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News and updates, February 2006

Feb 28, 2006

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: primeform : Message: Primality proof of (34*10^15768-43)/9 - need help! (Yahoo! Groups primeform)

Feb 27, 2006

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) ----------

Feb 24, 2006

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)

Feb 23, 2006

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) ----------

Feb 21, 2006

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) ----------

Feb 20, 2006 (2nd)

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)

Feb 20, 2006

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) ----------

Feb 18, 2006

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>]

Feb 17, 2006

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 = P36 P36 = 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) ----------

Feb 14, 2006 (2nd)

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) ----------

Feb 14, 2006

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) ----------

Feb 12, 2006

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>]

Feb 11, 2006

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) ----------

Feb 10, 2006 (2nd)

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) ----------

Feb 10, 2006

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) ----------

Feb 9, 2006 (3rd)

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) ----------

Feb 9, 2006 (2nd)

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) ----------

Feb 9, 2006

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) ----------

Feb 7, 2006 (2nd)

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) ----------

Feb 7, 2006

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>

Feb 5, 2006 (4th)

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)

Feb 5, 2006 (3rd)

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) ----------

Feb 5, 2006 (2nd)

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

Feb 5, 2006

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) ----------

Feb 4, 2006 (2nd)

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>

Feb 4, 2006

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>

Feb 3, 2006 (2nd)

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>

Feb 3, 2006

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) ----------

Feb 2, 2006 (3rd)

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) ----------

Feb 2, 2006 (2nd)

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>

Feb 2, 2006

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) ----------

Feb 1, 2006 (2nd)

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>

Feb 1, 2006

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>