From challenge-administrator@majordomo.rsasecurity.com Wed Jan 30 16:03:13 2002 Return-Path: Received: from pathfinder.securitydynamics.com (securecare.securitydynamics.com [205.181.76.19]) by shire.ontko.com (8.9.3/8.9.3/Debian 8.9.3-21) with SMTP id QAA00316 for ; Wed, 30 Jan 2002 16:03:12 -0500 X-Authentication-Warning: shire.ontko.com: Host securecare.securitydynamics.com [205.181.76.19] claimed to be pathfinder.securitydynamics.com Received: from cameos.rsasecurity.com by pathfinder.securitydynamics.com via smtpd (for shire.ontko.com [199.164.165.1]) with SMTP; 31 Jan 2002 00:00:39 UT Received: (from daemon@localhost) by cameos.majordomo.rsasecurity.com (8.8.8+Sun/notrash) id PAA23262; Wed, 30 Jan 2002 15:54:46 -0500 (EST) Date: Wed, 30 Jan 2002 15:54:46 -0500 (EST) Message-Id: <200201302054.PAA23262@cameos.majordomo.rsasecurity.com> From: challenge-administrator@majordomo.rsasecurity.com (RSA Factoring Challenge Administrator) To: rayo@ontko.com X-IMAPbase: 1128097135 1 Status: RO X-Status: X-Keywords: X-UID: 1 Partition Honor Roll 155 digits - 159 digits ----------------------- July 11, 1999 p(20411) Factors: 2 * 3 * 11 * 29 * 848895853065326903846850872662871 * 6201836822446859331288885027828037990142905211086373214149414897759197954468581207450840847526958330265830998410382003 Date: Oct 20, 1996 Method: TD, ECM (using Lips): p33, restp118 Time: 3 mips years Name: Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski) Adress: University of Saarland - Informatik (FB 14) -, Im Stadtwald, 66041 Saarbruecken -Germany- email: fberger@cs.uni-sb.de , denny@cs.uni-sb.de Phone: germany 681 - 3024168 Recd: October 20, 1996 --------------------------------------------------------------- p(20431) Factors 3 * 7 * 7 * 7 * 31 * 457 * 2521 * 318001 * 49991546837 * 148848117787 * 138520347005984911584679583055235672055316856937949527743101133911863813470805473972347048398302046899562814577213829 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(20441) Factors: 2 * 2 * 5 * 953 * 342107 * 71838317946857964438212811464585581 * p110 Date: February 3, 1997 Method: Trial division and ECM for last factor (program MIPS.ecm2.3000000.nonshared from Peter Montgomery) Time: 3079s on SGI R10000 Name: Paul Zimmermann Address: INRIA Lorraine, 615 rue du Jardin Botanique, BP 101, F-54600 Villers-les-Nancy Email: Paul.Zimmermann@inria.fr Phone: +33 03 83 59 30 21 Recd: February 3, 1996 --------------------------------------------------------------- p(20443) Factors: 2 * 3 * 3 * 5 * 9241 * 51539 * 316577 * 4200103543 * 24191100218240618240882919217597 * 9724255955776609656803607879457001127690946132671466044485212949209594323845001719594468808994711 Date: May 26, 1995 Method: trial division, ecm (p32 with first step 1000000) Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: May 26, 1994 --------------------------------------------------------------- p(20477) Factors: 3 * 3 * 11 * 17 * 59 * 71 * 3967 * 202949 * 183577484513 * 1065617734453432669 * 4638642951074161044503856803 * 3525103316038818896571948974466169201427628859619100943242771357493919985478025659 Date: Jun 17, 1994 Method: TD, ECM (using Lips): p12, p19, p28, restp82 Time: 1 mips year Name: Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski) Adress: University of Saarland - Informatik (FB 14) -, Im Stadtwald, 66041 Saarbruecken -Germany- email: fberger@cs.uni-sb.de , denny@cs.uni-sb.de Phone: germany 681 - 3024168 Recd: June 17, 1994 --------------------------------------------------------------- p(20479) Factors: 5 * 5 * 5 * 71 * 238031 * 1622311 * 55490777362407432518124612006180931 * 97188043488941883890994388405038131838273330966679718503622659517603571843339346763162660294420324654117 Date: Apr 02, 1996 Method: TD, ECM (using Lips): p7, p35, restp104 Time: 4 mips years Name: Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski) Adress: University of Saarland - Informatik (FB 14) -, Im Stadtwald, 66041 Saarbruecken -Germany- email: fberger@cs.uni-sb.de , denny@cs.uni-sb.de Phone: germany 681 - 3024168 Recd: May 10, 1996 --------------------------------------------------------------- p(20507) = 23720498920370980257405512175548368988882056898298623877115198265129252717070183028255927198368903744327792672055549549575914098343810135525831219172280020 (155 digits) Factors: 2 * 2 * 3 * 3 * 5 * 1439 * 30859 * 5361758709057450524926807 * 69787919435504473985769838242549978060433 * 7930875914849500932244004007661895700511201874124104264296698549515677427156819 Date: November 14, 1999 Method: trial division, ecm, ecm/fft (p41 with program MIPS.ecm2.30000000.shared from Peter Montgomery) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com --------------------------------------------------------------- >From jed49821@eastmail.com Sun Nov 14 19:33:57 PST 1999 p(20509) Factors 2 * 3 * 5 * 677 * 514867 * 858338225221 * 3914675614373 * 42533529827123 * 16157343079909938880380608949869154658903247252067019541140399507842541941176552809608221828044079974208953 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(20533) Factors: 2 * 3 * 3 * 11 * 117851 * 80274737 * 34734481541 * 47167187311134506203147200541 * 4707775384662388838183852937831511515217 * 2069563081600606751853277468196383255183893208352386801188859 Date: October 1, 1993 Method: TD, ECM : p8 p11 p29 , PPMPQS :p40 restp61 (using LIPS) Time: ECM 209 mips days , PPMPQS 20 mips years Name: Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski) address: University of Dortmund, University of Saarland - Informatik (FB 14) -, Postfach 1150, 66041 Saarbruecken -Germany- email: denny@cs.uni-sb.de fberger@cs.uni-sb.de Phone: germany 681 - 3024168 Recd: October 1, 1993 --------------------------------------------------------------- p(20543) Factors: 2 * 3 * 3 * 5 * 5 * 7 * 11 * 9533 * 3312275555299817 * 57114796557200526781804151953 * 