From challenge-administrator@majordomo.rsasecurity.com Wed Jan 30 16:03:19 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 QAA00330 for ; Wed, 30 Jan 2002 16:03:18 -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 00:00:45 UT Received: (from daemon@localhost) by cameos.majordomo.rsasecurity.com (8.8.8+Sun/notrash) id PAA23143; Wed, 30 Jan 2002 15:54:43 -0500 (EST) Date: Wed, 30 Jan 2002 15:54:43 -0500 (EST) Message-Id: <200201302054.PAA23143@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 145 digits - 149 digits ----------------------- July 11, 1999 p(17923) Factors: 41 * 307 * 3543913 * 241977137370942196222920520081805090539 * 102629111109381834201808060815260791677282566199569554908049197269250747421804750340160970653647 Date: October 26, 1998 Method: trial division, ecm, ecm/fft (p39 with program MIPS.ecm2.8000000.shared from Peter Montgomery) Time: 168th curve with 8000000 ecm/fft, on an SGI O2 (R5000, 200Mhz) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: October 26, 1998 --------------------------------------------------------------- p(17929) Factors: 2 * 5 * 13 * 588043 * 1524773 * 2299236034322807 * PRP115 Date: April 17, 1991 Method: ECM (p16) Time: 6E-3 (2 MIP-days) Name: Peter L. Montgomery Recd: April 16, 1991 --------------------------------------------------------------- p(17939) Factors: 2 * 5 * 7 * 75029 * 240376510321 * 840110410827486302515709 * PRP103 Date: February 10, 1992 Method: ECM (p12, p24 - first limit 300000) Time: 0.14 Name: Peter L. Montgomery Recd: February 10, 1992 --------------------------------------------------------------- p(17957) Factors: 157 * 257 * 1913503114355671 * 1310230868966975385883 * PRP104 Date: July 19, 1991 Method: ECM (p16, p22) Time: 0.06 Name: Peter L. Montgomery Recd: July 19, 1991 --------------------------------------------------------------- p(17959) Factors: 5 * 11 * 1171 * 48583474708493 * PRP126 Date: March 21, 1991 Method: ECM Time: 7E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(17971) Factors: 13 * 31 * 349 * 1543 * PRP136 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(17977) Factors: 421 * 71126179 * 27768606956639974811179 * p112 Date: December 23, 1992 Method: ecm (p23 with first limit 240000 - found in step 1) Time: 31 CPU hours on RS/6000, model 220 (timing), 340 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 23, 1992 --------------------------------------------------------------- p(17987) Factors: 13 * 19603 * 27427 * 2974589 * 97269353561 * PRP118 Method: P-1 Time: 3E-5 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(17989) Factors: 2 * 5 * 5 * 1693 * 2130349973 * PRP131 Date: March 21, 1991 Method: ECM Time: 3E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18013) Factors: 5 * 11 * 41 * 27437121015347643883 * 22177696162784735675206682330775427 * 1900464018695436905778404226120948020325209087350728628861659698969417379418532962631093 Date: February 27, 1998 Method: trial division, ecm (p35 with first limit 1400000) Time: about 1000th curve Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: February 27, 1998 --------------------------------------------------------------- p(18041) Factors: 13 * 3019 * 9319 * 25841 * 2045987073209147 * 175937852759688643063923874262771398696341578588856297017982060858872408141982064021322274308169732976980124855085881 Date: 10 May 1991 Method: TD + ECM (p16), Miller-Rabin for primality test. Time: 0.0003 Name: Paul C Leyland Recd: May 10, 1991 --------------------------------------------------------------- p(18043) Factors: 3 * 1377679 * 1039086038828439977191 * PRP117 Date: June 5, 1991 Method: ECM (p22) Time: 0.04 (2 MIP-weeks) Name: Peter L. Montgomery Recd: June 5, 1991 --------------------------------------------------------------- p(18047) Factors: 2 * 2 * 2 * 2 * 3 * 3 * 3 * 19 * 5607650569928279 * 510313011673504501849 * 2166428663303448310701320243951 * 4967386350938366813084629876373989 * p41 Date: 9 November 1993 Method: TD, ECM (p16, p21, p30), PPMPQS (p34, p41) Time: 0.4 ECM, negligible PPMPQS Name: Paul C Leyland Recd: November 9, 1993 --------------------------------------------------------------- p(18049) Factors: 2 * 2 * 2 * 2 * 5 * 5 * 7 * 17 * 67 * 29915047 * 424528169781040530247255464186772073 * 90625198059073304857866210710696354325015529938367703748989943051773486693493878816731317097337 Date: March 15, 1999 Method: trial division, ecm, ecm (p36 with first limit 3000000, GMP-ECM