352462 x 456173 with sparse part having weight 38619267. Pruned matrix : 299185 x 301011 with weight 22581981. Total sieving time: 29.04 hours. Total relation processing time: 0.34 hours. Matrix solve time: 3.59 hours. Time per square root: 0.16 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: 33.13 hours. --------- CPU info (if available) ----------
By suberi / GGNFS-0.77.1-20060513-pentium4
(2·10158-11)/9 = (2)1571<158> = 32 · 7 · 3373 · 244846033 · C144
C144 = P48 · P97
P48 = 136373220163038473408001030523801101796795796597<48>
P97 = 3131903903250503659877494912285800041740438149611919544242941413416214051230896603159433989608979<97>
Number: 22221_158 N=427107820527460481965800659937090806025710492398582629787910040201168839154848698242923514230339462348863549244998158835338352432003242848844463 ( 144 digits) SNFS difficulty: 158 digits. Divisors found: r1=136373220163038473408001030523801101796795796597 (pp48) r2=3131903903250503659877494912285800041740438149611919544242941413416214051230896603159433989608979 (pp97) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 61.35 hours. Scaled time: 42.08 units (timescale=0.686). Factorization parameters were as follows: n: 427107820527460481965800659937090806025710492398582629787910040201168839154848698242923514230339462348863549244998158835338352432003242848844463 m: 20000000000000000000000000000000 c5: 125 c0: -22 skew: 1 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3600001) Primes: RFBsize:283146, AFBsize:282598, largePrimes:5660000 encountered Relations: rels:5693705, finalFF:658134 Max relations in full relation-set: 28 Initial matrix: 565809 x 658134 with sparse part having weight 41765004. Pruned matrix : 492727 x 495620 with weight 28196709. Total sieving time: 50.11 hours. Total relation processing time: 0.26 hours. Matrix solve time: 10.76 hours. Time per square root: 0.21 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: 61.35 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1
(28·10154-1)/9 = 3(1)154<155> = 29 · 523 · 356947 · 1279301069<10> · 329796478307462684783<21> · C116
C116 = P51 · P65
P51 = 300621016513776590359526923103344706640342409501697<51>
P65 = 45307905222633353862121896072140996414543098670746516403110579681<65>
Number: 31111_154 N=13620508524137886095135775437549085410611631881407400493766199272054663054717943584997443021365877512209360023218657 ( 116 digits) SNFS difficulty: 156 digits. Divisors found: r1=300621016513776590359526923103344706640342409501697 (pp51) r2=45307905222633353862121896072140996414543098670746516403110579681 (pp65) Version: GGNFS-0.77.1 Total time: 48.44 hours. Scaled time: 32.22 units (timescale=0.665). Factorization parameters were as follows: name: 31111_154 n: 13620508524137886095135775437549085410611631881407400493766199272054663054717943584997443021365877512209360023218657 m: 10000000000000000000000000000000 c5: 14 c0: -5 skew: 2 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 2700001) Relations: rels:5727743, finalFF:603263 Initial matrix: 434263 x 603263 with sparse part having weight 48582766. Pruned matrix : 391440 x 393675 with weight 21231753. Total sieving time: 43.42 hours. Total relation processing time: 0.32 hours. Matrix solve time: 4.55 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 48.44 hours. --------- CPU info (if available) ----------
By Bryan Koen / GGNFS-0.77.1-20060513-pentium3 gnfs
10151+9 = 1(0)1509<152> = 47 · 59 · 1259 · 7127 · 2966921 · 11067807493<11> · 72688089600520497603686170777972481<35> · C90
C90 = P42 · P48
P42 = 304041896967341114744845407635505771861889<42>
P48 = 553800538862497459614953502422358377149435369453<48>
Number: 10009_151 N=168378566377289441526058266352233242122150864612576030629541165580379898372848314405476717 ( 90 digits) Divisors found: r1=304041896967341114744845407635505771861889 (pp42) r2=553800538862497459614953502422358377149435369453 (pp48) Version: GGNFS-0.77.1-20060513-pentium3 Total time: 7.78 hours. Scaled time: 4.87 units (timescale=0.626). Factorization parameters were as follows: name: 10009_151 n: 168378566377289441526058266352233242122150864612576030629541165580379898372848314405476717 m: 397102947624127176218 deg: 4 c4: 6771336 c3: -9421734641 c2: -17097857456607989 c1: 52700057966859489 c0: 20139528042945550388527 skew: 1635.250 type: gnfs # adj. I(F,S) = 50.521 # E(F1,F2) = 2.015879e-04 # GGNFS version 0.77.1-20060513-pentium3 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=58.00000000, seed=1149781811. # maxskew=2000.0 # These parameters should be manually set: rlim: 700000 alim: 700000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.4 alambda: 2.4 qintsize: 40000 type: gnfs Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [350000, 750001) Primes: RFBsize:56543, AFBsize:56325, largePrimes:1619047 encountered Relations: rels:1627644, finalFF:155272 Max relations in full relation-set: 28 Initial matrix: 112945 x 155272 with sparse part having weight 13574909. Pruned matrix : 100318 x 100946 with weight 6869840. Polynomial selection time: 0.17 hours. Total sieving time: 6.85 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.47 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: gnfs,89,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,25,25,44,44,2.4,2.4,40000 total time: 7.78 hours. --------- CPU info (if available) ---------- x86info v1.12b. Dave Jones 2001-2003 Feedback to <davej@redhat.com>. Found 1 CPU -------------------------------------------------------------------------- Family: 6 Model: 8 Stepping: 10 Type: 0 Brand: 2 CPU Model: Pentium III-M (Coppermine) [cD0] Original OEM Instruction TLB: 4KB pages, 4-way associative, 32 entries Instruction TLB: 4MB pages, fully associative, 2 entries Data TLB: 4KB pages, 4-way associative, 64 entries L2 unified cache: Size: 256KB 8-way associative. line size=32 bytes. L1 Instruction cache: Size: 16KB 4-way associative. line size=32 bytes. Data TLB: 4MB pages, 4-way associative, 8 entries L1 Data cache: Size: 16KB 4-way associative. line size=32 bytes. 1.0Ghz processor (estimate).
By Wojciech Florek / GMP-ECM 6.0.1 B1=250000
10199+3 = 1(0)1983<200> = 13 · 4533299 · 259556761 · 111011352372742720485057131<27> · C157
C157 = P33 · C125
P33 = 505135145839533539009957298516389<33>
C125 = [11658292768317820781554389954230436794449000313821548811563233466427335134152895851328952839749423751087120161554182716468331<125>]
By Yousuke Koide / GMP-ECM
(10607-1)/9 = (1)607<607> = 10857536471<11> · C597
C597 = P34 · C563
P34 = 8030222013165659643947340265695409<34>
C563 = [12743791025705280337647107449763389196590743381995489997602359492550670282914658786866644132251081530183945513634942367344940945849768823651695138554796618106799788799265038643749276286863772813091423307583327488336703425138962767003020761379082230966326019896681052112375556339576356383468466444597317090588231683659499086434219490053020977894894071243326908124169207137882751682358057098873428276903560922268298083613125322614771267815515696194827324894983730224274660295001335913828824662433094826344709281811146432335327830920101507170509517110651808908417249<563>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Bryan Koen / GMP-ECM 6.1 B1=3000000
10151+9 = 1(0)1509<152> = 47 · 59 · 1259 · 7127 · 2966921 · 11067807493<11> · C125
C125 = P35 · C90
P35 = 72688089600520497603686170777972481<35>
C90 = [168378566377289441526058266352233242122150864612576030629541165580379898372848314405476717<90>]
By Bryan Koen / GMP-ECM 6.1 B1=3000000
10149+9 = 1(0)1489<150> = 7 · 13 · 1289 · 14111809 · 2038469620239917<16> · C122
C122 = P26 · P96
P26 = 80577406982383442189446811<26>
P96 = 367794702512173851463405661443194990091070675569301662648266498490154427340333411671971726316077<96>
By Wojciech Florek / Msieve v. 1.03
10140+9 = 1(0)1399<141> = 47017 · 74498093 · 6280399637<10> · 378185559992276358710822426933737<33> · C86
C86 = P36 · P50
P36 = 275290255655372346657479721190470389<36>
P50 = 43663331382360791758121439349427121020054742354629<50>
By Bryan Koen / GMP-ECM 6.1 B1=3000000
10140+9 = 1(0)1399<141> = 47017 · 74498093 · 6280399637<10> · C118
C118 = P33 · C86
P33 = 378185559992276358710822426933737<33>
C86 = [12020089659015344816036119415930027908760447367801456885997889765522261556089961580681<86>]
By Bryan Koen / GGNFS-0.77.1-20060513-pentium3
10138+9 = 1(0)1379<139> = 876233 · 3884165579644422661<19> · C114
C114 = P44 · P70
P44 = 78273652233899717283899884219650481533344701<44>
P70 = 3753764830682790162556690001403905303929149813189408310793058874824593<70>
Number: 10009_138 N=293820882924708172219936720052802603554401992112281932163797281493515360316752301778857178250591701547951981031693 ( 114 digits) SNFS difficulty: 138 digits. Divisors found: r1=78273652233899717283899884219650481533344701 (pp44) r2=3753764830682790162556690001403905303929149813189408310793058874824593 (pp70) Version: GGNFS-0.77.1-20060513-pentium3 Total time: 17.78 hours. Scaled time: 11.13 units (timescale=0.626). Factorization parameters were as follows: n: 293820882924708172219936720052802603554401992112281932163797281493515360316752301778857178250591701547951981031693 m: 1000000000000000000000000000 c5: 1000 c0: 9 skew: 1 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1525001) Primes: RFBsize:78498, AFBsize:63873, largePrimes:1570583 encountered Relations: rels:1573135, finalFF:171984 Max relations in full relation-set: 28 Initial matrix: 142438 x 171984 with sparse part having weight 15803147. Pruned matrix : 133995 x 134771 with weight 10765947. Total sieving time: 16.39 hours. Total relation processing time: 0.22 hours. Matrix solve time: 1.04 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 17.78 hours. --------- CPU info (if available) ---------- x86info v1.12b. Dave Jones 2001-2003 Feedback to <davej@redhat.com>. Found 1 CPU -------------------------------------------------------------------------- Family: 6 Model: 8 Stepping: 10 Type: 0 Brand: 2 CPU Model: Pentium III-M (Coppermine) [cD0] Original OEM Instruction TLB: 4KB pages, 4-way associative, 32 entries Instruction TLB: 4MB pages, fully associative, 2 entries Data TLB: 4KB pages, 4-way associative, 64 entries L2 unified cache: Size: 256KB 8-way associative. line size=32 bytes. L1 Instruction cache: Size: 16KB 4-way associative. line size=32 bytes. Data TLB: 4MB pages, 4-way associative, 8 entries L1 Data cache: Size: 16KB 4-way associative. line size=32 bytes. 1.0Ghz processor (estimate).
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(5·10163+13)/9 = (5)1627<163> = 7 · 491 · 1046680382986660661<19> · 26988494111082482595723749<26> · C116
C116 = P33 · P35 · P49
P33 = 217331380417265405385792427178641<33>
P35 = 55344255753515407497857400669052247<35>
P49 = 4757296669612601389627040223185439915807754519687<49>
Number: 55557_163 N=57220971289632372895013854360486568742682462018091052842231747397803851776811199836976065406658831179664130202209649 ( 116 digits) Divisors found: r1=217331380417265405385792427178641 (pp33) r2=55344255753515407497857400669052247 (pp35) r3=4757296669612601389627040223185439915807754519687 (pp49) Version: GGNFS-0.77.1 Total time: 72.54 hours. Scaled time: 48.24 units (timescale=0.665). Factorization parameters were as follows: name: 55557_163 n: 57220971289632372895013854360486568742682462018091052842231747397803851776811199836976065406658831179664130202209649 skew: 63091.21 # norm 1.03e+16 c5: 10980 c4: -567513282 c3: -288483363928883 c2: -42686857066294 c1: -10217904753094925098120 c0: 805345242548038392245007424 # alpha -6.11 Y1: 920218306469 Y0: -22049094785443788512841 # Murphy_E 5.16e-10 # M 21548108821676313080445840778074574074874607909847815919519715036737519808444584049118282893032989879028308785080208 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 Sieved special-q in [2250000, 3630001) Relations: rels:7694457, finalFF:806287 Initial matrix: 631773 x 806287 with sparse part having weight 63262568. Pruned matrix : 555050 x 558272 with weight 30385169. Polynomial selection time: 1.52 hours. Total sieving time: 60.64 hours. Total relation processing time: 1.09 hours. Matrix solve time: 8.75 hours. Time per square root: 0.54 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 72.54 hours. --------- CPU info (if available) ----------
By Wojciech Florek / Msieve v. 1.03
10152+3 = 1(0)1513<153> = 43613668999<11> · 12179717710063<14> · 128492693814335713<18> · 2456091372331436862367783336363<31> · C81
C81 = P38 · P44
P38 = 15820959142195526790315426273379632223<38>
P44 = 37703736485632074700837740810673485387490687<44>
By Alfred Reich / Msieve v. 1.06
10144+3 = 1(0)1433<145> = 134060221 · 895346379774329815520794224163<30> · C106
C106 = P43 · P64
P43 = 3312794646750731247992525345573307418477327<43>
P64 = 2514863810750094284798767186768560521807692068531696374269371643<64>
By Bryan Koen / GMP-ECM 6.1 B1=1000000
10152+3 = 1(0)1513<153> = 43613668999<11> · 12179717710063<14> · 128492693814335713<18> · C112
C112 = P31 · C81
P31 = 2456091372331436862367783336363<31>
C81 = [596509274447291814464580040316696780259376731908870341805954675607430656897607201<81>]
10122+9 = 1(0)1219<123> = 797 · 87324709 · C112
C112 = P32 · P80
P32 = 46442319103878729137347867918441<32>
P80 = 30937885895272059997914839937905492541094892096918455339201066688438011910438513<80>
10129+9 = 1(0)1289<130> = 383 · 470957 · 925380361 · C112
C112 = P29 · P84
P29 = 26662284559638260051010569411<29>
P84 = 224699616945787993015228728987794854226294266940075097993481422453900414417478640009<84>
By Wojciech Florek / GMP-ECM 6.0.1 B1=250000
10160+3 = 1(0)1593<161> = 72 · 823 · C156
C156 = P28 · P129
P28 = 2418343914073834818913548979<28>
P129 = 102538278668961192433911894438328850160845843852041786502290291129164567462464059585048892813551072785448461295685350000183704391<129>
By Bryan Koen / GGNFS-0.77.1-20060513-pentium3
10141+3 = 1(0)1403<142> = 23 · 179 · 644783 · 1095239290136891<16> · C117
C117 = P51 · P66
P51 = 803739638634605270206280169488592754569025676064749<51>
P66 = 427938295026116307934098302562270778494869844206815199155275017447<66>
Number: 10003_141 N=343950970602199819231512078234382265236200797813972452208461451756224073663979763523341432993779852136795871276675803 ( 117 digits) SNFS difficulty: 141 digits. Divisors found: r1=803739638634605270206280169488592754569025676064749 (pp51) r2=427938295026116307934098302562270778494869844206815199155275017447 (pp66) Version: GGNFS-0.77.1-20060513-pentium3 Total time: 21.59 hours. Scaled time: 13.51 units (timescale=0.626). Factorization parameters were as follows: n: 343950970602199819231512078234382265236200797813972452208461451756224073663979763523341432993779852136795871276675803 m: 10000000000000000000000000000 c5: 10 c0: 3 skew: 1 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:99998, largePrimes:2680955 encountered Relations: rels:2643376, finalFF:256210 Max relations in full relation-set: 28 Initial matrix: 200085 x 256210 with sparse part having weight 22916201. Pruned matrix : 182362 x 183426 with weight 14089073. Total sieving time: 19.25 hours. Total relation processing time: 0.24 hours. Matrix solve time: 1.90 hours. Time per square root: 0.19 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: 21.59 hours. --------- CPU info (if available) ---------- x86info v1.12b. Dave Jones 2001-2003 Feedback to <davej@redhat.com>. Found 1 CPU -------------------------------------------------------------------------- Family: 6 Model: 8 Stepping: 10 Type: 0 Brand: 2 CPU Model: Pentium III-M (Coppermine) [cD0] Original OEM Instruction TLB: 4KB pages, 4-way associative, 32 entries Instruction TLB: 4MB pages, fully associative, 2 entries Data TLB: 4KB pages, 4-way associative, 64 entries L2 unified cache: Size: 256KB 8-way associative. line size=32 bytes. L1 Instruction cache: Size: 16KB 4-way associative. line size=32 bytes. Data TLB: 4MB pages, 4-way associative, 8 entries L1 Data cache: Size: 16KB 4-way associative. line size=32 bytes. 1.0Ghz processor (estimate).
By Tyler Cadigan / PRIMO 2.2.0 beta 6
The prime number (34·10773-7)/9 was certified by PRIMO. All prime numbers under 1000 digits in our tables have been certified.
By Alexander Mkrtychyan / Msieve v. 1.06
10167+3 = 1(0)1663<168> = 613 · 3042701 · 5418606523951<13> · 210504879244969399<18> · 104420640192739457415377<24> · C105
C105 = P50 · P56
P50 = 12671007740661978399849262965676367229484426614023<50>
P56 = 35524907704428477072483751792823172988116747462504646589<56>
Thu Jun 01 07:44:48 2006 Msieve v. 1.06 Thu Jun 01 07:44:48 2006 random seeds: b14be000 1f671996 Thu Jun 01 07:44:48 2006 factoring 450136380509115586818824476925994457819859020646634121016333059079851013391762916786707134979013526517547 (105 digits) Thu Jun 01 07:44:49 2006 using multiplier of 13 Thu Jun 01 07:44:49 2006 sieve interval: 9 blocks of size 65536 Thu Jun 01 07:44:49 2006 processing polynomials in batches of 6 Thu Jun 01 07:44:49 2006 using a sieve bound of 3943937 (140000 primes) Thu Jun 01 07:44:49 2006 using large prime bound of 591590550 (29 bits) Thu Jun 01 07:44:49 2006 using double large prime bound of 6160815113841750 (44-53 bits) Thu Jun 01 07:44:49 2006 using trial factoring cutoff of 60 bits Thu Jun 01 07:44:49 2006 polynomial 'A' values have 14 factors Thu Jun 01 07:44:49 2006 restarting with 3042 full and 194490 partial relations Sat Jun 03 05:48:23 2006 140203 relations (33009 full + 107194 combined from 2073320 partial), need 140096 Sat Jun 03 05:48:47 2006 begin with 2073320 relations Sat Jun 03 05:48:50 2006 reduce to 338226 relations in 11 passes Sat Jun 03 05:48:50 2006 attempting to read 33009 full and 338226 partial relations Sat Jun 03 05:49:15 2006 recovered 33009 full and 338226 partial relations Sat Jun 03 05:49:15 2006 recovered 364498 polynomials Sat Jun 03 05:49:16 2006 attempting to build 107194 cycles Sat Jun 03 05:49:17 2006 found 107194 cycles in 6 passes Sat Jun 03 05:49:17 2006 distribution of cycle lengths: Sat Jun 03 05:49:17 2006 length 2 : 23465 Sat Jun 03 05:49:17 2006 length 3 : 23358 Sat Jun 03 05:49:17 2006 length 4 : 19359 Sat Jun 03 05:49:17 2006 length 5 : 14682 Sat Jun 03 05:49:17 2006 length 6 : 10184 Sat Jun 03 05:49:17 2006 length 7 : 6633 Sat Jun 03 05:49:17 2006 length 8 : 4199 Sat Jun 03 05:49:17 2006 length 9+: 5314 Sat Jun 03 05:49:17 2006 largest cycle: 21 relations Sat Jun 03 05:49:18 2006 140000 x 140064 system, weight 9718057 (avg 69.38/col) Sat Jun 03 05:49:19 2006 reduce to 138118 x 138182 in 3 passes Sat Jun 03 06:08:39 2006 lanczos halted after 2185 iterations Sat Jun 03 06:08:41 2006 recovered 58 nontrivial dependencies Sat Jun 03 06:10:00 2006 prp50 factor: 12671007740661978399849262965676367229484426614023 Sat Jun 03 06:10:00 2006 prp56 factor: 35524907704428477072483751792823172988116747462504646589 Sat Jun 03 06:10:01 2006 elapsed time 46:25:13
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(34·10176-7)/9 = 3(7)176<177> = 13 · 829 · 318683 · 11176757 · 3948411858562751<16> · 428211044560044339671392979782357<33> · C112
C112 = P38 · P75
P38 = 11694279611466984831142203943332807419<38>
P75 = 497748584082412889125755168559358506745646837820266378957660155569774344887<75>
Number: 37777_176 N=5820811118471521231475918967207027515179168849013239199862519224248461311165696923761581519214488363575258316653 ( 112 digits) Divisors found: r1=11694279611466984831142203943332807419 (pp38) r2=497748584082412889125755168559358506745646837820266378957660155569774344887 (pp75) Version: GGNFS-0.77.1 Total time: 53.33 hours. Scaled time: 35.47 units (timescale=0.665). Factorization parameters were as follows: name: 37777_176 n: 5820811118471521231475918967207027515179168849013239199862519224248461311165696923761581519214488363575258316653 skew: 32740.23 # norm 7.73e+14 c5: 7800 c4: 790299208 c3: -34647393104357 c2: -702585806193034208 c1: 6659086119635802079482 c0: 123094738763234464057267500 # alpha -5.03 Y1: 484020890317 Y0: -3754712135906934550109 # Murphy_E 8.03e-10 # M 4302948463608880647102223092922936267994757185578952181911465511761176268904489859460161461822645693421840905721 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2750001) Relations: rels:7677602, finalFF:705015 Initial matrix: 499803 x 705015 with sparse part having weight 61142504. Pruned matrix : 419449 x 422012 with weight 24554381. Polynomial selection time: 0.52 hours. Total sieving time: 45.83 hours. Total relation processing time: 0.77 hours. Matrix solve time: 5.74 hours. Time per square root: 0.47 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 53.33 hours. --------- CPU info (if available) ----------
By Tyler Cadigan / PRIMO 2.2.0 beta 6
The following 11 prime numbers under 1000 digits were certified by PRIMO.
10700+7, 10999+7, (5·10461+1)/3, (5·10840+1)/3, (5·10847+1)/3, (7·10522-1)/3, (7·10597-1)/3, (13·10727-1)/3, (53·10439+1)/9, (61·10785-7)/9, (61·10799-7)/9.
By Bryan Koen / GGNFS-0.77.1-20060513-pentium3
10138+3 = 1(0)1373<139> = 103 · 990513749998083607<18> · 34585142462197870945875655226509<32> · C87
C87 = P42 · P45
P42 = 515100320152004920978466573096213025512461<42>
P45 = 550200369707475541148787748643398354924032907<45>
Number: 10003_138
N=283408386584072121357621650236515295775168451662180323194828514316327126544738502554127
( 87 digits)
SNFS difficulty: 138 digits.
Divisors found:
r1=515100320152004920978466573096213025512461 (pp42)
r2=550200369707475541148787748643398354924032907 (pp45)
Version: GGNFS-0.77.1-20060513-pentium3
Total time: 21.08 hours.
Scaled time: 13.20 units (timescale=0.626).
Factorization parameters were as follows:
n: 283408386584072121357621650236515295775168451662180323194828514316327126544738502554127
m: 1000000000000000000000000000
c5: 1000
c0: 3
skew: 1
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1750001)
Primes: RFBsize:78498, AFBsize:64158, largePrimes:1602887 encountered
Relations: rels:1611027, finalFF:169149
Max relations in full relation-set: 28
Initial matrix: 142722 x 169149 with sparse part having weight 16717764.
Pruned matrix : 135569 x 136346 with weight 11997191.
Total sieving time: 19.46 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 1.25 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 21.08 hours.
--------- CPU info (if available) ----------
x86info v1.12b. Dave Jones 2001-2003
Feedback to <davej@redhat.com>.
Found 1 CPU
--------------------------------------------------------------------------
Family: 6 Model: 8 Stepping: 10 Type: 0 Brand: 2
CPU Model: Pentium III-M (Coppermine) [cD0] Original OEM
Instruction TLB: 4KB pages, 4-way associative, 32 entries
Instruction TLB: 4MB pages, fully associative, 2 entries
Data TLB: 4KB pages, 4-way associative, 64 entries
L2 unified cache:
Size: 256KB 8-way associative.
line size=32 bytes.
L1 Instruction cache:
Size: 16KB 4-way associative.
line size=32 bytes.
Data TLB: 4MB pages, 4-way associative, 8 entries
L1 Data cache:
Size: 16KB 4-way associative.
line size=32 bytes.
1.0Ghz processor (estimate).By Tyler Cadigan / PRIMO 2.2.0 beta 6
The following 227 prime numbers under 1000 digits were certified by PRIMO.
(10767+53)/9, (10684+71)/9, (10720+71)/9, (11·10876+7)/9, (11·10811+43)/9, (11·10812+43)/9, (11·10547+61)/9, (4·10887+11)/3, (13·10735+23)/9, (13·10529+41)/9, (14·10537+31)/9, (14·10831+31)/9, (5·10629+7)/3, (5·10720+7)/3, (17·10843+1)/9, 2·10761+9, (19·10543-1)/9, (19·10584-1)/9, (19·10833-1)/9, (19·10754+17)/9, (19·10951+17)/9, (7·10657+17)/3, (22·10499+41)/9, (23·10733+31)/9, (25·10936-61)/9, (25·10482-7)/9, (26·10876-71)/9, (26·10494-53)/9, (26·10598-53)/9, (26·10449-17)/9, 3·10484-7, 3·10865-7, 3·10593+7, (28·10692+53)/9, (28·10797+71)/9, (29·10649-11)/9, (29·10949-11)/9, (29·10963-11)/9, (29·10519+61)/9, (29·10603+61)/9, (10978+11)/3, (31·10758+23)/9, (31·10512+41)/9, (32·10957+31)/9, (11·10673-17)/3, (11·10780-17)/3, (11·10498+1)/3, (34·10776+11)/9, (35·10538-71)/9, (35·10509+1)/9, (35·10710+1)/9, 4·10949-9, (37·10589-1)/9, (37·10973-1)/9, (37·10513+53)/9, (38·10630+7)/9, (38·10724+7)/9, (13·10715-7)/3, (13·10804-7)/3, (13·10456+11)/3, (13·10467+11)/3, (13·10607+11)/3, (13·10828+11)/3, (13·10638+17)/3, (4·10722+23)/9, (41·10702-23)/9, (41·10621+31)/9, (14·10652+1)/3, (43·10925-61)/9, (44·10595-17)/9, (44·10637-17)/9, (44·10776-17)/9, (44·10618+1)/9, 5·10495-3, 5·10966-3, 5·10531+3, 5·10706+3, 5·10757+9, (46·10447+17)/9, (46·10487+17)/9, (46·10445+71)/9, (46·10543+71)/9, (46·10633+71)/9, (46·10757+71)/9, (47·10494-11)/9, (47·10614-11)/9, (47·10710-11)/9, (47·10475+7)/9, (47·10505+7)/9, (47·10835+7)/9, (47·10922+7)/9, (47·10638+43)/9, (16·10575+17)/3, (16·10715+17)/3, (49·10476-31)/9, (49·10834-31)/9, (49·10795-13)/9, (49·10564+23)/9, (49·10620+23)/9, (49·10619+41)/9, (49·10759+41)/9, (5·10540-23)/9, (5·10528+13)/9, (5·10960+13)/9, (17·10868-11)/3, (17·10651+7)/3, (17·10884+7)/3, (17·10938+7)/3, (52·10866-7)/9, (52·10992-7)/9, (53·10816-71)/9, (53·10858-71)/9, (53·10462-17)/9, (53·10608+1)/9, 6·10806+7, (55·10533-1)/9, (55·10616-1)/9, (55·10718-1)/9, (55·10787-1)/9, (55·10647+17)/9, (55·10973+53)/9, (55·10953+71)/9, (56·10433-11)/9, (56·10766-11)/9, (19·10755-7)/3, (19·10455+11)/3, (58·10613-31)/9, (58·10470-13)/9, (58·10887+23)/9, (58·10627+41)/9, (58·10687+41)/9, (58·10699+41)/9, (59·10597-41)/9, (59·10681-41)/9, (59·10617-23)/9, (59·10696+13)/9, (61·10713+11)/9, (62·10732-17)/9, (62·10501+1)/9, (62·10515+1)/9, (62·10627+1)/9, (62·10641+1)/9, (62·10725+1)/9, 7·10568-9, 7·10639-9, 7·10842-9, 7·10969-9, (64·10938+17)/9, (65·10837+7)/9, (22·10489-7)/3, (22·10592-7)/3, (22·10634-7)/3, (22·10908-1)/3, (67·10451+41)/9, (67·10772+41)/9, (68·10734-41)/9, (68·10931-41)/9, (68·10646-23)/9, (68·10814-23)/9, (68·10967+31)/9, (23·10434-17)/3, (23·10721-17)/3, (23·10822-17)/3, (23·10883-17)/3, (23·10498-11)/3, (23·10868-11)/3, (23·10879-11)/3, (23·10717+7)/3, (23·10968+7)/3, (7·10624+11)/9, 8·10698+9, (73·10474-1)/9, (73·10902-1)/9, (73·10745+17)/9, (73·10641+53)/9, (73·10675+53)/9, (73·10594+71)/9, (74·10436+7)/9, (74·10524+43)/9, (74·10530+43)/9, (74·10657+43)/9, (25·10848+17)/3, (76·10486-31)/9, (76·10627-31)/9, (76·10999-31)/9, (76·10442-13)/9, (76·10469+41)/9, (77·10471-41)/9, (77·10637+31)/9, (26·10481-11)/3, (26·10608-11)/3, (26·10741-11)/3, (26·10879-11)/3, (26·10453+7)/3, (26·10611+7)/3, (26·10883+7)/3, (79·10480-61)/9, 9·10549-7, 9·10765-7, 9·10973-7, 9·10588+7, 9·10776+7, 9·10906+7, (82·10473+53)/9, (82·10685+53)/9, (82·10701+53)/9, (83·10520-11)/9, (83·10456+7)/9, (83·10678+7)/9, (83·10471+43)/9, (83·10561+43)/9, (83·10664+43)/9, (28·10448+11)/3, (28·10539+11)/3, (28·10784+11)/3, (28·10814+11)/3, (85·10581-13)/9, (86·10573-41)/9, (86·10897-41)/9, (86·10981-41)/9, (29·10635-17)/3, (29·10940-17)/3, (29·10944-17)/3, (88·10784-61)/9, (88·10447-43)/9, (89·10529-17)/9, 10990-3.
