From maro 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 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 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 Wed Aug 25 03:47:45 2004 3,1677M c234 644838232111522679335349578277194759. c198 Eric Brier and Christophe Clavier From christophe.clavier 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 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 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 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 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 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 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 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 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 Thu Oct 28 10:53:36 2004 3,1431L : c154 = p40 * p114 p40 = 3927892755414960353222801138344493547469 p114 = 487064336631755853101136765463511604804130773735941478314387532805730726209019436937698145520323678644840445409077 From christophe.clavier Thu Nov 4 04:59:58 2004 3,1437M : c228 = p37 * c192 p37 = 3398498146142284897724797703967083713 c192 = 146115380499508207535919587778834604659072089638324943159442197833458075843542774650593725078007126981600649696411122378062121559188357009483417550044074202762833936552274773579668480188393259 From maro 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 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 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 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 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 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 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 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 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 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 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 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 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 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 Date: Mon, 01 Sep 2008 04:47:48 -0600 From: Rocke Verser Subject: Factorization of 3^960+1 I have completed the factorization of 3^960+1, as shown below. The primitive part of 3^960+1 is factored as: primitive.of.3^960+1 = 495361.1843201.1455208537217840158394426881.200451274365805063668773322241.p176 To the best of my knowledge, the p28.p30.p176 factorizations were not previously known. Cheers! -- Rocke Verser A factor was found for primitive.of.3^960+1 using GMP-ECM using factor method ECM Candidate number: 21163520232630639991587184449192363590412111727747655255157404882686773733719774635531174519992444318435405196247396064013860484251383133928126527200113068649599534378834596301917368871656546434315863247621704015225382191661697352961 Factor: 1455208537217840158394426881 Factor Type: probable Factor Length: 28 Co-Factor: 14543290319813817395673241090128445101945893565153702230193069067265249380092115156855690289969683904113825131573190833000223588573294997017958593879194273964598320422562861519012397335401760565286034087681 Co-Factor Type: Composite Co-Factor Length: 206 B1: 250000 Sigma: 334528841 A factor was found for primitive.of.3^960+1_1 using GMP-ECM using factor method ECM Candidate number: 14543290319813817395673241090128445101945893565153702230193069067265249380092115156855690289969683904113825131573190833000223588573294997017958593879194273964598320422562861519012397335401760565286034087681 Factor: 200451274365805063668773322241 Factor Type: probable Factor Length: 30 Co-Factor: 72552745627716268153936384264631098004395035082053242627095698316767639216542500440992580564438112590450036791042786736020532535210409924630684392562879708847728056257072963841 Co-Factor Type: Probable Co-Factor Length: 176 B1: 1000000 Sigma: 3754240073 Date: Tue, 02 Sep 2008 02:48:20 -0600 From: Rocke Verser Subject: Factorization of 3^648+1 I have completed the factorization of 3^648+1, as shown below. The primitive part of 3^648+1 is factored as: primitive.of.3^648+1 = 23849414895235393.11737389581320622965551361.1589571835054110407091053013448488769.p129 To the best of my knowledge, the c165=p37.p129 factorization was not previously known. [See also, cyclotomic polynomial x^108+1, x=729] Cheers! -- Rocke Verser A factor was found for primitive.of.3^648+1_1 using GMP-ECM using factor method ECM Candidate number: 467017108234695206238902604234549878026998780537787172233478174916889732197044033717502787827011488418355518185973555697608095413667237087812702819083990622574889377 Factor: 1589571835054110407091053013448488769 Factor Type: probable Factor Length: 37 Co-Factor: 293800568137769966145245151636844667736020095102516769401696757816211815927266356815606317880971293377236053869670293424696040033 Co-Factor Type: Probable Co-Factor Length: 129 B1: 1000000 Sigma: 3137973503 Date: Sat, 13 Sep 2008 10:35:47 -0600 From: Rocke Verser I have completed the factorization of 3^945-1, as shown below. The primitive part of 3^945-1 is factored as: primitive.of.3^945-1 = 13766761.1483457221.71056301875021.243828451380420964460938501. 