From challenge-administrator@majordomo.rsasecurity.com Wed Jan 30 16:03:26 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 QAA00354 for ; Wed, 30 Jan 2002 16:03:24 -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 00:00:51 UT Received: (from daemon@localhost) by cameos.majordomo.rsasecurity.com (8.8.8+Sun/notrash) id PAA23161; Wed, 30 Jan 2002 15:54:44 -0500 (EST) Date: Wed, 30 Jan 2002 15:54:44 -0500 (EST) Message-Id: <200201302054.PAA23161@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 140 digits - 144 digits ----------------------- July 11, 1999 p(16729) Factors: 5 * 30851 * 7617483638387284258923280179056666689 * 8932092366740425355288842550948851250652179708315094734801536288265007775763307595139413226453371 Date: August 30, 1998 Method: trial division, ecm, ecm/fft (p37 with program MIPS.ecm2.8000000.shared from Peter Montgomery) Time: 58th 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 30, 1998 --------------------------------------------------------------- p(16741) Factors: 2 * 7 * 38424851765621295443657 * P116 Date: 13 August 1992 Method: TD, ECM (p23) Time: 0.25 Name: Paul C Leyland Recd: August 13, 1992 --------------------------------------------------------------- p(16747) Factors: 2 * 281 * PRP137 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(16759) Factors: 2 * 5 * 11 * 11 * 16211038058513 * 780607108636800721 * 12942366362376297503131 * P83 Date: 13 August 1992 Method: TD, P-1 (p14), P+-1 (p18), ECM (p23) Time: 0.3 Name: Paul C Leyland & Peter L Montgomery Recd: August 13, 1992 --------------------------------------------------------------- p(16763) = 14671351266450161394530634705729545067981369939416139618365725882497076455702498572403955902010724756946127816836592090436026181694900423545 (140 digits) Factors: 5 * 7 * 1737268684890488600694497053 * 14007603043245951279780982242411877578731776408133 * 17225476864500422107513801709840685391781789929646931239677763 Date: May 10, 1996 (found); January 3, 2000 (sent) Method: trial division, ecm, ppmpqs (two largest factors) Time: approximately 150 mips years Name: Bruce Dodson, Arjen K. Lenstra Email: arjen.lenstra@citicorp.com (was: lenstra@bellcore.com) ------------------------------------------------------------------ p(16787) Factors: 3 * 7 * 315521963 * 13985922851027 * PRP117 Date: April 17, 1991 Method: Pollard Rho (p9), ECM (p14) Time: 6E-3 (2 MIP-days) Name: Peter L. Montgomery Recd: April 16, 1991 --------------------------------------------------------------- p(16823) Factors: 3 * 3 * 7 * 89 * 16530139871231151854714498726866397 * 119125617474348668155320521675019073009879 * 2397759139053604367972445525292967503733446516034557068542579 Date: September 5, 1998 Method: trial division, ecm/fft (p35 with program MIPS.ecm2.8000000.shared from Peter Montgomery, then p42 with MIPS.ecm2.16000000.shared) Time: 286th curve with 16000000 ecm/fft, on an SGI Octane Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: September 5, 1998 --------------------------------------------------------------- p(16829) Factors: 2 * 2 * 2 * 2 * 2 * 3 * 5 * 41 * 4679 * 33889 * 38068628793943019 * 1925427180919539516341752773697868917 * 122771154174977161102939617651969291615197263745515935980370849796250462363 Date: Nov 16, 1993 Method: TD, ECM (using Lips): p17, p37, restp75 Time: ca. 3 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: November 16, 1993 --------------------------------------------------------------- p(16831) Factors: 2 * 2 * 7 * 7 * 47 * 13057788638551 * 2297408510053957999333 * 956674472707118202710139970781198728696605719 * 108327112628785397392452479468898151969859593718219204381 Date:September 16, 1993 Method: TD, ECM : p14 p22 , PPMPQS :p45 restp57 (using LIPS) Time: ECM ca. 14 mips days , PPMPQS 30 mips years 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: September 16, 1993 --------------------------------------------------------------- p(16843) Factors: 2 * 2 * 2 * 2 * 7 * 86350319697307 * 11680589971265249 * PRP108 Date: April 1, 1991 Method: ECM (p17 before p13) Time: 8E-4 Name: Peter L. Montgomery Recd: April 1, 1991 --------------------------------------------------------------- p(16871) Factors: 2 * 5 * 53 * 71 * 44111 * 2102256536279363713 * 6150044766769839601804641427579177 * 