523022486854639372914072655637153913919573566150315694907459640917419323565613677154071841356633716001 Date: September 14, 1993 Method: ecm (1st step 500K, 100th curve, c131 = p29*p102) Name: Bruce Dodson, Matt Fante Recd: September 14, 1993 --------------------------------------------------------------- p(20549) Factors 5 * 5 * 7 * 41 * 79 * 228539 * 266138628775326798713318473960428941967143884321968606653047092247548804422896471482254832393435489741883619426625023979212670813456137743464871 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(20551) Factors: 5 * 5 * 7 * 6703 * 810023 * 8180210381117 * 6932755055524901 * 235505013126622797185062510075070181389 * 2765483241667459405500593647685258791900873864216696171869313810577156555393 Date: Sep 29, 1994 Method: TD, ECM (using Lips): p13, p16, p39, restp76 Time: 2 mips years Name: Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski) Adress: University of Saarland - Informatik (FB 14) -, Im Stadtwald, 66041 Saarbruecken -Germany- email: fberger@cs.uni-sb.de , denny@cs.uni-sb.de Phone: germany 681 - 3024168 Recd: September 29, 1994 --------------------------------------------------------------- p(20563) Factors 29 * 1346522733711509773307352514745754989905863858674201116088321844152625223828334436459833643587130224556641180488650354043103574402147005818086294447135257 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(20593) Factors: 2 * 2 * 2 * 2 * 3 * 3 * 3 * 479 * 35894770108772835385661858657 * 6864616843549326613428926280581272769123440669746349249025417387462252737470925645564556010581676062782340288730943619257 Date: Jul 16, 1996 Method: TD, ECM (using Lips): p29, restp121 Time: 1 mips year Name: Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski) Adress: University of Saarland - Informatik (FB 14) -, Im Stadtwald, 66041 Saarbruecken -Germany- email: fberger@cs.uni-sb.de , denny@cs.uni-sb.de Phone: germany 681 - 3024168 Recd: July 16, 1996 --------------------------------------------------------------- p(20599) Factors 5 * 5 * 5 * 5 * 5 * 7 * 7 * 53 * 47123 * 1413439 * 233255567 * 4140031770330097 * 103029124625870848013148781679475322096373174465772077669313232895461768510370694457219879069230151859760770807621 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(20611) Factors 2 * 5 * 1709909 * 51729603774197 * 67643696861315732806583319904436534122475735691732546011251601523654500701477060731838991194329948413291704226091157870747580954507353 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(20627) Factors 7 * 7 * 2917 * 92593 * 5211431677493018140010248499322299899573517802025990875896767029074296361902596866635572514167681214687577671513655400284705960560013254058333801 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(20639) Factors: 2 * 2 * 5 * 5 * 17 * 1699 * 230618081 * 2033627859257 * 39137526897763879770052155471697 * 109292328820437860719103872162987692507392267 * 13242136611479681646594900275024861776401045418721771 Date: Aug 13, 1996 Method: TD, ECM (using Lips): p9, p13, p32; MPQS: p45, p53 Time: ECM: 3 mips years, MPQS: 1 week on 16 nodes of an Intel ipsc860 hypercube Name: Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski) Adress: University of Saarland - Informatik (FB 14) -, Im Stadtwald, 66041 Saarbruecken -Germany- email: fberger@cs.uni-sb.de , denny@cs.uni-sb.de Phone: germany 681 - 3024168 Recd: December 20, 1996 --------------------------------------------------------------- p(20641) = 78101681395439250951140202076930571761801632263168289083441600393078073049897262122170167187080868406673039349845547163492483220228094170205065330115674070 (155 digits) Factors: 2 * 3 * 5 * 7 * 11 * 11 * 187027 * 2806597 * 16526501 * 7031958875584177973 * 15813415567433228646299257181647715046680408592063665707 * 3186312987133216755470669854487899966114567396723511540903 Date: May 13, 1998 (found); December 30, 1999 (sent) Method: trial division, ecm, ppmpqs (two largest factors) Time: approximately 200 mips years for ppmpqs Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com --------------------------------------------------------------- p(20663) Factors: 2 * 5 * 19 * 19 * 61 * 193 * 104827 * 219972007534195284163959429823 * 45053443153112783974736391971 * 2150335972043704280558183774599753468354853471705947723881097827025240273159090899689 Date: September 10, 1993 Method: ecm (1st step 500K, 38th curve, c113 = p29*p85 after p30 found) Name: Bruce Dodson, Matt Fante Recd: September 10, 1993 --------------------------------------------------------------- p(20681) Factors: 2 * 47 * 47 * 91558808643835604808281 * 47800370122531964224008158633085161759 * 5760600877463010600868043758224329641934314897833921199577092673458935735283865378948252051 Date: Aug 13, 1996 Method: TD, ECM (using Lips): p23, p38, restp91 Time: 2 mips years Name: Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski) Adress: University of Saarland - Informatik (FB 14) -, Im Stadtwald, 66041 Saarbruecken -Germany- email: fberger@cs.uni-sb.de , denny@cs.uni-sb.de Phone: germany 681 - 3024168 Recd: December 20, 1996 --------------------------------------------------------------- p(20707) Factors: 3 * 3 * 19 * 1329841114262564888082517 * 616817164747276916330776163094203294086803150348209671968888769714622814273229334193506522817069772487263955258503950304203402197 Date: Jun 23, 1993 Method: TD, ECM (using Lips): p25, restp129 Time: ECM ca. 1.3 mips-years Name: Franz-Dieter Berger, Thomas Denny, Johannes Buchmann email: fberger@cs.uni-sb.de , denny@cs.uni-sb.de Recd: June 23, 1993 _______________________________________________________________ p(20717) Factors: 11 * 166349 * 1395770473 * 7411688563 * 2545493033027694152323 * PRP109 Date: April 1, 1992 Method: P-1 (first p10), ECM (second p10, p22; p22 found first) Name: Peter L. Montgomery Recd: April 1, 1992 --------------------------------------------------------------- p(20719) = 