From maro at isl.ntt.co.jp Mon Jun 21 00:27:40 2004 Recently I noticed that you made the 3LM extension table: http://www.cerias.purdue.edu/homes/ssw/cun/3LM I factored one of composites in the table c146 in 3,1377L = p36 . p110 p36 = 704104974521439858171605401239347119 Using GMP-ECM5 with B1=1000000 and sigma=1845881170 Best regards, Kazumaro Aoki at NTT Labs From maro at isl.ntt.co.jp Wed Jun 23 05:40:33 2004 I have found a new factor from the extended 3LM table: c118 in 3,1755M = p43 . p75 p36 = 5505826412841262001746359790144119203350351 Using GMP-ECM5 with B1=3000000 and sigma=3535901284 Best regards, Kazumaro Aoki at NTT Labs From maro at isl.ntt.co.jp Tue Aug 17 20:40:15 2004 Dear Paul Leyland and Sam Wagstaff, I found a new factor from the extended 3LM table: c162 in 3,1533L = p42 . p120 p42 = 377667606055574411584732518101496032645221 Using GMP-ECM5 with B1=11000000 and sigma=4046627650 Best regards, Kazumaro Aoki at NTT Labs From christophe.clavier at gemplus.com Wed Aug 25 03:47:45 2004 3,1677M c234 644838232111522679335349578277194759. c198 Eric Brier and Christophe Clavier From christophe.clavier at gemplus.com Thu Aug 26 03:34:01 2004 We have completed the factorization of the cofactor 3,1209M of the Cunningham number 3^1209+1. Indeed we have: 3^1209+1 = (3^403+1) * L * M where M = 3^403 + 3^202 + 1 = (157 * 373 * 10141 * 541447 * 3058399) * 16927 * 8972095773130410261992977 * c143 = (157 * 373 * 10141 * 541447 * 3058399) * 16927 * 8972095773130410261992977 * p33 * p111 c143 = 12754175694129254423402176873479515123689464602925293735270309499164984219435318572984978076958987069641894952816535980351001979954826703621951 p33 = 104214141181351378302389476423069 p111 = 122384309360998247235940063561872388083050908764579475105027694483402759508625480620330895961457722359120285579 The factor was found on "Thu Aug 26 07:10:50 2004" by an own implementation of ECM with B1=3e6 and B2=3e8. The winning curve is y^2 = x^3 + a*x + b with, a = 33482550341955995897206738996119 b = 73142796697094925033942968637382 and the starting point on the curve is (x0:y0:1) with, x0 = 97703386305791345886438815068059 y0 = 43527859869911081895442225018727 The factorisation of the curve order is: #E = 104214141181351364460048296663544 = 2^3 * 3^2 * 2383 * 5717 * 11779 * 642419 * 1162081 * 12081997 Credits must conjointly go to Eric Brier and Christophe Clavier. Cheers, Eric & Christophe PS : Thanks to reply to both discoverers From christophe.clavier at gemplus.com Mon Aug 30 04:37:49 2004 3,1299M : c202 = p35 * p167 p35 = 72294725439409852600619119163684989 p167 = 15699907553631673835088720676147779193076555382157913339177784853763686462870506492752576492212322736133645158157557950634628006965882177348385366381692092784577773463 3,1311L : c166 = p39 * p128 p39 = 197019064534643578236470519860924797481 p128 = 24624103610260039837348488899328442714177239840580062653770727338167664176632475997131522634436835090168518875067102706634790209 3,1323L : c163 = p34 * p129 p34 = 6984887381669898746134586894281501 p129 = 979562403808828867075765886633895815352051381300114533470493760314957159184077629379465205692080362373464501731587793419918611163 3,1335M : c133 = p37 * p40 * p57 p37 = 3204904531701877804575792123993929101 p40 = 1456709174321118298895999730143218667581 p57 = 699311248614694211384238575278356628471513758163123019941 3,1371L : c178 = p39 * p139 p39 = 217554631041972451443797098558007039161 p139 = 8219997427023679689845086671767373275595114711013355877154304804873573858286898549100074762819464488994227185246976991956244294089994748297 3,1377L : c146 = p36 * p110 p36 = 704104974521439858171605401239347119 p110 = 25527169167475025741711447858437911746090312837179294874375780792977629770384821984587744266010289678674379909 3,1383L : c213 = p37 * c176 p37 = 2673259958697812507617881136246428379 c176 = 87724317262438544425315980406445983190184321534203602277930250842665644923215843006435781457338211528606913033917014768222117615364368580740620638776002299173838812719571749357 From christophe.clavier at gemplus.com Fri Sep 3 01:55:12 2004 3,1557L : c169 = p36 * c134 p36 = 108599989773642835219110454527234001 c134 = 34682686763403822263489875756284522174289169971781674021070596819516629513395252327931822542622388786719450260589139257645779334507451 