1976623082766064034092656723587121792900190812935254167585176709700676220017867 Date: September 22, 1993 Method: ecm (c113 = p34*p79, first limit 10^6, found in 1st step before 8*10^5) Name: Bruce Dodson, Matt Fante Email: bad0@lehigh.edu Recd: September 22, 1993 --------------------------------------------------------------- p(16879) Factors: 2 * 2 * 5 * 5 * 114113 * 397151 * 6309223 * 21358476259 * PRP110 Method: P-1 Time: 4E-5 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(16883) Factors: 3 * 7 * 761 * 1289 * 168439319 * 948363593731 * 29411363287112531 * PRP96 Date: April 17, 1991 Method: P-1 (p9), ECM (p12, p17) Time: 6E-3 (2 MIP-days) Name: Peter L. Montgomery Recd: April 16, 1991 --------------------------------------------------------------- p(16889) Factors: 3 * 3 * 5 * 7 * 7 * 17 * 163 * 64661 * 69566677281355577 * 272453871773682316219 * 5547982571104561696587498367844369557 * 1218313726821617416124347324647494562784232673219729839 Date: November 3, 1992 Method: ppmpqs Time: seven hours on a 16K MasPar Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: November 3, 1992 --------------------------------------------------------------- p(16901) Factors: 2 * 2 * 37 * 76103 * 9915342534233 * PRP120 Date: March 21, 1991 Method: ECM Time: 7E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(16903) Factors: 5 * 7 * 7 * 9311 * 67483788922749885102936740927440117 * 6696889697976686454892455016912532965611857 * 56321463476532560291040232897575369861974703757605606053 Date: October 1, 1998 Method: trial division, ecm/fft (p35 with program MIPS.ecm2.8000000.shared from Peter Montgomery), ppmpqs (two largest factors) Time: approximately 15 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: October 1, 1998 --------------------------------------------------------------- p(16921) Factors: 13 * 1019 * 971456214373 * 559858969952453 * 14719529051626147271 * 40852086892904075311065307859 * 305864989048240083192580542811 * 52274089059785321340088462879301 Date: 17 September 1991 Time: 0.1 Method: TD, ECM (p12, p15, p20, p30 - first limit 200000), PPMPQS (p29, p32) p30 was found before p20, and both before the PPMPQS run. Name: Peter L Montgomery & Paul C Leyland Recd: September 17, 1991 --------------------------------------------------------------- p(16927) Factors: 2 * 21503 * 1529220647 * 3636328753 * 61035692533 * PRP106 Method: Pollard Rho + P-1 Time: 7E-5 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(16931) Factors: 2 * 2 * 7 * 7 * 13 * 227 * 1570007 * 2123532517 * 1779404518834461451106638053005866162077187 * 22265925719183864923870699944737786865933058932626632302767477813221966497053 Date: July 10, 1998 Method: ECM (p43 with first limit 3200000) Time: about 10 curves with first bound at 2*10e6 or 3.2*10e6 (for p43) Name: Eric Prestemon Email: ecp@io.com Phone: 650-842-6546 Recd: July 10, 1998 --------------------------------------------------------------- p(16943) Factors: 5 * 5 * 991 * 169199 * 1059503 * 226628021 * 3742197912210854539487871662444159442000139 * 22813905681527214622146730695132777648626555454025859637099299858729431127 Date: November 27, 1998 Method: trial division, ecm, ecm/fft (p43 with program MIPS.ecm2.30000000.shared from Peter Montgomery) Time: 493rd curve with 30000000 ecmfft, on an SGI Octane Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: November 27, 1998 --------------------------------------------------------------- p(16963) Factors: 2 * 7 * 30509 * 2220183942433 * PRP123 Method: P-1 Time: 8E-6 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(16979) Factors: 2 * 2 * 2 * 2 * 3 * 5 * 5 * 11 * 31 * 43 * 53 * 359895313 * PRP123 Method: Pollard Rho Time: 4E-5 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(16981) Factors: 7 * 11 * 173 * 457 * 98869 * 215797 * 3428159272889213 * 533148007925631331 * 144013127677782934047266621547941 * 3646126634442843357692681366913262446094651326693580009007 Date: December 14, 1992 Method: p-1, p18 (ECM), p33.p58 (ppmpqs); primality of the factors done using ECPP. Time: 30810s on a Dec3100 (ECM), time for ppmpqs unknown due to bugs. 