version 3b, by P. Zimmermann (Inria)) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: March 15,1999 --------------------------------------------------------------- p(18059) Factors: 3 * 5 * 29 * 427421 * 83171733180474049373473985630777 * 113871720582430200664490308532463149754746932976443 * 2291946834626961668494053488658612105644300748716862451 Date: September 10, 1995 Method: trial division, ecm, ppmpqs (two largest factors) Time: approximately 50 mips years Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 1, 1995 --------------------------------------------------------------- p(18061) Factors: 5 * 20190112383094068571086009831559789 * 40744975081862774918795704854837097813385362864344671049236470125736864547336605742310629449363853618990751173 Date: Apr 02, 1995 Method: TD, ECM (using Lips): p35, restp110 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: April 2, 1995 --------------------------------------------------------------- p(18077) Factors: 2 * 2 * 2 * 2 * 17 * 137 * PRP141 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18089) Factors: 5 * 7 * 31 * 41011723801721 * 3165322024978949411 * 2762738154171638951071957 * 3477482115750502108488403 * P61 Date: 26 May 1992 Method: TD, ECM (p14, p19, first p25), PPMPQS (second p25, p61) Time: 0.4 (0.15 ECM, 0.25 PPMPQS) Name: Paul C Leyland & Peter L Montgomery Recd: May 26, 1992 --------------------------------------------------------------- p(18097) Factors: 2 * 5 * 11 * 2909 * 2334361 * 15555983 * 73286460987981870526244357447962757 * 6795585002817296145130467011430557547309291826387294538967663858092689712688996916219153319 Date: August 12, 1998 Method: trial division, ecm, ecm/fft (p35 with program MIPS.ecm2.8000000.shared from Peter Montgomery) Time: 44th curve with 8000000 ecm/fft, on an SGI O2 (R5000, 200Mhz) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: August 12, 1998 --------------------------------------------------------------- p(18119) Factors: 2 * 5 * 829 * 1217 * 170887 * PRP133 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18127) Factors: 2 * 2 * 2 * 3 * 17 * 96157 * 27578259529 * 9312498203250083 * 735253944381966418144117 * 621028772191894903843449676721791 * 1671380707656539768667029690883249609108314462142573901 Date: September 30, 1992 Method: Pollard Rho (p11), ECM (p16, p24), ECM/FFT (p33 - first limit 400000) Time: 0.16 MIP year Name: FactOregon (Joe Buhler, Peter Montgomery, Robby Robson, Russell Ruby) Recd: September 30, 1992 --------------------------------------------------------------- p(18131) Factors: 2 * PRP145 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18133) Factors: 2 * 2 * 3 * 5 * 5 * 5 * 491 * PRP140 Date: March 21, 1991 Method: Trial Division Time: 1E-6 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18143) Factors: 3 * 3 * 2099 * 2351 * 95252464717 * PRP127 Date: March 21, 1991 Method: ECM Time: 3E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18149) Factors: 2 * 3 * 5 * 5 * 5 * 7 * 7 * 151 * 1009 * 569236446202556825188231 * 29114602129171659470376509 * 102054507804557386425519886021896567600641754912041683242861221366267580490798223839397 Date: May 31, 1994 Method: trial division, ecm (p26 with first step 240000, p24 with 500000) Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: May 31, 1994 --------------------------------------------------------------- p(18169) Factors: 2 * 2 * 2 * 5 * 595848088153 * PRP132 Date: April 1, 1991 Method: ECM (p12) Time: 8E-4 Name: Peter L. Montgomery Recd: April 1, 1991 --------------------------------------------------------------- p(18191) Factors: 2 * 5 * 5 * 7 * 17962193 * 127944743 * 37597109946772877 * 6025593423304737728924258540418433871 * 77322731045890844249805798125148675235540672061128916894102401006181953349 Date: April 1, 1996 Method: trial division, ecm (p37 with first step 1400000, after 2400 curves) Name: Bruce Dodson, Arjen K. Lenstra Email: arjen@galois.maths.su.oz.au Recd: March 31, 1996 --------------------------------------------------------------- p(18199) Factors: 2 * 5 * 5 * 5 * 43 * PRP142 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18211) Factors: 5 * 11 * 1831 * 559654681 * PRP132 Method: P-1 Time: 1E-5 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18223) Factors: 3 * 5507 * 7937 * 3872650489 * 193869132588353 * 546324601028039 * 81209098846453967 * 1254922510520127437 * 52630005102103878921397389917207 * 66089084550824415099278678792419 