By Wataru Sakai / GMP-ECM 6.0.1, GMP-ECM 6.1
(61·10163-7)/9 = 6(7)163<164> = 9266672567<10> · 5673581071735727<16> · C139
C139 = P35(1305...) · P35(2240...) · P70
P35(1305...) = 13053999710108279553984814365912541<35>
P35(2240...) = 22402313059656738339109313460161689<35>
P70 = 4408286195992575892384026018410003380146235251197963945518892063985397<70>
(61·10169-7)/9 = 6(7)169<170> = 679517 · 2099650316119<13> · C152
C152 = P33 · C120
P33 = 462133680259364512974037301324911<33>
C120 = [102795098400219410634465090516194534805474053557213593780153631997610268197607479386423556429973192979895429973931816909<120>]
(61·10170-7)/9 = 6(7)170<171> = 89 · 59149 · 73106034559740600637<20> · C145
C145 = P33 · C112
P33 = 455443373077175325700179430733987<33>
C112 = [3866894270110480495299331929349939555976910470220605286134629327779460046947883016645268141896942460825185552203<112>]
(61·10172-7)/9 = 6(7)172<173> = 1155709 · 4691776423<10> · C158
C158 = P30 · P42 · P86
P30 = 609460208105001402610217070871<30>
P42 = 463915191687646936303192442868799163452747<42>
P86 = 44209700384489934180137596183593901714505219083957722275135118923645544441308317835503<86>
(61·10193-7)/9 = 6(7)193<194> = 59 · 3853 · C189
C189 = P30 · P160
P30 = 163127799506136496038335489929<30>
P160 = 1827714372782507311292761526282412035783631956330528107609297122108841522030987601896279600559024296237981269384421792628912505034582472939235971142099110239319<160>
(61·10196-7)/9 = 6(7)196<197> = 4159 · 4464781 · 226180181 · C179
C179 = P38 · C142
P38 = 15615154400366770009282227004370183921<38>
C142 = [1033468904117966617164744053188712951295398238274545348816534213750285722018672609129914860028868584067980435445547786740892587358674249064463<142>]
(61·10199-7)/9 = 6(7)199<200> = 67 · 2686555097433200453529295711<28> · C171
C171 = P27 · P33 · P112
P27 = 605308283558156762793357649<27>
P33 = 181507461190783917343467817300507<33>
P112 = 3427249105123054795888760122109345886233343024535902715535737986060352180735446845218692299323082077938308290447<112>
(2·10159+7)/9 = (2)1583<159> = 298723 · 134414293495679<15> · C139
C139 = P35 · P105
P35 = 28564470286657715379909548819111177<35>
P105 = 193752446812631227185571963969853916284322191569677049783345080351097717812535867500285661692155668121347<105>
(2·10170+7)/9 = (2)1693<170> = 12930304574921414314033<23> · C148
C148 = P43 · P105
P43 = 3177578812262362929721778663715578834608987<43>
P105 = 540856932080673148371720800720497574973083187669508000817425748253849426512467650834585100482455000456813<105>
(2·10174+7)/9 = (2)1733<174> = 32653 · C169
C169 = P34 · C135
P34 = 8605748596807443176651449709360011<34>
C135 = [790816538438140615000153862079160056073471252421369321942539171949977923538944145405594829029895279514855025343464426448291871504794881<135>]
(2·10187+7)/9 = (2)1863<187> = 3 · 7121 · 703861 · 9726089 · 765326106386707<15> · 437824737463030830793<21> · C134
C134 = P28 · P32 · P75
P28 = 5263877762821122828884893157<28>
P32 = 48391846941817862159960485307009<32>
P75 = 178022660365682865284769924756205427705493239580961443647315723443038756623<75>
(2·10197+7)/9 = (2)1963<197> = 1621 · 141974874916545385999<21> · 2232227063658151482511<22> · C152
C152 = P32 · C120
P32 = 43577960060843625073819999006811<32>
C120 = [992630718271618283341033880453341958342128797919820395767331503484855179680778194512437518931403483604755119718794009097<120>]
By Makoto Kamada / GGNFS-0.77.1-20060513-pentium4
(8·10183+1)/9 = (8)1829<183> = 72 · 43 · 461 · 467 · 27107 · 9068209 · 23313817858784804426409706148665366375211175744287<50> · C114
C114 = P53 · P62
P53 = 17172336853874519123559347693340353363432157819381763<53>
P62 = 19912205285236655490930714577233779462660321205072785210366107<62>
Number: 88889_183 N=341939096661584400227553288107254525079031934616327634095069075719584264530732473440793216775647315692905629106641 ( 114 digits) SNFS difficulty: 124 digits. Divisors found: r1=17172336853874519123559347693340353363432157819381763 (pp53) r2=19912205285236655490930714577233779462660321205072785210366107 (pp62) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 3.48 hours. Scaled time: 3.06 units (timescale=0.879). Factorization parameters were as follows: n: 341939096661584400227553288107254525079031934616327634095069075719584264530732473440793216775647315692905629106641 m: 10000000000000000000000000000000 c4: 1 c2: -5 c0: 25 skew: 2.24 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, 850001) Primes: RFBsize:78498, AFBsize:63591, largePrimes:1360471 encountered Relations: rels:1359532, finalFF:174303 Max relations in full relation-set: 28 Initial matrix: 142154 x 174303 with sparse part having weight 7785807. Pruned matrix : 128927 x 129701 with weight 4603124. Total sieving time: 3.19 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.23 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,124,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 3.48 hours. --------- CPU info (if available) ----------
By Bryan Koen / GMP-ECM 6.1
10138+3 = 1(0)1373<139> = 103 · 990513749998083607<18> · C118
C118 = P32 · C87
P32 = 34585142462197870945875655226509<32>
C87 = [283408386584072121357621650236515295775168451662180323194828514316327126544738502554127<87>]
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(8·10177+1)/9 = (8)1769<177> = 7 · 29 · 163 · 10723 · 6035986569923<13> · 380857470122232181070000528210631041570306701<45> · C112
C112 = P32 · P80
P32 = 54739137296048956120640580620887<32>
P80 = 19908513669930269360597071221167439859525827759440362292604313670802851972278387<80>
Number: 88889_177 N=1089774863138580484872984968817045844294765683283798979147942631744722199904541170863376042427550881656470869269 ( 112 digits) Divisors found: r1=54739137296048956120640580620887 (pp32) r2=19908513669930269360597071221167439859525827759440362292604313670802851972278387 (pp80) Version: GGNFS-0.77.1 Total time: 39.45 hours. Scaled time: 23.51 units (timescale=0.596). Factorization parameters were as follows: name: 88889_177 n: 1089774863138580484872984968817045844294765683283798979147942631744722199904541170863376042427550881656470869269 skew: 36330.36 # norm 2.48e+15 c5: 5820 c4: -160561218 c3: -103428289141967 c2: 106685185438483196 c1: 22587835698887125868428 c0: 5319801337068504126612240 # alpha -6.19 Y1: 124019362819 Y0: -2847625443342581414407 # Murphy_E 9.82e-10 # M 622533092526007148420631005709468983895694441684678411183890427592736842958130944535980867733197098436365974294 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2450001) Relations: rels:7552865, finalFF:730865 Initial matrix: 500372 x 730865 with sparse part having weight 57563517. Pruned matrix : 402098 x 404663 with weight 19977007. Polynomial selection time: 0.50 hours. Total sieving time: 33.31 hours. Total relation processing time: 0.60 hours. Matrix solve time: 4.61 hours. Time per square root: 0.43 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 39.45 hours. --------- CPU info (if available) ----------
By Kazumaro Aoki / GMP-ECM
(10577-1)/9 = (1)577<577> = 8147324243<10> · C567
C567 = P36 · C531
P36 = 938481850248139268016449056596865441<36>
C531 = [145317063102710861820499228904524399066849909129219189300595865487766749556421082708313313982046013295421851928598056080304609057683996269997168542682627544996557610063342531571550391683940782938558316925981737405043174224057225444684519563619355417209749868847265821610326528137035528572329838382261312815748193325315149971534888035173399493417165233051071970445677091792860412089498091494812744864695247159254664667237171078605676809481110779919742695465749073598859163974452510897573796809940497098416296446123048494164664199197<531>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Alexander Mkrtychyan / GGNFS-0.77.1-20060513-pentium4
10135+3 = 1(0)1343<136> = 113 · 209694391 · 3187745395872205735627<22> · C104
C104 = P31 · P73
P31 = 4126491370074199286802782631529<31>
P73 = 3208264562687349553112271518304371303840051419576548379085824235751916727<73>
Number: 10003_135 N=13238876030844222881517187707728521701393691806109836301501637811754088940555731331591745916106732685583 ( 104 digits) SNFS difficulty: 135 digits. Divisors found: r1=4126491370074199286802782631529 (pp31) r2=3208264562687349553112271518304371303840051419576548379085824235751916727 (pp73) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 5.14 hours. Scaled time: 3.29 units (timescale=0.639). Factorization parameters were as follows: n: 13238876030844222881517187707728521701393691806109836301501637811754088940555731331591745916106732685583 m: 1000000000000000000000000000 c5: 1 c0: 3 skew: 1.25 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 1000001) Relations: rels:1483040, finalFF:174625 Initial matrix: 142575 x 174625 with sparse part having weight 11401173. Pruned matrix : 136556 x 137332 with weight 6638985. Total sieving time: 4.66 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.35 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 5.14 hours. --------- CPU info (if available) ---------- Number: 10003_135 N=13238876030844222881517187707728521701393691806109836301501637811754088940555731331591745916106732685583 ( 104 digits) Divisors found: r1=4126491370074199286802782631529 (pp31) r2=3208264562687349553112271518304371303840051419576548379085824235751916727 (pp73) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 12.23 hours. Scaled time: 10.47 units (timescale=0.856). Factorization parameters were as follows: name: 10003_135 n: 13238876030844222881517187707728521701393691806109836301501637811754088940555731331591745916106732685583 skew: 15091.32 # norm 1.78e+014 c5: 15300 c4: 42172857 c3: -16843114753885 c2: -6385923654261920 c1: 1080586713066062557585 c0: 1600614640292011265372783 # alpha -5.36 Y1: 85171659001 Y0: -61295925167544543480 # Murphy_E 2.14e-009 # M 1415068216635383107428986942648757487027085459449481691813363559400817105834292943797372282379140929763 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 Sieved special-q in [1150000, 2050001) Relations: rels:4579325, finalFF:479215 Initial matrix: 338276 x 479215 with sparse part having weight 37900481. Pruned matrix : 287943 x 289698 with weight 14497215. Total sieving time: 10.16 hours. Total relation processing time: 0.21 hours. Matrix solve time: 1.68 hours. Time per square root: 0.17 hours. 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: 12.23 hours. --------- CPU info (if available) ----------
By Alexander Mkrtychyan / GGNFS-0.77.1-20060513-pentium4
10125+9 = 1(0)1249<126> = 7 · 13 · 384889 · 723939179 · C109
C109 = P27 · P83
P27 = 104798542417408554023904481<27>
P83 = 37632735246204919539474660114544096567452721600807355325578711593030532758062764009<83>
Number: 10009_125 N=3943855800982512204047076283279173934267476357842898027812986502106895423798672694305963146974921925060624329 ( 109 digits) SNFS difficulty: 125 digits. Divisors found: r1=104798542417408554023904481 (pp27) r2=37632735246204919539474660114544096567452721600807355325578711593030532758062764009 (pp83) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 1.96 hours. Scaled time: 1.68 units (timescale=0.856). Factorization parameters were as follows: n: 3943855800982512204047076283279173934267476357842898027812986502106895423798672694305963146974921925060624329 m: 10000000000000000000000000 c5: 1 c0: 9 skew: 1.55 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 600001) Relations: rels:2183785, finalFF:208639 Initial matrix: 113175 x 208639 with sparse part having weight 18310937. Pruned matrix : 100818 x 101447 with weight 4612940. Total sieving time: 1.74 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.12 hours. Time per square root: 0.03 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: 1.96 hours. --------- CPU info (if available) ----------
By Alexander Mkrtychyan / GGNFS-0.77.1-20060513-pentium4
10126+3 = 1(0)1253<127> = 523 · 219931704421459<15> · C109
C109 = P54 · P56
P54 = 225003335227519500209690385071854069954197019410358111<54>
P56 = 38638611863595333536671213995256267949387191415100091789<56>
Number: 10003_126 N=8693816537870552796189791836347215234147282169892521208207622196514133941968184404004410089386067533460650579 ( 109 digits) SNFS difficulty: 126 digits. Divisors found: r1=225003335227519500209690385071854069954197019410358111 (pp54) r2=38638611863595333536671213995256267949387191415100091789 (pp56) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.71 hours. Scaled time: 2.32 units (timescale=0.856). Factorization parameters were as follows: n: 8693816537870552796189791836347215234147282169892521208207622196514133941968184404004410089386067533460650579 m: 10000000000000000000000000 c5: 10 c0: 3 skew: 1 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 700001) Relations: rels:2364119, finalFF:237060 Initial matrix: 113082 x 237060 with sparse part having weight 23525055. Pruned matrix : 102455 x 103084 with weight 5247156. Total sieving time: 2.45 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.14 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: 2.71 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(5·10160+31)/9 = (5)1599<160> = 3 · 83 · 191 · 11897 · 28176527153<11> · 18501477700637<14> · 113560929621493<15> · C114
C114 = P42 · P73
P42 = 110326591238035710584592040607678556416233<42>
P73 = 1503329914327084129827562239789927074395898119591880527859360579326768337<73>
Number: 55559_160 N=165857264953875455413997705152619856437429539839930319261236162874151164125325354773712814415336747189600137214521 ( 114 digits) Divisors found: r1=110326591238035710584592040607678556416233 (pp42) r2=1503329914327084129827562239789927074395898119591880527859360579326768337 (pp73) Version: GGNFS-0.77.1 Total time: 62.57 hours. Scaled time: 37.29 units (timescale=0.596). Factorization parameters were as follows: name: 55559_160 n: 165857264953875455413997705152619856437429539839930319261236162874151164125325354773712814415336747189600137214521 skew: 66068.60 # norm 7.20e+15 c5: 3600 c4: -247115952 c3: 212958230220305 c2: -666236161802342372 c1: -347144910357299009278472 c0: -149742468887770791438169544 # alpha -5.62 Y1: 269559540643 Y0: -8564195791010614904981 # Murphy_E 5.45e-10 # M 48686816090489950110783223909642057313547960725390427311092854386814467166976067367315514213453959993934165254017 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2950001) Relations: rels:7451217, finalFF:605225 Initial matrix: 500754 x 605225 with sparse part having weight 50049963. Pruned matrix : 460141 x 462708 with weight 28300107. Total sieving time: 53.74 hours. Total relation processing time: 0.63 hours. Matrix solve time: 7.64 hours. Time per square root: 0.57 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 62.57 hours. --------- CPU info (if available) ----------
By Makoto Kamada / GGNFS-0.77.1-20060513-pentium4
10137+3 = 1(0)1363<138> = C138
C138 = P36 · P45 · P58
P36 = 485528403184829992818506125204327553<36>
P45 = 148422974169957271956708475508014083532747879<45>
P58 = 1387663704324682066869289940523411644503592736304905992069<58>
Number: 10003_137 N=100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 ( 138 digits) SNFS difficulty: 137 digits. Divisors found: r1=485528403184829992818506125204327553 (pp36) r2=148422974169957271956708475508014083532747879 (pp45) r3=1387663704324682066869289940523411644503592736304905992069 (pp58) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 8.57 hours. Scaled time: 7.53 units (timescale=0.879). Factorization parameters were as follows: n: 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 m: 1000000000000000000000000000 c5: 100 c0: 3 skew: 1 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1525001) Primes: RFBsize:78498, AFBsize:64158, largePrimes:1561033 encountered Relations: rels:1553398, finalFF:160894 Max relations in full relation-set: 28 Initial matrix: 142720 x 160894 with sparse part having weight 14946696. Pruned matrix : 137740 x 138517 with weight 11497237. Total sieving time: 7.96 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.50 hours. Time per square root: 0.04 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: 8.57 hours. --------- CPU info (if available) ----------
By Wojciech Florek / GMP-ECM 6.0.1 B1=250000
10165+3 = 1(0)1643<166> = 38239 · 1693194240447509<16> · C146
C146 = P31 · P115
P31 = 1588184880884744278485835046657<31>
P115 = 9724910962239622540990620193028590711568046948990342160048211399738346880582051939871864183726938718963260603503529<115>
By Kazumaro Aoki / GMP-ECM
10283+1 = 1(0)2821<284> = 11 · 1699 · 241117 · 61945573305222690279363663578823967<35> · 151168348012920493188164812150408056175148228488823<51> · C189
C189 = P47 · P142
P47 = 49019999488937337866558715558211303750925973449<47>
P142 = 4834389726736518293852244130660191969670797610633948645694761977558159678896763591712097243317272920296826630341374217553659008741548305187653<142>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Wojciech Florek / Msieve v. 1.03
10139+3 = 1(0)1383<140> = 13 · 327203583643<12> · 21557806404758500426320572531<29> · C99
C99 = P46 · P54
P46 = 1048720107311272779271661501804277089838257303<46>
P54 = 103985894904565220127485054041767990985479311662142569<54>
Tue May 30 01:53:59 2006 Msieve v. 1.03 Tue May 30 01:53:59 2006 random seeds: e5a24ffa 3215051b Tue May 30 01:53:59 2006 factoring 109052098863174370952569599747648629418311788803478577891274670334454933699104045854505718091431407 (99 digits) Tue May 30 01:54:00 2006 using multiplier of 17 Tue May 30 01:54:00 2006 sieve interval: 9 blocks of size 65536 Tue May 30 01:54:00 2006 processing polynomials in batches of 6 Tue May 30 01:54:00 2006 using a sieve bound of 2538791 (92941 primes) Tue May 30 01:54:00 2006 using large prime bound of 380818650 (28 bits) Tue May 30 01:54:00 2006 using double large prime bound of 2787999993955500 (43-52 bits) Tue May 30 01:54:00 2006 using trial factoring cutoff of 57 bits Tue May 30 01:54:00 2006 polynomial 'A' values have 13 factors Tue May 30 09:38:34 2006 93395 relations (22839 full + 70556 combined from 1378715 partial), need 93037 Tue May 30 09:38:35 2006 begin with 1378715 relations Tue May 30 09:38:36 2006 reduce to 218992 relations in 11 passes Tue May 30 09:38:36 2006 attempting to read 22839 full and 218992 partial relations Tue May 30 09:38:41 2006 recovered 22839 full and 218992 partial relations Tue May 30 09:38:41 2006 recovered 230899 polynomials Tue May 30 09:38:41 2006 attempting to build 70556 cycles Tue May 30 09:38:41 2006 found 70556 cycles in 6 passes Tue May 30 09:38:42 2006 distribution of cycle lengths: Tue May 30 09:38:42 2006 length 2 : 16484 Tue May 30 09:38:42 2006 length 3 : 16165 Tue May 30 09:38:42 2006 length 4 : 12533 Tue May 30 09:38:42 2006 length 5 : 9319 Tue May 30 09:38:42 2006 length 6 : 6470 Tue May 30 09:38:42 2006 length 7 : 4127 Tue May 30 09:38:42 2006 length 8 : 2464 Tue May 30 09:38:42 2006 length 9+: 2994 Tue May 30 09:38:42 2006 largest cycle: 21 relations Tue May 30 09:38:42 2006 92941 x 93005 system, weight 6096558 (avg 65.55/col) Tue May 30 09:38:42 2006 reduce to 91325 x 91389 in 3 passes Tue May 30 09:42:18 2006 lanczos halted after 1447 iterations Tue May 30 09:42:18 2006 recovered 62 nontrivial dependencies Tue May 30 09:43:31 2006 prp46 factor: 1048720107311272779271661501804277089838257303 Tue May 30 09:43:31 2006 prp54 factor: 103985894904565220127485054041767990985479311662142569 Tue May 30 09:43:32 2006 elapsed time 07:49:33
By Alexander Mkrtychyan / GGNFS-0.77.1-20060513-pentium4
10124+3 = 1(0)1233<125> = 7 · 43 · 8179 · 23257479000261691<17> · C102
C102 = P42 · P60
P42 = 278215836815846300810499872638251601851541<42>
P60 = 627753020605636868785440299879864836902467148030812554348147<60>
Number: 10003_124 N=174650831941472467445289919450500673291473034301660439617172819294158790322600074782094487475522444527 ( 102 digits) SNFS difficulty: 125 digits. Divisors found: r1=278215836815846300810499872638251601851541 (pp42) r2=627753020605636868785440299879864836902467148030812554348147 (pp60) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.02 hours. Scaled time: 1.30 units (timescale=0.640). Factorization parameters were as follows: n: 174650831941472467445289919450500673291473034301660439617172819294158790322600074782094487475522444527 m: 10000000000000000000000000 c5: 1 c0: 30 skew: 1.97 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [400000, 600001) Relations: rels:2190943, finalFF:218685 Initial matrix: 113035 x 218685 with sparse part having weight 19064751. Pruned matrix : 99519 x 100148 with weight 4369458. Total sieving time: 1.81 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.12 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: 2.02 hours. --------- CPU info (if available) ----------
By Makoto Kamada / GGNFS-0.77.1-20060513-pentium4
10116+9 = 1(0)1159<117> = 111256744554457<15> · C102
C102 = P28 · P28 · P47
P28 = 3052729705599278798406752741<28>
P28 = 5505231043723870085469276793<28>
P47 = 53482259761111102005149456829292624252000374149<47>
Number: 10009_116 N=898821913228396280023466116957629527519011387394111616097834533727168556480812558017319934505640764337 ( 102 digits) SNFS difficulty: 116 digits. Divisors found: r1=3052729705599278798406752741 (pp28) r2=5505231043723870085469276793 (pp28) r3=53482259761111102005149456829292624252000374149 (pp47) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 1.32 hours. Scaled time: 1.17 units (timescale=0.880). Factorization parameters were as follows: n: 898821913228396280023466116957629527519011387394111616097834533727168556480812558017319934505640764337 m: 100000000000000000000000 c5: 10 c0: 9 skew: 1 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:64158, largePrimes:1940389 encountered Relations: rels:1896820, finalFF:138845 Max relations in full relation-set: 28 Initial matrix: 113323 x 138845 with sparse part having weight 10525760. Pruned matrix : 102932 x 103562 with weight 6044808. Total sieving time: 1.08 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.17 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: 1.32 hours. --------- CPU info (if available) ----------
By Makoto Kamada / GGNFS-0.77.1-20060513-pentium4
10116+3 = 1(0)1153<117> = 613 · 5581 · C110
C110 = P32 · P39 · P40
P32 = 31409912863227233240324396659219<32>
P39 = 285562837995982349446361585842661944753<39>
P40 = 3258810312307206854209463561699139379393<40>
Number: 10003_116 N=29229911670129924034382560499340427043163518264164157522332383263771015210369135785508569771653007041778020451 ( 110 digits) SNFS difficulty: 116 digits. Divisors found: r1=31409912863227233240324396659219 (pp32) r2=285562837995982349446361585842661944753 (pp39) r3=3258810312307206854209463561699139379393 (pp40) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 1.75 hours. Scaled time: 1.54 units (timescale=0.879). Factorization parameters were as follows: n: 29229911670129924034382560499340427043163518264164157522332383263771015210369135785508569771653007041778020451 m: 100000000000000000000000 c5: 10 c0: 3 skew: 1 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:63918, largePrimes:2331143 encountered Relations: rels:2714082, finalFF:499083 Max relations in full relation-set: 28 Initial matrix: 113082 x 499083 with sparse part having weight 42387208. Pruned matrix : 65921 x 66550 with weight 6428247. Total sieving time: 1.57 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.09 hours. Time per square root: 0.03 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: 1.75 hours. --------- CPU info (if available) ----------
By Makoto Kamada / GGNFS-0.77.1-20060513-pentium4
10114+9 = 1(0)1139<115> = 61 · 197 · C110
C110 = P41 · P70
P41 = 28209372385446691031827707934227981145697<41>
P70 = 2949921878782510902524946201902765360019176183479097760119909220054841<70>
Number: 10009_114 N=83215444786552384122493134725805109428309894316385121078472164433718898227511026046434218190896230340351169177 ( 110 digits) SNFS difficulty: 115 digits. Divisors found: r1=28209372385446691031827707934227981145697 (pp41) r2=2949921878782510902524946201902765360019176183479097760119909220054841 (pp70) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 1.29 hours. Scaled time: 1.14 units (timescale=0.879). Factorization parameters were as follows: n: 83215444786552384122493134725805109428309894316385121078472164433718898227511026046434218190896230340351169177 m: 100000000000000000000000 c5: 1 c0: 90 skew: 2.46 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, 400000) Primes: RFBsize:49098, AFBsize:64158, largePrimes:2037023 encountered Relations: rels:2085053, finalFF:208794 Max relations in full relation-set: 28 Initial matrix: 113320 x 208794 with sparse part having weight 16430199. Pruned matrix : 86059 x 86689 with weight 4402841. Total sieving time: 1.12 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.10 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: 1.29 hours. --------- CPU info (if available) ----------
By Makoto Kamada / GGNFS-0.77.1-20060513-pentium4
10111+3 = 1(0)1103<112> = 22483 · C107
C107 = P49 · P59
P49 = 3811103616383696520035255018963138889550371472027<49>
P59 = 11670648336895389594887395705639732998619139278066767263683<59>
Number: 10003_111 N=44478050082284392652226126406618333852243917626651247609304808077213894942845705644264555441889427567495441 ( 107 digits) SNFS difficulty: 111 digits. Divisors found: r1=3811103616383696520035255018963138889550371472027 (pp49) r2=11670648336895389594887395705639732998619139278066767263683 (pp59) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 1.46 hours. Scaled time: 1.26 units (timescale=0.864). Factorization parameters were as follows: n: 44478050082284392652226126406618333852243917626651247609304808077213894942845705644264555441889427567495441 m: 10000000000000000000000 c5: 10 c0: 3 skew: 1 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:63918, largePrimes:2285539 encountered Relations: rels:2658142, finalFF:499848 Max relations in full relation-set: 28 Initial matrix: 113082 x 499848 with sparse part having weight 39448818. Pruned matrix : 61151 x 61780 with weight 5357858. Total sieving time: 1.31 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.06 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.46 hours. --------- CPU info (if available) ----------
100...003 and 100...009 have been extended to n=200. The factors contained in 100...003, 100...009, 99...991 and 99...997 are shared with Wojciech Florek's Numbers b^n +/- (b-1).