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 14, 1992 --------------------------------------------------------------- p(16993) Factors: 2 * 37 * 197 * 229589 * 41709986105661746826529 * p109 Date: December 14, 1992 Method: ecm (first limit 240000, p23 in step 1 after 44 curves) Time: < 15 hours on RS/6000, model 220 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 14, 1992 --------------------------------------------------------------- p(17011) Factors: 3 * 11 * 118311613722744115932193500716689484719 * 42812493696032247947226183760928738001570829391802003022397694779355993812105082513834036463302607141 Date: March 20, 1999 Method: trial division, ecm (p39 with first limit 3000000, GMP-ECM by P. Zimmermann (Inria)) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: March 20, 1999 --------------------------------------------------------------- p(17021) Factors: 2 * 41 * 61 * 239 * 1451 * 1377137 * 4304261494481330745382904837 * 17925548196073400367840949737450078895732902273982212577056041206752755804579219878088753450097761 Date: Apr 11, 1994 Method: TD, ECM (using Lips): p7, p28, restp98 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: April 11, 1994 --------------------------------------------------------------- p(17027) = 195442285190507926749811494730126724581700375210022166183595582100226400873714608807529708842403254264862789323895878083107487250659112107172 (141 digits) Factors: 2 * 2 * 8456211009525899927 * 58968298512166599200779233231624330520082633 * 97986023294775910354260293598747300672847882373962254147569325110694286823623 Date: July 2, 1999 Method: trial division, ecm, ecm/fft (p44 with program MIPS.ecm2.30000000.shared from Peter Montgomery) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com --------------------------------------------------------------- p(17029) = 199298778896312406789058349163984150220800887841072834663480147481914396832800549815049150979457764017065666937038471960517072761325365218980 (141 digits) Factors: 2 * 2 * 3 * 3 * 5 * 7 * 3187 * 29629 * 1777920712109823045241570821106745671349063 * 942155626141860014467107969774383416806123840555639086383957373162078689314165203159227 Date: May 30, 1999 Method: trial division, ecm, ecm/fft (p43 in Step 1, with program MIPS.ecm2.16000000.shared from Peter Montgomery, before 13000000) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com --------------------------------------------------------------- >From bad0@CS0.CC.Lehigh.EDU Mon May 31 14:30:08 EST 1999 p(17033) Factors: 2 * 7 * 37 * 10401583 * 15847841 * 72736297 * PRP116 Method: Pollard Rho + P-1 Time: 1E-5 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(17041) Factors: 659 * 691 * 929 * 720228308224823857801 * PRP111 Date: November 12, 1991 Method: ECM (p21) Time: 0.1 Name: Peter L. Montgomery Recd: November 12, 1991 --------------------------------------------------------------- p(17047) Factors: 3 * 3 * 2693 * 124199 * 569021 * 454257529211098507 * 3915076288851265709613772251377 * 77999117832855403276221556283339326816803214669546862686727037312613266048911 Date: Jul 25, 1994 Method: TD, ECM (using Lips): p18, p31, restp77 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 25, 1994 --------------------------------------------------------------- p(17053) Factors: 2 * 2 * 2 * 2 * 157 * 1180807 * 77721639199515757682763432636637 * 1092845557292965153341221239000132243871376940198355382077798882490558042939743801473021056461653273 Date: Oct 31, 1994 Method: TD, ECM (using Lips): p7, p32, restp100 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 31, 1994 --------------------------------------------------------------- p(17077) Factors: 2 * 2 * 2 * 2 * 2 * 3 * 19 * 19 * 85903 * 5105141 * 91735558436693250704587 * PRP102 Date: June 16, 1991 Method: ECM (p23 - first limit 90000) Time: 0.05 (2.5 MIP-weeks) Name: Peter L. Montgomery Recd: June 16, 1991 --------------------------------------------------------------- p(17099) Factors: 2 * 3 * 5 * 5 * 5 * 7 * 7 * 2069 * 97960929461 * 4271513395291710089 * PRP104 Date: April 1, 1991 Method: P-1 (p11), ECM (p19) Time: 8E-4 Name: Peter L. Montgomery Recd: April 1, 1991 --------------------------------------------------------------- p(17107) Factors: 5 * 151 * 2243 * PRP135 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(17117) Factors: 79 * 197 * 266947 * PRP132 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(17123) Factors: 2 * 2 * 2 * 2 * 3 * 60773 * 888077 * 3177574358920937 * 34171227653223673 * PRP97 