Date: 17 June 1991 Method: TD, Pollard Rho (p10), ECM (two p15, p17, p19), PPMPQS (two p32), Miller-Rabin for primality test. Time: 0.02 Name: Peter L Montgomery & Paul C Leyland Recd: June 17, 1991 --------------------------------------------------------------- p(18233) Factors: 2 * 2 * 3 * 7 * 11 * 107 * 5741 * 6323 * 1698920249082609711611426517413559768311 * 3436560838018333487261917551075806314512082370782339218928655719720676139010375438107098033357 Date: November 23, 1998 Method: trial division, ecm/fft (p40 with program MIPS.ecm2.16000000.shared from Peter Montgomery) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: November 23, 1998 --------------------------------------------------------------- p(18251) = 24835236985764117198556819575546411068652427208522932926253251955593093368432790596345131967410550488570727479899928627774319985136285269612201607 (146 digits) Factors: 7 * 23 * 651966600340428593632996025625121 * 23565662132249150390316565016523448200856980084787 * 10040086117410728714373325028468511494222242135361853305165981 Date: May 2, 1997 (found); December 30, 1999 (sent) Method: trial division, ecm (p33 with first limit 1000000), ppmpqs (two largest factors) Time: approximately 150 mips years Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com ---------------------------------------------------------------- p(18253) Factors: 3 * 3 * 3 * 3 * 11 * 2278753 * 31271464823 * 6228359150809 * 43167981561598677853 * PRP94 Date: May 16, 1991 Method: P-1 (p11), ECM (p13, p20) Time: 0.02 Name: Peter L. Montgomery Recd: May 16, 1991 --------------------------------------------------------------- p(18257) Factors: 3 * 17 * 233 * 17195623 * 51807393283 * 79311803355148631582644300834981201 * 31303167815046587530899583820970037126197279616401374314113911800009285635422025259789421 Date: April 1, 1996 Method: trial division, ecm (p35 with first step 1400000) Name: Bruce Dodson, Arjen K. Lenstra Email: arjen@galois.maths.su.oz.au Recd: March 31, 1996 --------------------------------------------------------------- p(18269) Factors: 2 * 5 * 1187 * 2219111 * PRP136 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18287) Factors: 2 * 433 * 118973 * 666078280177 * 52144494065959051084703608637 * p97 Date: December 15, 1992 Method: ecm (52nd curve, first limit quickly up to 240000, p29 in 2nd step) Time: 16 CPU hours on RS/6000, model 220 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 15, 1992 --------------------------------------------------------------- p(18289) Factors: 2 * 2 * 2 * 3 * 3 * 5 * 7 * 11 * 5470247496563167 * PRP126 Date: April 17, 1991 Method: ECM (p16) Time: 6E-3 (2 MIP-days) Name: Peter L. Montgomery Recd: April 16, 1991 --------------------------------------------------------------- p(18301) Factors: 13 * 17 * 43 * 211 * 601 * 32493541419928847849802557 * 141945230473392372732035791 * 15076523629923048261027510938299 * 474958081486783808100678548737381999569354065397481381 Date: September 9, 1993 Method: TD, ECM : p26 p27 , PPMPQS :p32 restp54 (using LIPS) Time: ECM ca. 0.4 mips year , PPMPQS 1 day on a IPSC860 (16 nodes) Name: Heinz-Bernd Eggenstein, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski) Recd: September 10, 1993 --------------------------------------------------------------- p(18311) Factors: 2 * 2 * 7 * 37 * 43 * 47 * 91183 * PRP135 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18313) Factors: 3 * 3 * 3 * 7 * PRP144 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18329) Factors: 5 * 7 * 29 * 739 * 14923 * 10141 * 405077011 * 31428191 * 140466866476409444508547217 * p90 Date: December 13, 1992 Method: ecm (11th curve, p27 at start of 2nd step) Time: < 4 hours on RS/6000, model 220 Name: Bruce Dodson, Matt Fante Address: Math Dept, #14 Lehigh Univ, Bethlehem, PA 18015 Email: bad0@ns1.cc.lehigh.edu Phone: (215) 758-3753 Recd: December 13, 1992 --------------------------------------------------------------- p(18341) Factors: 2 * 3 * 13 * 3107838197 * PRP135 Method: P-1 Time: 5E-5 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18367) Factors: 127 * 329994183688545962486074403 * p118 Date: December 30, 1992 Method: ecm (p27 with first limit 240000) Time: 2.5 CPU days on RS/6000, model 220 (timing), 340 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 30, 1992 --------------------------------------------------------------- p(18371) Factors: 3 * 69456227 * 550718986931 * 