By Alexander Mkrtychyan / ggnfs-0.77.1-20050930-win32, ggnfs-0.77.1-20060513-win32 gnfs
(10177+17)/9 = (1)1763<177> = 79 · 199 · 337 · 1892299672990464278460298053559<31> · C140
C140 = P41 · P99
P41 = 30718605547911357038884474798678757669593<41>
P99 = 360791261643161040204601470623121686876253222118849993349356095607539068590369608206576778840865487<99>
From dependence 0, sqrt obtained: r1=30718605547911357038884474798678757669593 (pp41) r2=360791261643161040204601470623121686876253222118849993349356095607539068590369608206576778840865487 (pp99) Sieving time: ~100hrs 3x(2xXeon 2GHz HT) Special-q: [3700000;4285000)U[4700000;5285000)U[5700000;6275000)U[6700000;7275000)U[7700000;8275000)U[8700000;9275000) Matbuild time: 1h 13m (P4 3GHz) Matsolve time: 65hrs (Xeon 2GHz) SQRT time: 23m (Xeon 2GHz)
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(10187-7)/3 = (3)1861<187> = 353 · 280452841 · 1622017637<10> · 6455829493<10> · 8153771179<10> · 8323772467<10> · 13844844491<11> · 133121560007<12> · C116
C116 = P32 · P85
P32 = 17112512897645193474162457303709<32>
P85 = 1502130221517405323788789034763018633547019554207566438289495865206761369751410755243<85>
Number: 33331_187 N=25705222789659230129577349579323241908332956518982930455730238052034344376144780365717653648473188667077721115096287 ( 116 digits) Divisors found: r1=17112512897645193474162457303709 (pp32) r2=1502130221517405323788789034763018633547019554207566438289495865206761369751410755243 (pp85) Version: GGNFS-0.77.1 Total time: 74.90 hours. Scaled time: 44.64 units (timescale=0.596). Factorization parameters were as follows: name: 33331_187 n: 25705222789659230129577349579323241908332956518982930455730238052034344376144780365717653648473188667077721115096287 skew: 72066.11 # norm 4.77e+15 c5: 16020 c4: 1079678044 c3: -226377956377577 c2: -3869740926659501127 c1: 593017781651556008797213 c0: 556666633407509921583325059 # alpha -5.61 Y1: 29630664371 Y0: -17420947106597594755066 # Murphy_E 4.96e-10 # M 19075954865955788364877833372874227080287775471724129794572307966875364161158480220873129933185096115271356398268504 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 Sieved special-q in [2250000, 3630001) Relations: rels:7413410, finalFF:711122 Initial matrix: 631991 x 711122 with sparse part having weight 52523327. Pruned matrix : 591074 x 594297 with weight 34326604. Polynomial selection time: 1.58 hours. Total sieving time: 60.71 hours. Total relation processing time: 0.96 hours. Matrix solve time: 11.04 hours. Time per square root: 0.62 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 74.90 hours. --------- CPU info (if available) ----------
By Tyler Cadigan / PRIMO 2.2.0 beta 5, PRIMO 2.2.0 beta 6
(13·103883+23)/9 = 144...447<3884> and (13·103883+41)/9 = 144...449<3884> are twin primes. PRIMO took 61 days to certify them. These numbers are the new largest known quasi-repdigit twin primes in our tables. Congratulations!
[PRIMO - Primality Certificate] Version=2.2.0 beta 5 WebSite=http://www.ellipsa.net/ Format=3 ID=B2CD301B487E4 Created=03/01/2006 07:58:02 AM TestCount=555 Status=Candidate certified prime [Running Times] Initialization=1mn 13s 1stPhase=717h 33mn 5s 2ndPhase=199h 0mn 10s Total=916h 34mn 29s
[PRIMO - Primality Certificate] Version=2.2.0 beta 6 WebSite=http://www.ellipsa.net/ Format=3 ID=B2D1401C3126D Created=05/04/2006 08:13:59 am TestCount=525 Status=Candidate certified prime [Running Times] Initialization=1mn 17s 1stPhase=435h 46mn 42s 2ndPhase=120h 53mn 59s Total=556h 42mn 0s
By Alexander Mkrtychyan / ggnfs-0.77.1-20050930-win32, ggnfs-0.77.1-20060513-win32 gnfs
(10180+17)/9 = (1)1793<180> = 6949 · 135862068644287<15> · 21633659135200744087543<23> · 57990409560719099220689<23> · C116
C116 = P58 · P59
P58 = 1382900513606693483258913500529894818988671399169846834029<58>
P59 = 67835941890955693798711513601062800007163705809229580442097<59>
From dependence 2, sqrt obtained: r1=67835941890955693798711513601062800007163705809229580442097 (pp59) r2=1382900513606693483258913500529894818988671399169846834029 (pp58) --- name: 11113_180 n: 93810358881996442890482228144067883749540447348259571159075789651402467670223973413339539712829879169409153603718813 skew: 175108.69 # norm 1.75e+016 c5: 5400 c4: -1726380600 c3: -432331060735484 c2: 49069046496066798379 c1: 6386726768458004938997316 c0: -195736233629971911011199858171 # alpha -6.42 Y1: 118668961433 Y0: -28052497025194315455812 # Murphy_E 4.47e-010 # M 21556650053594647587355239452989933796097336626550949729236432534682743476314564571653393032526111986106295322015595 type: gnfs rlim: 4200000 alim: 4200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 special-q: [2100000;3300000) U [3800000;4050000) largePrimes: 7643593 , relations: 7698454, finalFF:735738 Pruning matrix with wt=0.700 Initial matrix is 592789 x 735738 with sparse part having weight 60694738. (total weight is 105658690) Matrix pruned to 534537 x 537564 with weight 32218417. Matrix solve time: 11 hrs Each dependency: 24 min
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
6·10154-1 = 5(9)154<155> = 57413 · 33391993 · 394480713417379755453806059<27> · C116
C116 = P55 · P62
P55 = 5080508476226699401820394941107809615305588790497635369<55>
P62 = 15615853062739861486377064170042789464317919964935221145123641<62>
Number: 59999_154 N=79336473848760530612842941919437624337465023282039573568924868671690972576856766205762376956791968689234595639658529 ( 116 digits) Divisors found: r1=5080508476226699401820394941107809615305588790497635369 (pp55) r2=15615853062739861486377064170042789464317919964935221145123641 (pp62) Version: GGNFS-0.77.1 Total time: 71.45 hours. Scaled time: 42.59 units (timescale=0.596). Factorization parameters were as follows: name: 59999_154 n: 79336473848760530612842941919437624337465023282039573568924868671690972576856766205762376956791968689234595639658529 skew: 84818.07 # norm 2.28e+16 c5: 29880 c4: 7478564061 c3: -707415992953978 c2: -45326205609016815484 c1: 1923709240675668423295402 c0: 33553695631315758691438543975 # alpha -7.35 Y1: 1705761963619 Y0: -19267108168052096703534 # Murphy_E 5.23e-10 # M 66752713575719543916592226157126688247860915181985985556033446618000744146215247187696635904247103461998592722806763 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 Sieved special-q in [2250000, 3570001) Relations: rels:7595337, finalFF:785196 Initial matrix: 631739 x 785196 with sparse part having weight 56191010. Pruned matrix : 561458 x 564680 with weight 27895824. Total sieving time: 60.75 hours. Total relation processing time: 1.09 hours. Matrix solve time: 9.02 hours. Time per square root: 0.60 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 71.45 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(22·10158-1)/3 = 7(3)158<159> = 140489219953<12> · 35002292573981<14> · 12758191547884466113<20> · C116
C116 = P46 · P70
P46 = 5876416527844272249936979378582409414757015853<46>
P70 = 1989116612667541745797449592887591507231608864101217927853626043037229<70>
Number: 73333_158 N=11688877738489155829430414188785043880605496839583412226210933921576972975907322546275114248757018500186648622191337 ( 116 digits) Divisors found: r1=5876416527844272249936979378582409414757015853 (pp46) r2=1989116612667541745797449592887591507231608864101217927853626043037229 (pp70) Version: GGNFS-0.77.1 Total time: 78.52 hours. Scaled time: 46.80 units (timescale=0.596). Factorization parameters were as follows: name: 73333_158 n: 11688877738489155829430414188785043880605496839583412226210933921576972975907322546275114248757018500186648622191337 skew: 59680.44 # norm 3.24e+16 c5: 20880 c4: -14234941084 c3: -306085187616580 c2: 23180516622910676703 c1: -735129018559166322145374 c0: 4488697936590608689274471535 # alpha -6.93 Y1: 486245336687 Y0: -14112712835610901808786 # Murphy_E 4.83e-10 # M 2568106766109560019945838462360232314677097972922575724213417769912041924975690663254191959635629891932025334885188 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 Sieved special-q in [2250000, 3690001) Relations: rels:7460294, finalFF:721699 Initial matrix: 631607 x 721699 with sparse part having weight 54496744. Pruned matrix : 587098 x 590320 with weight 34434946. Polynomial selection time: 1.53 hours. Total sieving time: 64.01 hours. Total relation processing time: 1.17 hours. Matrix solve time: 11.13 hours. Time per square root: 0.67 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 78.52 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
101490+1 = 1(0)14891<1491> = 101 · 3541 · 8941 · 10729 · 27961 · 62581 · 607921 · 14118155281<11> · 4672884738461<13> · 72286688991301<14> · 171815892427926701<18> · 136916416686052955621<21> · 2336398996447692315465181<25> · [110870679844269144354635709949582391774770890704083103791132633566371413253392265378550591815806580691669808595307539634355488864836833845471616794677024940025967620229919340559408262151273358247434378152195260280636870443948931086228877135378433246056449430881437009<267>] · C533 · [1351888791527812046439213882009622550983970447446930813907281321570614318590099348850147937665737601917016027689304215555619864311672420525464165912633730679733873139241622895458014281474880533521107162485558617384106966419668546077494971073918410836418351615825596959802566688270975816957817343681670940963553941306251076786071118381886951748734183323759331738970862212863946579098193981677634489961869774727417167109001620173536142186561428201966969394669482772192463087452587648096715535089953833204308363926463253547939370366391026176469926869119483259090839941<565>]
C533 = P32 · C502
P32 = 43449727365272099794386367962241<32>
C502 = [1605214440709619357797351581919800889833597416421394148739815672950024771161380823847360755208273655227157019000219766490046550207325155036864476602837123952047383195091299758360303040822482624716944164463773873136231905729534814986307576307291846151794615420341552185181793289760376366513402259834628028778708825939521820938434639815230158850634413284564675945198522078882483236008364966125191436705573836033815481341830782769681163394145324260216840198126909976526595416165428782222227927578041059481<502>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
6·10153-1 = 5(9)153<154> = 72 · 11923 · 10612859 · 331784113069<12> · 453413972988539<15> · C115
C115 = P54 · P62
P54 = 210419824853341366020370755446106047880424773709398731<54>
P62 = 30570327461743607247656827644966362380207522643930113459529683<62>
Number: 59999_153 N=6432602950209381566071417300565692922172746250322495126280992600135969399574714874192832413021554182913335977032273 ( 115 digits) Divisors found: r1=210419824853341366020370755446106047880424773709398731 (pp54) r2=30570327461743607247656827644966362380207522643930113459529683 (pp62) Version: GGNFS-0.77.1 Total time: 74.60 hours. Scaled time: 49.61 units (timescale=0.665). Factorization parameters were as follows: name: 59999_153 n: 6432602950209381566071417300565692922172746250322495126280992600135969399574714874192832413021554182913335977032273 skew: 105280.31 # norm 6.40e+15 c5: 3360 c4: 1711138388 c3: -142704087242572 c2: -16509405547813587843 c1: 579448197690139623628968 c0: 15834339481339862133738235344 # alpha -6.16 Y1: 916937538077 Y0: -18047092579177005337355 # Murphy_E 5.51e-10 # M 4649560124782638886169002085810032125698866907620478245677898408391415163706005214228115241540314236068560646898293 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 3150001) Relations: rels:7537636, finalFF:591893 Initial matrix: 500171 x 591893 with sparse part having weight 53046021. Pruned matrix : 466490 x 469054 with weight 32722150. Total sieving time: 65.33 hours. Total relation processing time: 0.80 hours. Matrix solve time: 7.93 hours. Time per square root: 0.53 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 74.60 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(10171+11)/3 = (3)1707<171> = 92679287 · 994403167 · 417175914199627907<18> · 42988602995074769083067<23> · C114
C114 = P42 · P72
P42 = 532370738642252747881930955732927552264431<42>
P72 = 378832148738346714803246790370049786475497092748031158119297214036870927<72>
Number: 33337_171 N=201679150845265397972899579405414196358211817136533655146698091272809044950702835327119509077953012871064520097537 ( 114 digits) Divisors found: r1=532370738642252747881930955732927552264431 (pp42) r2=378832148738346714803246790370049786475497092748031158119297214036870927 (pp72) Version: GGNFS-0.77.1 Total time: 60.55 hours. Scaled time: 36.21 units (timescale=0.598). Factorization parameters were as follows: name: 33337_171 n: 201679150845265397972899579405414196358211817136533655146698091272809044950702835327119509077953012871064520097537 skew: 64839.26
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(8·10194-17)/9 = (8)1937<194> = 3 · 457 · 7442198479<10> · 1853420236219<13> · 47262295153011259<17> · 15350897443886512393<20> · 64765061725005467929<20> · C114
C114 = P34 · P80
P34 = 6480369962419216676886015131553803<34>
P80 = 15436388905337558778371403302481752050799648156400720007183437167938419834568313<80>
Number: 88887_194 N=100033510990370769037783221436892148654237355566140936043342879059476911987097644903473741174361430890787438444339 ( 114 digits) Divisors found: r1=6480369962419216676886015131553803 (pp34) r2=15436388905337558778371403302481752050799648156400720007183437167938419834568313 (pp80) Version: GGNFS-0.77.1 Total time: 59.27 hours. Scaled time: 39.41 units (timescale=0.665). Factorization parameters were as follows: name: 88887_194 n: 100033510990370769037783221436892148654237355566140936043342879059476911987097644903473741174361430890787438444339 skew: 94843.55 # norm 3.78e+15 c5: 6720 c4: -454079855 c3: -166276676958541 c2: 4321868868486253437 c1: 621457987802746553015556 c0: -5759405241914086523773708032 # alpha -5.97 Y1: 1235364142463 Y0: -6832132952966350514215 # Murphy_E 6.59e-10 # M 53414084420105239531409507853870439225520878623788372429017774638301052821831186082132921294698619636722904152636 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2850001) Relations: rels:7428947, finalFF:618021 Initial matrix: 501237 x 618021 with sparse part having weight 51636023. Pruned matrix : 454628 x 457198 with weight 27725778. Polynomial selection time: 0.75 hours. Total sieving time: 50.46 hours. Total relation processing time: 0.67 hours. Matrix solve time: 6.82 hours. Time per square root: 0.57 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 59.27 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(64·10187-1)/9 = 7(1)187<188> = 3059423027<10> · 774835058906615644573<21> · 2096821980403022549357<22> · 46631924364211658379013<23> · C114
C114 = P34 · P80
P34 = 3085197246316846058441513572039351<34>
P80 = 99439936186422677023881388364394444639121093342721552571149678501567263064669351<80>
Number: 71111_187 N=306791817296274137578369995378342769784629428227128004530748464743913733873267850246802709850429363527789575631201 ( 114 digits) Divisors found: r1=3085197246316846058441513572039351 (pp34) r2=99439936186422677023881388364394444639121093342721552571149678501567263064669351 (pp80) Version: GGNFS-0.77.1 Total time: 66.32 hours. Scaled time: 44.11 units (timescale=0.665). Factorization parameters were as follows: name: 71111_187 n: 306791817296274137578369995378342769784629428227128004530748464743913733873267850246802709850429363527789575631201 skew: 72723.60 # norm 8.36e+15 c5: 4200 c4: 1314878496 c3: 29893165368154 c2: 5806505690884697260 c1: -80974786490363044819303 c0: -2809595739939450546389912905 # alpha -5.91 Y1: 506287004443 Y0: -9391120872173951113476 # Murphy_E 5.91e-10 # M 64411780652946857169721256341933818960526809823175485053028889724667874325524578817371689180174804384560712691116 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 3050001) Relations: rels:7784965, finalFF:703564 Initial matrix: 500178 x 703564 with sparse part having weight 64780933. Pruned matrix : 427184 x 429748 with weight 27215548. Polynomial selection time: 0.52 hours. Total sieving time: 58.35 hours. Total relation processing time: 0.75 hours. Matrix solve time: 6.21 hours. Time per square root: 0.49 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 66.32 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
101005+1 = 1(0)10041<1006> = 7 · 11 · 13 · 211 · 241 · 2011 · 2161 · 7237 · 9091 · 667321 · 248807851 · 7261216121<10> · 17830074841<11> · 851109498533797<15> · 45360300267343173645804799921<29> · 909090909090909090909090909090909090909090909090909090909090909091<66> · 220589842618680198991086731354678488275926380957742565496334997548411735059<75> · 302763019793435602569276039549096923630299122171140405303248730561741324305632792351835552866724155290700915085510738521559595248967375329278966176208018813174111240588000435579287968883246599299199382818469156370627492652751047813638818869931<243> · C523
C523 = P34 · C489
P34 = 5106142986008803018248662015009851<34>
C489 = [267065612248820557472520439776822436976316860200284961217319474767187378351419204646394707262722878914653395748869244344163867301798774915535042661263712198199655751422924668127752305623311241735515907241278561718322243002304418362598142142784047872257429459694724497453620868115224924909852592025982594685275509236743201047056443487859885626143200492047910061842042588027369301270574181306219963521753550999023466384773034942701929137632741459562769524551431233366749180168445321428112521<489>]
(101095-1)/9 = (1)1095<1095> = 3 · 31 · 37 · 41 · 271 · 439 · 2906161 · 30528601 · 743778751 · 2212293763<10> · 12171337159<11> · 1399205517511<13> · 99519941206321<14> · 1855193842151350117<19> · 49207341634646326934001739482502131487446637<44> · 39316310783659104892252157287077969239619734325044334592964583271<65> · 23593748551050409936688015200253053030029532433958916533719315706853<68> · [900009000090000900009000090000900009000090000900009000090000900009000090090900909009090090900909009090090900909009090090900909009090090900909009099090990909909099090990909909099090990909909099090990909909099090990909909999099990999909999099990999909999099990999909999099990999909999099991<288>] · C534
C534 = P36 · C499
P36 = 140932038048905130657965837325339961<36>
C499 = [2490959198534119854148888244888389656922469923333114578224491510740768956555767426487650605866819367218146558537719339947893409283320637700994215368076762244767408218909879904099720709997732498013277342080382591987824100057995391141148714118030303561287868930859755521892342961834650557591057337986666940122597723149999708447139377583307317514714358416876794090235604232173146119518484368738494673569394646876952276579416547854836399176089562703592384079831887087898586536197356767893761165757641671<499>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
10176-3 = (9)1757<176> = 1630871011403<13> · 274954356330508669<18> · 6165326947505579813146109111140967<34> · C113
C113 = P53 · P61
P53 = 15902473362316519828155848907387241210869028241932019<53>
P61 = 2274568355541311973196278737571018169468417735311027313697927<61>
Number: 99997_176 N=36171262684763804729310148527389239248018395875233064507433824238903582995595207747275554709544383072041835224613 ( 113 digits) Divisors found: r1=15902473362316519828155848907387241210869028241932019 (pp53) r2=2274568355541311973196278737571018169468417735311027313697927 (pp61) Version: GGNFS-0.77.1 Total time: 49.15 hours. Scaled time: 31.46 units (timescale=0.640). Factorization parameters were as follows: name: 99997_176 n: 36171262684763804729310148527389239248018395875233064507433824238903582995595207747275554709544383072041835224613 skew: 21661.12 # norm 1.39e+15 c5: 18480 c4: -1274308388 c3: -2753156212614 c2: -566135503557535436 c1: -1770382572121760880459 c0: 12586420686444448843600627 # alpha -5.30 Y1: 186177921679 Y0: -4553366263117725452040 # Murphy_E 7.67e-10 # M 6503063031704603377893240417849562075913973347253991849218632153429208960877388456019300122795172030561087003516 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2650001) Relations: rels:7231586, finalFF:566384 Initial matrix: 501020 x 566384 with sparse part having weight 46763514. Pruned matrix : 469008 x 471577 with weight 31217684. Total sieving time: 40.71 hours. Total relation processing time: 0.63 hours. Matrix solve time: 7.33 hours. Time per square root: 0.47 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 49.15 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(22·10195-1)/3 = 7(3)195<196> = 760607 · 924361 · 7110820979199464413<19> · 225671089237444355780867<24> · 1468739043177098162139599627<28> · C115
C115 = P47 · P68
P47 = 57840971850648197321146788506896562701289609689<47>
P68 = 76510951515688690163170103291651427855005889299208107899216779746183<68>
Number: 73333_195 N=4425467792885258554902155078021991736153936106228595784249517804196388210518384921317149581681328539846156557567087 ( 115 digits) Divisors found: r1=57840971850648197321146788506896562701289609689 (pp47) r2=76510951515688690163170103291651427855005889299208107899216779746183 (pp68) Version: GGNFS-0.77.1 Total time: 84.49 hours. Scaled time: 50.36 units (timescale=0.596). Factorization parameters were as follows: name: 73333_195 n: 4425467792885258554902155078021991736153936106228595784249517804196388210518384921317149581681328539846156557567087 skew: 170663.23 # norm 9.92e+15 c5: 1260 c4: 133094852 c3: -235094834885984 c2: -2109515795186569345 c1: 1527791730117853107692802 c0: -2793794243224810862467149600 # alpha -5.77 Y1: 302054157823 Y0: -20375937126109800578251 # Murphy_E 5.19e-10 # M 3076403489535678031464462710394205254422024861907700313351362960154556084852305858936583388784869574395611274292560 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 3450001) Relations: rels:7869880, finalFF:687897 Initial matrix: 500521 x 687897 with sparse part having weight 66175633. Pruned matrix : 440257 x 442823 with weight 30310998. Polynomial selection time: 0.52 hours. Total sieving time: 75.79 hours. Total relation processing time: 0.78 hours. Matrix solve time: 6.82 hours. Time per square root: 0.59 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 84.49 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(2·10166+43)/9 = (2)1657<166> = 23 · 239 · 223681 · 4808529001<10> · 27380724157<11> · 49555413624314842798663<23> · C114
C114 = P48 · P67
P48 = 109487586728603959180419389601246000593684286667<48>
P67 = 2529994022553427102516108528949076661299677585064796901468164965163<67>
Number: 22227_166 N=277002939967167951016685502103671381318776877865988131419624426806168301114704336309326219472752500352276560381721 ( 114 digits) Divisors found: r1=109487586728603959180419389601246000593684286667 (pp48) r2=2529994022553427102516108528949076661299677585064796901468164965163 (pp67) Version: GGNFS-0.77.1 Total time: 68.07 hours. Scaled time: 40.57 units (timescale=0.596). Factorization parameters were as follows: name: 22227_166 n: 277002939967167951016685502103671381318776877865988131419624426806168301114704336309326219472752500352276560381721 skew: 35022.57 # norm 2.16e+15 c5: 18240 c4: 3324342576 c3: -75210684545821 c2: -3889995031532597485 c1: 41149321063516891001327 c0: 225554783497329843951341475 # alpha -5.11 Y1: 661875331123 Y0: -6859467162763553226608 # Murphy_E 5.83e-10 # M 169113702666968308599370405410246605720862169449212140169193171897561787349105029174955912873471203511474794908184 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 3050001) Relations: rels:7820687, finalFF:710792 Initial matrix: 500744 x 710792 with sparse part having weight 65707739. Pruned matrix : 426298 x 428865 with weight 27132479. Total sieving time: 60.31 hours. Total relation processing time: 0.73 hours. Matrix solve time: 6.55 hours. Time per square root: 0.47 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 68.07 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
10957+1 = 1(0)9561<958> = 7 · 112 · 13 · 23 · 59 · 1277 · 4093 · 8779 · 357281 · 599144041 · 49561573447<11> · 183411838171<12> · 638453709757<12> · 135080726389891<15> · 8793273568581345414847<22> · 154083204930662557781201849<27> · 1274194732898148471766404179653<31> · [486459602951209423461970749393767073577709990315453869054236545173346054197523047637756449380382360041196303992701358542477479985899282299202659134981413322115768441437335973512015267176836292140179486592703400778357473505777445415009505803673230073891473294849<261>] · C539
C539 = P33 · C506
P33 = 156318278601913796169958831669567<33>
C506 = [66203514277021933018367219154147693778936535037473098541895109470133101615260456904766124804243260059004061482523868396627422842510506272739618129760738873068588643277236787555047257507825557038938807521179427472188374447895999544336201041507230424796520553176789792857470904436544840504491242651630080934330545370540473441479395984110121956451559196947095558755351350931089697373180296334055005865225493893072152234214689358450841228924816239504156756948896041357344696275396252307079534359595606264813659<506>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(4·10175+23)/9 = (4)1747<175>= 74 · 151 · 4077068417<10> · 912028673482967<15> · 18287204296526384115739261382729<32> · C114
C114 = P43 · P72
P43 = 1474496589385636624872422204643590358428021<43>
P72 = 122264617559167997611060160283499497988751361155452737911400912906085147<72>
Number: 44447_175 N=180278761593532432612303389060257361960331553150960921382583597306562657112851496908359299109733878279188096704087 ( 114 digits) Divisors found: r1=1474496589385636624872422204643590358428021 (pp43) r2=122264617559167997611060160283499497988751361155452737911400912906085147 (pp72) Version: GGNFS-0.77.1 Total time: 66.44 hours. Scaled time: 40.99 units (timescale=0.617). Factorization parameters were as follows: name: 44447_175 n: 180278761593532432612303389060257361960331553150960921382583597306562657112851496908359299109733878279188096704087 skew: 37257.24 # norm 1.97e+15 c5: 2640 c4: -3066352960 c3: -2045340552093 c2: 4202550017261824270 c1: 5428663167547359316208 c0: -351827258170714110587019840 # alpha -5.13 Y1: 940460856101 Y0: -9265702850142573753067 # Murphy_E 5.77e-10 # M 73472187332863004272367469093365019774637426525363658693875390400459913791531866622534228469633558335064213728171 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 3050001) Relations: rels:7715758, finalFF:666113 Initial matrix: 501371 x 666113 with sparse part having weight 60549670. Pruned matrix : 442462 x 445032 with weight 28621695. Polynomial selection time: 0.59 hours. Total sieving time: 57.53 hours. Total relation processing time: 0.71 hours. Matrix solve time: 7.08 hours. Time per square root: 0.52 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 66.44 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(5·10164-41)/9 = (5)1631<164> = 3 · 117526809611<12> · 54250638606310858569979433501919015383<38> · C115
C115 = P43 · P73
P43 = 1474584781590694929005726294763938095505713<43>
P73 = 1969675536474541734600499776776117471857256864782569029241086440347327593<73>
Number: 55551_164 N=2904453570756846986973383368766510254862338723725138737049038603407688954012735912987940359365696468744723414038809 ( 115 digits) Divisors found: r1=1474584781590694929005726294763938095505713 (pp43) r2=1969675536474541734600499776776117471857256864782569029241086440347327593 (pp73) Version: GGNFS-0.77.1 Total time: 67.75 hours. Scaled time: 40.38 units (timescale=0.596). Factorization parameters were as follows: name: 55551_164 n: 2904453570756846986973383368766510254862338723725138737049038603407688954012735912987940359365696468744723414038809 skew: 80450.98 # norm 1.20e+16 c5: 17820 c4: 4393654356 c3: -433753330947111 c2: -27350320194916868196 c1: 1177687194802812552792514 c0: 15113021087910275283692837108 # alpha -6.45 Y1: 2090837063779 Y0: -11026236084453321843579 # Murphy_E 5.28e-10 # M 223818122459110710984661179910979783697925729433915265008233972170338542245360401390459830340040811696130589483131 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 3050001) Relations: rels:7459470, finalFF:591118 Initial matrix: 500042 x 591118 with sparse part having weight 51454791. Pruned matrix : 465016 x 467580 with weight 31354404. Total sieving time: 58.56 hours. Total relation processing time: 0.63 hours. Matrix solve time: 7.92 hours. Time per square root: 0.64 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 67.75 hours. --------- CPU info (if available) ----------
By Bruce Dodson / GMP-ECM
10399+1 = 1(0)3981<400> = 72 · 11 · 13 · 127 · 2689 · 459691 · 909091 · 1458973 · 425991366045253<15> · 909090909090909091<18> · 247025236977306025681323889<27> · 753201806271328462547977919407<30> · 61828645758322140842666144519962696417487<41> · 72021403933746126426491665754465510017877<41> · 17499101101496101893247811440257935152097401<44> · C159
C159 = P49 · P110
P49 = 9284668536078237580134472469990637899155265743957<49>
P110 = 13147963643704652632557279758698587212033283223333451187877069162714784603584406816150353817835190742091970171<110>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Yousuke Koide / GMP-ECM
10903+1 = 1(0)9021<904> = 72 · 11 · 13 · 127 · 2689 · 3613 · 459691 · 909091 · 57009401 · 2182600451<10> · 212057054080446499<18> · 120525789336558438197<21> · 7306116556571817748755241<25> · 304768036847074491064894608014695867632997<42> · 3605696680890791382725432167911038465896663<43> · 6798855735656881396055959081077830421892567<43> · 1752088930844817629923654387608505754917704006063078641900632201094124478044555887071171166365583553287053602700568010683873135238140340718711012045219107751867190380847<169> · C504
C504 = P38 · C467
P38 = 43304701938592897922269981296083376277<38>
C467 = [21013886489517971344330040348864764437934906646797649893170202970198245328335882505499980396675911865555101856779577300554075531457771872695017237088972173632109249163225374752369335580275541978505985802453671153658648150573384500193528998265661485199395999980819844420791561304482876541398168140686809355351611618717081565145452820471364641262390976246981616092354714230772892990579479051048942179341131112862748124387554407607082664991040927358250555874030530718383<467>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Jason Papadopoulos's Msieve Version 1.06 was released.