156006929215110670517466423975433750558628342724155136925950355809404207969368395291356759986487685939826690135945362234838752577845786769030272635117437255 (156 digits) Factors: 5 * 11 * 5563 * 608065904261527748927327868474069227 * 838535564411252390708841880728461277712493540996694558822411172775677088823985633854041495359255861577226787855241 Date: May 25, 1999 Method: trial division, ecm/fft (p36 with program MIPS.ecm2.16000000.shared from Peter Montgomery) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com --------------------------------------------------------------- p(20731) Factors: 2 * 2 * 213337 * 4051309479857 * 654129049495591 * 703427220200777087 * PRP105 Date: April 1, 1992 Method: P-1 (p13), ECM (p15, p18) Name: Peter L. Montgomery Recd: April 1, 1992 --------------------------------------------------------------- p(20747) = 199927489142421807768996909544813448784288133282882564515746074795258299400594920588393743176235683654521262184177899230173861405938402667506562386250585233 (156 digits) Factors: 226231 * 6560495354899585703588598796768566666493009 * 6191961923842799882370420682175292915628984391 * 21754819643894078617275115658673989388420355418322475161556097 Date: July 13, 1999 Method: ecm, ecm/fft (p43 with program MIPS.ecm2.16000000.shared from Peter Montgomery), gnfs (two largest factors, with CWI's NFS code) Time: 2 cpudays polyn selection, 32 cpudays sieving (SGI workstations, R10000, 175 Mhz) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com --------------------------------------------------------------- p(20753) Factors: 2 * 7 * 11 * 11 * 13 * 19 * 41 * 17492087 * 277335611203641845044702145401 * 364142615511230657754415936994657572237 * 6957205281066526206070839279693377813394886682271195526205802393816221561 Date: April 18, 1997 Method: trial division, ecm (p30), ecm/fft (p39 with program MIPS.ecm2.3000000.nonshared from Peter Montgomery) Time: 200 curves on Centre Charles Hermite's R4K-R8K, R10K sgi's, after 2500 curves with first limit 1400000 at Lehigh Univ Address: http://www.loria.fr/CCH (for "Centre Charles Hermite") Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: April 18, 1997 --------------------------------------------------------------- p(20759) = 222341119445364512426165854410244591755883827483880572756978073256424017830274135311067912568539770107498992954197592279785009747907848380291593606510836700 (156 digits) Factors: 2 * 2 * 5 * 5 * 2953 * 136194901 * 94134759761047121 * 125807226343887636828456879323839020151 * 466809715680917811942304833532909215497542527862870541927769358501279259573015456032909 Date: October 10, 1999 Method: trial division, ecm, ecm/fft (p39 with program MIPS.ecm2.8000000.shared from Peter Montgomery) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com p(23873) = 80255132763585135131819545092356479593986201561986090889076085331209609885443044309140947368807334312261323462819103666451726719806184574067439401847430648132955683493 (167 digits) Factors: 19 * 19 * 41 * 59 * 487 * 3079 * 9157 * 76423 * 10123530321432894237234967334171900147432147 * 8651308779313095913899638700302401725783194747329564424788856145475871214417338822632625199513661668247 p(20771) Factors: 2 * 2 * 3 * 7 * 61 * 123451729 * 4118716655738432269 * 43325423715180667107769 * 1093034023939235724332583221 * 2004052464470471589913245903454760821309408215221681387177322148691548868243 Date: Mar 9, 1993 Method: TD, ECM (using Lips): p9 ,p19, p23, p28, restp76 Time: ECM ca. 0.4 mip year Name: Franz-Dieter Berger, Thomas Denny, Johannes Buchmann Adress: University of Saarland - Informatik (FB 14) -, Im Stadtwald, 6600 Saarbruecken -Germany- email: fberger@cs.uni-sb.de , denny@cs.uni-sb.de Phone: germany 681 - 3024168 Recd: March 9, 1993 --------------------------------------------------------------- p(20773) Factors: 13183 * 5050996414129138101822173942149 * 2621660268855378846367085973731509957751 * 2766868748463179852974860117628582956793 * 521056995456550726282821746352231888862577 Date: March 14, 1999 Method: trial division, ecm (p31), ecm/fft (p40 = 276... then p42=521... with program MIPS.ecm2.16000000.shared from Peter Montgomery; cofactor p40=262...) Time: 204 curves between the p40 ecmfft factor and the p42 Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: March 13, 1999 --------------------------------------------------------------- p(20789) Factors: 2 * 2 * 3 * 5 * 569 * 1647179 * 1106812149095265967496478732521 * 12967798808625461177662387969 * 39558944351897066081912813871925326013259 * 9081148666624123749559593202721398240524691769 Date: April 1, 1996 Method: trial division, ecm (p31, p29), ppmpqs (two largest factors) Time: approximately 0.5 mips year Name: Bruce Dodson, Arjen K. Lenstra Email: arjen@galois.maths.su.oz.au Recd: March 31, 1996 --------------------------------------------------------------- p(20807) Factors 3 * 11 * 11 * 151 * 151 * 1423 * 4951 * 24203 * 74750551 * 4423198122983 * 9967251457346569477873 * 73100881949792213353669682814776241372381486749860631935126455518622010792887869727837478959791 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(20809) Factors: 3 * 5 * 7 * 7 * 11 * 37 * 2617 * 6419807 * 3599347448810539583725333 * PRP116 Date: April 1, 1992 Method: ECM (p25) Name: Peter L. Montgomery Recd: April 1, 1992 --------------------------------------------------------------- p(20849) Factors 5 * 5 * 5 * 5 * 472859 * 168332735009 * 44279085114379 * 3890595736082628679 * 57505232551778445685280187382308549260631233451672868637544393079139529311156083007873870284301852764013 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(20857) Factors 2 * 3 * 7 * 37 * 340363316875259352949902157599484389514344805580454513029787469838796873158961471767216750153088547105813851230601564575261180152986404361027598927152623 