341163958996898010807677761 * 14638765156493152640753385617 * 134260517423008739693654247554072256998018320622017089732215087102552353 Date: August 8, 1993 Methods: Rho (p8), p-1 (p12), ECM (p29), ppmpqs (p27 and largest factor) Time: 25 hours on a 16K MasPar for ppmpqs Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: August 9, 1993 --------------------------------------------------------------- p(18379) Factors: 2 * 2 * 2 * 2 * 3 * 3 * 3 * 5 * 7 * 37 * 251177 * 532789 * PRP130 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18397) Factors: 2 * 2 * 3 * 3 * 73 * 3209 * 15199 * 880007 * 7329545389 * 826760580703217 * 682027972473415704830399616516007 * 210775432100435972949104218112480451622020852941782525705879554556723069 Date: Dec 27, 1994 Method: TD, ECM (using Lips): p10, p15, p33, restp72 Time: 7 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 27, 1994 --------------------------------------------------------------- p(18427) Factors: 5 * 5 * 7 * 409 * PRP142 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18433) Factors: 3 * 5 * 17 * 349 * 28387 * 138407 * 315736581717049 * 5062122540046012956030962718161 * 36948603899346185864425477276277071109 * 6674136237671519514663177740215657401262431240907 Date: Sep 2, 1994 Method: TD, ECM (using Lips): p15, p31; MPQS (ipsc860):p38, p49 Time: ECM: 5 mips years, MPQS 48 hours on 16 nodes of an Intel ipsc860 hypercubeName: 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 7, 1994 --------------------------------------------------------------- p(18439) Factors: 2 * 3 * 5 * 1163 * 6489570566740759469407 * 13296778295720175227927 * 1439043308496666318424620872286295658509 * 33653416634935710389115854716549125613446086247250179944063 Date:May 19, 1993 Method: TD, ECM : p22 p23 , PPMPQS :p40 restp59 (using LIPS) Time: ECM 53 mips days , PPMPQS ca. 14 mips years 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 - 3024167 Recd: May 19, 1993 --------------------------------------------------------------- p(18443) Factors: 3 * 7 * 7 * 181792464371789080216628647 * 106975049563923102950357283192958763 * 52954578879229324268813098344575605374540443172674830854328161068849375806579943651 Date: Oct 1, 1994 Method: TD, ECM (using Lips): p27, p36, restp83 Time: 6y 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 1, 1994 --------------------------------------------------------------- p(18451) Factors: 11 * 84922980066474991167102606565712123 * 174695503995204191712603909455455614874469419304776374432620517405400853917156596533821097458406621779947592153 Date: Aug 13, 1996 Method: TD, ECM (using Lips): p35, restp111 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 17, 1996 --------------------------------------------------------------- p(18457) Factors: 3 * 3 * 7 * 7 * 607726380933218623 * PRP126 Date: April 17, 1991 Method: ECM (p18) Time: 6E-3 (2 MIP-days) Name: Peter L. Montgomery Recd: April 16, 1991 --------------------------------------------------------------- p(18461) Factors: 3 * 3 * 5 * 1423307 * 1625817601 * 29531947189 * PRP119 Date: April 1, 1991 Method: P-1 (p10), ECM (p11) Time: 8E-4 Name: Peter L. Montgomery Recd: April 1, 1991 --------------------------------------------------------------- p(18481) Factors: 2 * 3 * 13 * 73 * 66617944923088326737 * PRP123 Date: April 17, 1991 Method: ECM (p20) Time: 6E-3 (2 MIP-days) Name: Peter L. Montgomery Recd: April 16, 1991 --------------------------------------------------------------- p(18493) Factors: 2 * 2 * 2 * 5 * 650609 * 652549 * 710813 * 1572564006240751 * 4459069373454099623296858452791291 * 2859173161375152465666850721668697013680066220966778331425832025375994275855013 Date: Oct 1, 1994 Method: TD, ECM (using Lips): p16, p34, restp79 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: October 1, 1994 --------------------------------------------------------------- p(18503) Factors: 7 * 131 * 193 * 566505782187074909 * 314825276455062785735033 * PRP100 Date: February 25, 1992 Method: ECM (p18, p24 - first limit 300000) Time: 0.13 Name: Peter L. Montgomery Recd: February 25, 1992 --------------------------------------------------------------- p(18517) = 303075065083022387767771687053301232451409640418772192628146650785305604102359288481828135670577729919695600913819326835127339169935349873027505582 (147 digits) Factors: 2 * 1873 * 4019 * 31907 * 145806081567144861509 * 6871170875293919844169035330954414719637664532517913 * 