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(2·10167-17)/3 = (6)1661<167> = 7 · 7461472332473<13> · 431563732881502259<18> · 5375549665816933543013<22> · C114
C114 = P35 · P37 · P44
P35 = 13261436963852796014111335957348117<35>
P37 = 1573557102101571405377857101955399229<37>
P44 = 26366061185051453095178144268786977977763221<44>
Number: 66661_167 N=550197165033613611769376863626601856258906596716272891854586217441612353242352244972984468385524424237232803855253 ( 114 digits) Divisors found: r1=13261436963852796014111335957348117 (pp35) r2=1573557102101571405377857101955399229 (pp37) r3=26366061185051453095178144268786977977763221 (pp44) Version: GGNFS-0.77.1 Total time: 61.41 hours. Scaled time: 36.60 units (timescale=0.596). Factorization parameters were as follows: name: 66661_167 n: 550197165033613611769376863626601856258906596716272891854586217441612353242352244972984468385524424237232803855253 skew: 70471.01 # norm 4.20e+15 c5: 1800 c4: 1368602079 c3: -12250040256487 c2: -1093635789305396793 c1: 39849855690633737457906 c0: -1783344159885267576523734080 # alpha -5.53 Y1: 805473164171 Y0: -12503883379418569316817 # Murphy_E 5.79e-10 # M 529423451654234320505526908635372534366477001369404131995810074889560862579154671691751730713159012157786351594722 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2950001) Relations: rels:7611348, finalFF:653939 Initial matrix: 500098 x 653939 with sparse part having weight 56597179. Pruned matrix : 441743 x 444307 with weight 26893096. Total sieving time: 53.70 hours. Total relation processing time: 0.64 hours. Matrix solve time: 6.54 hours. Time per square root: 0.53 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 61.41 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
10888+1 = 1(0)8871<889> = 17 · 593 · 1777 · 5882353 · 7228321 · 9999999900000001<16> · 14645119755678294049<20> · 1686340623946037268128160202360893760539460370996627318701517706745362561551433406408094266441822934232698145025463743674536256340640809274873526138279915682968128161887015177082630691231028669477234384485666273187182124789224283305059021924114671146711635919055647554806087689713153457<286> · C547
C547 = P34 · P514
P34 = 2430356574005120498845908043009873<34>
P514 = 2187319485856065660460480283212234313654078652411870459451330169647543812240431617143716447792186692975247051510538424479092940669136785288465781753693717009207146283270615110366556378727360748704592078063629885737548293485907528075546515396905912717472464716164833417809029422074335902030196371245199471373470169818790769381981258258611278976650676287419191207657093916768283363951628318877273133525031558244951861839766442570991470244423599118239355710932138403326127489420348476636642367374646669593814227877889<514>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(10162+11)/3 = (3)1617<162> = 1433 · 124841369 · 1336592833641954403<19> · 36720308617555078459<20> · C113
C113 = P35 · P79
P35 = 15839391943642481226131981562976091<35>
P79 = 2396790507959344653148912568029143521446310165683450943135628493061398785885083<79>
Number: 33337_162 N=37963704262370013974982229977530646773584991859960923446485591042890017200918324520218776946038568609153002550553 ( 113 digits) Divisors found: r1=15839391943642481226131981562976091 (pp35) r2=2396790507959344653148912568029143521446310165683450943135628493061398785885083 (pp79) Version: GGNFS-0.77.1 Total time: 57.23 hours. Scaled time: 37.88 units (timescale=0.662). Factorization parameters were as follows: name: 33337_162 n: 37963704262370013974982229977530646773584991859960923446485591042890017200918324520218776946038568609153002550553 skew: 82628.90 # norm 5.80e+15 c5: 5400 c4: 2402492435 c3: -113085781430568 c2: -14669915217540964944 c1: 360170614013768543148208 c0: 13321767032890434723398144064 # alpha -6.38 Y1: 693271831747 Y0: -5880177126467717739035 # Murphy_E 6.89e-10 # M 34645119737512916872622338715117151998917211253417099047843164366198507059196910860745581897837412972482767998816 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2850001) Relations: rels:7665727, finalFF:700241 Initial matrix: 500331 x 700241 with sparse part having weight 60604941. Pruned matrix : 422361 x 424926 with weight 24830799. Polynomial selection time: 0.52 hours. Total sieving time: 50.08 hours. Total relation processing time: 0.70 hours. Matrix solve time: 5.45 hours. Time per square root: 0.48 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 57.23 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(82·10165-1)/9 = 9(1)165<166> = 3 · 4651 · 3815909 · 109337069 · 24597499837<11> · 119473647151415430355631209<27> · C111
C111 = P44 · P68
P44 = 52584546422938872199993496426580755318657669<44>
P68 = 10127846063825475829007266635111227567710236342483257149233524822111<68>
Number: 91111_165 N=532568191507609461751810844266510060172332169466526373634275624269343840855863338282742074685691230272530919259 ( 111 digits) Divisors found: r1=52584546422938872199993496426580755318657669 (pp44) r2=10127846063825475829007266635111227567710236342483257149233524822111 (pp68) Version: GGNFS-0.77.1 Total time: 47.69 hours. Scaled time: 28.42 units (timescale=0.596). Factorization parameters were as follows: name: 91111_165 n: 532568191507609461751810844266510060172332169466526373634275624269343840855863338282742074685691230272530919259 skew: 44253.41 # norm 2.76e+15 c5: 13260 c4: -2952571022 c3: -64159933967618 c2: 5169908297278730197 c1: 65757180348379498133862 c0: -972969186385581959161825911 # alpha -6.14 Y1: 183357985723 Y0: -2092994245773555980588 # Murphy_E 8.58e-10 # M 266349246250008411579281465016211195175095228656302106749506815357893863129981722202192551134409014791788528244 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 Sieved special-q in [1600000, 2500001) Relations: rels:7502896, finalFF:632541 Initial matrix: 459786 x 632541 with sparse part having weight 56622491. Pruned matrix : 394614 x 396976 with weight 24147845. Polynomial selection time: 0.50 hours. Total sieving time: 41.44 hours. Total relation processing time: 0.68 hours. Matrix solve time: 4.57 hours. Time per square root: 0.49 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 47.69 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(83·10176+61)/9 = 9(2)1759<177> = 977189933 · 677436880567<12> · 4398981358728402973<19> · 4561677112603872026693843<25> · C113
C113 = P40 · P73
P40 = 7192656946027737524918319855947986687571<40>
P73 = 9652098648828096511437545492127071883766346870809662669210109599313691731<73>
Number: 92229_176 N=69424234390238348459735580768786661626522690519560994858731457507032720590703701430297457624005875684018103175401 ( 113 digits) Divisors found: r1=7192656946027737524918319855947986687571 (pp40) r2=9652098648828096511437545492127071883766346870809662669210109599313691731 (pp73) Version: GGNFS-0.77.1 Total time: 60.14 hours. Scaled time: 39.99 units (timescale=0.665). Factorization parameters were as follows: name: 92229_176 n: 69424234390238348459735580768786661626522690519560994858731457507032720590703701430297457624005875684018103175401 skew: 34725.81 # norm 9.38e+15 c5: 27840 c4: 1952949260 c3: 239570943857341 c2: 28653622092714987 c1: 4208411463039264573491 c0: -524927595336302835681939143 # alpha -6.17 Y1: 829057423733 Y0: -4779333281932956287892 # Murphy_E 6.01e-10 # M 1944097459749997755277490881319499555332311992419460999696824029213840783552124833372077496272187035996537581197 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2950001) Relations: rels:7512522, finalFF:623442 Initial matrix: 499633 x 623442 with sparse part having weight 54825480. Pruned matrix : 451822 x 454384 with weight 29284529. Polynomial selection time: 0.50 hours. Total sieving time: 51.68 hours. Total relation processing time: 0.79 hours. Matrix solve time: 6.71 hours. Time per square root: 0.46 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 60.14 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
10816+1 = 1(0)8151<817> = 97 · 353 · 449 · 641 · 1409 · 69857 · 206209 · 58627969 · 3156663361<10> · 66554101249<11> · 75118313082913<14> · 39127329514182768921189838418689<32> · 8274466617334672110426476083265843201<37> · [20613661601050142213000575997849301836417547662874985098970766781932900988120507408603473644982986488160619644274811516746717894883553676903578704941377044565165542482689618096760494994922455997632250274389555329<212>] · C471
C471 = P37 · P435
P37 = 4444442797021732533861519689020084897<37>
P435 = 182168885688800471032070314606442908018600300417083944518739710393647902382617378829742666164078393724922058999479539245587167427080499185116669904781913921946772253903767015005946741838709655930349163084737589584381983926389625045094948824590259228606134828950677303795021460411056135766667281810175120746691826141507834669471110707839979934576289109001841823875933756134673970083682689775540524930437792688282436257038622290979346977<435>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(22·10168-1)/3 = 7(3)168<169> = 7 · 56123 · 446327841017<12> · 430461185535167573<18> · 1409905188331436013487<22> · C113
C113 = P56 · P58
P56 = 13084049258809821588896439090996621938307031288296648457<56>
P58 = 5266746964258109491400138988161479038453646038826462079387<58>
Number: 73333_168 N=68910376714040195406347745240503361261758316416576282636203495308149851640887510416264286216165380927075165055859 ( 113 digits) Divisors found: r1=13084049258809821588896439090996621938307031288296648457 (pp56) r2=5266746964258109491400138988161479038453646038826462079387 (pp58) Version: GGNFS-0.77.1 Total time: 53.51 hours. Scaled time: 31.89 units (timescale=0.596). Factorization parameters were as follows: name: 73333_168 n: 68910376714040195406347745240503361261758316416576282636203495308149851640887510416264286216165380927075165055859 skew: 36941.64 # norm 5.22e+15 c5: 15600 c4: 4190341915 c3: 3039365141531 c2: -8922979585383379554 c1: 94148034217382755246189 c0: -5421494257068971161432225 # alpha -6.41 Y1: 975922912999 Y0: -5358309014913334727634 # Murphy_E 7.37e-10 # M 6599696211979593814265749664234017177559052514922972069100058083737370758216219483967420220531197055536338039220 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2750001) Relations: rels:7879379, finalFF:790755 Initial matrix: 500653 x 790755 with sparse part having weight 69627103. Pruned matrix : 390126 x 392693 with weight 22520690. Polynomial selection time: 0.53 hours. Total sieving time: 46.94 hours. Total relation processing time: 0.63 hours. Matrix solve time: 4.96 hours. Time per square root: 0.46 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 53.51 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
10849+1 = 1(0)8481<850> = 7 · 11 · 13 · 1699 · 241117 · 9170899 · 715880197 · 7198295568559013885196835567543447<34> · 61945573305222690279363663578823967<35> · 151168348012920493188164812150408056175148228488823<51> · [236981781933948043228112220789227624908212542569354344676500735171191136986262759275099377257787061318322981899812820646487731505276950534191352836827590738081581753192002166353465640625197<189>] · C515
C515 = P34 · C482
P34 = 1941850545413860134349140850659019<34>
C482 = [11974596042808172532294983252939558878410189694663843068971765344308532913676645715309213363442627278076993492211166595880998184306177956628823075306750747898909101048339462363861018906574913448147471222095530123865763276293471254728437236511524459858068517800257650185047651380759211520548387242736820413514544025166081207894531393549080448211783134185139166833148694113912674297086397341821453080768324146339882473885456877565040591000305223469402926705116035907018404340127773009<482>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Yousuke Koide / GMP-ECM
10816+1 = 1(0)8151<817> = 97 · 353 · 449 · 641 · 1409 · 69857 · 206209 · 58627969 · 3156663361<10> · 66554101249<11> · 75118313082913<14> · 8274466617334672110426476083265843201<37> · [20613661601050142213000575997849301836417547662874985098970766781932900988120507408603473644982986488160619644274811516746717894883553676903578704941377044565165542482689618096760494994922455997632250274389555329<212>] · C503
C503 = P32 · C471
P32 = 39127329514182768921189838418689<32>
C471 = [809639191841064628525439231464999860397773607701980496081352666339504925459847421412079302897545851796994671960772729238488139832762235263695725908656072122047265685298946436141716959730769253735737488429705565187437664314635095937428340389980720185899033798436170265716087449200924809607342324420823123105586292160476218717903066160195563389157166475672526475982627558029455580472138762318157710719436530508723203208044400504432618748282362705740783507784354366160306369<471>]
10822+1 = 1(0)8211<823> = 101 · 9901 · 718606649 · 40160350429<11> · 144389656548047821<18> · 2834523818368583744706086149<28> · [3430756550790484778909640352209879033892610315578901813821345434990400007261052844057102137330186660253398361164679549479441003751370060990401385264590147924466884786339105844110638415462294590233248989402615229312388735660453351624541145759819967937881<253>] · C500
C500 = P35 · C466
P35 = 16254031864650930002850269462824009<35>
C466 = [1518251219423747541558249786341574895284479899305883251990246801255766909229333395434458469693549966383795065664136418817339096752250299235950034967670343929013892055001964056060297891256021051404942653075694117320359458606226902427876452489321855322434222068318126282515684656661189152027802914755789408960326502178798522971472567196598942110678827737509377973305601271034834784135339840915115044044544939389765778113496729595022312073212316740002281949880005471741<466>]
10837+1 = 1(0)8361<838> = 7 · 11 · 13 · 19 · 373 · 1117 · 5023 · 44641 · 52579 · 70541929 · 3590254957<10> · 14175966169<11> · 261315626851<12> · 909090909090909090909090909091<30> · 183372282864547916749018225828651<33> · 18381907262281244633158190677786966663091011<44> · 4887054837129490444185770642291712106451445708466643483270887621857163512076927093556902832792696796518529880218993484798134507347686651311824503<145> · C525
C525 = P36 · C490
P36 = 108131551600520034721722272883130729<36>
C490 = [7045616588486799878229908819910336923888220571062351357216159107348231895397024661050209344237746338927104332618758413991185539098879237656670503260201568098865214938494573500927612773398337686887554455654975502630496905550466931864411689596634310312025533326809689061042921776515817300848267597128380147428873265628242289520724784622861753110448953054107116821206466090015933935448825960415332332679426815216857782017220038922288778308959959611010035857100841026102213598239576198581831053<490>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(34·10190-7)/9 = 3(7)190<191> = 37 · 109 · 6609437 · 60793981 · 16209889148099957<17> · 3026164475092149900973<22> · 5559395425785366046547<22> · C113
C113 = P47 · P67
P47 = 17700270697562795473798575278495575252228893343<47>
P67 = 4829510199492607911626007156104654630552733041153862475787361617117<67>
Number: 37777_190 N=85483637867659658567202674170495654476226505771174948815394154314847353949058264254404667624789110546175796152131 ( 113 digits) Divisors found: r1=17700270697562795473798575278495575252228893343 (pp47) r2=4829510199492607911626007156104654630552733041153862475787361617117 (pp67) Version: GGNFS-0.77.1 Total time: 57.54 hours. Scaled time: 38.27 units (timescale=0.665). Factorization parameters were as follows: name: 37777_190 n: 85483637867659658567202674170495654476226505771174948815394154314847353949058264254404667624789110546175796152131 skew: 29076.08 # norm 1.07e+16 c5: 36540 c4: -12185242756 c3: 256023137714363 c2: 11051642456086268502 c1: 18000780073429467449288 c0: -153367693679452411321236672 # alpha -6.17 Y1: 878574755927 Y0: -4718764285096744772323 # Murphy_E 6.34e-10 # M 75966605504227469208499904048510806763470040437426901577401200590832189731289766473179388615073537509657719698494 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2850001) Relations: rels:7507727, finalFF:633645 Initial matrix: 500994 x 633645 with sparse part having weight 54977270. Pruned matrix : 448761 x 451329 with weight 28155882. Total sieving time: 50.19 hours. Total relation processing time: 0.63 hours. Matrix solve time: 6.24 hours. Time per square root: 0.49 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 57.54 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(61·10173-7)/9 = 6(7)173<174> = 71 · 233 · 24742957991<11> · 31809119701353051742109<23> · 39660267116313906346259099<26> · C112
C112 = P28 · P29 · P56
P28 = 3760357206641161646188454939<28>
P29 = 17434053596101093960844893121<29>
P56 = 20021041886655596186926329100373757874861254953098046101<56>
Number: 67777_173 N=1312544851288681061657320385726742235100077386920141929455960788027209627857570783929880133267056183525631510519 ( 112 digits) Divisors found: r1=3760357206641161646188454939 (pp28) r2=17434053596101093960844893121 (pp29) r3=20021041886655596186926329100373757874861254953098046101 (pp56) Version: GGNFS-0.77.1 Total time: 43.90 hours. Scaled time: 26.21 units (timescale=0.597). Factorization parameters were as follows: name: 67777_173 n: 1312544851288681061657320385726742235100077386920141929455960788027209627857570783929880133267056183525631510519 skew: 24484.59 # norm 3.26e+15 c5: 20160 c4: -6931159530 c3: -62708438404343 c2: 2275074974729497200 c1: 32786546490054575521986 c0: 5415945762602193956372053 # alpha -6.42 Y1: 308438021903 Y0: -2305306742891941527290 # Murphy_E 8.41e-10 # M 54595772227758935359404905948683395924693960067717954361230432600020289149931447345402724142563475095733714275 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2550001) Relations: rels:7400610, finalFF:656339 Initial matrix: 500217 x 656339 with sparse part having weight 52225852. Pruned matrix : 433326 x 435891 with weight 23330329. Total sieving time: 37.25 hours. Total relation processing time: 0.59 hours. Matrix solve time: 5.59 hours. Time per square root: 0.47 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 43.90 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(25·10189-7)/9 = 2(7)189<190> = 23 · 53 · 37013 · 547635411247<12> · 330088629807359<15> · 3327653778948571<16> · 22683909170999073431738750101<29> · C112
C112 = P39 · P73
P39 = 856086520823564452415849992209116593237<39>
P73 = 5270401796810904687788561074505843101960974063751693547717781294407477621<73>
Number: 27777_189 N=4511919937574110062022680359046714142686606807038938468754742182604387963067074666966204626047764872601837449177 ( 112 digits) Divisors found: r1=856086520823564452415849992209116593237 (pp39) r2=5270401796810904687788561074505843101960974063751693547717781294407477621 (pp73) Version: GGNFS-0.77.1 Total time: 57.21 hours. Scaled time: 34.09 units (timescale=0.596). Factorization parameters were as follows: name: 27777_189 n: 4511919937574110062022680359046714142686606807038938468754742182604387963067074666966204626047764872601837449177 skew: 148044.23 # norm 4.56e+15 c5: 720 c4: -73626874 c3: -110867117727798 c2: 454455646419441839 c1: 510055059250966394606382 c0: 3954090739576303650823513256 # alpha -5.57 Y1: 234260784469 Y0: -5746536105901399508307 # Murphy_E 7.19e-10 # M 3185822251552743801476745947087601288349612792255263001652175728055263652166107759270387802466612664245102359504 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2850001) Relations: rels:7502977, finalFF:656719 Initial matrix: 500172 x 656719 with sparse part having weight 54894770. Pruned matrix : 438101 x 440665 with weight 25287702. Polynomial selection time: 0.50 hours. Total sieving time: 50.16 hours. Total relation processing time: 0.64 hours. Matrix solve time: 5.43 hours. Time per square root: 0.48 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 57.21 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(83·10169+61)/9 = 9(2)1689<170> = 3 · 112 · 306725482387<12> · 158097431899383477583<21> · 5128036316381592220298959<25> · C112
C112 = P50 · P62
P50 = 19700081684465458593403806555789969994895088533657<50>
P62 = 51860316780454489279897084658059454426917923044301608049721421<62>
Number: 92229_168 N=1021652476757208163560581079259281054181213711730300692671570682687015568804053712776559333447913768270232366597 ( 112 digits) Divisors found: r1=19700081684465458593403806555789969994895088533657 (pp50) r2=51860316780454489279897084658059454426917923044301608049721421 (pp62) Version: GGNFS-0.77.1 Total time: 48.14 hours. Scaled time: 28.69 units (timescale=0.596). Factorization parameters were as follows: name: 92229_168 n: 1021652476757208163560581079259281054181213711730300692671570682687015568804053712776559333447913768270232366597 skew: 42379.53 # norm 2.26e+15 c5: 5700 c4: 2476189901 c3: 2818036125079 c2: -3965150761651559721 c1: 20159536553490602897396 c0: 628219114223343985647383680 # alpha -5.92 Y1: 299274416299 Y0: -2822810127643404054087 # Murphy_E 8.41e-10 # M 998581722717076005120486833807822888215121894318500192856457073627922103911622034888560960264551830549271253187 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2650001) Relations: rels:7817263, finalFF:794068 Initial matrix: 500946 x 794068 with sparse part having weight 68271744. Pruned matrix : 385474 x 388042 with weight 21626578. Polynomial selection time: 0.52 hours. Total sieving time: 41.98 hours. Total relation processing time: 0.73 hours. Matrix solve time: 4.45 hours. Time per square root: 0.47 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 48.14 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
2·10168-9 = 1(9)1671<169> = 7 · 1087 · 8537489959<10> · 367694783292840547667053261930530350154041<42> · C113
C113 = P53 · P61
P53 = 17966034076031944574391153471623679589453353622292711<53>
P61 = 4660500063909969005743702902671272798968399002082218677735511<61>
Number: 19991_168 N=83730702959555558644286753585554649649572317505120979221312693092511006979457450320140886370830911981249481160321 ( 113 digits) Divisors found: r1=17966034076031944574391153471623679589453353622292711 (pp53) r2=4660500063909969005743702902671272798968399002082218677735511 (pp61) Version: GGNFS-0.77.1 Total time: 58.38 hours. Scaled time: 34.80 units (timescale=0.596). Factorization parameters were as follows: name: 19991_168 n: 83730702959555558644286753585554649649572317505120979221312693092511006979457450320140886370830911981249481160321 skew: 62536.04 # norm 1.67e+15 c5: 4800 c4: 542418002 c3: -30527202903432 c2: -187460816726501101 c1: 39811099175404160316726 c0: -1109743373310044488384538995 # alpha -5.38 Y1: 185480496509 Y0: -7052262054420382279818 # Murphy_E 6.92e-10 # M 75632762796499756649388024022841439022310180894940132867887513639978626189449917333412097122871594278740117554634 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2850001) Relations: rels:7719597, finalFF:707777 Initial matrix: 500741 x 707777 with sparse part having weight 61382861. Pruned matrix : 422570 x 425137 with weight 24650963. Total sieving time: 51.42 hours. Total relation processing time: 0.60 hours. Matrix solve time: 5.83 hours. Time per square root: 0.53 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 58.38 hours. --------- CPU info (if available) ----------
By CWI
10238+1 = 1(0)2371<239> = 29 · 101 · 281 · 2381 · 28559389 · 121499449 · 1491383821<10> · 275855329893529<15> · 2324557465671829<16> · 20087794479102305428621<23> · C152
C152 = P64 · P89
P64 = 5582637833682557709253612812885341475900082138954691763178176941<64>
P89 = 13712255219708533473813623053189821987961076229175414555827926545777661379291311684923609<89>Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(68·10198+13)/9 = 7(5)1977<199> = 33 · 2837 · 7305413 · 124068676637<12> · 403212889427768888832067867<27> · 1562091434865214888463863633<28> · C123
C123 = P57 · P66
P57 = 258170928787318894541525466230371667081514748966348106999<57>
P66 = 669249700255497765647229643415437163131542241223547798847162206127<66>
Number: 75557_198 N=172780816705596629436477571893915454694951908049723289731935734705261274963726310234006475949636958455314893409923089382873 ( 123 digits) Divisors found: r1=258170928787318894541525466230371667081514748966348106999 (pp57) r2=669249700255497765647229643415437163131542241223547798847162206127 (pp66) Version: GGNFS-0.77.1 Total time: 257.55 hours. Scaled time: 161.74 units (timescale=0.628). Factorization parameters were as follows: name: 75557_198 n: 172780816705596629436477571893915454694951908049723289731935734705261274963726310234006475949636958455314893409923089382873 skew: 242002.32 # norm 4.69e+16 c5: 5040 c4: 620918512 c3: -1283681869942759 c2: -25445850424152104787 c1: 26848786049597838801584727 c0: 58141808848337734262122548867 # alpha -5.97 Y1: 1075588169161 Y0: -509346087624359811646142 # Murphy_E 2.15e-10 # M 4224800078277202070226350581168509253931390803546482563682347130827643033159196813348775910046698793869083997859267081664 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [2500000, 7780001) Relations: rels:8271672, finalFF:788713 Initial matrix: 697784 x 788713 with sparse part having weight 89212794. Pruned matrix : 662576 x 666128 with weight 65904764. Total sieving time: 227.99 hours. Total relation processing time: 4.58 hours. Matrix solve time: 24.26 hours. Time per square root: 0.72 hours. Prototype def-par.txt line would be: gnfs,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000 total time: 257.55 hours. --------- CPU info (if available) ----------
By Kazumaro Aoki / GMP-ECM
(10371-1)/9 = (1)371<371> = 107 · 239 · 2969 · 4649 · 51199 · 1659431 · 1325815267337711173<19> · 47198858799491425660200071<26> · C304
C304 = P50 · C255
P50 = 26628696860763170757415075888614691991511099147227<50>
C255 = [222341721027911715633671961706217915116678982524266600828809108331318320649681568887402437710769278163500186590283610898584016236491957089336867945678571711723875925300701888125177904675751179148227068623232948215760382265117676642381699264210177060167843<255>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Bruce Dodson / GMP-ECM
10283+1 = 1(0)2821<284> = 11 · 1699 · 241117 · 61945573305222690279363663578823967<35> · C239
C239 = P51 · C189
P51 = 151168348012920493188164812150408056175148228488823<51>
C189 = [236981781933948043228112220789227624908212542569354344676500735171191136986262759275099377257787061318322981899812820646487731505276950534191352836827590738081581753192002166353465640625197<189>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Torbjörn Granlund / GMP-ECM
10395+1 = 1(0)3941<396> = 11 · 1423 · 9091 · 9615060929<10> · 6295632499623851<16> · 4539787279569136988691351491<28> · 24966203549341539495819194854679625225811<41> · 66443174541490579097997510158021076958392938976011506949065646573<65> · C229
C229 = P47 · P182
P47 = 36135553580039597739744803188558136917651907171<47>
P182 = 42660530392229903351072436102344244250617560023502875336329183331096805000157530395542396500243031769146588091361465456452731316179986315200680926557940585563325081869311166989363491<182>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(32·10183-23)/9 = 3(5)1823<184> = 11 · 19 · 17397387712532638583<20> · 90684212543160708737<20> · 15029772282548630768461<23> · C120
C120 = P40 · P81
P40 = 1923668077538699854190851222644599554517<40>
P81 = 372960566449273440535593005370695937455230440600272291890122994647120883283696071<81>
Number: 35553_183 N=717452335859218360167438927623765212076802428464127319102516042017826581473819680378277934646358498808266801495823202707 ( 120 digits) Divisors found: r1=1923668077538699854190851222644599554517 (pp40) r2=372960566449273440535593005370695937455230440600272291890122994647120883283696071 (pp81) Version: GGNFS-0.77.1 Total time: 146.56 hours. Scaled time: 87.35 units (timescale=0.596). Factorization parameters were as follows: name: 35553_183 n: 717452335859218360167438927623765212076802428464127319102516042017826581473819680378277934646358498808266801495823202707 skew: 103830.10 # norm 4.16e+16 c5: 18360 c4: 9620368916 c3: 7177488075314 c2: -81657829878091490664 c1: 1933461944338510949361607 c0: -313681924961620863382406111 # alpha -5.66 Y1: 1710720816299 Y0: -131335908490248459876552 # Murphy_E 2.70e-10 # M 481970025387192072510914688544626149162622798462491063577737582196652254614879116165880736905817348899803797752005002797 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 Sieved special-q in [2250000, 5190001) Relations: rels:7895878, finalFF:708277 Initial matrix: 631562 x 708277 with sparse part having weight 69096069. Pruned matrix : 599687 x 602908 with weight 50233403. Polynomial selection time: 1.50 hours. Total sieving time: 125.46 hours. Total relation processing time: 2.04 hours. Matrix solve time: 16.85 hours. Time per square root: 0.70 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: 146.56 hours. --------- CPU info (if available) ----------
By Makoto Kamada / PFGW
(14·1011279-11)/3 = 4(6)112783<11280> is PRP. This is the 26th prime or PRP of the form 466...663 including 43.