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(20873) Factors: 2 * 11 * 322963 * 29710171 * 553162828961705883281 * 117436485578607998335593041934839 * 44424480462981791968783683417859886446097398490510451664173507574218241630630144474975681 Date: Jan, 6, 1994 Method: TD, ECM (using Lips) : p8, p21, p33 , restp89 Time: ca. 4 MipsYears Name: Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski) Adress: University of Saarland - Informatik (FB 14) -, Im Stadtwald, 66041 Saarbruecken -Germany- email: fberger@cs.uni-sb.de , denny@cs.uni-sb.de Phone: germany 681 - 3024168 Recd: January 6, 1994 --------------------------------------------------------------- p(20887) Factors 13 * 17 * 2917 * 463987 * 829463143 * 16077681640853527403 * 172814172174360475707224174463102084573913230856795056766920348720852015628796254744562795132964531199750412620013663 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(20897) Factors: 2 * 2 * 2 * 2 * 3 * 11 * 163 * 1559 * 1088537 * 8118772230569369 * PRP126 Date: April 1, 1992 Method: P-1 (p16) Name: Peter L. Montgomery Recd: April 1, 1992 --------------------------------------------------------------- p(20899) Factors: 2 * 2 * 2 * 5 * 5 * 7 * 3847 * 4633157 * 10153331 * 223673617 * 75912131 * 229965436484560157130353990522117797 * 774646094835285579892873937908923386068553450137212347990029395403479856560237616363 Date: April 10, 1998 Method: trial division, ecm (p36 with first limit 1400000) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: April 10, 1998 --------------------------------------------------------------- p(20921) Factors 7 * 7 * 4291387237 * 4425075564688815818024508988054442446625594734843248962462707596312107657846066257869945261914532411766098450103737193320384456093446715947823461 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(20929) Factors: 2 * 2 * 2 * 2 * 5 * 5 * 13 * 787 * 24033465814652057 * 98386245243349616808256549 * 103186870961023527736649206832096366635333191011696387320555822612302962079387337653259230798626631091673603 Date: July 27, 1993 Method: TD, ECM (using Lips): Time: ECM ca. 0.7 mips years Name: Franz-Dieter Berger, Thomas Denny, Johannes Buchmann Adress: University of Saarland - Informatik (FB 14) -, Im Stadtwald, 66041 Saarbruecken -Germany- email: fberger@cs.uni-sb.de , denny@cs.uni-sb.de Phone: germany 681 - 3024168 Recd: August 3, 1993 --------------------------------------------------------------- p(20939) Factors 3 * 5 * 11 * 1259 * 217724959 * 1722790288117 * 1766097469087365656635487 * 7924624404695966908182844680632309798741208964680934971048402297621085075644088685267399149165832713718077 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(20947) Factors: 4317979 * 3601021271 * 10838187306404872847 * 23864427196741378053458301234280433 * 290974893322205484963129985209715726269979974968687731631250164649445058594367123924181 Date: April 13, 1998 Method: ecm (p35 with first limit 1400000) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: April 13, 1998 --------------------------------------------------------------- p(20959) Factors 5 * 3701 * 13279141 * 250234493 * 21153919618039929926160463053008004931904023305595585237022392548671339973994308453328718541081899282317096817014511956011920087568603611 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(20963) = 1347421342031296351824523584392403960250779393113153804811226146684169040011102214448531022258366384862918134908944956559328831955539040757042041162697126289 (157 digits) Factors: 3 * 7 * 7 * 13 * 5323243 * 765899476337 * 464247646789280185775563746929773240709113 * 2237652192504905648765509636784481311553692059 * 166476285193864892763615529864840395048699100967 Date: May 12, 1999 Method: trial division, ecm, ecm/fft (p42 with program MIPS.ecm2.16000000.shared from Peter Montgomery), ecm (p48 = 166.., cofactor p46 = 223..., with first limit 3000000, GMP-ECM 4 by P. Zimmermann (Inria)) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com --------------------------------------------------------------- p(20981) Factors: 5 * 7 * 11467 * 1486629917 * 1289873973563198604733261 * PRP118 Date: April 1, 1992 Method: ECM (p10, p25 - first limit 30000) Name: Peter L. Montgomery Recd: April 1, 1992 --------------------------------------------------------------- p(21001) Factors 5 * 1567 * 3037 * 10861 * 22003733389991 * 331124385761521270711943922762289308630118871566019732952518119260354360341579621258334116156075601332335185999047181330230089186981 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(21011) Factors: 3 * 7 * 74141831 * 8926005859 * 53104695779 * 59021399986421 * 5809827825770619693606853603 * 8124950261946457931874989803348952280458993632447515297350228081568906090472708695089 Date: Feb 11, 1994 Method: TD, ECM (using Lips): p8, p10, p11, p14, p28, restp85 Time: 50 mips days Name: Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski) Adress: University of Saarland - Informatik (FB 14) -, Im Stadtwald, 66041 Saarbruecken -Germany- email: fberger@cs.uni-sb.de , denny@cs.uni-sb.de Phone: germany 681 - 3024168 Recd: February 11, 1994 --------------------------------------------------------------- p(21013) Factors: 2 * 2 * 2 * 13499 * 142324205301619511 * 154472968820052963099030821 * 881428826069406864006749331136520202753243197379172091713830817515639525335396800173704554466395911674731133 Date: August 27, 1993 Method: ecm (12th curve with 1st step 100K, C135 = p27*p108) Name: Bruce Dodson, Matt Fante Recd: August 27, 1993 --------------------------------------------------------------- p(21017) Factors 134921 * 542263 * 111869773 * 198686729 * 47933893327 * 27808848331908714297604903856094018791336766828203383735677277558932881053718298470894808076741409566800409008620361817 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(21019) Factors 3 * 5 * 7 * 7 * 47 * 89 * 58771 * 269327 * 