3,1299L : c160 = p35 * p126 p35 = 24518336107758964004567688595327267 p126 = 391801889306169273087360829989070973523355356940964819637041116921136587473012443283133350862122867674705201290415097141378211 From christophe.clavier at gemplus.com Thu Sep 9 01:44:50 2004 3,1443M : c168 = p38 * p131 p38 = 17897550933983682381524022832723680547 p131 = 24641993237208973245915534707333516083866757855156379713003513836245528854283583368267183262262990237512136476481528947723351408757 3,1455M : c135 = p34 * p102 p34 = 1565183882137144946648898538725391 p102 = 588732453011753508013694503091100490261928459157514647309296941697666832507096172127852923090672844101 3,1473M : c214 = p36 * c178 p36 = 419701010039666236565045972319840541 c178 = 9392184058866892027225793962402705356703031067553603711692538613241512802460819955475898527247404819112894581072571468361456518086145391773184817482452709873397220743572550918247 3,1485M : c172 = p33 * c139 p33 = 728533568225878800721661003585941 c139 = 7867367539262740526357986080871712730691717228424552566253272499360425543450939724888979252972257011767004722354248344212108059625550126381 From christophe.clavier at gemplus.com Fri Sep 17 09:42:21 2004 3,1791M : c281 = p38 * p243 p38 = 78541858916736851129320066561505080849 p243 = 129803822729382437174756280986669648785650081927776830108806450780883818984104377920454880078018109768263827081072647321498369486661559822452580677987998789487837646296815944601693403711785869806518184821365945124409000934505252191103360070747 3,1383M : c194 = p39 * p156 p39 = 101230960987312031866957790447845050391 p156 = 244426577552942124333180821391655985484321330121681177392741652016188840520386781840726300913915237531131314889814495269356309232646689600096727491163577243 3,1521M : c179 = p34 * p34 * p112 p34 = 5851380513076385535484370482767823 p34 = 8002439729908294163002140206186911 p112 = 1174131098667391081033842907084422050486157065767468498802915243298908943070470792867431859010920163736965806247 From christophe.clavier at gemplus.com Mon Sep 27 09:22:31 2004 3,1563L : c232 = p35 * c197 p35 = 34519678373151698155933989949555159 c197 = 37624918654207220603566069436484134155570183764757237605223098019692642105061973852665534377528558492954936280373434333584867515842170837890381681378974395107974342279162849953177720466778861767357 3,1347M : c163 = p34 * p129 p34 = 9616790564899660933918984330332787 p129 = 159129663612215806956902501181249741589602013005447136085759909536154333582488511852828056237406679733458206246186845473468369007 3,1617L : c197 = p36 * c161 p36 = 238958551200611078500890308107077823 c161 = 47177277943194767050546613198911025603296643415336943789318399913338214081495229058742483264350732233884484579851094584752331704535481658397879775274054500438553 From maro at isl.ntt.co.jp Tue Oct 12 20:22:41 2004 I found factors from the extended 3LM table: c165 in 3,1617M = p45 . c121 p42 = 121934855918652005425425185516541065340216577 Using GMP-ECM5 with B1=43000000 and sigma=2642837151 c121 in 3,1617M = p48 . p73 p48 = 476266745652632045310161945284909891520767955887 Using GMP-ECM5 with B1=43000000 and sigma=3381238981 Best regards, Kazumaro Aoki at NTT Labs From christophe.clavier at gemplus.com Fri Oct 15 09:13:49 2004 3,1293L : c166 = p42 * c124 p42 = 654939898481980657804817856776510924445547 c124 = 3174173963124030911468212309336233783723661742440492597090227332140430147322372605862953005457414079187854433713436156353037 3,1389M : c157 = p41 * p117 p41 = 52230324397879426011825816300492539615257 p117 = 158756751973047219056656112485888435250504009653077589945254444751525665687725978577133528407135856626219383730986383 From christophe.clavier at gemplus.com Mon Oct 25 01:49:55 2004 3,1461L : c196 = p37 * p159 p37 = 4001107679969153471668159060060172149 p159 = 413324127416399227914450536430536165793427316860061109382246242158507886547853177970318425804030483617668830764751927976080704305529264936028814620018564578087 3,1743M : c225 = p36 * c190 p36 = 165718850995790755889408413510958659 c190 = 4996928928282317103640650450704446114345728504411650039872369101384461980322807948057251334961079160764963010183052910298099789060722662179217774469010445475943037113504602163670829201181029 