629755643184739590613492402190952749146647554168945586694494347 Date: July 27, 1999 Method: trial division, ecm, gnfs (two largest factors, with CWI's NFS code and Arjen's lattice siever) Time: 6 cpudays polyn selection, 137.5 cpudays line sieving (SGI workstations, R10000, 175 Mhz), 9.5 cpudays lattice sieving (450Mhz Pentium) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com --------------------------------------------------------------- p(18521) Factors: 3 * 3 * 251 * 98395882200873721087155729709585756538621 * 1415584189821750521370854564212218517245355121312467350210272352731800235260891987756795673695613075923 Date: Aug 13, 1996 Method: TD, ECM (using Lips): p41, restp103 Time: 9 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: January 24, 1997 --------------------------------------------------------------- p(18523) Factors: 1109 * 2717692577 * PRP135 Date: March 21, 1991 Method: ECM Time: 5E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18539) Factors: 5 * 37 * 83 * 9931 * 86647265219 * 26149276231703 * 110193339460313121013587859218554699 * 336598039802449639123748111065303067 * 29062763432685211713113035567770511061371411 Date: February 13, 1997 Method: trial division, ecm/fft (p36 with program MIPS.ecm2.3000000.nonshared from Peter Montgomery), ppmpqs (two largest factors: p36', p44) Time: 5 ecm/fft runs on SGI R10000 (Origin 2000) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: February 14, 1997 --------------------------------------------------------------- p(18541) Factors: 7 * 7 * 7 * 7 * 11 * 80747 * 726599 * 3374403987541 * 2302115109392422072372759 * 93977809520379499833780212783053 * PPR63 Date: November 30, 1992 Method: TD + p-1 + ECM (P13, P25, P32; B1 up to 320000) Time: ca. 0.04 MIPSyears (a few hours an an i486-33 and SparcStation ELC each) Name: Heinz-Bernd Eggenstein Address: Universitaet Dortmund, FB Informatik, LS II, Baroper Str. 103, 4700 Dortmund, Federal Republic of Germany Email: eggenste@cantor.informatik.uni-dortmund.de Recd: November 30, 1992 --------------------------------------------------------------- p(18553) Factors: 3 * 3 * 73 * 271 * 283 * 142271 * 23885879671980167740607 * p112 Date: December 29, 1992 Method: ecm (p23 with first limit 240000) Time: 40 CPU hours on RS/6000, model 220 (timing), 340 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 29, 1992 --------------------------------------------------------------- p(18583) Factors: 3 * 3 * 7 * 47 * 109539893 * 142190753 * 785015769619 * 67318454807341 * 25340429346413519454458868045947262002835274151 * 9103664710409361006570175622051368371012919663987148767 Date: October 23, 1993 Method: trial division, ecm (p9, p9, p12, p14), ppmpqs (two largest factors) Time: 90 hours on a 16K MasPar for ppmpqs Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 23, 1993 --------------------------------------------------------------- p(18587) Factors: 12774917 * 6218841061 * 68033913851 * 204243795936433946929 * 24181270643357925546978843737 * 21865212980994265005324233011514469162473626444095612708733880014689787 Date: March 20, 1993 Method: p-1, ECM (250951 and 2677133 in 2nd phase); primality with ECPP Time: 33159s on a 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: March 20, 1993 --------------------------------------------------------------- p(18593) Factors: 7 * 19 * 107 * 6007 * 1412737104953 * 3627248041591 * PRP115 Date: April 17, 1991 Method: ECM (two p13) Time: 6E-3 (2 MIP-days) Name: Peter L. Montgomery Recd: April 16, 1991 --------------------------------------------------------------- p(18617) Factors: 5 * 5 * 11 * 19 * 277 * 406447 * 8754289 * 12382009147429486707440882387 * 9659036918749481682944212703443927 * 1254520225780855111301146106518187640019582134925763137848961359079 Date: February 19, 1994 Method: TD, ECM : p7 p29 , PPMPQS :p34 restp67 (using LIPS) Time: ECM 10 mips days , PPMPQS 50 day on a IPSC860 (16 nodes) Name: Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski) address: 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: February 19, 1994 --------------------------------------------------------------- p(18637) Factors: 2 * 2 * 2 * 2 * 2 * 11 * 1069 * 56354251 * 41665178037922593242291830626784777 * 1054220594429557317579687918975202260824687572307736817075967111919592829143432176044016605913423529 Date: Mar 31, 1995 Method: TD, ECM (using Lips): p8, p35, restp100 Time: 8 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: March 31, 1995 --------------------------------------------------------------- p(18661) Factors: 3 * 41 * 670156212399900616845801660103 * PRP116 Date: February 25, 1992 Method: ECM (p30 - first limit 300000) Time: 0.13 Name: Peter L. Montgomery Recd: February 25, 1992 --------------------------------------------------------------- p(18671) Factors 353453 * 649787862461 * 6641373917713 * 54906617719098270521965801 * 16743617880283359512761979407047903404132003 * 912402389740016558614087909619494807179331201739 Date: February 19, 1993 Method: ecm, ppmpqs Time: 8 hours on a 16K MasPar (ppmpqs) Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: February 19, 1993 --------------------------------------------------------------- p(18679) Factors: 2 * 5 * 59 * 28521471549847 * 12239243788740167 * 126074661047 * 241115638902334482927677907985067 * 220197157539354142243859746314069077843569108684270640765696970391904759 Date: November 21, 1993 Method: ecm (c104 = p33*p72, first limit 10^6) Name: Bruce Dodson, Matt Fante Email: bad0@lehigh.edu Recd: November 22, 1993 --------------------------------------------------------------- p(18691) Factors: 5 * 47 * 6901980236603 * 15195641511731 * PRP119 Date: April 21, 1991 Method: P-1 (p13), ECM (p14) Time: 8E-3 (3 MIP days) Name: Peter L. Montgomery Recd: April 21, 1991 --------------------------------------------------------------- p(18701) Factors: 2 * 11 * 19 * 31 * 359 * 1610380621 * 330485261988370879318930295101 * 683682996573145420370674935381066841861988997243920768496263703528810206960999846828370364184932289051 Date: Nov 03, 1994 Method: TD, ECM (using Lips): p10, p30, restp102 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: November 3, 1994 --------------------------------------------------------------- p(18713) Factors: 12013433 * 220546529986579208162110391 * P114 Date: June 3, 1993 Method: Rho (p8), ECM (p27) Time: 0.5 Name: Paul C Leyland --------------------------------------------------------------- p(18719) Factors: 2 * 2 * 3 * 3 * 3 * 3 * 5 * 19 * 269 * 3420701 * PRP134 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18731) = 2238809630536043429624786547017359870251899269418758276330531384846786966456440926598259884831796533220032552178398869797633986798241472619896845473 (148 digits) Factors: 3 * 41 * 369731 * 1421908817607366101501 * 34653690832460610668915418541327640612693 * 999090767491474300911052406463714107808223035729316130974021951170310534102897 Date: November 8, 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 --------------------------------------------------------------- p(18743) Factors: 3 * 19 * 1019 * 5407 * 6176869 * 959726374378621 * PRP118 Date: March 21, 1991 Method: ECM Time: 4E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18749) Factors: 2 * 2 * 2 * 5 * 5 * 5 * 3163 * 14407 * 360534883 * 68948533517258070859947650102639239031 * 2337196778725048743184641550718012359099294929612379625799626932530454800414601569774578813 Date: December 5, 1998 Method: trial division, ecm, ecm/fft (p38 with program MIPS.ecm2.16000000.shared from Peter Montgomery) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd:December 5, 1998 --------------------------------------------------------------- p(18757) Factors: 7 * 561894376373195642453676081899 * 4209673662399724309153078108252170459259 * 172263750480128514675524894714330738108145581905009927230723302807195961052907 Date: August 5, 1998 Method: trial division, ecm/fft (p30 with program MIPS.ecm2.3000000.nonshared from Peter Montgomery, then p40 with program MIPS.ecm2.8000000.shared) Time: 4th curve with 8000000 ecm/fft, on an SGI O2 (R5000, 200Mhz) at Lehigh University Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: August 5, 1998 --------------------------------------------------------------- p(18773) Factors: 457 * 503 * 2906472887477539 * 22354965400019965562981 * 221645757096013785732087399072189072963538663076326277939887863468965266175784840475937080089485333785751 Date: 13 May 1991 Method: TD + ECM (p16, p23), Miller-Rabin for primality test. Time: 0.01 Name: Paul C Leyland & Peter L Montgomery Recd: May 13, 1991 --------------------------------------------------------------- p(18787) Factors: 11 * 53 * 2740603 * 464477167353382555238454214511 * 5081419834017012466661978995877440156276466608736738164641292746431980734109796059646730073387026153780289687 Date: Feb 20, 1995 Method: TD, ECM (using