3057487 * 10901616601 * 3800363035477 * 357882858588988196706438878347640366205360481650614332655746141826694954880477740927572213518395500158719565817 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(21031) Factors 5 * 5 * 5 * 5 * 5 * 17 * 23 * 223 * 5916023 * 1520994358839476193445382144906739067281244612376005076229593929127110087064086896993108279163186503456707574367424125085252044102736401555861 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(21059) Factors: 5 * 197 * 6317 * 8263 * 30503591429 * 2176608000799 * 5449946073136771 * 7783835797633395317 * 221432011271095573848960470126075587 * 97808853419824234592283447441321865426183145686035869 Date: December 26, 1992 Method: TD, p-1, ECM, ppmpqs; primality with ECPP Time: ppmpqs used 55083 min on DecStation 5000 Name: Reynald Lercier, Francois Morain Address: LIX. Ecole Polytechnique, F-91128 Palaiseau Cedex FRANCE Email: lercier@poly.polytechnique.fr or morain@poly.polytechnique.fr phone: +33 1 69 33 45 89 Recd: December 26, 1992 --------------------------------------------------------------- p(21067) Factors: 2 * 3 * 3 * 3 * 202614607115387998057 * 5417226633854124647876313842187977 * 38312055765059114315838245340706735165661 * 1481775355920891264469500689281252934345450752008487298747383 Date: December 28, 1998 Method: trial division, ecm, ecm/fft (p34 with program MIPS.ecm2.8000000.shared from Peter Montgomery, then p41 with ecm2.16000000) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: December 28, 1998 -------------------------------------------------------------- p(21089) Factors 5 * 7 * 7 * 1005761 * 15548208407 * 32387366230236803 * 165764662079668849943 * 364375461154135169971 * 3123378313499602111272551 * 174392940619467405112447444907698318804314534158421225457 Date: April 2, 1992 Method: ecm Time: a few hours on a DEC 5000 Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 2, 1992 --------------------------------------------------------------- p(21139) Factors: 3 * 3 * 3 * 3 * 5 * 5 * 233713 * 397051 * 1424545940053999949801 * 23654792585655974162759716738023869644011857583253075107805290090528635580051813027352703418893573103107200425400094139293 Date: August 23, 1993 Method: ecm (p22*p122 on 3rd curve) Name: Bruce Dodson, Matt Fante Recd: August 23, 1993 --------------------------------------------------------------- p(21143) Factors 43 * 491 * 787 * 4241 * 5483 * 10891 * 1558519413373729526460054372189392803482162395767700213830979999071827310130977920042403875278691724636709580557835485900233088866760544737 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(21157) Factors 2 * 17 * 29 * 3127173013 * 2404893669755602555193416031829966423161473469321730259458183776735400757193343862272077076203387914500901071988427051937113675412951672302932867 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(21163) Factors: 2 * 2 * 2 * 107 * 2251 * 102181 * 224080006002187569203 * 462422960099460408110807147085344119 * 383102206313110780927617584752668059474069247487548393503512956831136210297127412379671181 Date: December 4, 1998 Method: trial division, ecm, ecm/fft (p36 with program MIPS.ecm2.16000000.shared from Peter Montgomery) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: December 4, 1998 --------------------------------------------------------------- p(21169) Factors 2 * 3 * 5 * 41 * 563 * 77047 * 40266409320649 * 3834538015561738969407590126162548566066301841037120180847374229326361267079511201488143184493636135189031646249329589161524918506599 Date: April 1, 1992 Method: trial division, ecm Time: very short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 1, 1992 --------------------------------------------------------------- p(21187) Factors: 7 * 7 * 53 * 457 * 3073981 * 35936123 * 10196967075663269987674261493780609108227 * 7215396575222864836803635113347629138013237760736033247023023381047407041416336829940807932578037 Date: October 13, 1998 Method: trial division, ecm (p41 with first limit 3000000, GMP-ECM version 3, by P. Zimmermann (Inria)) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: October 13, 1998 --------------------------------------------------------------- p(21191) Factors: 2 * 839 * 7121 * 56272574336658492733 * 86660282060939026308040580450704707527 * 171445521665298040874143639940094111793617415620116262828937693780978657875869323210391251937 Date: February 17, 1997 Method: trial division, ecm/fft (p38 with program MIPS.ecm2.3000000.nonshared from Peter Montgomery) Time: under 50 curves on Centre Charles Hermite's R4K-R8K, R10K sgi's Address: http://www.loria.fr/CCH (for "Centre Charles Hermite") Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: February 18, 1997 --------------------------------------------------------------- p(21193) Factors: 3 * PRP157 Name: Heinz-Bernd Eggenstein Address: Repkestr. 26, W-4712 Werne, Federal Republic of Germany Email: eggenste@cantor.informatik.uni-dortmund.de Recd: July 1, 1992 --------------------------------------------------------------- p(21211) Factors: 3 * 3 * 3 * 3 * 195967 * 22152121 * 668966013724063513 * 25985206760370790061 * 30051071352584845299273252635833 * 64804036329212834575894776247245043588152985166325208447368629960357801543 Date: Jul 15, 1994 Method: TD, ECM (using Lips): p8, p18, p20, p32, restp74 Time: 1 mips year Name: Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski) Adress: University of Saarland - Informatik (FB 14) -, Im Stadtwald, 66041 Saarbruecken -Germany- email: fberger@cs.uni-sb.de , denny@cs.uni-sb.de Phone: germany 681 - 3024168 Recd: July 15, 1994 --------------------------------------------------------------- p(21227) = 13693973437475259957493704953135858300283470686349253247033509546919954562975571372864242469273197422164768417588874237720463792708764360345806141103640880100 (158 digits) Factors: 2 * 2 * 5 * 5 * 13 * 43 * 730973911 * 33150314926426059866572378714304269 * 1067571042050710775007672454090449008095683348448488967 * 9469593854324918187225600789406519893994041809313253963 Date: February 11, 1998 (found); January 3, 2000 (sent) Method: trial division, ecm (p35 with first limit 1000000), ppmpqs (two largest factors) Time: approximately 150 mips years for ppmpqs Address: http://www.loria.fr/CCH (for "Centre Charles Hermite") Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann --------------------------------------------------------------- p(21247) Factors: 2 * 11 * 73 * 353 * 641 * 5297 * 62071 * 848367356790312113 * 3722801819780922457 * PRP104 Method: TD + p-1 + ECM (P18, P19) Time: ca. 0.033 MIPS years (17h on an i486-33 PC) Name: Heinz-Bernd Eggenstein Address: Repkestr. 