437926273109426034305860414748221. 843741327089277331721090872660165662167232052209572695487111440354649004343187602338083414935717149720018448968509641} To the best of my knowledge, the c176=p27.p33.p117 factorizations were not previously known. Cheers! -- Rocke Verser A factor was found for primitive.of.3^945-1_1 using GMP-ECM using factor method ECM Candidate number: 90093758127479257718615416494034530036128629896284812922067127202934875285116433270538817045300966554619558850607091555799975134487912012506967670096121676944220530100279447161 Factor: 243828451380420964460938501 Factor Type: probable Factor Length: 27 Co-Factor: 369496494840608427547345455938466071481368354805369518259924654147335592470292282240118010414427732026120297755441292332035442275201949664918626098661 Co-Factor Type: Composite Co-Factor Length: 150 B1: 250000 Sigma: 2914447901 A factor was found for primitive.of.3^945-1_1_1 using GMP-ECM using factor method ECM Candidate number: 369496494840608427547345455938466071481368354805369518259924654147335592470292282240118010414427732026120297755441292332035442275201949664918626098661 Factor: 437926273109426034305860414748221 Factor Type: probable Factor Length: 33 Co-Factor: 843741327089277331721090872660165662167232052209572695487111440354649004343187602338083414935717149720018448968509641 Co-Factor Type: Probable Co-Factor Length: 117 B1: 3000000 Sigma: 2229082644 Date: Wed, 17 Sep 2008 23:46:41 -0600 From: Rocke Verser I have completed the factorization of 3^693-1, as shown below. The primitive part of 3^693-1 is factored as: primitive.of.3^693-1 = 8480390689 . 103600005401243737 . 18640970977551223539934315621 . 159726751678525658083898531371647932938681 . 2303553067912647527083722959256790534926418329636639482985280187359007831437 To the best of my knowledge, the p29.p42.p76 factorizations were not previously known. Cheers! -- Rocke Verser A factor was found for primitive.of.3^693-1_1 using GMP-ECM using factor method ECM Candidate number: 6858741131247212949113923303420781185659290945012374097750990799720432877804395786921492133819908711814494098423244745887239471680971869372219737 Factor: 18640970977551223539934315621 Factor Type: probable Factor Length: 29 Co-Factor: 367939048856789402645880142437273568798169390258336513569733592581580991831802903945447991821713512722706468505114597 Co-Factor Type: Composite Co-Factor Length: 117 B1: 250000 Sigma: 2473630057 A factor was found for primitive.of.3^693-1_1_1 using GMP-ECM using factor method ECM Candidate number: 367939048856789402645880142437273568798169390258336513569733592581580991831802903945447991821713512722706468505114597 Factor: 159726751678525658083898531371647932938681 Factor Type: probable Factor Length: 42 Co-Factor: 2303553067912647527083722959256790534926418329636639482985280187359007831437 Co-Factor Type: Probable Co-Factor Length: 76 B1: 11000000 Sigma: 2340304646 Date: Sat, 4 Apr 2009 07:08:49 +0000 (GMT) Subject: 3,1785M completed From Valerio Sisti Scuola del Corso Arezzo Italy Dear Professor Wagstaff I have found a new penultimate factor from the extended 3LM table: C125 in 3,1785M = p47 . p79 p47 = 11684493917749480329477000912638408177177293141 Using GGNFS and Msieve - Thanks Chris Monico and Jason Papadopoulos. Best regards Valerio Sisti Wed May 20 03:59:36 2009 From Valerio Sisti Scuola del Corso Arezzo Italy Dear Professor Wagstaff I found two prime factors completing an entry from the extended 3LM table: c167 in 3,1785L = p41 * c127 p41 = 11602837029074603473099331048901180822811 Using Msieve (in ECM mode) c127 in 3,1785L = p52 * p75 p52 = 8168664655496021662526746022020996941523461342977701 Using GGNFS and Msieve (May 8 - May 19, 2009) Best regards Valerio Sisti Wed Jul 15 06:45:17 2009 >From Valerio Sisti Scuola del Corso Arezzo Italy Dear Professor Wagstaff I have completed another entry from the extended 3LM table: c146 in 3,1359L = p40 * c106 p40 = 6899030887465321400524120466233864197943 Using Msieve (in ECM mode) c106 in 3,1359L = p49 * p58 p49 = 