From christophe.clavier at gemplus.com Thu Oct 28 10:53:36 2004 3,1431L : c154 = p40 * p114 p40 = 3927892755414960353222801138344493547469 p114 = 487064336631755853101136765463511604804130773735941478314387532805730726209019436937698145520323678644840445409077 From christophe.clavier at gemplus.com Thu Nov 4 04:59:58 2004 3,1437M : c228 = p37 * c192 p37 = 3398498146142284897724797703967083713 c192 = 146115380499508207535919587778834604659072089638324943159442197833458075843542774650593725078007126981600649696411122378062121559188357009483417550044074202762833936552274773579668480188393259 From maro at isl.ntt.co.jp Fri Nov 5 08:09:41 2004 I found a factor from the extended 3LM table: c124 in 3,1293L = p51 . p74 p51 = 265287347170307102473334860992823790658456216950833 Using GMP-ECM5 with B1=11000000 and sigma=1227917157 Best regards, Kazumaro Aoki at NTT Labs From christophe.clavier at gemplus.com Mon Nov 15 08:38:01 2004 3,1731L : c254 = p31 * c223 p31 = 9620165017104637878779546452501 c223 = 1646763098247641310437983515996223911780751490476206319495697634935389164860289666696673764935950494483646288445225019704178226334624068459020788741650400901280369184708945862278202957831503073468035577699905466174777278107 3,1749M : c234 = p31 * p203 p31 = 6039140016670342659598900465549 p203 = 21148181949374608678249357006334414413702540085806470705398897000729752368024704685306862541134701003798735457009614028613116723324601418928273763475905777298379241455002360540104842866391856375045279587 From maro at isl.ntt.co.jp Mon Nov 15 20:32:01 2004 I found factors from the extended 3LM table: c161 in 3,1617L = p44 . c118 p42 = 39176411954757684279286049848109010550909057 Using GMP-ECM5 with B1=11000000 and sigma=4046627650 c118 in 3,1617L = p45 . p73 p45 = 166463779642956973878860171631999409509399613 Using GMP-ECM5 with B1=43000000 and sigma=3451517535 Best regards, Kazumaro Aoki at NTT Labs From maro at isl.ntt.co.jp Wed Nov 17 20:24:41 2004 I found factors from the extended 3LM table: c134 in 3,1557L = p55 . p80 p55 = 1268413494411135671239686038243358243539607519968737801 Using GMP-ECM5 with B1=43000000 and sigma=1073421943 Best regards, Kazumaro Aoki at NTT Labs From maro at isl.ntt.co.jp Sat Feb 5 06:41:47 2005 I found factors from the extended 3LM table: c112 in 3,1683M = p54 . p59 p54 = 110995096534055033775812456877810354806490499839538741 p59 = 89684744058358371782836080654176665490827739409519835653337 using our GNFS code with Kleinjung's polynomial selection code. It takes about 2 days in a P4 2.8GHz PC. Best regards, Kazumaro Aoki at NTT Labs From aoki.kazumaro at lab.ntt.co.jp Sun Jul 31 23:05:19 2005 I factored 116 digits cofactor in 3,1455L using GNFS. 3,1455Lc116 = p55 . p63 p55 = 3146955858766457814647982108433483105173251986980374041 p63 = 303009812924778824178065624113774042812430103863443808702143391 Kazumaro Aoki at NTT Labs From paul at leyland.vispa.com Tue Oct 11 06:38:21 2005 Sam, I realise that this is of no immediate interest to the Cunningham tables but it may become so at some point in the future. I and a few others have been factoring numbers of the form n*a^n\pm1 with n<=1000 and a<=12, the so-called generalized Cullen and Woodall numbers. This morning I completed the factorization of GW(3,729), which is also 3^735-1, when P-1 found a p39.p88 factorization. Presumably the 3- table will eventually be extended to index 750 or so, in which case this entry may prove useful. Note that algebraic factors are not given separately, but separating them is essentially trivial. 729 2.11.11.13.71.421.491.1093.4019.4561.6301.8233.32341.47041.51157. .131713.368089.1616161.87459121.2664097031.26751945361. .58770727715103776715586741. .254395969103901649521223867932173929. .536827955723741125410788967206335237321. .4430152977536859072181134657493233649089245714747389001639572141363110009421.P88 Regards, Paul From alexander.kruppa at mytum.de Thu Jan 19 05:42:15 2006 Here is a p42 of 3,823- which had no known primitive prime factors before. Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=3988002431 Step 1 took 58539ms Step 2 took 25095ms ********** Factor found in step 2: 974228888530699445757319146555496498314349 Found probable prime factor of 42 digits: 974228888530699445757319146555496498314349 Composite cofactor (phi(823,3))/974228888530699445757319146555496498314349 has 351 digits Alex From wesolowski.ids.pl June 29 2007 Arkadiusz would like to dedicate the discovery to his mother, Barbara. (3^2531-1) = (2(trivial) * 76628557 * Prime1200) Arkadiusz Wesolowski (prime proof by ECPP) From wesolowski.ids.pl August 19 2007 I completed the factorization of the Cunningham number 3^2131-1. (3^2131-1) = (2 * 459589675789 * 147045472166651 * Prime991) Arkadiusz Wesolowski From wesolowski.ids.pl August 30 2007 (3^2417-1) = (2 * 4767160283 * Prime1144) The factor was found on August 28, 2007. Prime proof by ECPP. Arkadiusz Wesolowski From dagdex at yahoo.it Mon Oct 8 05:27:52 2007 From: Dagobert Dexter >From Valerio Sisti , Scuola del Corso Arezzo Italy Illustre signor Sam Wagstaff I have completed the factorization of the Aurifeuillian 3,1245M in the extended table 3LM. M = 3^415+3^208+1 = c199 c199 = c43 * c156 c43 = 271*1993*57957241*9839624437*3511321676267937799 (algebric part) c156 = p26 * p41 * p43 * p47 p26 = 91693819532064792506744551 p41 = 52756883599525473146299535861842572044371 p43 = 2352841863097081277716466456704233668694601 p47 = 82238530244732182031635554132790553456887049461 From dagdex at yahoo.it Sat Jan 19 09:04:05 2008 from Valerio Sisti Scuola del Corso Arezzo Italy Dear Professor Wagstaff I have found a new factor from the extended 3LM table: c182 in 3,1479L = p43 . c140 p43 = 1195496928653800716779761036930067651090617 Using GMP-ECM6.1.3 with B1=5e6 Also I submit the complete factorization of 5,474+ (5^474+1)/5^158+1)/601=43609*157651060477*1133101180287529*3367254562316010241*10074918917599232092884277* *58400466995304188804026921*30967644304103854956320826397*29674700910032777583435863458273573*P55 Using GMP-ECM6.1.3 and Msieve1.22 Best regards Valerio Sisti Scuola del Corso Arezzo Italy Date: Fri, 25 Jan 2008 10:01:19 +0100 (CET) From: Dagobert Dexter From Valerio Sisti Scuola del Corso Arezzo Italy Dear Professor Wagstaff I have found a new factor from the extended 3LM table: C155 in 3,1269L = p37 . p118 p37 = 2985388008268680178763152029796515313 Using GMP-ECM6.1.3 with B1=5e6 and sigma=377109790 Best regards Valerio Sisti From tom at womack.net Sun Jan 27 13:36:06 2008 I've done the C145 of 2^1365+1 by GNFS: Sun Jan 27 15:37:48 2008 prp54 factor: 307125743850143133483913160596928028514251505520546641 Sun Jan 27 15:37:48 2008 prp91 factor: 568873176907329522682244333977278165991761609611850302082958068765036652 8080737234892225491 { the complete factorisation of 2^1365+1 is, thanks to its many algebraic factors, now easy if cumbersome to write down as 3 3 11 43 131 211 281 331 547 2731 5419 35491 86171 107251 131041 224771 409891 436801 664441 1210483 1564921 2511601 7623851 22366891 1185685411 25829691707 105310750819 4663895387971 39537592800161 171525190684121 571403921126076957182161 292653113147157205779127526827 327061478509556968075523586322717436918466721 307125743850143133483913160596928028514251505520546641 568873176907329522682244333977278165991761609611850302082958068765036652 8080737234892225491 } Tom From dagdex at yahoo.it Mon Feb 25 04:49:59 2008 from Valerio Sisti Scuola del Corso Arezzo Italy Dear Professor Wagstaff I have found three new factors from the extended 3LM table: 1) c199 in 3,1443L = p45 . c154 p45 = 327989896957482033146397865633925722501302373 Using GMP-ECM6.1.3 with B1=5e6 and sigma=2846841166 2) c219 in 3,1521L = p39 . c181 p39 = 114910003172322436455447319908539210773 Using GMP-ECM6.1.3 with B1=5e6 and sigma=1442026316 3) c162 in 3,1785M = p37 . c125 p37 = 3487112551339276492962187385415678301 Using GMP-ECM6.1.3 with B1=5e6 and sigma=3311715559 Best regards Valerio Sisti From: Dagobert Dexter Date: Thu, 13 Mar 2008 16:49:48 +0100 (CET) Subject: factors for the extended 3LM table from Valerio Sisti Scuola del Corso Arezzo Italy Dear Professor Wagstaff I have found two new penultimate factors from the extended 3LM table: C256 in 3,1797L = p34 . p222 p34 = 7856091882646592100947226223272217 Using GMP-ECM6.1.3 with B1=5e6 and sigma=3147864373 C198 in 3,1677M = p39 . p159 p39 = 623946491284066832337611657335109969863 Using GMP-ECM6.1.3 with B1=5e6 and sigma=2759787378 Best regards Valerio Sisti