(14·1019677-11)/3 = 4(6)196763<19678> is PRP. This is the 27th prime or PRP of the form 466...663 including 43.
Primality testing (14*10^11279-11)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 167 Running N-1 test using base 193 Running N-1 test using base 223 Running N+1 test using discriminant 3, base 1+sqrt(3) Running N+1 test using discriminant 3, base 3+sqrt(3) Running N+1 test using discriminant 3, base 4+sqrt(3) Calling N+1 BLS with factored part 0.04% and helper 0.01% (0.13% proof) (14*10^11279-11)/3 is Fermat and Lucas PRP! (136.2094s+0.0010s) Primality testing (14*10^19677-11)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 139 Running N+1 test using discriminant 191, base 2+sqrt(191) Calling N-1 BLS with factored part 0.18% and helper 0.04% (0.57% proof) (14*10^19677-11)/3 is Fermat and Lucas PRP! (208.3531s+0.0015s)
Note:
(14·1011279-11)/3-1 = 42·R11279, 11279 is prime.
(14·1019677-11)/3-1 = 42·R19677, 19677 = 3 · 7 · 937.
By Yousuke Koide / GMP-ECM
10563+1 = 1(0)5621<564> = 11 · 12498601 · 579098423 · 5089082809028683211<19> · 29283791702184825961<20> · C508
C508 = P35 · P474
P35 = 36265008707438890601092610924794499<35>
P474 = 232401494054570096143564993567696213375160353588417043090684984008451459670563877848647221789116648084601933880604986363761579421580159899581971059471764334988754554032162111036734709558829222890387903668986840084368851089124293184850568488971261475110622313574444779882860262870083592445443612475383694609460996337539641013578225997858543638658915937776380907660097061600787534395165252920449980799649154737825244060326194223564696221792437925158704683354257701429283783173<474>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, Msieve v. 1.03
(86·10159+31)/9 = 9(5)1589<160> = 11 · 79 · 11174459 · 1502356653904533350741<22> · C129
C129 = P35 · P95
P35 = 32925940611028209913897631506414729<35>
P95 = 19892914848838805121187170889842741939087687000043733872145367908159923963535199308109148910261<95>
(86·10197+31)/9 = 9(5)1969<198> = 11 · 383 · 389 · 6551821 · 889779406597<12> · 16240097980183799<17> · 6326590128437676415873<22> · C135
C135 = P36 · P50 · P51
P36 = 257061712718000124573629082190241723<36>
P50 = 17202872520442432210877384770546939996230403362031<50>
P51 = 220127243508692213597620396060520447620885683353701<51>
(83·10152+61)/9 = 9(2)1519<153> = 53 · 49553849717<11> · 317701005474431<15> · C127
C127 = P34 · P47(1095...) · P47(2796...)
P34 = 3608239190673295798991471185907989<34>
P47(1095...) = 10951667146070503349365880660080570035257139853<47>
P47(2796...) = 27969723271484245196929127184512281242928180627<47>
(83·10158+61)/9 = 9(2)1579<159> = C159
C159 = P39 · C121
P39 = 117545651888135840815842818880953169751<39>
C121 = [7845651518440422046274124148055206572053296058018576850355756519442414234698093136206369834368093919414710356459458036979<121>]
(83·10165+61)/9 = 9(2)1649<166> = 11 · 53 · 15467 · 624066075792757767593189<24> · C136
C136 = P32 · P43 · P62
P32 = 77015221797071783144018776142779<32>
P43 = 1363983398260425583802572468420050762256249<43>
P62 = 15600722535588390596249739026257013695088784067038703180701031<62>
(83·10170+61)/9 = 9(2)1699<171> = 7883 · 19441 · 2000351 · 2106457109<10> · C148
C148 = P32 · P117
P32 = 10246654667775461302966534591093<32>
P117 = 139374886901991284309920528691380173177220939093427095206182914573598399192602401679574826904949867314936196243568889<117>
(83·10182+61)/9 = 9(2)1819<183> = 773 · 5849 · C177
C177 = P26 · P152
P26 = 18323924688912353458934957<26>
P152 = 11131558409804658552975136550245961802897585754926764622588590174425550785078755590086633257634460716644299002312941445512090775542751313517232875571261<152>
(83·10187+61)/9 = 9(2)1869<188> = 3 · 11 · 92051 · 30067547 · C175
C175 = P32 · C143
P32 = 84311270917687423566615482497229<32>
C143 = [11975936863183358248554497011506440623051685644174883289393187724496404341718218435134527037287517064098894745988460538796464883046662025611401<143>]
(83·10188+61)/9 = 9(2)1879<189> = 446309 · 1434847 · 11812329767321731<17> · C162
C162 = P33 · P129
P33 = 813358403948275531485764881346537<33>
P129 = 149891436995987972781929490337435011368175402050551513955225614585203280820778471440295188112515448467155816910188061801267258909<129>
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
3·10167-1 = 2(9)167<168> = 7 · 7643 · 5308447 · 22854213927330216399615920416772214007<38> · C119
C119 = P59 · P61
P59 = 39688758719895871031552328771144713882109670630545445702193<59>
P61 = 1164549798963657623144995222566231913164712125722393092919267<61>
Number: 29999_167 N=46219535988371850084418374386615219342097027661120626172731378243865022947240172061060017102055950948979932685073852531 ( 119 digits) Divisors found: r1=39688758719895871031552328771144713882109670630545445702193 (pp59) r2=1164549798963657623144995222566231913164712125722393092919267 (pp61) Version: GGNFS-0.77.1 Total time: 127.93 hours. Scaled time: 76.25 units (timescale=0.596). Factorization parameters were as follows: name: 29999_167 n: 46219535988371850084418374386615219342097027661120626172731378243865022947240172061060017102055950948979932685073852531 skew: 124276.53 # norm 6.35e+16 c5: 3780 c4: 9000258924 c3: -554045092292200 c2: -39482819237992107286 c1: 3932121986615762035288899 c0: 70617401508006264190233896568 # alpha -6.80 Y1: 977912957527 Y0: -104103375987437644398895 # Murphy_E 3.22e-10 # M 38938266427990170016457106322341826580574242911371250299063807152482269131899914371350670090841862042894144699664069961 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 Sieved special-q in [2250000, 4770001) Relations: rels:7833087, finalFF:739482 Initial matrix: 632170 x 739482 with sparse part having weight 66718778. Pruned matrix : 591810 x 595034 with weight 42684964. Polynomial selection time: 1.71 hours. Total sieving time: 109.90 hours. Total relation processing time: 1.73 hours. Matrix solve time: 13.85 hours. Time per square root: 0.75 hours. Prototype def-par.txt line would be: gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 127.93 hours. --------- CPU info (if available) ----------
By Bruce Dodson / GMP-ECM
10610+1 = 1(0)6091<611> = 101 · 3541 · 6101 · 21961 · 27961 · 51241 · 1587221 · 9818561 · 81183810541<11> · 217345835281<12> · 555818110301<12> · 28474644365651641<17> · 8950221294967070861<19> · 17751033585336286181<20> · 17716886277230798340041<23> · 101444162656037151745878558385892753596849<42> · 75743388768260974116327848920184337528059461788181539337429709<62> · [24117462560776940857674798510867129035516104161041003845211930699998253738773357627145166937584558542746371549244626963892247670300659074689156318263222623146762142584127818541<176>] · C185
C185 = P50 · P136
P50 = 39069669288697789469488625615834711944836425801981<50>
P136 = [1642269048916396301246801744101379821902073519810571143520576971928815724659633161556699837755221303434764527770131486856721570324295821<136>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Yousuke Koide / GMP-ECM
10557+1 = 1(0)5561<558> = 11 · 88007 · 179268223 · 344577275324047<15> · C529
C529 = P38 · C491
P38 = 20862619931001299769258280552030071437<38>
C491 = [80155126803992958974081271951622621798563080439375689086151511748888857024774801881444988889327039297111156006793190146899843106382703618789533002233930062113834145634448902443144669556151584614671871116613397376475754027410164847877952704878442901102913032214159979400648826552464374616727772570384213045693621664436916530380113597719242206587830138898336553329158672161855285016711264338141948902686341480347249217048265971292294117681897203483787177184016190823523188622792220861985797929<491>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(14·10178-41)/9 = 1(5)1771<179> = 18077 · 970583 · 1735406205257<13> · 1745824177303<13> · 390328319148709270682251559<27> · C117
C117 = P41 · P76
P41 = 82809502531065408728209262767741242648467<41>
P76 = 9053460294396930637785159619418341915179225744274958113717340351294912094247<76>
Number: 15551_178 N=749712543163762808092051180657424884788820203073702176064721437535025801283241160904783569650296980815170595794069349 ( 117 digits) Divisors found: r1=82809502531065408728209262767741242648467 (pp41) r2=9053460294396930637785159619418341915179225744274958113717340351294912094247 (pp76) Version: GGNFS-0.77.1 Total time: 90.52 hours. Scaled time: 60.19 units (timescale=0.665). Factorization parameters were as follows: name: 15551_178 n: 749712543163762808092051180657424884788820203073702176064721437535025801283241160904783569650296980815170595794069349 skew: 37242.91 # norm 6.09e+15 c5: 64800 c4: 6759976239 c3: -240101464909709 c2: -7631822091175545737 c1: 136429241778261841168464 c0: 1961043974935176328332864300 # alpha -5.23 Y1: 3236659220977 Y0: -25862042449072322628529 # Murphy_E 4.05e-10 # M 349385423445357336464828299975167497040480146975800760950577244763433429412923324641596525897204278449812482008715321 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 Sieved special-q in [2250000, 3990001) Relations: rels:7690204, finalFF:756389 Initial matrix: 631392 x 756389 with sparse part having weight 61408642. Pruned matrix : 578158 x 581378 with weight 35000223. Polynomial selection time: 2.42 hours. Total sieving time: 74.78 hours. Total relation processing time: 1.15 hours. Matrix solve time: 11.46 hours. Time per square root: 0.70 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 90.52 hours. --------- CPU info (if available) ----------
By Greg Childers
(34·1015768-43)/9 = 3(7)157673<15769> is prime!
It was proved using the CHG code of John Renze. The method of proof and the certificates are available at http://www.pa.uky.edu/~childers/certs/P15769.zip
Congratulations!
The related informations are here: Primality proof of (34*10^15768-43)/9 - need help! (Yahoo! Groups primeform)
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(4·10165-7)/3 = 1(3)1641<166> = 11 · 172 · 15451 · 9309257 · 118373216867<12> · 1155975658715129283281353<25> · C116
C116 = P42 · P75
P42 = 205021964377232851384274581785018821440921<42>
P75 = 103937930788557133839808815846377770465549706196596461958171966641700024737<75>
Number: 13331_165 N=21309558743574854304397255469491373814945851188552387301145377958263470546801882078579306491878134755335591684062777 ( 116 digits) Divisors found: r1=205021964377232851384274581785018821440921 (pp42) r2=103937930788557133839808815846377770465549706196596461958171966641700024737 (pp75) Version: GGNFS-0.77.1 Total time: 82.16 hours. Scaled time: 54.56 units (timescale=0.664). Factorization parameters were as follows: name: 13331_165 n: 21309558743574854304397255469491373814945851188552387301145377958263470546801882078579306491878134755335591684062777 skew: 74051.52 # norm 2.34e+16 c5: 15480 c4: 3522388296 c3: -263035411418048 c2: 17484999314447126873 c1: 419940854699164050454894 c0: -9021914749412741504826452520 # alpha -6.42 Y1: 232981020679 Y0: -16895086808506470960631 # Murphy_E 4.68e-10 # M 14447464806211217445904309749906213471132462194430118712249412815602202665304715034718787861457069930890043834109555 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 Sieved special-q in [2250000, 3810001) Relations: rels:7611728, finalFF:765966 Initial matrix: 632522 x 765966 with sparse part having weight 59940352. Pruned matrix : 572389 x 575615 with weight 32817222. Total sieving time: 69.56 hours. Total relation processing time: 1.39 hours. Matrix solve time: 10.53 hours. Time per square root: 0.69 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 82.16 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
10526+1 = 1(0)5251<527> = 101 · 5261 · 119929 · C516
C516 = P35 · C482
P35 = 13268398183394556944627542607703521<35>
C482 = [11826809890140660378338391428621739420944914204418270540548648343005259897590744879396431744264495055674553364129755077045241978687202365722448940256802260852123723223687570098653961560376654250917493622678295282473622845068332813346356170074002662358220640333931566540952269342710885379205798802761321264162169247021611517911394262594009242131813723180126329212661624008170532159618167368524165159364853029744154010198135065779112334150003021894547007767944159586907077014505010249<482>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(28·10157+17)/9 = 3(1)1563<158> = 35 · 11 · 15241 · 30689 · 20857099 · 305736526979514144882409<24> · C115
C115 = P52 · P63
P52 = 5531052712936917961623275670908807144590636709264557<52>
P63 = 705523257741806994604431331044786408191814533429843056689276487<63>
Number: 31113_157 N=3902286328772913985808676036444149479620450834825575137775166222776897795611767518523557612486876817421306202571259 ( 115 digits) Divisors found: r1=5531052712936917961623275670908807144590636709264557 (pp52) r2=705523257741806994604431331044786408191814533429843056689276487 (pp63) Version: GGNFS-0.77.1 Total time: 72.69 hours. Scaled time: 48.34 units (timescale=0.665). Factorization parameters were as follows: name: 31113_157 n: 3902286328772913985808676036444149479620450834825575137775166222776897795611767518523557612486876817421306202571259 skew: 111063.39 # norm 1.68e+16 c5: 4200 c4: 3846257440 c3: -55901044728118 c2: -31732745539522374884 c1: -796641630993524085413841 c0: 32181874432829360357010466365 # alpha -6.43 Y1: 1288462748353 Y0: -15617352258803599959586 # Murphy_E 4.96e-10 # M 2091860557216746714576578794995371925399048065820019879931480116988906787342221899432500462446408416880157916828661 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 3150001) Relations: rels:7440531, finalFF:577703 Initial matrix: 499902 x 577703 with sparse part having weight 50403483. Pruned matrix : 469571 x 472134 with weight 32720714. Polynomial selection time: 0.50 hours. Total sieving time: 62.31 hours. Total relation processing time: 0.91 hours. Matrix solve time: 8.41 hours. Time per square root: 0.56 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 72.69 hours. --------- CPU info (if available) ----------
By Makoto Kamada / GGNFS-0.77.1-20050930-pentium4
(7·10151-1)/3 = 2(3)151<152> = 17 · 4794211 · C144
C144 = P62 · P83
P62 = 21673976374827387979429628274383243276327347868031316908486251<62>
P83 = 13209066428165039913538933609092428550233210679041990355672812502768300544328111909<83>
Number: 23333_151 N=286292993697574666040961059240887337977030230507454208631953796597032317092590274755426950561506653034048690773755526175623222322447946115863159 ( 144 digits) SNFS difficulty: 151 digits. Divisors found: r1=21673976374827387979429628274383243276327347868031316908486251 (pp62) r2=13209066428165039913538933609092428550233210679041990355672812502768300544328111909 (pp83) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 26.78 hours. Scaled time: 16.44 units (timescale=0.614). Factorization parameters were as follows: n: 286292993697574666040961059240887337977030230507454208631953796597032317092590274755426950561506653034048690773755526175623222322447946115863159 m: 1000000000000000000000000000000 c5: 70 c0: -1 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:176833, largePrimes:5577813 encountered Relations: rels:5534752, finalFF:516451 Max relations in full relation-set: 28 Initial matrix: 353202 x 516451 with sparse part having weight 46378725. Pruned matrix : 284926 x 286756 with weight 24102058. Total sieving time: 23.94 hours. Total relation processing time: 0.24 hours. Matrix solve time: 2.51 hours. Time per square root: 0.09 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: 26.78 hours. --------- CPU info (if available) ----------
By Herman te Riele / GMP-ECM
10382+1 = 1(0)3811<383> = 101 · 77929 · 106961 · C371
C371 = P47 · C324
P47 = 13968004259021399202183274452648726337203224861<47>
C324 = [850393064402012666744482907848502515341494454491910072839871008358233226408384942430276781401143673123159329816093549352983410346709470834405150582792012803493237246693515128580540497732985722494237458711874709969154969748305639862674398403145342742584691000307403742442619500709721633892588569975004520484288234238028276889<324>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(71·10162-17)/9 = 7(8)1617<163> = 3 · 243502289 · 116444549857<12> · 128270027616314750452923569549<30> · C114
C114 = P43 · P72
P43 = 3386184936137402790776200334857258952729771<43>
P72 = 213518991010401372381688432413728927073750464555050022709806288337774787<72>
Number: 78887_162 N=723014790938678651721147391990553557307168178882364588086043927423948319684735855253124973472587538762189468083777 ( 114 digits) Divisors found: r1=3386184936137402790776200334857258952729771 (pp43) r2=213518991010401372381688432413728927073750464555050022709806288337774787 (pp72) Version: GGNFS-0.77.1 Total time: 65.96 hours. Scaled time: 39.38 units (timescale=0.597). Factorization parameters were as follows: name: 78887_162 n: 723014790938678651721147391990553557307168178882364588086043927423948319684735855253124973472587538762189468083777 skew: 46149.34 # norm 7.15e+15 c5: 12060 c4: -2736605976 c3: -44691865616191 c2: -3100143244501198126 c1: 20887871137226227608648 c0: 1061224024356544925135754180 # alpha -5.93 Y1: 762409635149 Y0: -9027378239651588136263 # Murphy_E 5.82e-10 # M 605779985268998323829240402100043274437028440935658503297164474505831869806567549361974091435657964544874132311457 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2950001) Relations: rels:7527514, finalFF:620031 Initial matrix: 501181 x 620031 with sparse part having weight 52823587. Pruned matrix : 455494 x 458063 with weight 28473787. Total sieving time: 57.75 hours. Total relation processing time: 0.62 hours. Matrix solve time: 6.99 hours. Time per square root: 0.60 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 65.96 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GMP-ECM 6.0.1 B1=11000000
(86·10156+31)/9 = 9(5)1559<157> = 13 · 487 · 53117 · 33675667 · 16469890637<11> · C131
C131 = P35 · P97
P35 = 45896092494621654893425012753765729<35>
P97 = 1116265380604458192056463779508427484700133652377805812712655330066850140540194073278282658605887<97>
(86·10172+31)/9 = 9(5)1719<173> = 32 · 23 · 59 · 79 · 1791454139<10> · 398614507270289<15> · C144
C144 = P34 · P111
P34 = 1342363415950343403713077647628357<34>
P111 = 103318380622337348816390846078358788840032723949972204188865763768829298668657709947217898275209152529423007011<111>
(86·10175+31)/9 = 9(5)1749<176> = 3 · 11 · 2849423 · C169
C169 = P36 · C133
P36 = 662096372245323070905807054281026159<36>
C133 = [1534842682831474675191613986513705075285853096908253230732277917454586669752032261197652469052432398524331417918409196804434169528839<133>]
(86·10184+31)/9 = 9(5)1839<185> = 3 · 349 · 13883077929495122457509792250269<32> · C151
C151 = P40 · P112
P40 = 3240633863300248064298285243088031837323<40>
P112 = 2028586508296212038657801271877882169058285697615801859876284958434006470077093431789681527730924938652681378831<112>
(86·10193+31)/9 = 9(5)1929<194> = 3 · 11 · 2699 · 46103930161<11> · 8491960607515969<16> · C163
C163 = P33 · C131
P33 = 193493468565567926104105693906747<33>
C131 = [14162074932095004056081428092843431186530927733017519258696552135554878856011970657843644107064766187698663624963481176743381279999<131>]
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(61·10153-7)/9 = 6(7)153<154> = 3 · 251 · 67901 · 16902449019944461<17> · 104893886986106263<18> · C113
C113 = P36P36 = 517325769482943481148002669266260899<36>
P78 = 144528086508799010588986000906479628320347052391513546996479503285853448618037<78>
Number: 67777_153 N=74768103565061870641605399739627354138013930489466959869231758097217372256549377910964390885085630752041839235263 ( 113 digits) Divisors found: r1=517325769482943481148002669266260899 (pp36) r2=144528086508799010588986000906479628320347052391513546996479503285853448618037 (pp78) Version: GGNFS-0.77.1 Total time: 61.92 hours. Scaled time: 36.84 units (timescale=0.595). Factorization parameters were as follows: name: 67777_153 n: 74768103565061870641605399739627354138013930489466959869231758097217372256549377910964390885085630752041839235263 skew: 55526.94 # norm 8.28e+15 c5: 12120 c4: -3386768743 c3: -88626093878374 c2: 243661300839375176 c1: 105379193533510512818766 c0: 1364060466056181859258457439 # alpha -5.81 Y1: 950254522657 Y0: -5728577268569493660032 # Murphy_E 6.06e-10 # M 16703589613663589708930353481129128065019775689439043582974894461469132433722410551782136824363891658249732324655 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2950001) Relations: rels:7552137, finalFF:638676 Initial matrix: 500743 x 638676 with sparse part having weight 56983765. Pruned matrix : 448464 x 451031 with weight 28731156. Polynomial selection time: 0.51 hours. Total sieving time: 53.34 hours. Total relation processing time: 0.95 hours. Matrix solve time: 6.62 hours. Time per square root: 0.52 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 61.92 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(71·10160-17)/9 = 7(8)1597<161> = 89 · 3491 · 78791 · 163337 · 494927 · 20992251737<11> · 25597988189016413<17> · C113
C113 = P53 · P61
P53 = 11466231815762675161044743195594232084784560019479973<53>
P61 = 6469758533064433639393094558069579940474812145379136995723789<61>
Number: 78887_160 N=74183751132125462572090856533831080834569538057811826337065936337992030749034836183025904719268995337840525177697 ( 113 digits) Divisors found: r1=11466231815762675161044743195594232084784560019479973 (pp53) r2=6469758533064433639393094558069579940474812145379136995723789 (pp61) Version: GGNFS-0.77.1 Total time: 53.10 hours. Scaled time: 31.65 units (timescale=0.596). Factorization parameters were as follows: name: 78887_160 n: 74183751132125462572090856533831080834569538057811826337065936337992030749034836183025904719268995337840525177697 skew: 38798.92 # norm 5.62e+15 c5: 39840 c4: -3837797312 c3: -158075269926546 c2: 997159671338664115 c1: 26196821511285852635928 c0: 601719853765070500366044775 # alpha -6.41 Y1: 475417808587 Y0: -4508154323163695216034 # Murphy_E 7.04e-10 # M 29623494024761047815194465994502172767121530326872775601150064441321500367062841145203088741769412509398727691366 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2750001) Relations: rels:7649183, finalFF:703646 Initial matrix: 500694 x 703646 with sparse part having weight 60474912. Pruned matrix : 420736 x 423303 with weight 24158497. Polynomial selection time: 0.56 hours. Total sieving time: 45.88 hours. Total relation processing time: 0.66 hours. Matrix solve time: 5.49 hours. Time per square root: 0.51 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 53.10 hours. --------- CPU info (if available) ----------
By Maksym Voznyy / GGNFS-0.77.1-20050930-pentium4
(7·10159-43)/9 = (7)1583<159> = 2198881 · 107554406636101703<18> · 108269558050928644841579<24> · C113
C113 = P54 · P59
P54 = 508913280753558081579008581881689241407143447291728103<54>
P59 = 59686408469391464479233088678668511871451520317771224765303<59>
Number: c113 N=30375205950554965254665724980216207052946917800227062425483231705034695663566872449662848892149586008209464410209 ( 113 digits) SNFS difficulty: 160 digits. Divisors found: r1=508913280753558081579008581881689241407143447291728103 (pp54) r2=59686408469391464479233088678668511871451520317771224765303 (pp59) Version: GGNFS-0.77.1-20050930-pentium4 Total time: -568.07 hours. Scaled time: -263.02 units (timescale=0.463). Factorization parameters were as follows: n: 30375205950554965254665724980216207052946917800227062425483231705034695663566872449662848892149586008209464410209 m: 100000000000000000000000000000000 c5: 7 c0: -430 skew: 2.5 type: snfs qintsize: 10000 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, 3790001) Primes: RFBsize:283146, AFBsize:283047, largePrimes:5637721 encountered Relations: rels:5645068, finalFF:636944 Max relations in full relation-set: 28 Initial matrix: 566258 x 636944 with sparse part having weight 41222443. Pruned matrix : 513332 x 516227 with weight 29866484. Total sieving time: 64.60 hours. Total relation processing time: -645.06 hours. Matrix solve time: 12.25 hours. Time per square root: 0.14 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: -568.07 hours. --------- CPU info (if available) ----------
By Patrick Keller / GMP-ECM B1=1000000
(85·10186+41)/9 = 9(4)1859<187> = 72 · 73 · 2963 · 13879 · 15569 · 249311 · C167
C167 = P38 · C130
P38 = 13535091039564671486279847232684736987<38>
C130 = [1222093145661488304689087334206869992908799364801631751346153045069664958899170583005647688332917002870930209205870065660169052657<130>]
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
(37·10168-1)/9 = 4(1)168<169> = 681773 · 358640627 · 925410356462034774743<21> · 2027784404324172549427<22> · C112
C112 = P56 · P57
P56 = 61132896250125153035803780936000573049046898692303340201<56>
P57 = 146564511853610321058927580714084417649617753103996081381<57>
Number: 41111_168 N=8959913097096997938824188495967634805981158290247231678875205600280440323115153722167798653658628998881324897581 ( 112 digits) Divisors found: r1=61132896250125153035803780936000573049046898692303340201 (pp56) r2=146564511853610321058927580714084417649617753103996081381 (pp57) Version: GGNFS-0.77.1 Total time: 49.32 hours. Scaled time: 32.79 units (timescale=0.665). Factorization parameters were as follows: name: 41111_168 n: 8959913097096997938824188495967634805981158290247231678875205600280440323115153722167798653658628998881324897581 skew: 40427.59 # norm 2.40e+15 c5: 26100 c4: 2196431592 c3: -127573556116769 c2: -3240983120379717400 c1: 93050782877412745697718 c0: 784802897791216925783383232 # alpha -5.73 Y1: 331254086647 Y0: -3214636746423654432877 # Murphy_E 7.34e-10 # M 6577919040614998762593170428792988826678863704808659218722799705188626767732335579311257019642666960033159299411 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2650001) Relations: rels:7281400, finalFF:599694 Initial matrix: 500888 x 599694 with sparse part having weight 47516870. Pruned matrix : 457312 x 459880 with weight 26788343. Polynomial selection time: 0.51 hours. Total sieving time: 41.75 hours. Total relation processing time: 0.62 hours. Matrix solve time: 5.95 hours. Time per square root: 0.49 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 49.32 hours. --------- CPU info (if available) ----------
By Patrick Keller / GGNFS-0.77.1-20050930-pentium4 gnfs
(10187+53)/9 = (1)1867<187> = 7 · 71 · 197 · 4523 · 90019 · 131374937 · 44730961183<11> · 764090474173501457<18> · 1003033405098351401377991<25> · C112
C112 = P38 · P75
P38 = 16462583911544611673142425725427372749<38>
P75 = 375919771891371586331252948799948552812814320677059444957657343601244135613<75>
Number: 2 N=6188610788770414212796511211495988489540391349491968058312867831046678507555599713712584325000581110482056610137 ( 112 digits) Divisors found: r1=16462583911544611673142425725427372749 (pp38) r2=375919771891371586331252948799948552812814320677059444957657343601244135613 (pp75) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 27.41 hours. Scaled time: 18.26 units (timescale=%1.3lf). Factorization parameters were as follows: name: 2 n: 6188610788770414212796511211495988489540391349491968058312867831046678507555599713712584325000581110482056610137 skew: 21795.31 # norm 8.31e+014 c5: 38880 c4: -120636723 c3: -5646870886264 c2: -84505874040617561 c1: -12229642424486779772215 c0: -10006425163572188338251900 # alpha -5.32 Y1: 1030176524267 Y0: -2756598296849159231369 # Murphy_E 7.71e-010 # M 3327217392231341839193020182372575084355003187604176097066870872073360700330416454572036356484618763494826886338 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 200000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2750001) Relations: rels:7750950, finalFF:745908 Initial matrix: 500763 x 745908 with sparse part having weight 63844677. Pruned matrix : 405254 x 407821 with weight 22768815. Polynomial selection time: 0.52 hours. Total sieving time: 22.26 hours. Total relation processing time: 0.33 hours. Matrix solve time: 4.08 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,200000 total time: 27.41 hours. --------- CPU info (if available) ----------