2022294677035020074854486664093028261522434362123 Using GGNFS and Msieve (14th-15th July 2009) Per aspera ad astra Valerio Sisti Thu Aug 20 03:46:29 2009 >From Valerio Sisti, Scuola del Corso Arezzo, Italy Dear Sam Here are six more completed entries from extended Cunningham Tables, done mainly using GMP-ECM 6.2.3 3,724+ (3^724+1)/(3^4+1)=95569*12866929*1378763610289096643037119101193*p302 7,426+ (7^426+1)/(7^142+1)/(13*181)=5805529*61096921*14520980034353029*177975632= 3460738853*1307129149621472226319357*183379247600051304020496173940481*p132 11,303- (11^303-1)/(11^101-1)/(7*19)=607*549643*72993247727041*148050455165687645= 16541*224121152998661467362601857061*p135 12,342+ (12^342+1)/(12^114+1)/(73*122138321401)=27361*310604401*12348362809*30422= 3696426737*4676888770289898553*38929814623432765735561*34678079311256579060= 765180713*4926117284784160987559042600200729*p93 12,349+ (12^349+1)/13=136796833*6657213955019705244277781494659747139*p331 12,603M (12^201+1+2^201*3^101)/1657=37948886981947*165005354024346709*20954239462= 618482188564604919*210469877070599169710131278720871*1100121132262297102406= 82655743829157534683*p82 Best regards Valerio Sisti From: Valerio Sisti, Scuola del Corso Arezzo Italy Subject: 3,1485M completed Tue Sep 2, 2009 Using gGNFS, I found the penultimate prime factor of 3,1485M: c139 in 3,1485M = p54 * p86 p54 = 408357497164678483608973463538490157762187609740820571 Best wishes Valerio Sisti From: Valerio Sisti, Scuola del Corso Arezzo Italy Thu Sep 17 08:31:40 2009 Subject: an entry from extended Cunningham tables completed I submit the complete factoring of 3^630+1 (the primitive part is a c138): c138 = p4 * p65 * p70 p4 = 7561 p65 = 12590175379400132061492944820636383346706910611864696890158853481 (done with GGNFS in about 10 days) Best regards, Valerio Sisti From Valerio Sisti Dear Professor Wagstaff I have found a new factor from the extended 3LM table: C140 in 3,1479L = p55 . p86 p55 = 1315924956569789619337671062640003985324619492796255289 Using GGNFS and Msieve (September 1 - October 31, 2009) Best regards Valerio Sisti From: Timothy Sorbera Date: Mon, 9 Nov 2009 12:54:26 -0600 Subject: 3,1275M factored I have factored 722246167593210213600721845300936312325604542109808942638322762195652109906484317713234362910371878925978582792087245538684104125860958452511801 from 3,1275M as 28307046970942456068307849275575041770247062269862468071803789660351 * 25514712584982993649721349633001246398829959056614327094684863451960879218951. (c144 = p68 * p77) Timothy Sorbera (Mini-Geek) From: Serge Batalov Subject: 3,1419M factored Hello, Sam, I have factored an (extension 3LM tables') cofactor for 3,1419M. Input number is 1124518356445127013154461024095440659590350025108 741627429522049756647344780534236641635921304596942953499982922342948589845 7680738686849968750522693107562008229014579782076367 (176 digits) Using B1=6000000, B2=14270867530, polynomial Dickson(12), sigma=1618754349 Step 1 took 27646ms Step 2 took 14353ms ********** Factor found in step 2: 29168058670862674378104507538208850016837 Found probable prime factor of 41 digits: 29168058670862674378104507538208850016837 Probable prime cofactor has 135 digits Serge Batalov Date: Thu, 26 Nov 2009 14:51:22 +0000 (GMT) Subject: another entry from extended Cunningham tables completed From: Valerio Sisti, Scuola del Corso, Arezzo, Italy Dear Professor Wagstaff I found the penultimate factor of 3^750+1, using GGNFS and Msieve. The primitive factors already known were 9001, 11055001, 9490983001, 48724437074406251254164683458269001 and the cofactor was c136 = 153318412608659106299749452376331289294580001575230227951498583592\ 5338848875117272184688764108454343026894934982188211887071580608728001 c136 = p49 * p87 p49 = 3101836296928589193693596667339803928446660439001 p87 = 494282734264453734837010600360756824124572973262503221472801347816485913508464077289001 Best regards Valerio Sisti Date: Wed, 2 Dec 2009 08:03:44 +0000 (GMT) Subject: a factor of 3,1509L from Valerio Sisti, Scuola del Corso, Arezzo, Italy Dear Sam Wagstaff, I found a new factor from the extended 3LM table: c191 in 3,1509L = p40 . c151 p40 = 4737233752020545884052798695412419254883 Using GMP-ECM 6.2.3 with B1 = 5e6 and sigma = 3061742896 Best regards, Valerio Sisti Date: Fri, 29 Jan 2010 02:14:32 -0800 (PST) Subject: 3,1485L completed from Valerio Sisti, Scuola del Corso, Arezzo, Italy Dear Professor Wagstaff I have found a new factor from the extended 3LM table: C145 in 3,1485L = p46 . p99 p46 = 5474245653260990986533436821246647816715166891 Using GGNFS and Msieve Sincerely Valerio Sisti