26, W-4712 Werne, Federal Republic of Germany Email: eggenste@cantor.informatik.uni-dortmund.de Recd: July 2, 1992 --------------------------------------------------------------- p(21283) Factors: 2 * 2 * 3 * 5 * 7 * 11 * 301843 * 17691166770845669 * 874917964985083499930214431659 * 231523522795519655419818460293725931947 * 4472979107682975458538293092584739631614581145681411238547332959 Date: March 1, 1997 Method: trial division, ecm (p39 then p30, both with first limit 1000000) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: March 1, 1997 --------------------------------------------------------------- p(21313) = 29055568663110468883545021637823961166479350930198319614143879563834215809601030024209069614788992716203936336888388948838731387676747767146138735781250239427 (158 digits) Factors: 7 * 7 * 11 * 285457 * 45158543 * 178344421763769125019247123651129189 * 16820538508863054278478915922719677109169775461309 * 1393992926962627146188962256782163740199309598752547749143 Date: May 19, 1997 (found); January 3, 2000 (sent) Method: trial division, ecm (p36 with first limit 1000000, ppmpqs (two largest factors) Time: approximately 75 mips years Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com --------------------------------------------------------------- p(21317) Factors: 2 * 7 * 181 * 643129 * 1856365657 * 94638789373 * 27938319314050709133217 * PRP106 Method: TD, p-1, ECM (P10, P11, P23) Time: 0.016MIPS years ~ 0,5 TI ["Tera Instructions"] ~ 2 trillion clock-cycles (36 h on an IBM compat 286AT, 16 MHz clock)[lucky, avg. time substantially higher] Name: Heinz-Bernd Eggenstein Address: Repkestr. 26, W-4712 Werne, Federal Republic of Germany Email: eggenste@cantor.informatik.uni-dortmund.de Recd: July 1, 1992 --------------------------------------------------------------- p(21319) Factors: 2 * 2 * 2 * 2 * 3 * 5 * 46997 * 761713 * 17104855624751 * 14556909606337931827158170399399 * 14313194259642660283139373042982887223692242411325499460307194990298534406445914990039419892589508643 Date: February 14, 1997 Method: trial division, ecm/fft (p32 with program MIPS.ecm2.3000000.nonshared from Peter Montgomery) Time: under 50 curves on Centre Charles Hermite's R4K-R8K, R10K sgi's Address: http://www.loria.fr/CCH (for "Centre Charles Hermite") Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: February 14, 1997 --------------------------------------------------------------- p(21323) Factors: 5 * 7 * 45170693 * 1466567667729175073 * 2123029452431 * 75629429246970771775676880335621 * 85172895634655676727666399834873073134625760322908399572340735937746281101441841535169 Date: September 5, 1993 Method: ecm (1st step 500K, 21st curve, C118 = p32*p86) Name: Bruce Dodson, Matt Fante Recd: September 5, 1993 --------------------------------------------------------------- p(21341) Factors: 2 * 3 * 3 * 7 * 563 * 124633 * 2534449 * 40949581 * 3762768857736953 * 1067104143436305467029 * 95052634868964270374232364285401023745253160869 * 105957511284844493202366813400482858717758381092243 Date: October 10, 1993 Method: trial division, ecm (p16, p22), ppmpqs (two largest factors) Time: 19 hours on a 16K MasPar for ppmpqs Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 10, 1993 --------------------------------------------------------------- p(21377) Factors: 2 * 2 * 2 * 2 * 2 * 2 * 83 * 90260748980204951 * PRP138 Time: 0.006 MIPS years (14 h on IBM compat. 286AT, 16 MHz clock) Name: Heinz-Bernd Eggenstein Address: Repkestr. 26, W-4712 Werne, Federal Republic of Germany Email: eggenste@cantor.informatik.uni-dortmund.de Recd: July 1, 1992 --------------------------------------------------------------- p(21383) Factors: 2 * 2 * 3 * 5 * 7 * 7 * 15593926262263 * 82563299931567028103 * PRP122 Method: TD + ECM (P14, P20) Time: 0.015 MIPS years (ca. 32 h on an IBM compat. 286AT, 16 MHz clock) Name: Heinz-Bernd Eggenstein Address: Repkestr. 26, W-4712 Werne, Federal Republic of Germany Email: eggenste@cantor.informatik.uni-dortmund.de Recd: July 1, 1992 --------------------------------------------------------------- p(21391) Factors 3 * 109 * 256014890282380236295571 * 685739413450783777267278245918755910683478686755719331485688652553873846405406509319903537910620215757658887527400211129168589016287 Date: October 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 1, 1992 --------------------------------------------------------------- p(21397) Factors: 7 * 7 * 103688747 * 149593229 * 2208534296035559 * PRP125 Method: TD + ECM Time: 0.006 MIPSyears (13 h on an IBM compat. 286AT, 16 MHz clock) Name: Heinz-Bernd Eggenstein Address: Repkestr. 26, W-4712 Werne, Federal Republic of Germany Email: eggenste@cantor.informatik.uni-dortmund.de Recd: July 1, 1992 --------------------------------------------------------------- p(21401) Factors: 11 * 19 * 7583 * 204517 * 28590931 * 38652975212768355727175030777 * 89575573018324132503615538374568604029377563 * 1952232022418053461995164302351934782884661216808051261651465500017 Date: May 15, 1998 Method: trial division, ecm, ecm/fft (p29 with program MIPS.ecm2.3000000.nonshar ed, p44 with program MIPS.ecm2.8000000.shared from Peter Montgomery) Time: 96th curve on Lehigh's Origin2000, after 3400 curves with first limit 1400 000 Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: May 15, 1998 --------------------------------------------------------------- p(21407) Factors: 2 * 5 * 11 * 283 * 289680991 * PRP145 Method: TD + ECM Time: short Name: Heinz-Bernd Eggenstein Address: Repkestr. 