By Maksym Voznyy / GGNFS-0.77.1-20050930-pentium4
(46·10151-1)/9 = 5(1)151<152> = 3 · 100613 · 11252677 · 17561028246989<14> · 254884347047509<15> · C112
C112 = P36 · P77
P36 = 163142891746432375615001387087556691<36>
P77 = 20607383487557504808781535006630386430436651273368978693125608058034215922407<77>
Number: c112 N=3361948133487812075077922500985184449851754373875089188887233786612314488240147798191074701287201289454469675237 ( 112 digits) SNFS difficulty: 152 digits. Divisors found: r1=163142891746432375615001387087556691 (pp36) r2=20607383487557504808781535006630386430436651273368978693125608058034215922407 (pp77) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 40.64 hours. Scaled time: 19.02 units (timescale=0.468). Factorization parameters were as follows: n: 3361948133487812075077922500985184449851754373875089188887233786612314488240147798191074701287201289454469675237 m: 1000000000000000000000000000000 c5: 460 c0: -1 skew: 0.4 type: snfs qintsize: 20000 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, 1960001) Primes: RFBsize:176302, AFBsize:176118, largePrimes:5294119 encountered Relations: rels:5123433, finalFF:422966 Max relations in full relation-set: 28 Initial matrix: 352487 x 422966 with sparse part having weight 34954044. Pruned matrix : 312226 x 314052 with weight 22744841. Total sieving time: 31.87 hours. Total relation processing time: 0.43 hours. Matrix solve time: 8.25 hours. Time per square root: 0.10 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: 40.64 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1 gnfs
8·10158-3 = 7(9)1577<159> = 47 · 73 · 163 · 7715837 · 5875170743947<13> · 18583538108533323516211<23> · C112
C112 = P30 · P82
P30 = 288901606894446877454247126479<30>
P82 = 5877596490240672347764431371309125446211638140185245222440610912673511074017720739<82>
Number: 79997_158 N=1698047070707691395420746408981023416719231061576173416181875824650185270803056769051905000529016826215834347981 ( 112 digits) Divisors found: r1=288901606894446877454247126479 (pp30) r2=5877596490240672347764431371309125446211638140185245222440610912673511074017720739 (pp82) Version: GGNFS-0.77.1 Total time: 49.27 hours. Scaled time: 32.76 units (timescale=0.665). Factorization parameters were as follows: name: 79997_158 n: 1698047070707691395420746408981023416719231061576173416181875824650185270803056769051905000529016826215834347981 skew: 34286.38 # norm 4.83e+15 c5: 9000 c4: -4462864515 c3: -64241300805211 c2: 1453846801432205282 c1: -26683572554404993280571 c0: 263662311370362904945670067 # alpha -6.21 Y1: 359421792191 Y0: -2851982598484250583104 # Murphy_E 7.76e-10 # M 1118129559379046546854714597668784376529084592686110336061756095364521516843937336546128904918463162740256522637 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2650001) Relations: rels:7253879, finalFF:587691 Initial matrix: 500957 x 587691 with sparse part having weight 45582024. Pruned matrix : 461255 x 463823 with weight 27086263. Polynomial selection time: 0.50 hours. Total sieving time: 41.11 hours. Total relation processing time: 0.75 hours. Matrix solve time: 6.45 hours. Time per square root: 0.45 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 49.27 hours. --------- CPU info (if available) ----------
By Patrick Keller / GGNFS-0.77.1-20050930-pentium4 gnfs
(79·10165-7)/9 = 8(7)165<166> = 181787 · 6947861 · 471250250494729967<18> · 146631661811942550414576793<27> · C111
C111 = P33 · P78
P33 = 505183798145073606671326082895157<33>
P78 = 199086528382066627439016425618280593244587507522519767719428521573572672432733<78>
Number: 2 N=100575288567569414650753061908992433831162812137784021232130567965686212874475190732266862757968646178973974081 ( 111 digits) Divisors found: r1=505183798145073606671326082895157 (pp33) r2=199086528382066627439016425618280593244587507522519767719428521573572672432733 (pp78) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 25.27 hours. Scaled time: 16.88 units (timescale=%1.3lf). Factorization parameters were as follows: name: 2 n: 100575288567569414650753061908992433831162812137784021232130567965686212874475190732266862757968646178973974081 skew: 41634.78 # norm 4.86e+015 c5: 14160 c4: 2304193002 c3: -83720342315739 c2: 1686585772450806812 c1: 45998111723386131551140 c0: -776680905380863451921695600 # alpha -6.55 Y1: 767339486963 Y0: -1480056448132856254239 # Murphy_E 9.24e-010 # M 1117747378090499295948109067179419719161638564223783773069029778808966385056414571852861383687546909976534536 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1600000, 2350001) Relations: rels:7212017, finalFF:564444 Initial matrix: 459888 x 564444 with sparse part having weight 45344626. Pruned matrix : 415592 x 417955 with weight 24057004. Total sieving time: 20.47 hours. Total relation processing time: 0.38 hours. Matrix solve time: 4.22 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 25.27 hours. --------- CPU info (if available) ----------
By Patrick Keller / GGNFS-0.77.1-20050930-pentium4 gnfs
(5·10167+13)/9 = (5)1667<167> = 32 · 4027 · 10463 · 12941 · 44897457148379489<17> · 1519650041086432620438421693<28> · C111
C111 = P37 · P75
P37 = 1001555099341379538477781614644711869<37>
P75 = 165668185679698740547711081846511427600993641940174707427260998637343088981<75>
Number: 2 N=165925816166136783147225072078845728669837032683683114399003933918276111210507446722985872485375711425173815489 ( 111 digits) Divisors found: r1=1001555099341379538477781614644711869 (pp37) r2=165668185679698740547711081846511427600993641940174707427260998637343088981 (pp75) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 26.12 hours. Scaled time: 17.27 units (timescale=%1.3lf). Factorization parameters were as follows: name: 2 n: 165925816166136783147225072078845728669837032683683114399003933918276111210507446722985872485375711425173815489 skew: 39402.35 # norm 2.87e+015 c5: 2760 c4: -1796268948 c3: -3542165988808 c2: -153924170064893167 c1: -1523943674560155151998 c0: -77864042459289411013639504 # alpha -5.39 Y1: 325574065619 Y0: -2268867260185188064005 # Murphy_E 7.81e-010 # M 68795449822125752170511759654875711714200059898916396981004545201485519359004288023996397211130284425818863789 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 Sieved special-q in [1600000, 2500001) Relations: rels:7293097, finalFF:562048 Initial matrix: 461329 x 562048 with sparse part having weight 47664987. Pruned matrix : 421158 x 423528 with weight 26372876. Total sieving time: 20.36 hours. Total relation processing time: 0.38 hours. Matrix solve time: 5.19 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,200000 total time: 26.12 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1
(83·10151+61)/9 = 9(2)1509<152> = 3 · 11 · 17 · 733 · 40329493663<11> · C136
C136 = P58 · P79
P58 = 4266817943380179456442463705074607914097928139686406991771<58>
P79 = 1303292406197656724391669573637441907482304621617005899880147521482913023505621<79>
Number: 92229_151 N=5560911424235291114762797245319179861381456751514177216307994652416449166451578809099682022150998090569967412440150646011850523319244791 ( 136 digits) SNFS difficulty: 152 digits. Divisors found: r1=4266817943380179456442463705074607914097928139686406991771 (pp58) r2=1303292406197656724391669573637441907482304621617005899880147521482913023505621 (pp79) Version: GGNFS-0.77.1 Total time: 51.11 hours. Scaled time: 30.46 units (timescale=0.596). Factorization parameters were as follows: name: 92229_151 n: 5560911424235291114762797245319179861381456751514177216307994652416449166451578809099682022150998090569967412440150646011850523319244791 m: 1000000000000000000000000000000 c5: 830 c0: 61 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2500001) Relations: rels:5525717, finalFF:420091 Initial matrix: 352078 x 420091 with sparse part having weight 41285447. Pruned matrix : 342863 x 344687 with weight 26911075. Total sieving time: 45.82 hours. Total relation processing time: 0.32 hours. Matrix solve time: 4.78 hours. Time per square root: 0.19 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: 51.11 hours. --------- CPU info (if available) ----------
By Patrick Keller / GGNFS-0.77.1-20050930-pentium4 gnfs
(85·10174+41)/9 = 9(4)1739<175> = 7 · 2017 · 11063449 · 13431161 · 862560884921<12> · 617545692656011875106207177777<30> · C115
C115 = P45 · P70
P45 = 950310447883283935373995072876758274438818959<45>
P70 = 8892912596211804531600808855278331945835416961840108159359737857615713<70>
By Yousuke Koide / GMP-ECM B1=48e6, GGNFS-0.77.1 gnfs
10465+1 = 1(0)4641<466> = 7 · 11 · 13 · 211 · 241 · 373 · 2161 · 9091 · 11161 · 44641 · 3590254957<10> · 3925963357681<13> · 5167617497664851<16> · 22672589441232691<17> · 909090909090909090909090909091<30> · 6548241632713397411808073416931<31> · 553114664478262993662992814601370587114291<42> · 18381907262281244633158190677786966663091011<44> · 4857900688365130469291831549890842547443917376935406225054646143856579892970236911030721<88> · C152
C152 = P46 · P49 · P58
P46 = 3093888678771257769541252942946202755752229401<46>
P49 = 1158334526259936604206939942487445760921582415411<49>
P58 = 3092189186638711651761630213691413266133197806226014052371<58>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1
(8·10152-71)/9 = (8)1511<152> = 3 · 43 · 1853927 · 4204279 · 7297846909<10> · 54055784093<11> · C117
C117 = P50 · P67
P50 =41852930861153999543319597376037498948438646374273<50>
P67 = 5354400016690058007150197629839830971822257922958622091177046313833<67>
Number: 88881_152 N=224097333701490818996657378545506420449477157334788271342455411233177004466153550173305245966022827936168245135218409 ( 117 digits) SNFS difficulty: 152 digits. Divisors found: r1=41852930861153999543319597376037498948438646374273 (pp50) r2=5354400016690058007150197629839830971822257922958622091177046313833 (pp67) Version: GGNFS-0.77.1 Total time: 47.04 hours. Scaled time: 28.04 units (timescale=0.596). Factorization parameters were as follows: name: 88881_152 n: 224097333701490818996657378545506420449477157334788271342455411233177004466153550173305245966022827936168245135218409 m: 1000000000000000000000000000000 c5: 800 c0: -71 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2400001) Relations: rels:5420617, finalFF:427342 Initial matrix: 352737 x 427342 with sparse part having weight 39372434. Pruned matrix : 342345 x 344172 with weight 24241100. Total sieving time: 41.88 hours. Total relation processing time: 0.33 hours. Matrix solve time: 4.69 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: 47.04 hours. --------- CPU info (if available) ----------
By Patrick Keller / GMP-ECM B1=1000000, Msieve v. 1.03
(29·10184+7)/9 = 3(2)1833<185> = 3 · 1609 · 141209 · 51361763 · 40099719731363732494892431187567<32> · C137
C137 = P38 · P44 · P55
P38 = 92263672187280138504843095427211568801<38>
P44 = 37954749951041472756030401435183280403544987<44>
P55 = 6554471536158162812921217408651094733184278319197338043<55>
Sat Feb 04 12:56:59 2006 Sat Feb 04 12:56:59 2006 Sat Feb 04 12:56:59 2006 Msieve v. 1.03 Sat Feb 04 12:56:59 2006 random seeds: ea6ba580 6866eb26 Sat Feb 04 12:56:59 2006 factoring 248773328216101756750898896613176208821881925232865782829696275230827569801647842746392670997040441 (99 digits) Sat Feb 04 12:57:01 2006 using multiplier of 1 Sat Feb 04 12:57:01 2006 sieve interval: 9 blocks of size 65536 Sat Feb 04 12:57:01 2006 processing polynomials in batches of 6 Sat Feb 04 12:57:01 2006 using a sieve bound of 2577437 (94049 primes) Sat Feb 04 12:57:01 2006 using large prime bound of 386615550 (28 bits) Sat Feb 04 12:57:01 2006 using double large prime bound of 2864855634283950 (43-52 bits) Sat Feb 04 12:57:01 2006 using trial factoring cutoff of 56 bits Sat Feb 04 12:57:01 2006 polynomial 'A' values have 13 factors Sat Feb 04 21:41:54 2006 56404 relations (17959 full + 38445 combined from 1160498 partial), need 94145 Sat Feb 04 21:41:55 2006 elapsed time 08:44:56 Sat Feb 04 22:05:29 2006 Sat Feb 04 22:05:29 2006 Sat Feb 04 22:05:29 2006 Msieve v. 1.03 Sat Feb 04 22:05:29 2006 random seeds: d6651c40 32698dee Sat Feb 04 22:05:29 2006 factoring 248773328216101756750898896613176208821881925232865782829696275230827569801647842746392670997040441 (99 digits) Sat Feb 04 22:05:30 2006 using multiplier of 1 Sat Feb 04 22:05:30 2006 sieve interval: 9 blocks of size 65536 Sat Feb 04 22:05:30 2006 processing polynomials in batches of 6 Sat Feb 04 22:05:30 2006 using a sieve bound of 2577437 (94049 primes) Sat Feb 04 22:05:30 2006 using large prime bound of 386615550 (28 bits) Sat Feb 04 22:05:30 2006 using double large prime bound of 2864855634283950 (43-52 bits) Sat Feb 04 22:05:30 2006 using trial factoring cutoff of 56 bits Sat Feb 04 22:05:30 2006 polynomial 'A' values have 13 factors Sat Feb 04 22:05:44 2006 restarting with 17959 full and 1160498 partial relations Sun Feb 05 00:06:02 2006 94364 relations (21827 full + 72537 combined from 1416464 partial), need 94145 Sun Feb 05 00:06:19 2006 begin with 1416464 relations Sun Feb 05 00:06:20 2006 reduce to 227453 relations in 12 passes Sun Feb 05 00:06:20 2006 attempting to read 21827 full and 227453 partial relations Sun Feb 05 00:06:35 2006 recovered 21827 full and 227453 partial relations Sun Feb 05 00:06:35 2006 recovered 240062 polynomials Sun Feb 05 00:06:35 2006 attempting to build 72537 cycles Sun Feb 05 00:06:35 2006 found 72537 cycles in 6 passes Sun Feb 05 00:06:36 2006 distribution of cycle lengths: Sun Feb 05 00:06:36 2006 length 2 : 16159 Sun Feb 05 00:06:36 2006 length 3 : 15890 Sun Feb 05 00:06:36 2006 length 4 : 12995 Sun Feb 05 00:06:36 2006 length 5 : 9994 Sun Feb 05 00:06:36 2006 length 6 : 6811 Sun Feb 05 00:06:36 2006 length 7 : 4521 Sun Feb 05 00:06:36 2006 length 8 : 2736 Sun Feb 05 00:06:36 2006 length 9+: 3431 Sun Feb 05 00:06:36 2006 largest cycle: 22 relations Sun Feb 05 00:06:37 2006 94049 x 94113 system, weight 6254417 (avg 66.46/col) Sun Feb 05 00:06:37 2006 reduce to 92804 x 92868 in 3 passes Sun Feb 05 00:10:09 2006 lanczos halted after 1470 iterations Sun Feb 05 00:10:09 2006 recovered 61 nontrivial dependencies Sun Feb 05 00:11:12 2006 prp44 factor: 37954749951041472756030401435183280403544987 Sun Feb 05 00:11:12 2006 prp55 factor: 6554471536158162812921217408651094733184278319197338043 Sun Feb 05 00:11:13 2006 elapsed time 02:05:44
By Maksym Voznyy / GGNFS-0.77.1-20050930-pentium4 gnfs
(86·10190+31)/9 = 9(5)1899<191> = 32 · 67 · 5471 · 611551 · 73815411636669551483<20> · 3170631581865285261257<22> · 6091316752293331060196299481596117<34> · C104
C104 = P33 · P71
P33 = 457211761022060630937323603497523<33>
P71 = 72663753848976855418724955088071884465133486342364370534508053286036233<71>
Number: c104 N=33222722859764244370420434977799235487750656254904937398689327484258018049044115562830311699136103750859 ( 104 digits) Divisors found: r1=457211761022060630937323603497523 (pp33) r2=72663753848976855418724955088071884465133486342364370534508053286036233 (pp71) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 16.86 hours. Scaled time: 7.82 units (timescale=0.464). Factorization parameters were as follows: name: c104 n: 33222722859764244370420434977799235487750656254904937398689327484258018049044115562830311699136103750859 skew: 27227.55 # norm 1.38e+014 c5: 1200 c4: -337183344 c3: -2381651633066 c2: 248938736692896209 c1: 1114387600843598108660 c0: -8590490841004470211810724 # alpha -5.80 Y1: 4931580409 Y0: -122589077603127855687 # Murphy_E 2.20e-009 # M 18111450033633959611018991800622801867540539784088860242535444057580236296942281954789823965040069650824 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 10000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1880001) Primes: RFBsize:169511, AFBsize:169766, largePrimes:4290847 encountered Relations: rels:4240040, finalFF:381754 Max relations in full relation-set: 28 Initial matrix: 339352 x 381754 with sparse part having weight 25810384. Pruned matrix : 304178 x 305938 with weight 16837141. Total sieving time: 13.97 hours. Total relation processing time: 0.26 hours. Matrix solve time: 2.44 hours. Time per square root: 0.19 hours. 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: 16.86 hours. --------- CPU info (if available) ----------
By Patrick Keller / GMP-ECM B1=1000000
(35·10173-53)/9 = 3(8)1723<174> = 11 · 19 · C172
C172 = P36 · C137
P36 = 106607187862536784442950213557216101<36>
C137 = [17453911169924557576039346133779902931162217477346570291829558559498426489621005591757758283994513516027454699330159557616319274222151687<137>]
(35·10194-53)/9 = 3(8)1933<195> = 61 · 617 · 7789 · 2163952582499<13> · 2326287941625511<16> · C159
C159 = P34 · P125
P34 = 6746993270905212529064277315866309<34>
P125 = 39057761165108223751807608888821277864278277187051226632566244066718880660497494906726063888182641266851221458785471976443931<125>
By Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, msieve 0.87
(86·10160+31)/9 = 9(5)1599<161> = 3 · 53 · 1613 · 3079 · 459013 · C147
C147 = P32 · P116
P32 = 14670887812170112648165750204273<32>
P116 = 17969391859802737625411698238094111071046415301119204415487275818924623166672293418294215899020175769928316811952687<116>
(86·10161+31)/9 = 9(5)1609<162> = 11 · 89 · 6781 · 10463 · 219000841 · 8485143186446374631<19> · C124
C124 = P35 · P44 · P47
P35 = 11172612558877304373318878010640487<35>
P44 = 11130475485219139561224467027642134977104237<44>
P47 = 59531916804317723800843666035300551575340273843<47>
(86·10165+31)/9 = 9(5)1649<166> = 11 · 198206262227<12> · 282920348903<12> · 56062580707273403<17> · C126
C126 = P33 · P93
P33 = 377200546525010742136261811904529<33>
P93 = 732548361104222114744378742455560736263367357613585076402263537276085872187790224738590321427<93>
(86·10185+31)/9 = 9(5)1849<186> = 11 · 79 · 109 · 89785291 · 1340814637898597<16> · C158
C158 = P30 · C129
P30 = 106445252032344079296136072207<30>
C129 = [787244138386490929876920510164611857119065256566549011183789719145870310160312863127858597915954078318413882086128479743889883711<129>]
(86·10190+31)/9 = 9(5)1899<191> = 32 · 67 · 5471 · 611551 · 73815411636669551483<20> · 3170631581865285261257<22> · C138
C138 = P34 · C104
P34 = 6091316752293331060196299481596117<34>
C104 = [33222722859764244370420434977799235487750656254904937398689327484258018049044115562830311699136103750859<104>]
(86·10199+31)/9 = 9(5)1989<200> = 32 · 11 · 53 · 541 · 89137 · 76090631637580657<17> · C172
C172 = P43 · P130
P43 = 4579335276299329109975930690686129256408537<43>
P130 = 1083817023802321703870503348039561161116538975431193722884499511083415580850112440288729259296754840574728575471510509230597499349<130>
By Patrick Keller / GMP-ECM B1=1000000
(29·10159+7)/9 = 3(2)1583<160> = 112 · C158
C158 = P33 · P125
P33 = 372612991204438824699686544369853<33>
P125 = 71468081761631228566085263364605922699893745503722687075347744609858409705036759488616306116194486173125016207819151185682771<125>
By Sinkiti Sibata / GGNFS-0.77.1
(2·10153+43)/9 = (2)1527<153> = 233 · 705525417997694941<18> · C133
C133 = P62 · P71
P62 = 96031666888365515991851317657490644554037610309664332640312809<62>
P71 = 14076815976438800641016953391829954431437624223094892290351236824633151<71>
Number: 22227_153 N=1351820102698192661030117440553977431729482875555439502902724093183979899791774244560611952035579693882883059470179897275225311331159 ( 133 digits) SNFS difficulty: 155 digits. Divisors found: r1=96031666888365515991851317657490644554037610309664332640312809 (pp62) r2=14076815976438800641016953391829954431437624223094892290351236824633151 (pp71) Version: GGNFS-0.77.1 Total time: 61.83 hours. Scaled time: 36.91 units (timescale=0.597). Factorization parameters were as follows: name: 22227_153 n: 1351820102698192661030117440553977431729482875555439502902724093183979899791774244560611952035579693882883059470179897275225311331159 m: 10000000000000000000000000000000 c5: 1 c0: 2150 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 3000001) Relations: rels:5698313, finalFF:582672 Initial matrix: 434096 x 582672 with sparse part having weight 46776643. Pruned matrix : 402398 x 404632 with weight 22177700. Total sieving time: 56.12 hours. Total relation processing time: 0.51 hours. Matrix solve time: 5.00 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 61.83 hours. --------- CPU info (if available) ----------
By Patrick Keller / GMP-ECM B1=1000000, GGNFS-0.77.1-20050930-pentium4 gnfs
(85·10168+41)/9 = 9(4)1679<169> = 7 · C169
C169 = P35 · C134
P35 = 30130007026272762236778552242458213<35>
C134 = [44779490028988984693345170298727232692672656093119287564674642677206820719270872412399590798774417897156369411429035099199813230155339<134>]
(85·10157+41)/9 = 9(4)1569<158> = 3 · 11 · 59 · 1450887150073<13> · C143
C143 = P29 · P114
P29 = 34449651002043481561963796153<29>
P114 = 970492098520818280676751308577374007361564345427698728787511704586443471464476736368328800135769189312717343166243<114>
(85·10164+41)/9 = 9(4)1639<165> = 13 · 9275757052376397976700267<25> · C139
C139 = P32 · P53 · P56
P32 = 26101001656469946963507262643981<32>
P53 = 14014284289662546774664694573536712383889671549051637<53>
P56 = 21411919469099025577565743587014582313214956323407880927<56>
Number: 1 N=300072726627314093320520489979175841355383288041487938215482381207181324448972896973431534123803458670427499 ( 108 digits) Divisors found: r1=14014284289662546774664694573536712383889671549051637 (pp53) r2=21411919469099025577565743587014582313214956323407880927 (pp56) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 14.13 hours. Scaled time: 9.34 units (timescale=%1.3lf). Factorization parameters were as follows: name: 1 n: 300072726627314093320520489979175841355383288041487938215482381207181324448972896973431534123803458670427499 skew: 14413.92 # norm 2.07e+015 c5: 68040 c4: -5486491074 c3: -107839267366391 c2: 814095232497087056 c1: 297733551779803293509 c0: 3472766926728906384353725 # alpha -6.26 Y1: 281101122991 Y0: -337985656024213877229 # Murphy_E 1.25e-009 # M 240851906692879690151436063888151202315772228258486233467638719578063636840097221853916840815252756913542175 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 Sieved special-q in [1250000, 2600001) Relations: rels:4653173, finalFF:470989 Initial matrix: 365488 x 470989 with sparse part having weight 38723282. Pruned matrix : 330933 x 332824 with weight 19140939. Total sieving time: 11.34 hours. Total relation processing time: 0.25 hours. Matrix solve time: 2.40 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 14.13 hours. --------- CPU info (if available) ----------
By Patrick Keller / GMP-ECM B1=1000000
(85·10163+41)/9 = 9(4)1629<164> = 32 · 11 · 31 · 157 · C159
C159 = P32 · P128
P32 = 13105568177894521477105321529233<32>
P128 = 14956294955922037005060865998514952333966593107588242623067398373503949070814552736812565807968312337312378522414968886212851241<128>
By Makoto Kamada / GGNFS-0.77.1-20050930-pentium4
(10154-7)/3 = (3)1531<154> = 210030505454134151<18> · 2949482315206615051<19> · C118
C118 = P39 · P79
P39 = 988766704612729363725673840229579328631<39>
P79 = 5441977445653925374118919046362314202378090727425848505434921132007141558367001<79>
Number: 33331_154 N=5380846105516030294514527973878351422932507055981674764039604926065238659321190766317777113182762829421115190284905631 ( 118 digits) SNFS difficulty: 155 digits. Divisors found: r1=988766704612729363725673840229579328631 (pp39) r2=5441977445653925374118919046362314202378090727425848505434921132007141558367001 (pp79) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 34.82 hours. Scaled time: 21.38 units (timescale=0.614). Factorization parameters were as follows: name: 33331_154 n: 5380846105516030294514527973878351422932507055981674764039604926065238659321190766317777113182762829421115190284905631 m: 10000000000000000000000000000000 c5: 1 c0: -70 skew: 5 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:217251, largePrimes:5599946 encountered Relations: rels:5549582, finalFF:541091 Max relations in full relation-set: 28 Initial matrix: 434131 x 541091 with sparse part having weight 42032926. Pruned matrix : 365380 x 367614 with weight 26967032. Total sieving time: 29.75 hours. Total relation processing time: 0.24 hours. Matrix solve time: 4.74 hours. Time per square root: 0.09 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: 34.82 hours. --------- CPU info (if available) ----------
By Patrick Keller / GMP-ECM B1=1000000
(85·10183+41)/9 = 9(4)1829<184> = 11 · 280294841 · 127720032577<12> · 532735528664257<15> · C149
C149 = P32 · P117
P32 = 48044979146898568326453523893341<32>
P117 = 937022319203434101741528181490976533217713016698050847685313060556924953332107679500036871906546985351198581558955351<117>
By Patrick Keller / GMP-ECM B1=1000000
(85·10160+41)/9 = 9(4)1599<161> = 3 · 50179757 · 14484627089<11> · C143
C143 = P34 · P109
P34 = 4356375194869062990627509092203103<34>
P109 = 9942463665136438161089813056493194640029957518925315720288546609296010178713411105011178503140721671112406457<109>
(85·10171+41)/9 = 9(4)1709<172> = 112 · 427052687177<12> · 919355421421<12> · 1442197769764018515817<22> · C126
C126 = P33 · P93
P33 = 728961914628469704246275138502451<33>
P93 = 189102158969065391485449428344208719851426050660814594754935684284783697027367063614273413071<93>
By Patrick Keller / GMP-ECM B1=1000000
(85·10195+41)/9 = 9(4)1949<196> = 11 · 251 · 2161031 · 27117551 · 1356870133<10> · 1739134559<10> · C161
C161 = P32 · C129
P32 = 25433652459414927499870617826399<32>
C129 = [972564350491546545147205599284218262224405374403653035025318106240841093313007765387765814323889960983051835806443072289350847213<129>]
(85·10153+41)/9 = 9(4)1529<154> = 11 · 677 · C151
C151 = P30 · P121
P30 = 532169908190609312922547459373<30>
P121 = 2383113620910345920040953299352597741758366084543329896306152414094100094570766140265306051858235710984214902514068075779<121>
(85·10191+41)/9 = 9(4)1909<192> = 11 · 994241 · 3853279 · 101912461631<12> · C168
C168 = P29 · C140
P29 = 14619811588998591301047585107<29>
C140 = [15041548193948732237377921782760162860444904346066707049385208315027780859557363470765425247552446374119213069706352597065891744437122468593<140>]
By Patrick Keller / GMP-ECM B1=1000000
(35·10195-53)/9 = 3(8)1943<196> = 11 · 353 · C193
C193 = P32 · C161
P32 = 13489623807653598428959653177019<32>
C161 = [74243477544933195199721018884564753532476736984037248212062263178045358729126496935286755527092585387779607938542329058870850264718140427333783944788315471979579<161>]
By Sinkiti Sibata / GGNFS-0.77.1
(2·10154+7)/9 = (2)1533<154> = 3 · 13 · 83 · 227 · 62851 · 910523 · 11950907 · 226326480869<12> · C119
C119 = P34 · P85
P34 = 2678614065727037627558566220314891<34>
P85 = 7294061730828789765648309600745906429764528886149847086345196093357863550959590237333<85>
