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News and updates, December 2006

Dec 28, 2006 (2nd)

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)

Dec 28, 2006

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) ----------

Dec 26, 2006 (2nd)

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)

Dec 26, 2006

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) ----------

Dec 25, 2006 (2nd)

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>]

Dec 25, 2006

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.

Dec 23, 2006

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) ----------

Dec 21, 2006 (2nd)

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)

Dec 21, 2006

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) ----------

Dec 20, 2006

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)

Dec 19, 2006

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>]

Dec 13, 2006

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) ----------

Dec 9, 2006

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)

Dec 8, 2006

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)

Dec 6, 2006

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) ----------

Dec 5, 2006 (2nd)

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)

Dec 5, 2006

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>

Dec 4, 2006 (2nd)

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>]

Dec 4, 2006

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) ----------

Dec 3, 2006

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) ----------