26, W-4712 Werne, Federal Republic of Germany Email: eggenste@cantor.informatik.uni-dortmund.de Recd: July 1, 1992 --------------------------------------------------------------- p(21467) Factors: 7 * 11 * 79657 * 3059135437 * 252182076425611 * 299412621245501 * 78581177925254304699367444012372864637528078239621196510893135543182108877441521388927758098494909744034613448087 Date: October 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 1, 1992 --------------------------------------------------------------- p(21481) Factors 2 * 3 * 7 * 7 * 7 * 81012989921 * 15039826919399 * 90447993180287 * 554505978056339383059316596978072918669084213947102862277512799796489913910359252875117604755525689142250131017336199 Date: October 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 1, 1992 --------------------------------------------------------------- p(21491) Factors: 3 * 3 * 17 * 23 * 79 * 113171563 * 257642416718899583773 578576235566570162663317 * PRP101 Date: October 4, 1992 Method: P-1 (p9), ECM (p21, p24, both with first limit 60000) Name: FactOregon (Joe Buhler, Peter Montgomery, Robby Robson, Russell Ruby) Recd: October 4, 1992 --------------------------------------------------------------- p(21493) Factors: 2 * 2 * 3 * 5 * 3947 * 29626543 * 18473141 * 30645121467427914570513521 * 35148197384787986842641755897721851349028072512995464944247954093780916691392222048938864476665933295539801900789 Date: August 29, 1993 Method: ecm (1st step 500K, one of six 1st curves, C139 = p26*p113) Name: Bruce Dodson, Matt Fante Recd: August 29, 1993 --------------------------------------------------------------- p(21499) = 147088261323979379016995393440905146674096734024103360849631328025357711292854546139995208443655491380876211229088775871221151746992103968607207192329340551375 (159 digits) Factors: 3 * 5 * 5 * 5 * 4051 * 405282613 * 266431617938998481134383024525190262221 * 4423969804600543961863478478927602073989 * 202688269487389515988321849431424520447961676142999733855994109671 Date: December 28, 1999 Method: trial division, ecm, ecm/fft (p40, then p39 with program MIPS.ecm2.8000000.shared from Peter Montgomery) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com --------------------------------------------------------------- p(21517) Factors 62927 * 2733648318902298842846346160705889887731058374858102701587798297846092184874857406738861745088233413170581616521850919290338819629132432736227051052302419 Date: October 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 1, 1992 --------------------------------------------------------------- p(21521) Factors 2 * 11 * 240433 * 295407881 * 189554245421 * 601332888190675525360665749424999841183257080904849840528232742559043168801494591062828200874997792828059133115416770926635913744499 Date: October 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 1, 1992 --------------------------------------------------------------- p(21529) Factors: 2 * 5 * 81203 * 145777 * 356264925943155204857285745790147 * 4527560257091529360235150455727084937594903043367655595452876363535298579637726724382979664279899932029379193539043 Date: September 7, 1998 Method: ECM (p33 with first limit 2000000, found in step 1) Name: Eric Prestemon Email: ecp@io.com Recd: September 7, 1998 --------------------------------------------------------------- p(21559) Factors: 2 * 3 * 5 * 17 * 47 * 197 * 14757397 * 166400016683 * 577890230419 * 1398562055933083019464695096928037089 * 26443307746835585174560079697352108656650744469314700554703608781176321942890673179757 Date: March 14, 1997 Method: trial division, ecm/fft (p37 with program MIPS.ecm2.3000000.nonshared from Peter Montgomery) Time: under 50 curves on Centre Charles Hermite's R4K-R8K, R10K SGIs Address: http://www.loria.fr/CCH (for "Centre Charles Hermite") Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: March 14, 1997 --------------------------------------------------------------- p(21563) Factors: 2 * 2 * 2 * 2 * 3 * 109 * 9137 * 187922474441059533163 * 724612995375319117961437 * PRP107 Date: October 4, 1992 Method: ECM (p21, p24 - latter with first limit 30000) Name: FactOregon (Joe Buhler, Peter Montgomery, Robby Robson, Russell Ruby) Recd: October 4, 1992 --------------------------------------------------------------- p(21577) Factors: 11 * 59 * 29333 * 506573 * 190186056943 * 6644638766115258163324058923 * PRP107 Date: October 4, 1992 Method: ECM (p12, p28 -- first limit 50000) Name: FactOregon (Joe Buhler, Peter Montgomery, Robby Robson, Russell Ruby) Recd: October 4, 1992 --------------------------------------------------------------- p(21587) = 316054504682946119549589570820968505338321364178455505274925228383162923800516239010081462290256074170544035709005162017709539803516337482297382922371346898293 (159 digits) Factors: 7 * 11 * 1559 * 23314179884868133430999449883136804034168433 * 112928874883123017681775768579898543212430873007560055960840724068741341482174788510214528218371077429866120847 Date: December 11, 1999 Method: trial division, ecm/fft (p44 with program MIPS.ecm2.8000000.shared from Peter Montgomery) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com --------------------------------------------------------------- p(21589) Factors: 2 * 5 * 13 * 13 * 13 * 47 * 9181 * 16614769 * 77793457541 * 5882271715295259253976042857 * 241069537755345986193322022221566574701570290843 * 18508067931477229469586892148473843135511537095747614217 Date: March 15, 1995 Method: trial division, ecm, ppmpqs (two largest factors) Time: approximately 30 mips years Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: March 15, 1995 --------------------------------------------------------------- p(21599) Factors 2 * 5 * 5 * 5 * 7 * 11 * 43 * 317 * 6691 * 61091 * 148501 * 4860607 * 17413331396346602177 * 260183117076394151961797131805076051020074054702451276176577859260932812228393900422981803920176604307377999901 Date: October 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 1, 1992 --------------------------------------------------------------- p(21601) Factors 2 * 2 * 2 * 2 * 3 * 3 * 3 * 89 * 331 * 193043 * 824191 * 11293739 * 77888833029781 * 2720142396010241 * 552303189338715247 * 2331858969199206991311391547994288587 * 57197784606228472041919942170510420214862966396743 Date: October 1, 1992 Method: ecm and ppmpqs Time: short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 1, 1992 --------------------------------------------------------------- p(21611) Factors 2 * 7 * 13 * 37 * 18181 * 394529 * 15672614939 * 11932601556901 * 58982676572464067 * 730583373216117229367864377946643346225080494131941106952549560541199198776357595890757589392943683265361 Date: October 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 1, 1992 --------------------------------------------------------------- p(21613) Factors: 2 * 3 * 7 * 58662698851 * 1615545605909 * 969290944859561111264010568200196897 * 5959232365804186019480664708908336459121006723713 * 17226747211903186128824918256554452448167246276757 Date: January 3, 1999 Method: trial division, ecm, ecm (p36 with first limit 3000000, GMP-ECM version 3, by P. Zimmermann (Inria)), ppmpqs (two largest factors) Time: approximately 15 mips years for ppmpqs Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: January 3, 1999 --------------------------------------------------------------- p(21647) Factors 2 * 5 * 5 * 13 * 1584343 * 134443591 * 2961817803941 * 3574305603880937201 * 362921225417367404158375648073839821314294548526339642276299088595960316888257704390272208252342571359064866609 Date: October 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 1, 1992 --------------------------------------------------------------- p(21649) Factors 2 * 3 * 5 * 5 * 7 * 7 * 19 * 29 * 79 * 38120389 * 71490474509559401 * 620761716316659004178974124446533464700611493816497349213274299477078054601593999780238905912493519311525201845940967527366739 Date: October 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 1, 1992 --------------------------------------------------------------- p(21661) Factors 2 * 2 * 3 * 3 * 17 * 17 * 41 * 6143 * 4416527 * 6284624993 * 8257576504676990446214240232806409990765579227471114438469304136645510645337078311645000253109988754857305503694644493115340026293957 Date: October 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 1, 1992 --------------------------------------------------------------- p(21673) Factors: 31 * 491 * 1326041 * 4298850429989809 * 1054859311346299139141606981755923691 * 18122752955857391029353827001600343199 * 401767747555933864950218614293237431680859812987940606615039 Date: October 4, 1993 Method: trial division, ecm (p38), ppmpqs (p37 and largest factor) Time: four days on idle time of ~30 workstations (ppmpqs) Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 4, 1993 --------------------------------------------------------------- p(21683) Factors: 2 * 3 * 21031 * 18780137 * 14925575237 * 5767086590081396563543961 * 1154101093827326556633150477799 * 3086995410184102196625116260709586193262685750418299823551073769793256784260805341 Date: January 18, 1997 Method: trial division, ecm (p31 with first step 1400000) Name: Bruce Dodson, Arjen K. Lenstra Email: arjen.lenstra@citicorp.com Recd: January 18, 1997 --------------------------------------------------------------- p(21701) Factors: 2 * 3 * 3 * 3 * 47 * 2388131003 * 9436241539 * 555005755501 * 3159449395549136497 * 44163813962664986413 * PRP87 Date: October 4, 1992 Method: P-1 (p12), ECM (two p10, p19, p20) Name: FactOregon (Joe Buhler, Peter Montgomery, Robby Robson, Russell Ruby) Recd: October 4, 1992 --------------------------------------------------------------- p(21713) Factors 2 * 37 * 103 * 673 * 112489733 * 118492180176858661 * 13782631919514016839015238742980455110504077798984154853308552910023552032233410947578756818263809236433888185664999317557391443 Date: October 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 1, 1992 --------------------------------------------------------------- p(21727) Factors: 5 * 31 * 431 * 19991 * 27103058002589 * 8710515661487130853 * 18594060267689184799 * PRP99 Date: October 4, 1992 Method: ECM (p14, p19, p21) Name: FactOregon (Joe Buhler, Peter Montgomery, Robby Robson, Russell Ruby) Recd: October 4, 1992 --------------------------------------------------------------- p(21751) = 1309302390402950631688792799038587659902376391049609736863582308805779992154734188628263551495821558614424835665312664886659876066300485352751839025496313400358 (160 digits) Factors: 2 * 103 * 14699 * 24831943365249324152528483455839003527 * 17413025717215694446176683008080894473825773806590684507308194741167804632799534433481360092030825706935415833344041 Date: September 10, 1999 Method: trial division, ecm (p38 with first limit 3000000, GMP-ECM 4 by P. Zimmermann (Inria)) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com --------------------------------------------------------------- >From bad0@CS0.CC.Lehigh.EDU Tue Sep 14 12:56:55 PDT 1999 p(21863) Factors: 11 * 3280631383 * 961583686136412881 * 12872535373674371729 * PRP112 Date: October 4, 1992 Method: ECM (p10, p18, p20) Name: FactOregon (Joe Buhler, Peter Montgomery, Robby Robson, Russell Ruby) Recd: October 4, 1992 ---------------------------------------------------------------