Number: 22223_154 N=19537976348479297709241108486263881541684093534372921346678597304513214562602235530128310041656777831832213020684025703 ( 119 digits) SNFS difficulty: 155 digits. Divisors found: r1=2678614065727037627558566220314891 (pp34) r2=7294061730828789765648309600745906429764528886149847086345196093357863550959590237333 (pp85) Version: GGNFS-0.77.1 Total time: 44.63 hours. Scaled time: 26.60 units (timescale=0.596). Factorization parameters were as follows: name: 22223_154 n: 19537976348479297709241108486263881541684093534372921346678597304513214562602235530128310041656777831832213020684025703 m: 10000000000000000000000000000000 c5: 1 c0: 35 skew: 2 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 2600001) Relations: rels:5734822, finalFF:622092 Initial matrix: 433711 x 622092 with sparse part having weight 48174864. Pruned matrix : 382626 x 384858 with weight 19449566. Total sieving time: 39.59 hours. Total relation processing time: 0.39 hours. Matrix solve time: 4.49 hours. Time per square root: 0.16 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: 44.63 hours. --------- CPU info (if available) ----------
By CWI / GMP-ECM
(10383-1)/9 = (1)383<383> = 852559 · 1628675880394909638591813700831880313095925587<46> · C331
C331 = P47 · C285
P47 = 23181229247696012268805890210990826546682789683<47>
C285 = [345192952476958960147823998139683616642758281269013129543194636356033777495389903234686281133559196454018224515556815842464194616108378684266847054423006039422253677029609403326167675526846676838304378980263488424464689785323765671486102372923974370891369373572968024442734473362642049<285>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Patrick Keller / GMP-ECM B1=1000000, Msieve v. 1.03
(29·10197+7)/9 = 3(2)1963<198> = 11 · 21487 · 43969 · 344695237 · 1684161325078097<16> · 4370874144876529<16> · 1167476286104917223<19> · C131
C131 = P32 · P41 · P58
P32 = 58538086613548548979322909890333<32>
P41 = 27331887467833258552502650566280944366953<41>
P58 = 6541795177200537912720111371200600941834147753875171749613<58>
Mon Jan 30 00:27:51 2006 Msieve v. 1.03 Mon Jan 30 00:27:51 2006 random seeds: f48bdf24 eb4aed3e Mon Jan 30 00:27:51 2006 factoring 178799609620859433102456092550449953189558502392026811425674771874894588929096911710737173707739189 (99 digits) Mon Jan 30 00:27:52 2006 using multiplier of 1 Mon Jan 30 00:27:52 2006 sieve interval: 9 blocks of size 65536 Mon Jan 30 00:27:52 2006 processing polynomials in batches of 6 Mon Jan 30 00:27:52 2006 using a sieve bound of 2572489 (94118 primes) Mon Jan 30 00:27:52 2006 using large prime bound of 385873350 (28 bits) Mon Jan 30 00:27:52 2006 using double large prime bound of 2854963469885100 (43-52 bits) Mon Jan 30 00:27:52 2006 using trial factoring cutoff of 56 bits Mon Jan 30 00:27:52 2006 polynomial 'A' values have 13 factors Mon Jan 30 00:28:08 2006 restarting with 15020 full and 918731 partial relations Mon Jan 30 03:21:36 2006 94326 relations (22749 full + 71577 combined from 1400538 partial), need 94214 Mon Jan 30 03:21:37 2006 begin with 1400538 relations Mon Jan 30 03:21:38 2006 reduce to 224123 relations in 10 passes Mon Jan 30 03:21:38 2006 attempting to read 22749 full and 224123 partial relations Mon Jan 30 03:21:43 2006 recovered 22749 full and 224123 partial relations Mon Jan 30 03:21:43 2006 recovered 235484 polynomials Mon Jan 30 03:21:43 2006 attempting to build 71577 cycles Mon Jan 30 03:21:43 2006 found 71577 cycles in 6 passes Mon Jan 30 03:21:45 2006 distribution of cycle lengths: Mon Jan 30 03:21:45 2006 length 2 : 16449 Mon Jan 30 03:21:45 2006 length 3 : 15837 Mon Jan 30 03:21:45 2006 length 4 : 12749 Mon Jan 30 03:21:45 2006 length 5 : 9690 Mon Jan 30 03:21:45 2006 length 6 : 6646 Mon Jan 30 03:21:45 2006 length 7 : 4252 Mon Jan 30 03:21:45 2006 length 8 : 2620 Mon Jan 30 03:21:45 2006 length 9+: 3334 Mon Jan 30 03:21:45 2006 largest cycle: 21 relations Mon Jan 30 03:21:45 2006 94118 x 94182 system, weight 6188121 (avg 65.70/col) Mon Jan 30 03:21:45 2006 reduce to 92662 x 92726 in 3 passes Mon Jan 30 03:25:00 2006 lanczos halted after 1467 iterations Mon Jan 30 03:25:00 2006 recovered 64 nontrivial dependencies Mon Jan 30 03:26:02 2006 prp41 factor: 27331887467833258552502650566280944366953 Mon Jan 30 03:26:02 2006 prp58 factor: 6541795177200537912720111371200600941834147753875171749613 Mon Jan 30 03:26:02 2006 elapsed time 02:58:11
(29·10184+7)/9 = 3(2)1833<185> = 3 · 1609 · 141209 · 51361763 · C168
C168 = P32 · C137
P32 = 40099719731363732494892431187567<32>
C137 = [22952740803469060968111049404977261126816846627377021815399203618706658891312214574568337698722128170320166788147251434819194627650881241<137>]
By Patrick Keller / GMP-ECM B1=1000000
(29·10200+7)/9 = 3(2)1993<201> = 19 · 31469 · 200361424120519799<18> · 58874401726386398612126252576411<32> · C146
C146 = P36 · P110
P36 = 606815175214790313738987778416739217<36>
P110 = 75287329942185691582016605126251222192589334987378940003905961066870448780390121188605939719076412292159168861<110>
By Patrick Keller / GMP-ECM B1=1000000, GGNFS-0.77.1-20050930-pentium4 gnfs
(29·10186+7)/9 = 3(2)1853<187> = 367 · 6869 · 24173692225247190029<20> · 817085648520860204729531<24> · C137
C137 = P33 · P34 · P71
P33 = 148875337781562336091206119274899<33>
P34 = 5595198805825978240661829971576263<34>
P71 = 77686768150478058338957220040145869488476905274432941974964154046333127<71>
Number: 32223_186 N=434672912384034472276489075857058056092971658726960112621499647289367910737488108932999434401951383764401 ( 105 digits) Divisors found: r1=5595198805825978240661829971576263 (pp34) r2=77686768150478058338957220040145869488476905274432941974964154046333127 (pp71) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 9.48 hours. Scaled time: 4.83 units (timescale=%1.3lf). Factorization parameters were as follows: name: 1 n: 434672912384034472276489075857058056092971658726960112621499647289367910737488108932999434401951383764401 skew: 43423.78 # norm 3.55e+014 c5: 2700 c4: -32793540 c3: -22483127152441 c2: 82849481010709582 c1: 14402080289847793642392 c0: -46281243702985892444165040 # alpha -6.74 Y1: 17831828861 Y0: -174325078919840638189 # Murphy_E 2.18e-009 # M 75917951504007049919756011760453746537937058616496215661199923963867940747621339656342162085021060087616 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [1250000, 1950001) Relations: rels:4463965, finalFF:492216 Initial matrix: 366964 x 492216 with sparse part having weight 33506857. Pruned matrix : 311533 x 313431 with weight 13262973. Total sieving time: 7.31 hours. Total relation processing time: 0.23 hours. Matrix solve time: 1.80 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 9.48 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1
(4·10153+23)/9 = (4)1527<153> = 3 · 17 · 19 · 81017 · 241784369429<12> · C134
C134 = P46 · P89
P46 = 1470703507530817065767950099767404004845089349<46>
P89 = 15920774731201487385655812078291835754560386012725533646207019291393849532640008894695559<89>
Number: 44447_153 N=23414739239786028749269162319365649597012527790011081766399867486328722607760076327047273100135171383472611229438026705790715508501091 ( 134 digits) SNFS difficulty: 155 digits. Divisors found: r1=1470703507530817065767950099767404004845089349 (pp46) r2=15920774731201487385655812078291835754560386012725533646207019291393849532640008894695559 (pp89) Version: GGNFS-0.77.1 Total time: 41.25 hours. Scaled time: 24.59 units (timescale=0.596). Factorization parameters were as follows: name: 44447_153 n: 23414739239786028749269162319365649597012527790011081766399867486328722607760076327047273100135171383472611229438026705790715508501091 m: 10000000000000000000000000000000 c5: 1 c0: 575 skew: 2 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 2500001) Relations: rels:5624531, finalFF:597924 Initial matrix: 433646 x 597924 with sparse part having weight 43829030. Pruned matrix : 383560 x 385792 with weight 18604471. Total sieving time: 36.47 hours. Total relation processing time: 0.33 hours. Matrix solve time: 4.29 hours. Time per square root: 0.16 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: 41.25 hours. --------- CPU info (if available) ----------
By Patrick Keller / GMP-ECM B1=1000000
(29·10200+7)/9 = 3(2)1993<201> = 19 · 31469 · 200361424120519799<18> · C178
C178 = P32 · C146
P32 = 58874401726386398612126252576411<32>
C146 = [45685494310321139538690186388518699890739761704723675271383671232036884261792667410604433223602786884855278216669151772545738533720768128503921837<146>]
By Patrick Keller / GMP-ECM B1=1000000
(35·10171-53)/9 = 3(8)1703<172> = 11 · 257 · 313 · 14547037 · C159
C159 = P36 · P123
P36 = 451637800707841604043591937013618243<36>
P123 = 668945230356071257795118498826470672455372523944031278211962172797587051335478238590834313058838878619295303466223808615463<123>
By Cedric Vonck / GGNFS-0.77.1-20050930-pentium4 gnfs
(10166+11)/3 = (3)1657<166> = 2269 · 5764399 · 19537095989<11> · 87732744049<11> · 301816485953164436063353<24> · C111
C111 = P53 · P59
P53 = 11206452347884993130940717654027456951433829993441411<53>
P59 = 43959969732682098946597196186987599511353917863039376632629<59>
Divisors found: r1=11206452347884993130940717654027456951433829993441411 (pp53) r2=43959969732682098946597196186987599511353917863039376632629 (pp59) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 37.53 hours. Scaled time: 20.19 units (timescale=0.538). Factorization parameters were as follows: name: c111 n: 492635306023768541594765890513052108909476061496811112954272759376577034953854526502589831415278876920382399519 skew: 25890.51 # norm 6.53e+014 c5: 14280 c4: -898725224 c3: -24028726065267 c2: 149970026802419081 c1: 8622273537997815680117 c0: 2369636294795826677063373 # alpha -5.25 Y1: 598043715709 Y0: -2030304024354184370578 # Murphy_E 9.11e-010 # M 344700207265714400774493844422343622305068913230711086885117440445706540058613325752159815816366332677658325980 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2400001) Primes: RFBsize:230209, AFBsize:231093, largePrimes:7527070 encountered Relations: rels:7440978, finalFF:621380 Max relations in full relation-set: 28 Initial matrix: 461385 x 621380 with sparse part having weight 53695434. Pruned matrix : 332381 x 334751 with weight 28979305. Total sieving time: 32.00 hours. Total relation processing time: 0.41 hours. Matrix solve time: 4.82 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 37.53 hours. --------- CPU info (if available) ----------
A very improvised snfs poly file for GGNFS is available on each contribution pages. Default parameters are required and the skew is not adjusted.
By Patrick Keller / GMP-ECM
(35·10179-53)/9 = 3(8)1783<180> = 11 · 1453 · C176
C176 = P28 · C148
P28 = 4823708954837782458566048329<28>
C148 = [5044128471268801172062513142983485358949897775689870766059301754241680504722143167099125805317082288533122296651679099968127315184968035371550200469<148>]
By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs
(5·10177+31)/9 = (5)1769<177> = 13 · 56345207 · 3866383109<10> · 242143359684157<15> · 272242916096747<15> · 1691532864670216129<19> · C112
C112 = P46 · P66
P46 = 5590949666318516260855679354188427787135841331<46>
P66 = 314649542503316748079738255963456709156720035705251552887876749141<66>
Number: 7638 N=1759189754666192572326725349064953542205081951959080946286724157353603060805175015430135904517498852334266546671 ( 112 digits) Divisors found: r1=5590949666318516260855679354188427787135841331 (pp46) r2=314649542503316748079738255963456709156720035705251552887876749141 (pp66) Version: GGNFS-0.77.1-20050930-athlon Total time: 23.44 hours. Scaled time: 15.47 units (timescale=%1.3lf). Factorization parameters were as follows: name: 7638 n: 1759189754666192572326725349064953542205081951959080946286724157353603060805175015430135904517498852334266546671 skew: 23920.37 # norm 1.64e+015 c5: 26760 c4: 2529054184 c3: -88766237821472 c2: -1536599333403767721 c1: 11040733049224213553472 c0: -20360395729652409608835548 # alpha -5.47 Y1: 739415148989 Y0: -2309737831355081448027 # Murphy_E 8.07e-010 # M 79677056783275846577819398475589618451768605930335261907244912079153872042265783015618928186592278468264372413 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2650001) Relations: rels:7206433, finalFF:570022 Initial matrix: 499190 x 570022 with sparse part having weight 44320846. Pruned matrix : 465373 x 467932 with weight 28459747. Total sieving time: 20.25 hours. Total relation processing time: 0.35 hours. Matrix solve time: 2.65 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 23.44 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1
(8·10152+1)/9 = (8)1519<152> = 276553 · 96941219 · 17522761249341089058283<23> · C117
C117 = P52 · P65
P52 = 9275450587465013271141450209568903221034440958615769<52>
P65 = 20399666486620694433547638703203893366675685859664738168665270201<65>
Number: 88889_152 N=189216098497416263473135181856600180019937737923795853280762266113886314312612554827066663044652111065432137324399569 ( 117 digits) SNFS difficulty: 152 digits. Divisors found: r1=9275450587465013271141450209568903221034440958615769 (pp52) r2=20399666486620694433547638703203893366675685859664738168665270201 (pp65) Version: GGNFS-0.77.1 Total time: 39.61 hours. Scaled time: 23.61 units (timescale=0.596). Factorization parameters were as follows: name: 88889_152 n: 189216098497416263473135181856600180019937737923795853280762266113886314312612554827066663044652111065432137324399569 m: 1000000000000000000000000000000 c5: 800 c0: 1 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2200001) Relations: rels:5656806, finalFF:560541 Initial matrix: 352461 x 560541 with sparse part having weight 49911832. Pruned matrix : 311880 x 313706 with weight 17483011. Total sieving time: 35.95 hours. Total relation processing time: 0.37 hours. Matrix solve time: 3.15 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: 39.61 hours. --------- CPU info (if available) ----------
By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs
(8·10166+1)/9 = (8)1659<166> = 3 · 557461665979<12> · 1225671932987<13> · 1106648171488609<16> · 8449459157386939<16> · C111
C111 = P48 · P64
P48 = 333087075628896812713251964530979547595195984979<48>
P64 = 1392325284264560906132614928910781331907389357350433733048086539<64>
Number: 3254 N=463765557259855051917117131486710479266089943564208828987238225638693593801271651567757735109441644551336097681 ( 111 digits) Divisors found: r1=333087075628896812713251964530979547595195984979 (pp48) r2=1392325284264560906132614928910781331907389357350433733048086539 (pp64) Version: GGNFS-0.77.1-20050930-athlon Total time: 19.29 hours. Scaled time: 11.85 units (timescale=%1.3lf). Factorization parameters were as follows: name: 3254 n: 463765557259855051917117131486710479266089943564208828987238225638693593801271651567757735109441644551336097681 skew: 36628.95 # norm 5.55e+015 c5: 16800 c4: -2384216080 c3: -58737157009298 c2: -3097661265535552497 c1: 9175246943003298098750 c0: 479467956148092230621982685 # alpha -6.74 Y1: 604398104101 Y0: -1941787400956269041544 # Murphy_E 9.07e-010 # M 391675059068029791990482987611213515275710334411496631346201367720880232500594510316273613195473518983785111212 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1600000, 2350001) Relations: rels:7130922, finalFF:535065 Initial matrix: 460667 x 535065 with sparse part having weight 42098767. Pruned matrix : 426581 x 428948 with weight 25847979. Total sieving time: 16.52 hours. Total relation processing time: 0.36 hours. Matrix solve time: 2.21 hours. Time per square root: 0.21 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 19.29 hours. --------- CPU info (if available) ----------
By Anton Korobeynikov / GGNFS-0.77.1-20050930-athlon
2·10155-1 = 1(9)155<156> = 5012795239<10> · C146
C146 = P72 · P75
P72 = 136754115856816167695867638454568058370179471864695591167031691027321981<72>
P75 = 291749166878241872177396255297205394204088421236507456460074010898849116061<75>
Number: snfs N=39897899368396683078640308292073846665253745067243908623573443351652528969376480849310828991552990102095809942178250620541654244896237621885436841 ( 146 digits) SNFS difficulty: 155 digits. Divisors found: r1=136754115856816167695867638454568058370179471864695591167031691027321981 (pp72) r2=291749166878241872177396255297205394204088421236507456460074010898849116061 (pp75) Version: GGNFS-0.77.1-20050930-athlon Total time: 141.14 hours. Scaled time: 66.90 units (timescale=0.474). Factorization parameters were as follows: n: 39897899368396683078640308292073846665253745067243908623573443351652528969376480849310828991552990102095809942178250620541654244896237621885436841 c5: 2 c0: -1 m: 10000000000000000000000000000000 skew: 100.0 type: snfs lss: 1 qintsize: 50000Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved rational special-q in [1500000, 3550001) Primes: RFBsize:216816, AFBsize:216491, largePrimes:5779940 encountered Relations: rels:5731745, finalFF:497024 Max relations in full relation-set: 28 Initial matrix: 433372 x 497024 with sparse part having weight 47577503. Pruned matrix : 403451 x 405681 with weight 35625976. Total sieving time: 129.13 hours. Total relation processing time: 0.88 hours. Matrix solve time: 10.85 hours. Time per square root: 0.28 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: 141.14 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1
(28·10151+17)/9 = 3(1)1503<152> = 3 · 11 · 19 · 47 · 53 · 743 · 5279 · 6760674071<10> · C129
C129 = P64 · P66
P64 = 1183424773474736884406097266107576876938774299229979351789940959<64>
P66 = 634750602886514005931448326915798097467522134045896246417437275273<66>
Number: 31113_151 N=751179588433925505819980439132160983509357836200324681542769367407649269891006424737915625504962455505240739186983603374500606807 ( 129 digits) SNFS difficulty: 152 digits. Divisors found: r1=1183424773474736884406097266107576876938774299229979351789940959 (pp64) r2=634750602886514005931448326915798097467522134045896246417437275273 (pp66) Version: GGNFS-0.77.1 Total time: 36.25 hours. Scaled time: 21.61 units (timescale=0.596). Factorization parameters were as follows: name: 31113_151 n: 751179588433925505819980439132160983509357836200324681542769367407649269891006424737915625504962455505240739186983603374500606807 m: 1000000000000000000000000000000 c5: 280 c0: 17 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2100001) Relations: rels:5476607, finalFF:488877 Initial matrix: 352462 x 488877 with sparse part having weight 42762285. Pruned matrix : 322831 x 324657 with weight 19033619. Total sieving time: 32.22 hours. Total relation processing time: 0.38 hours. Matrix solve time: 3.50 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 36.25 hours. --------- CPU info (if available) ----------
By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs
(52·10177-7)/9 = 5(7)177<178> = 5209 · 687901 · 3591592130707531<16> · 20758583474340401<17> · 163882620580891776606591883<27> · C111
C111 = P55 · P56
P55 = 5990130956546303578954044839627845137546757129595421161<55>
P56 = 22030613574269288396243921906995869107155224693130054301<56>
Number: 7205 N=131966260362939672544609184922691216201854675825526623713085165777457266196327622856980876044228227484894463461 ( 111 digits) Divisors found: r1=5990130956546303578954044839627845137546757129595421161 (pp55) r2=22030613574269288396243921906995869107155224693130054301 (pp56) Version: GGNFS-0.77.1-20050930-athlon Total time: 19.89 hours. Scaled time: 12.93 units (timescale=%1.3lf). Factorization parameters were as follows: name: 7205 n: 131966260362939672544609184922691216201854675825526623713085165777457266196327622856980876044228227484894463461 skew: 38293.48 # norm 4.68e+015 c5: 26460 c4: -1421202454 c3: -176948763340345 c2: -2446403972040051259 c1: 106057665132258845107595 c0: -6358896990066060629975025 # alpha -6.46 Y1: 616825309463 Y0: -1379039484047520995828 # Murphy_E 8.87e-010 # M 73243177485515507332517433451890715278931353287625047006678691986437432307082725942451292464863658852031109008 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 Sieved special-q in [1600000, 2400001) Relations: rels:7208189, finalFF:557042 Initial matrix: 460412 x 557042 with sparse part having weight 47165794. Pruned matrix : 419163 x 421529 with weight 26297790. Total sieving time: 17.25 hours. Total relation processing time: 0.35 hours. Matrix solve time: 2.10 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 19.89 hours. --------- CPU info (if available) ----------
By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs
(13·10164-1)/3 = 4(3)164<165> = 17 · 23 · 121291 · 1720324112526590653<19> · 22830290549856975884476811953<29> · C111
C111 = P45 · P66
P45 = 250560538262323237800920263917376214890034701<45>
P66 = 928500998327696518716189155494288425648796690706977226894213494177<66>
Number: 2007 N=232645709918092128212963626281842374753128885585849987283506411402099491993298681298998317099407771797991436077 ( 111 digits) Divisors found: r1=250560538262323237800920263917376214890034701 (pp45) r2=928500998327696518716189155494288425648796690706977226894213494177 (pp66) Version: GGNFS-0.77.1-20050930-athlon Total time: 23.62 hours. Scaled time: 15.31 units (timescale=%1.3lf). Factorization parameters were as follows: name: 2007 n: 232645709918092128212963626281842374753128885585849987283506411402099491993298681298998317099407771797991436077 skew: 14212.24 # norm 1.41e+014 c5: 17520 c4: -731536343 c3: -7203612784458 c2: 137854935490016143 c1: 757017358734400134189 c0: -3936459434010134648132846 # alpha -3.52 Y1: 140945592403 Y0: -1677383992046597419989 # Murphy_E 8.77e-010 # M 30919382169914387085751545851925427078681855413600291588789589589734820051013111462667174408849572806160572640 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 Sieved special-q in [1600000, 2500001) Relations: rels:7297886, finalFF:584279 Initial matrix: 460506 x 584279 with sparse part having weight 46858369. Pruned matrix : 409772 x 412138 with weight 22844098. Total sieving time: 21.23 hours. Total relation processing time: 0.28 hours. Matrix solve time: 1.92 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 23.62 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1
(4·10152+41)/9 = (4)1519<152> = 7 · 227 · 971 · 674759 · C140
C140 = P67 · P74
P67 = 1749054437074730839738212413266980681168427109942203394836261055113<67>
P74 = 24407446290192717863936113799240790417381456561254089477520149077854868713<74>
Number: 44449_152 N=42689952231524751722138041230328646463026795672759687658152146679145117324025601300082106418039877056208737757403079020376978414617472379569 ( 140 digits) SNFS difficulty: 152 digits. Divisors found: r1=1749054437074730839738212413266980681168427109942203394836261055113 (pp67) r2=24407446290192717863936113799240790417381456561254089477520149077854868713 (pp74) Version: GGNFS-0.77.1 Total time: 40.18 hours. Scaled time: 23.99 units (timescale=0.597). Factorization parameters were as follows: name: 44449_152 n: 42689952231524751722138041230328646463026795672759687658152146679145117324025601300082106418039877056208737757403079020376978414617472379569 m: 1000000000000000000000000000000 c5: 400 c0: 41 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2200001) Relations: rels:5353614, finalFF:451285 Initial matrix: 352740 x 451285 with sparse part having weight 39087828. Pruned matrix : 333599 x 335426 with weight 20667424. Total sieving time: 35.74 hours. Total relation processing time: 0.29 hours. Matrix solve time: 4.00 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 40.18 hours. --------- CPU info (if available) ----------
By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs
(10167+11)/3 = (3)1667<167> = 37 · 1223 · 1659737 · 2908723 · 447435816063229601<18> · 1294695630404312613929<22> · C111
C111 = P49 · P62
P49 = 8084500782190389840478406072564528309399381768737<49>
P62 = 32580465758870391821055101253905389293574411343938722240893569<62>
Number: 3051 N=263396800911714895792509875297859568219343048500407357011345512027494719081492325733089149289256654778588552353 ( 111 digits) Divisors found: r1=8084500782190389840478406072564528309399381768737 (pp49) r2=32580465758870391821055101253905389293574411343938722240893569 (pp62) Version: GGNFS-0.77.1-20050930-athlon Total time: 19.92 hours. Scaled time: 13.26 units (timescale=%1.3lf). Factorization parameters were as follows: name: 1 n: 263396800911714895792509875297859568219343048500407357011345512027494719081492325733089149289256654778588552353 skew: 44063.22 # norm 5.82e+015 c5: 31440 c4: -2042808076 c3: -259462411933762 c2: 3562919922588584576 c1: 78571915379339780403777 c0: -1247587394058679282894357380 # alpha -7.13 Y1: 449769722723 Y0: -1529773914367355424991 # Murphy_E 9.78e-010 # M 37620472442472730250295197130900633958251966432039131133767733126942109554102128164093057823374055476852748918 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 Sieved special-q in [1600000, 2300001) Relations: rels:7226550, finalFF:590752 Initial matrix: 460667 x 590752 with sparse part having weight 46800960. Pruned matrix : 405019 x 407386 with weight 21906508. Total sieving time: 17.67 hours. Total relation processing time: 0.25 hours. Matrix solve time: 1.81 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 19.92 hours. --------- CPU info (if available) ----------
By Cedric Vonck / GGNFS-0.77.1-20050930-pentium4 gnfs
2·10161-9 = 1(9)1601<162> = 11 · 8009 · 46649 · 5470052140709707519<19> · 21260817950106947166511<23> · C111
C111 = P44 · P68
P44 = 38623719592924262442438059227864671483234091<44>
P68 = 10834057799333342211229610150242910516634871944815694724812226195039<68>
Number: c111 N=418451610494985126825836635808849111611795791400042430454732256218470337626978790680198450889274838215059874549 ( 111 digits) Divisors found: r1=38623719592924262442438059227864671483234091 (pp44) r2=10834057799333342211229610150242910516634871944815694724812226195039 (pp68) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 38.14 hours. Scaled time: 21.67 units (timescale=0.568). Factorization parameters were as follows: name: c111 n: 418451610494985126825836635808849111611795791400042430454732256218470337626978790680198450889274838215059874549 skew: 3675.70 # norm 1.93e+014 c5: 32760 c4: -178083787 c3: 21650278439078 c2: 8917979542614550 c1: -49383796745086078804 c0: 13429828240883863427696 # alpha -3.65 Y1: 795881887993 Y0: -1664410687743954876989 # Murphy_E 8.91e-010 # M 10948574208808051795460323832426812352113482816811172364528579270127779274130082656672732319498982550206267293 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2500001) Primes: RFBsize:230209, AFBsize:230091, largePrimes:7793681 encountered Relations: rels:7932693, finalFF:773618 Max relations in full relation-set: 28 Initial matrix: 460383 x 773618 with sparse part having weight 72578266. Pruned matrix : 260552 x 262917 with weight 44454129. Total sieving time: 33.38 hours. Total relation processing time: 0.46 hours. Matrix solve time: 4.05 hours. Time per square root: 0.26 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 38.14 hours. --------- CPU info (if available) ----------
By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs
(7·10158-1)/3 = 2(3)158<159> = 1567 · 6272477 · 94340496413<11> · 411102666467<12> · 48861300224203<14> · C113
C113 = P37 · P76
P37 = 1447531832598287194675337087588890669<37>
P76 = 8654203791135258006846208256907995285539701724907372088440732832849802487071<76>