Lips): p7, p30, restp109 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: February 27, 1995 --------------------------------------------------------------- p(18793) Factors: 2 * 2 * 2 * 2 * 3 * 7 * 7 * 193 * 31957 * 15825473177 * 30187276897 * 45844419560978896644405788888790299 * 12551009026314564026766973169760943584084408629005069994895538737924416313138439547 Date: Oct 1, 1994 Method: TD, ECM (using Lips): p11, p11, p35, restp83 Time: 5 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 1, 1994 --------------------------------------------------------------- p(18797) Factors: 2 * 3 * 3 * 61 * 799273986885893 * 311682835960740609961 * PRP110 Date: April 17, 1991 Method: P-1 (p21 in 110 sec), ECM (p15) Time: 6E-3 (2 MIP-days) Name: Peter L. Montgomery Recd: April 16, 1991 --------------------------------------------------------------- p(18839) Factors: 2 * 5 * 7 * 19 * 19 * 123667 * 26168207146968840488942808344864382029 * 74783019313359006060676516050338788544152079001332875279484985230472997984769153414677275242214730273 Date: February 1, 1999 Method: trial division, ecm, ecm/fft (p38 with program MIPS.ecm2.8000000.shared from Peter Montgomery) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: February 1, 1999 --------------------------------------------------------------- p(18859) = 7364066815395395136808576798768597276323768019235849581589125413512476193015732136194226325657533791627245960346865315430218211821619976183875326165 (148 digits) Factors: 3 * 5 * 7 * 193 * 1160921081 * 585733808410699194683 * 4083543518715050287472966090028749340839632813053968723 * 130867237301513799881928065902009025199497247194893744906709 Date: December 28, 1998 (found); January 3, 2000 (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(18869) Factors: 2 * 5 * 5 * 5 * 5437 * PRP142 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18899) Factors: 3 * 3 * 5 * 5 * 11 * 1193 * 11345029 * 2365049873 * 4352555561 * PRP116 Date: March 21, 1991 Method: P-1 (p8, second p10), ECM (first p10) Time: 5E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18911) Factors: 2 * 2 * 3 * 3 * 17 * 23 * 47 * 181 * 467 * 1609 * 592168974391 * 55497056848171 * 107687124178369 * 304377001208707726108170057217727 * 123103789501299494701152640296568596215244376202558266201818113 Date: March 1st, 1993 Method: ECM, ppmpqs; primality of the factors with ECPP. Time: two weeks human time on an incredible variety of machines Name: Reynald Lercier, Francois Morain Address: LIX, Ecole Polytechnique, F-91128 Palaiseau Cedex FRANCE Email: lercier@polytechnique.fr or morain@polytechnique.fr phone: +33 1 69 33 45 89 Recd: March 1, 1993 --------------------------------------------------------------- p(18913) Factors: 2 * 149 * 4336662342378323591 * PRP127 Date: May 16, 1991 Method: ECM (p19). Also found by P+-1. Time: 0.02 Name: Peter L. Montgomery Recd: May 16, 1991 --------------------------------------------------------------- p(18917) Factors: 2 * 2 * 25006784713 * 80309297001971 * 2537189980641402843885010229600805270041 * 618896048163977569546780415239921932396456507373542220133187474358147279676625187151 Date: Feb 20, 1996 Method: TD, ECM (using Lips): p11, p14, p40, restp84 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: February 20, 1996 --------------------------------------------------------------- p(18947) Factors: 7 * 7 * 199 * 56946257 * 13554297803470987 * 19713995929081695037 * 40251560895467035037881 * 885895761368170291388532216764486999 * P43 Date: 27 February 1992 Method: TD, P-1 (p8), ECM (p17, p20, p23), PPMPQS (p36, p43) Time: 0.3 (ECM 0.13) Name: Peter L Montgomery & Paul C Leyland Recd: February 27, 1992 --------------------------------------------------------------- p(18959) Factors: 3 * 5 * 11 * 11 * 97 * 6702287 * PRP137 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18973) Factors: 224611 * PRP143 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(18979) Factors: 5 * 13 * 17 * 311 * 64679 * 104551 * 2402329 * 52953551494404961249 * 22900019541140695321785165596633 * 3309326002875283479303189910720891681778010999435572420285943313956956503657 Date: May 02, 1994 Method: TD, ECM (using Lips): p7, p20, p32, restp76 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: May 2, 1994 --------------------------------------------------------------- p(19001) Factors: 2 * 2 * 61 * 233621 * 431021 * 596200110419 * 1839959420779 * PRP112 Method: P-1 Time: 6E-5 Name: Peter L. Montgomery Recd: March 21, 1991 ---------------------------------------------------------------- p(19009) Factors: 5 * 285145277 * 75309106151 * 84962786994439853 * 11401370819770324153977081413 * P84 Date: 21 June 1993 Method: TD, P-1 (p9), ECM (p11, p17, p29) Time: 0.5 Name: Paul C Leyland Recd: June 21, 1993 --------------------------------------------------------------- p(19013) Factors: 3 * 3 * 7 * 7 * 24239 * 4261268338674046361319988873 * 2994000169930481672558671908900434599628639 * 225010771043629696784062185413627128434466650017784216182328620956824413 Date: August 27, 1998 Method: trial division, ecm, ecm/fft (p43 with program MIPS.ecm2.16000000.shared from Peter Montgomery) Time: 1261st curve with 16000000 ecm/fft, on an SGI Octane at Lehigh University Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: August 27, 1998 --------------------------------------------------------------- p(19031) Factors: 5 * 5 * 7 * 7 * 11 * 3767 * 7927 * 3274427735401 * 5507465102355137 * 66069347148874019 * PRP92 Date: April 17, 1991 Method: P-1 (p13), ECM (p16, p17) Time: 6E-3 (2 MIP-days) Name: Peter L. Montgomery Recd: April 16, 1991 --------------------------------------------------------------- p(19037) Factors: 3 * 3 * 5 * 113149 * 76110686960198271061 * PRP122 Date: June 16, 1991 Method: ECM (p20) Time: 0.05 (2.5 MIP-weeks) Name: Peter L. Montgomery Recd: June 16, 1991 --------------------------------------------------------------- p(19051) Factors: 2 * 2 * 2 * 203907718966967 * 2341707465498367 * 2968610743455271 * 101545786968402937083829 * 7606470321349394521245949 * 258580532245637340757909273 * 19251185199613503943130166289 Date: 22 July 1991 Time: 0.06 (ECM, PPMPQS < 0.005) Method: TD, ECM (p15, two p16, p24, p25), PPMPQS (p27, p29) Name: Peter L Montgomery & Paul C Leyland Recd: July 22, 1991 --------------------------------------------------------------- p(19069) Factors: 2 * 2 * 2 * 5 * 11 * 61 * 593 * 13597 * 263027969 * 3325184920111256831040648864877 * 27885873044042449777540626664487051863162949 * 9755250005786113682712487679063085286993209553172264941 Date: Jun 20, 1995 Method: TD, ECM (with FFT-Continuation): p9, p31, p44, restp55 Time: ECM approximately 60 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: June 21, 1995 --------------------------------------------------------------- p(19073) Factors: 2 * 2 * 3 * 7 * 19 * 13305981613924980319550797857546022609 * 5066825188663809681518076222461852545930193 * 496532448662680628496294197597545475384948880358732345521322506553 Date: September 21, 1998 Method: trial division, ecm/fft (p38 with program MIPS.ecm2.8000000.shared from Peter Montgomery), 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 Email: arjen.lenstra@citicorp.com Recd: September 21, 1998 --------------------------------------------------------------- p(19079) Factors: 5 * 5 * 7 * 11 * 17 * 757 * 148793 * 678763 * 17918469509 * 104016808735238331798721549 * 118638846425033571242865826913790832391 * 102074366243671816960346757616942576982683589614034651837 Date: January 20, 1993 Method: TD, p-1, ECM (p=3282451 in 2nd step), ppmpqs; primality with ECPP Time: ECM=67717s on a Ds3100; ppmpqs=Dieu seul le sait! 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: January 20, 1993 --------------------------------------------------------------- p(19087) Factors: 3 * 3 * 3 * 5 * 5 * 7 * 11 * 389 * 701 * 238627 * 297755411 * 1935344868495872293 * 166484568528513876450315495511 * 187381127803330253291015449091948783235759468114080302589802529039731231904631 Date: Jul 18, 1994 Method: TD, ECM (using Lips): p9, p19, p30, restp78 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: July 18, 1994 --------------------------------------------------------------- p(19121) Factors 4444523919103 * 43626923544302201 * 7954672598506064338046450189 * 114727472549865696422274515941 * 470192381050052429939633528427661996120330178816243584513977463 Date: February 18, 1993 Method: ecm (p28), ppmpqs (p30) Time: 8 hours on a 16K MasPar Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: February 18, 1993 --------------------------------------------------------------- p(19213) Factors: 3 * 3 * 3 * 7 * 43 * 107 * 635483 * 177495431209 * 20939990206259014806407195551 * P98 Date: 11 July 1993 Method: TD, Rho (p6), ECM (p12, p29) Time: 0.5 Name: Paul C Leyland Recd: June 11,1993 ---------------------------------------------------------------