Number: 1 N=12527235473461064690789740751463629224250685860494368593748060178562891242691247493191763713705069665306105040499 ( 113 digits) Divisors found: r1=1447531832598287194675337087588890669 (pp37) r2=8654203791135258006846208256907995285539701724907372088440732832849802487071 (pp76) Version: GGNFS-0.77.1-20050930-athlon Total time: 26.10 hours. Scaled time: 17.25 units (timescale=%1.3lf). Factorization parameters were as follows: name: 1 n: 12527235473461064690789740751463629224250685860494368593748060178562891242691247493191763713705069665306105040499 skew: 89208.53 # norm 3.49e+015 c5: 2760 c4: -1034197276 c3: -28219325036870 c2: 7094204249441952635 c1: -225125126489700920174112 c0: -346886755808856710520625020 # alpha -6.18 Y1: 434919627923 Y0: -5387556766897775617289 # Murphy_E 7.50e-010 # M 12155549874620238031766711571075608703631898509942543672223711551128349335307687833438143686070227069253819519139 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 5000Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2655001) Relations: rels:7505319, finalFF:659459 Initial matrix: 501526 x 659459 with sparse part having weight 55260502. Pruned matrix : 438001 x 440572 with weight 25312097. Total sieving time: 22.64 hours. Total relation processing time: 0.54 hours. Matrix solve time: 2.73 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 26.10 hours. --------- CPU info (if available) ----------
By Makoto Kamada / GGNFS-0.77.1-20050930-pentium4 gnfs
By Torbjörn Granlund / GMP-ECM
10810+1 = 1(0)8091<811> = 61 · 101 · 109 · 181 · 541 · 1621 · 3541 · 8101 · 9901 · 19441 · 27541 · 27961 · 68041 · 119881 · 153469 · 329941 · 2925721 · 4188901 · 39526741 · 49229101 · 68189581 · 999999000001<12> · 29639179139212862101<20> · 4999437541453012143121<22> · 13029637224192121671301<23> · 1105097795002994798105101<25> · 67128593062302476037266041<26> · 7997499229153265919258822361<28> · 59779577156334533866654838281<29> · 292833529380862495499652402770042860551961<42> · 141849229571534821256183437819902857798933927761<48> · 902957305935680526667861848839993076071896366838581<51> · 341796090604674881849636380229010216626944264336893367139245334739710314141368913850637159182300704681<102> · C108 · [21431956757675468974876300755804900832277300719777308299609301048389700236714216988820459065467670651445681992662548793310029766116893035870982334672674080173615607829147502498184662701<185>]
C108 = P43 · P65
P43 = 2187911623791867750065408022595894263802921<43>
P65 = 79802900676249574386310013540996547368285959759708473463717727701<65>
Number: 10001_810a N=174601694001874347255805749546028712001883150079648147890917445185989799312355477070999037232383781006414621 ( 108 digits) Divisors found: r1=2187911623791867750065408022595894263802921 (pp43) r2=79802900676249574386310013540996547368285959759708473463717727701 (pp65) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 18.72 hours. Scaled time: 11.51 units (timescale=0.615). Factorization parameters were as follows: name: 10001_810a n: 174601694001874347255805749546028712001883150079648147890917445185989799312355477070999037232383781006414621 skew: 5126.41 # norm 1.93e+14 c5: 103740 c4: 5489741268 c3: -13075289527817 c2: -139084549632406609 c1: 119742151420102586749 c0: 271623207935125340303085 # alpha -5.35 Y1: 259012632439 Y0: -278750831169188009758 # Murphy_E 1.45e-09 # M 134662390696672647263499356795199525153224044769487875113261803659845520946252776074226595599860047310328984 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, 2600001) Primes: RFBsize:183072, AFBsize:182575, largePrimes:4597622 encountered Relations: rels:4798738, finalFF:516298 Max relations in full relation-set: 28 Initial matrix: 365731 x 516298 with sparse part having weight 45217492. Pruned matrix : 265981 x 267873 with weight 25469744. Total sieving time: 15.82 hours. Total relation processing time: 0.35 hours. Matrix solve time: 2.37 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 18.72 hours. --------- CPU info (if available) ----------
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1
(34·10151-7)/9 = 3(7)151<152> = 37 · C151
C151 = P44 · P49 · P59
P44 = 36244743842331203919950327303612252533187707<44>
P49 = 1236569276238851873641077650635328609093214576107<49>
P59 = 22780916748875701195796464739236626157318164712696869631829<59>
Number: 37777_151 N=1021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021 ( 151 digits) SNFS difficulty: 152 digits. Divisors found: r1=36244743842331203919950327303612252533187707 (pp44) r2=1236569276238851873641077650635328609093214576107 (pp49) r3=22780916748875701195796464739236626157318164712696869631829 (pp59) Version: GGNFS-0.77.1 Total time: 46.75 hours. Scaled time: 31.09 units (timescale=0.665). Factorization parameters were as follows: name: 37777_151 n: 1021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021 m: 1000000000000000000000000000000 c5: 340 c0: -7 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2400001) Relations: rels:5359277, finalFF:399435 Initial matrix: 352217 x 399435 with sparse part having weight 36448166. Pruned matrix : 346243 x 348068 with weight 26257292. Total sieving time: 41.64 hours. Total relation processing time: 0.43 hours. Matrix solve time: 4.52 hours. Time per square root: 0.17 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: 46.75 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
10810+1 = 1(0)8091<811> = 61 · 101 · 109 · 181 · 541 · 1621 · 3541 · 8101 · 9901 · 19441 · 27541 · 27961 · 68041 · 119881 · 153469 · 329941 · 2925721 · 4188901 · 39526741 · 49229101 · 68189581 · 999999000001<12> · 29639179139212862101<20> · 4999437541453012143121<22> · 13029637224192121671301<23> · 1105097795002994798105101<25> · 67128593062302476037266041<26> · 7997499229153265919258822361<28> · 59779577156334533866654838281<29> · 141849229571534821256183437819902857798933927761<48> · 902957305935680526667861848839993076071896366838581<51> · 341796090604674881849636380229010216626944264336893367139245334739710314141368913850637159182300704681<102> · C149 · [21431956757675468974876300755804900832277300719777308299609301048389700236714216988820459065467670651445681992662548793310029766116893035870982334672674080173615607829147502498184662701<185>]
C149 = P42 · C108
P42 = 292833529380862495499652402770042860551961<42>
C108 = [174601694001874347255805749546028712001883150079648147890917445185989799312355477070999037232383781006414621<108>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Cedric Vonck / GGNFS-0.77.1-20050930-pentium4 gnfs
(28·10159+17)/9 = 3(1)1583<160> = 11 · 31 · 60558053 · 7212362800961<13> · 33539753385806481216611969<26> · C111
C111 = P51 · P61
P51 = 462536132185574572774501768659198144654440616697393<51>
P61 = 1346499340514681298574411447231016501419631070503438624796113<61>
Number: c111 N=622804596952087616912505747405171660214728457594249079875162518181585744977322568358844642895637638988043633409 ( 111 digits) Divisors found: r1=462536132185574572774501768659198144654440616697393 (pp51) r2=1346499340514681298574411447231016501419631070503438624796113 (pp61) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 35.69 hours. Scaled time: 21.20 units (timescale=0.594). Factorization parameters were as follows: name: c111 n: 622804596952087616912505747405171660214728457594249079875162518181585744977322568358844642895637638988043633409 skew: 40274.04 # norm 3.24e+015 c5: 24960 c4: 3358680112 c3: -154095379278068 c2: -5133738171144417744 c1: 97735448881250080837173 c0: 973118633560276453861668837 # alpha -6.68 Y1: 255538396069 Y0: -1902917132300748293272 # Murphy_E 9.18e-010 # M 204503118033941889104818766711331234716892044883651475030150490804811943446656433575566145287157210501727805036 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2400001) Primes: RFBsize:230209, AFBsize:230053, largePrimes:7688165 encountered Relations: rels:7775371, finalFF:751041 Max relations in full relation-set: 28 Initial matrix: 460347 x 751041 with sparse part having weight 67651935. Pruned matrix : 260052 x 262417 with weight 38209459. Total sieving time: 31.54 hours. Total relation processing time: 0.46 hours. Matrix solve time: 3.42 hours. Time per square root: 0.27 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 35.69 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1
(85·10151+41)/9 = 9(4)1509<152> = 3 · 11 · 263 · C149
C149 = P34 · P56 · P60
P34 = 4943181161334121867022094443412343<34>
P56 = 15942446963562877289932971560669341883979707656772226419<56>
P60 = 138084591641348859848844692898664238439608537558881691144443<60>
Number: 94449_151 N=10881950045448144307459896813508980809361037497919627197193737117691490315064459551151566360691835977007079668676626851531794497573965254573619592631 ( 149 digits) SNFS difficulty: 152 digits. Divisors found: r1=4943181161334121867022094443412343 (pp34) r2=15942446963562877289932971560669341883979707656772226419 (pp56) r3=138084591641348859848844692898664238439608537558881691144443 (pp60) Version: GGNFS-0.77.1 Total time: 45.03 hours. Scaled time: 26.84 units (timescale=0.596). Factorization parameters were as follows: name: 94449_151 n: 10881950045448144307459896813508980809361037497919627197193737117691490315064459551151566360691835977007079668676626851531794497573965254573619592631 m: 1000000000000000000000000000000 c5: 850 c0: 41 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2300001) Relations: rels:5470422, finalFF:459583 Initial matrix: 352868 x 459583 with sparse part having weight 41964979. Pruned matrix : 334801 x 336629 with weight 21806643. Total sieving time: 40.36 hours. Total relation processing time: 0.41 hours. Matrix solve time: 4.10 hours. Time per square root: 0.16 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: 45.03 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1
(89·10151+1)/9 = 9(8)1509<152> = 3 · 112 · 683 · 106781 · C142
C142 = P61 · P81
P61 = 9592561240368708557394631004994331725705539077245555042315551<61>
P81 = 389396106087029426819397405054446679770014664080460923953210556844866305408789611<81>
Number: 98889_151 N=3735305994400940222977603340946986263067520786719671553018228690399643253656412142170867746660925810754124002709470582364123614636317632540661 ( 142 digits) SNFS difficulty: 152 digits. Divisors found: r1=9592561240368708557394631004994331725705539077245555042315551 (pp61) r2=389396106087029426819397405054446679770014664080460923953210556844866305408789611 (pp81) Version: GGNFS-0.77.1 Total time: 40.47 hours. Scaled time: 24.20 units (timescale=0.598). Factorization parameters were as follows: name: 98889_151 n: 3735305994400940222977603340946986263067520786719671553018228690399643253656412142170867746660925810754124002709470582364123614636317632540661 m: 1000000000000000000000000000000 c5: 890 c0: 1 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2200001) Relations: rels:5400256, finalFF:457265 Initial matrix: 353142 x 457265 with sparse part having weight 41226568. Pruned matrix : 332763 x 334592 with weight 21288107. Total sieving time: 36.15 hours. Total relation processing time: 0.31 hours. Matrix solve time: 3.84 hours. Time per square root: 0.17 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: 40.47 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1
(4·10152-31)/9 = (4)1511<152> = 41 · 79 · 4231 · 19037823664438599021743461<26> · C120
C120 = P51 · P70
P51 = 166866328854011532118907641869784764648724705750463<51>
P70 = 1020886585728828363510597287873903676785706217228771834142475438673643<70>
Number: 44441_152 N=170351596736875709959179822326526166723291839274113159290765004032671542668674951513691570325256153664621191583653146709 ( 120 digits) SNFS difficulty: 152 digits. Divisors found: r1=166866328854011532118907641869784764648724705750463 (pp51) r2=1020886585728828363510597287873903676785706217228771834142475438673643 (pp70) Version: GGNFS-0.77.1 Total time: 42.82 hours. Scaled time: 25.60 units (timescale=0.598). Factorization parameters were as follows: name: 44441_152 n: 170351596736875709959179822326526166723291839274113159290765004032671542668674951513691570325256153664621191583653146709 m: 1000000000000000000000000000000 c5: 400 c0: -31 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2300001) Relations: rels:5546011, finalFF:491989 Initial matrix: 352175 x 491989 with sparse part having weight 44706048. Pruned matrix : 327635 x 329459 with weight 20162990. Total sieving time: 38.40 hours. Total relation processing time: 0.40 hours. Matrix solve time: 3.86 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 42.82 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1
(5·10151+13)/9 = (5)1507<151> = 7 · 337 · 709 · C145
C145 = P66 · P80
P66 = 244675379719578289333919494527112794313295764375089268344563909567<66>
P80 = 13575725494988365411487737203669177049217503397028681709211591765872759556449241<80>
Number: 55557_151 N=3321645790455038235796858506990636081217959819910994508057282977448881698190081711822116035849592955559900268249470745567977846482699307549788647 ( 145 digits) SNFS difficulty: 151 digits. Divisors found: r1=244675379719578289333919494527112794313295764375089268344563909567 (pp66) r2=13575725494988365411487737203669177049217503397028681709211591765872759556449241 (pp80) Version: GGNFS-0.77.1 Total time: 43.12 hours. Scaled time: 25.78 units (timescale=0.598). Factorization parameters were as follows: name: 55557_151 n: 3321645790455038235796858506990636081217959819910994508057282977448881698190081711822116035849592955559900268249470745567977846482699307549788647 m: 1000000000000000000000000000000 c5: 50 c0: 13 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2300001) Relations: rels:5749297, finalFF:559546 Initial matrix: 352970 x 559546 with sparse part having weight 51636734. Pruned matrix : 313574 x 315402 with weight 18663720. Total sieving time: 39.14 hours. Total relation processing time: 0.42 hours. Matrix solve time: 3.40 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: 43.12 hours. --------- CPU info (if available) ----------
By Cedric Vonck / GGNFS-0.77.1-20050930-pentium4 gnfs
(13·10164-31)/9 = 1(4)1631<165> = 3 · 43 · 112428709734049<15> · 12667023571737990991217609155379403223<38> · C111
C111 = P40 · P72
P40 = 1676745044461232317729000675458505147939<40>
P72 = 468913024426091623245443201751896636676035669103202976763622771817695493<72>
Number: c111 N=786247589989777914636073830302682947375520031653629043043502213698140564149219934257068310767319486956018538927 ( 111 digits) Divisors found: r1=1676745044461232317729000675458505147939 (pp40) r2=468913024426091623245443201751896636676035669103202976763622771817695493 (pp72) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 34.26 hours. Scaled time: 20.14 units (timescale=0.588). Factorization parameters were as follows: name: c111 n: 786247589989777914636073830302682947375520031653629043043502213698140564149219934257068310767319486956018538927 skew: 33636.57 # norm 3.04e+015 c5: 25920 c4: 3144008652 c3: -165915269317612 c2: -3366808236145090300 c1: 65987022536508996805519 c0: -83913059230236699400938539 # alpha -6.22 Y1: 168306501707 Y0: -1978718297937859459848 # Murphy_E 8.62e-010 # M 382289855528369169824421895336199655196115297917391454091611178216699183661511295281539641929425741668177499676 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2400001) Primes: RFBsize:230209, AFBsize:230419, largePrimes:7530904 encountered Relations: rels:7451513, finalFF:629444 Max relations in full relation-set: 28 Initial matrix: 460708 x 629444 with sparse part having weight 52954694. Pruned matrix : 325045 x 327412 with weight 28218188. Total sieving time: 29.63 hours. Total relation processing time: 0.40 hours. Matrix solve time: 3.93 hours. Time per square root: 0.29 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 34.26 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1
(5·10151-41)/9 = (5)1501<151> = 8807 · 2090089 · C141
C141 = P41 · P101
P41 = 11985535893412477734546646139854999516751<41>
P101 = 25181248688759856231710588775652390270239456503420879894844818915001826111432510170224977191479409487<101>
Number: 55551_151 N=301810760000077146934882355719805754244522020140143157553847294497017706100796642885120166592755779952215374038834393599733412999151844816737 ( 141 digits) SNFS difficulty: 151 digits. Divisors found: r1=11985535893412477734546646139854999516751 (pp41) r2=25181248688759856231710588775652390270239456503420879894844818915001826111432510170224977191479409487 (pp101) Version: GGNFS-0.77.1 Total time: 36.08 hours. Scaled time: 21.54 units (timescale=0.597). Factorization parameters were as follows: name: 55551_151 n: 301810760000077146934882355719805754244522020140143157553847294497017706100796642885120166592755779952215374038834393599733412999151844816737 m: 1000000000000000000000000000000 c5: 50 c0: -41 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2100001) Relations: rels:5700417, finalFF:582235 Initial matrix: 353156 x 582235 with sparse part having weight 52139676. Pruned matrix : 306424 x 308253 with weight 17013977. Total sieving time: 32.85 hours. Total relation processing time: 0.30 hours. Matrix solve time: 2.80 hours. Time per square root: 0.14 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: 36.08 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
(10613-1)/9 = (1)613<613> = 116511326129882791<18> · 1338285489332902166657911<25> · 1167883827993965201733843631<28> · C544
C544 = P36(1578...) · P36(4178...) · C473
P36(1578...) = 157818501697366913685542354577959717<36>
P36(4178...) = 417832220121515364538149502380148831<36>
C473 = [92529686120873990343331646774569359605383200587531417818236454390368869356415580228140609613497955460838507350423994235002078982421038981440839145461968437684528151941016349039119710736708391988071730726458391973172748638236782424739028612908524572972797032173010469396535113785013391541941058401658302567269148785675157132157433612203464707174823357971319412397911253267576408572089565418449213549477068089648406765856499332638101600661504414922416754050898040460592701003<473>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1
(4·10151-13)/9 = (4)1503<151> = 32 · 569 · 739 · 296843 · 2093219419<10> · C130
C130 = P57 · P73
P57 = 608858606877851551008985766196261799773945455000342152507<57>
P73 = 3104275453960187109937984286123825972776995247295782410574851825856126963<73>
Number: 44443_151 N=1890064828263309725274083499046605546833450559934940425099723669089227887530971292896451763065906695772892072780173366261700746241 ( 130 digits) SNFS difficulty: 151 digits. Divisors found: r1=608858606877851551008985766196261799773945455000342152507 (pp57) r2=3104275453960187109937984286123825972776995247295782410574851825856126963 (pp73) Version: GGNFS-0.77.1 Total time: 35.91 hours. Scaled time: 23.92 units (timescale=0.666). Factorization parameters were as follows: name: 44443_151 n: 1890064828263309725274083499046605546833450559934940425099723669089227887530971292896451763065906695772892072780173366261700746241 m: 1000000000000000000000000000000 c5: 40 c0: -13 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2100001) Relations: rels:5703153, finalFF:584406 Initial matrix: 352876 x 584406 with sparse part having weight 52535784. Pruned matrix : 305996 x 307824 with weight 17082130. Total sieving time: 32.57 hours. Total relation processing time: 0.36 hours. Matrix solve time: 2.85 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: 35.91 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1
(7·10151-43)/9 = (7)1503<151> = 33 · 29 · C148
C148 = P59 · P90
P59 = 45315988862875285213569229229556178268002361973050983850023<59>
P90 = 219200886965523354035724320238357087792206973888306661944263918310909301395050880685320197<90>
Number: 77773_151 N=9933304952462040584645948630622960124875833688094224492691925642117212998439052078898822193841350929473534837519511849013764722576983113381580814531 ( 148 digits) SNFS difficulty: 151 digits. Divisors found: r1=45315988862875285213569229229556178268002361973050983850023 (pp59) r2=219200886965523354035724320238357087792206973888306661944263918310909301395050880685320197 (pp90) Version: GGNFS-0.77.1 Total time: 45.55 hours. Scaled time: 30.33 units (timescale=0.666). Factorization parameters were as follows: name: 77773_151 n: 9933304952462040584645948630622960124875833688094224492691925642117212998439052078898822193841350929473534837519511849013764722576983113381580814531 m: 1000000000000000000000000000000 c5: 70 c0: -43 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2300001) Relations: rels:5323814, finalFF:394816 Initial matrix: 351642 x 394816 with sparse part having weight 35764287. Pruned matrix : 344365 x 346187 with weight 26333968. Total sieving time: 40.55 hours. Total relation processing time: 0.29 hours. Matrix solve time: 4.55 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 45.55 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS-0.77.1
(2·10153+61)/9 = (2)1529<153> = 47 · 45584453 · 28080199986351056858875439<26> · C118
C118 = P39 · P79
P39 = 671616835389977570079621109237856169919<39>
P79 = 5499853356503855968659112953597044134358448571426698521260112204765203148087759<79>
Number: 22229_153 N=3693794106404065858730314506980409104367505481133478480581009263807454409922295169004251243400306482394846724627921521 ( 118 digits) SNFS difficulty: 153 digits. Divisors found: r1=671616835389977570079621109237856169919 (pp39) r2=5499853356503855968659112953597044134358448571426698521260112204765203148087759 (pp79) Version: GGNFS-0.77.1 Total time: 56.97 hours. Scaled time: 37.88 units (timescale=0.665). Factorization parameters were as follows: name: 22229_153 n: 3693794106404065858730314506980409104367505481133478480581009263807454409922295169004251243400306482394846724627921521 m: 1000000000000000000000000000000 c5: 2000 c0: 61 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2700001) Relations: rels:5744016, finalFF:475866 Initial matrix: 352137 x 475866 with sparse part having weight 49699157. Pruned matrix : 333291 x 335115 with weight 25753267. Total sieving time: 51.98 hours. Total relation processing time: 0.44 hours. Matrix solve time: 4.41 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 56.97 hours. --------- CPU info (if available) ----------
By Wataru Sakai / GMP-ECM 6.0.1
3·10162-1 = 2(9)162<163> = 1586308304691323221318531843777<31> · C133
C133 = P36 · P98
P36 = 152512406662190891155427973892329217<36>
P98 = 12400194079641198397538641885769926694273799859212033454948583982801438301040530455353496340235711<98>
3·10167-1 = 2(9)167<168> = 7 · 7643 · 5308447 · C157
C157 = P38 · C119
P38 = 22854213927330216399615920416772214007<38>
C119 = [46219535988371850084418374386615219342097027661120626172731378243865022947240172061060017102055950948979932685073852531<119>]
By Sinkiti Sibata / GGNFS-0.77.1
(2·10152+61)/9 = (2)1519<152> = 19 · 661 · 3110104741<10> · C138
C138 = P36 · P103
P36 = 212106865486264043300787031493682199<36>
P103 = 2682271187373818595628680353095781651261120492663158413594580075578341939139175919064741649056564506009<103>
Number: 22229_152 N=568928133937980278199098064552428646633330057246257057269990790106201631376496707972280571278537623830907316340729803882559809990871833791 ( 138 digits) SNFS difficulty: 152 digits. Divisors found: r1=212106865486264043300787031493682199 (pp36) r2=2682271187373818595628680353095781651261120492663158413594580075578341939139175919064741649056564506009 (pp103) Version: GGNFS-0.77.1 Total time: 40.24 hours. Scaled time: 26.76 units (timescale=0.665). Factorization parameters were as follows: name: 22229_152 n: 568928133937980278199098064552428646633330057246257057269990790106201631376496707972280571278537623830907316340729803882559809990871833791 m: 1000000000000000000000000000000 c5: 200 c0: 61 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2200001) Relations: rels:5449459, finalFF:461888 Initial matrix: 352626 x 461888 with sparse part having weight 40268875. Pruned matrix : 331996 x 333823 with weight 20373572. Total sieving time: 35.71 hours. Total relation processing time: 0.34 hours. Matrix solve time: 4.04 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: 40.24 hours. --------- CPU info (if available) ----------
By Yousuke Koide / GMP-ECM
(10867-1)/9 = (1)867<867> = 3 · 37 · 613 · 42773 · 210631 · 2071723 · 52986961 · 93101929 · 1112647111<10> · 5363222357<10> · 234771432523<12> · 6270681177984151<16> · 13168164561429877<17> · 93195753455238027770502373<26> · 74451201112778571232641337987561693<35> · 25086158646798685749029022942725879293529996353937930044688310225209792405267161387550045665503080767367139652501504645587640324255739525766942448322852994756555563269219516158897234150632016254115138596672215506548424356751044570760748443769<242> · C465
C465 = P35 · C431
P35 = 20086446755059947304637543254330027<35>
C431 = [43847928340273007036683492466629425347593144386187849570352692715343015468508233711269987298844088842010811958146922848088904584451385409058136753439089940818345804415994995588939268929792742826083627766997939694984246400007687684923922833991165782358300738461285079416521540204902744071543408565874874731448917358285646695823461539103120712047524782671709937412975148617883482385473395336582811704194633808078648898999907547620693<431>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
By Sinkiti Sibata / GGNFS-0.77.1
(10153+71)/9 = (1)1529<153> = 7 · 5113880010251<13> · C139
C139 = P51 · P89
P51 = 102810924599828884362050857164373075486103832573319<51>
P89 = 30190454557728793269250249717674139102743562662711596919033095611883027825428747426710493<89>
Number: 11119_153 N=3103908547169215253162254552873669619616617637161201595918077528854736573322626119479853392157234575315036994281948666107068847843409136267 ( 139 digits) SNFS difficulty: 155 digits. Divisors found: r1=102810924599828884362050857164373075486103832573319 (pp51) r2=30190454557728793269250249717674139102743562662711596919033095611883027825428747426710493 (pp89) Version: GGNFS-0.77.1 Total time: 53.43 hours. Scaled time: 35.48 units (timescale=0.664). Factorization parameters were as follows: name: 11119_153 n: 3103908547169215253162254552873669619616617637161201595918077528854736573322626119479853392157234575315036994281948666107068847843409136267 m: 10000000000000000000000000000000 c5: 1 c0: 7100 skew: 2 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 2800001) Relations: rels:5486477, finalFF:518137 Initial matrix: 434532 x 518137 with sparse part having weight 39785945. Pruned matrix : 414550 x 416786 with weight 23920260. Total sieving time: 47.55 hours. Total relation processing time: 0.32 hours. Matrix solve time: 5.41 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 53.43 hours. --------- CPU info (if available) ----------
By Kenichiro Yamaguchi / GGNFS-0.77.1
10179-3 = (9)1787<179> = C179
C179 = P44 · P62 · P74
P44 = 47527552610960667080491218952801922312569073<44>
P62 = 38918563279240249010933742596447312973214118388632853991466677<62>
P74 = 54062702222061890579230284912359478718122077297383163210696543917211696057<74>
Number: 99997_179 N=99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 ( 179 digits) SNFS difficulty: 180 digits. Divisors found: r1=47527552610960667080491218952801922312569073 (pp44) r2=38918563279240249010933742596447312973214118388632853991466677 (pp62) r3=54062702222061890579230284912359478718122077297383163210696543917211696057 (pp74) Version: GGNFS-0.77.1 Total time: 623.03 hours. Scaled time: 484.09 units (timescale=0.777). Factorization parameters were as follows: name: 99997_175 n: 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 m: 1000000000000000000000000000000000000 c5: 1 c0: -30 type: snfs skew: 1 qintsize: 100000 Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [3700000, 8100001) Relations: rels:6798472, finalFF:1134568 Initial matrix: 1002617 x 1134568 with sparse part having weight 56588036. Pruned matrix : 947705 x 952782 with weight 39508237. Total sieving time: 606.40 hours. Total relation processing time: 0.97 hours. Matrix solve time: 15.38 hours. Time per square root: 0.28 hours. Prototype def-par.txt line would be: snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 623.03 hours. --------- CPU info (if available) ----------
Note: This is the second largest number factored by GGNFS in our tables. Congratulations!