Date: April 17, 1991 Method: P-1 (p16), ECM (p17) Time: 6E-3 (2 MIP-days) Name: Peter L. Montgomery Recd: April 16, 1991 --------------------------------------------------------------- p(17137) = 571506343245329246915014963591106959377926106170565517415487689052355154929268918544030525277635634544425633129514704520633533396059855648818 (141 digits) Factors: 2 * 17 * 71 * 10685956713374067942842540201 * 690824610064528061556773516832143448461459302022241323 * 32070267183512326259203369739497645279235428906030547269 Date: August 12, 1995 (found); December 30, 1999 (sent) Method: trial division, ecm, ppmpqs (two largest factors) Time: approximately 200 mips years Name: Bruce Dodson, Arjen K. Lenstra Email: arjen.lenstra@citicorp.com (was: lenstra@bellcore.com) ------------------------------------------------------------- p(17159) Factors: 2 * 2 * 5 * 31 * 10257437 * 168223372817 * PRP120 Date: April 17, 1991 Method: Pollard Rho (p8), ECM (p12) Time: 6E-3 (2 MIP-days) Name: Peter L. Montgomery Recd: April 16, 1991 --------------------------------------------------------------- p(17167) Factors: 2 * 2 * 2 * 17 * 29 * 41 * 1327 * 1787 * 825898207 * 2865274707257807184741593 * p96 Date: December 10, 1992 Method: ecm (12th curve, p25 in 2nd step) Time: < 5 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 10, 1992 --------------------------------------------------------------- p(17183) Factors 7 * 7 * 17 * 211 * 5035529 * 943327233786441593 * 3818145021682385609711 * 2352896108091062806391905023769 * 119224023967915132398811428313765982895265563577917208275839 Date: January 20, 1993 Method: ecm, ppmpqs Time: six hours on a 16K MasPar (ppmpqs) Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: January 20, 1993 --------------------------------------------------------------- p(17189) Factors: 2 * 5 * 7 * 157 * 769 * 4933 * 11447 * 26371 * 27919 * 385118333 * 13797627946789 * PRP96 Date: April 17, 1991 Method: P-1 (p9), ECM (p14) Time: 6E-3 (2 MIP-days) Name: Peter L. Montgomery Recd: April 16, 1991 --------------------------------------------------------------- p(17191) Factors: 2 * 5 * 23 * 29 * 1093 * 24701286367 * 280044932977 * PRP113 Date: April 17, 1991 Method: P-1 (p12), ECM (p11 - not until third ECM pass) Time: 6E-3 (2 MIP-days) Name: Peter L. Montgomery Recd: April 16, 1991 --------------------------------------------------------------- p(17207) Factors: 1123 * 2923069 * 652826744131415783 * PRP114 Date: May 2, 1991 Method: ECM (p18) Time: 0.02 Name: Peter L. Montgomery Recd: May 2, 1991 --------------------------------------------------------------- p(17231) Factors: 17 * 89681 * 57371748796157 * PRP122 Date: April 1, 1991 Method: ECM (p14) Time: 8E-4 Name: Peter L. Montgomery Recd: April 1, 1991 --------------------------------------------------------------- p(17239) Factors: 5 * 5 * 7 * 7 * 7 * 1650991 * 2063432770123 * 2965290528161283955599430579612201 * 17789734007006534064646839370032460636838712186916118858211550593808703166585613073539 Date: Feb 21, 1994 Method: TD, ECM (using Lips): p7, p13, p34, restp86 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: February 21, 1994 --------------------------------------------------------------- p(17257) Factors: 2 * 2 * 2 * 2 * 3 * 5 * 506281 * 10503974976731783 * PRP118 Date: May 2, 1991 Method: ECM (p17) Time: 0.02 Name: Peter L. Montgomery Recd: May 2, 1991 --------------------------------------------------------------- p(17291) Factors: 163 * 199 * 241 * 2003 * 767216282269 * 16729362935759227781 * 208266505097601563570152171 * 4261397367859217879153956864322828579 * 14309575782205295840979509886151840043 Date: October 15, 1993 Method: trial division, ecm (p12, p20), ppmpqs (three largest factors) Time: 35 hours on a 16K MasPar for ppmpqs Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 15, 1993 --------------------------------------------------------------- p(17293) Factors: 317653387964524057506085949680153489 * 8192228937613991480154865494183749542591840245359248118690542662680997795794385470449312487176758870758993 Date: Okt 17, 1995 Method: TD, ECM (using Lips): p36, restp106 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: November 21, 1995 --------------------------------------------------------------- p(17299) Factors: 3 * 3 * 3 * 5 * 5 * PRP139 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(17317) Factors: 3 * 251 * 3581 * 28100133780074413 * 14617243578508555289 * 208676018703242436663585890360160946491421 * 14207893494272469514029918520486848588564391254650028855457 Date: October 13, 1993 Method: trial division, ecm (p17, p20), ppmpqs (two largest factors) Time: 34 hours on a 16K MasPar for ppmpqs Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 13, 1993 --------------------------------------------------------------- p(17321) Factors: 12710684143083373 * 1849028731710740621 * 52682446929394963173933498687452563 * 2756936421549057651807487283648531499589598864444050276945818886006600991 Date: Jan 31, 1995 Method: TD, ECM (using Lips): p17, p19, p35, restp73 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 31, 1995 --------------------------------------------------------------- p(17327) Factors: 2 * 2 * 7 * 331 * 3031697811319059303467100829 * 41157695128075275649555482225821 * 3128408666064433276003089731190105936879111497869101532983182842490409671217173 Date: Feb 26, 1993 Method: TD, ECM (using Lips): p28, p32, restp79 Time: ECM ca. 0.8 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 2, 1993 --------------------------------------------------------------- p(17333) Factors: 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 1288034973407840501391017 * 1264771634822348528899646580163483 * 9193980231935930655023251655641185727030107079623443140747912120034761679933416249 Date: Apr 08, 1994 Method: TD, ECM (using Lips): p25, p34, restp82 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 8, 1994 --------------------------------------------------------------- p(17351) Factors: 3 * 5 * 7 * 19 * 7564673 * 265109768569365288953718877771 * 9270376770003439537757236994714378563333 * 123058498791276268056029163499118261160629323766181202538839523 Date: June 4, 1994 Method: trial division, ecm, ppmpqs (two largest factors) Time: 76 hours on 16K maspar for ppmpqs Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: June 4, 1994 --------------------------------------------------------------- p(17377) Factors: 2 * 2 * 2 * 2 * 2 * 2351 * 284041 * 3273493 * 9319275261937 * PRP112 Date: April 17, 1991 Method: ECM (p13) Time: 6E-3 (2 MIP-days) Name: Peter L. Montgomery Recd: April 16, 1991 --------------------------------------------------------------- p(17389) Factors: 2 * 5 * 239 * 2624963708628088260068273551 * p112 Date: December 29, 1992 Method: ecm (p28 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(17393) Factors: 3 * 7 * 7 * 11 * 331 * 39315083864381746026607 * 47507460637478428553 * 11054204311420329036478983707 * p66 Date: January 12, 1993 Method: ecm (p29 with first limit 480000 - small composite left from '92) Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: January 12, 1993 --------------------------------------------------------------- p(17401) Factors: 2 * 11 * 89 * 173 * 13691 * 12717387228555554110327 * 2268381355068847973282641640849813559817 * 55333739786759297538427437624013699764466339836803144231496086214930079 Date: January 8, 1996 Method: trial division, ecm (c111=p40*p71, with first step 1400000) Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: January 8, 1996 --------------------------------------------------------------- p(17417) Factors: 2971 * 37214184206411675075581 * p116 Date: December 11, 1992 Method: ecm (16th curve, p23 in 2nd step) Time: < 6 hours on RS/6000, model 220 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 11, 1992 --------------------------------------------------------------- p(17419) Factors: 2 * 5 * 11 * 11 * 242309165993 * 29281144868900813070239 * PRP106 Date: August 28, 1991 Method: ECM (p12, p23 - first limit 300000) Time: 0.07 Name: Peter L. Montgomery Recd: August 28, 1991 --------------------------------------------------------------- p(17431) Factors: 157 * 499 * 306517 * 19807483 * 6300613601 * 32517110529382428215620308161 * PRP87 Date: July 15, 1992 Method: td, p-1 (P6, P8, P10), ECM (P29) [1st limit 160000, 2nd limit 10080000, 248 curves used] Time: 0.5 MIPS years (ca. 240 h on an i486-DX33 PC under MS-DOS) 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: July 15, 1992 --------------------------------------------------------------- p(17443) Factors: 2 * 2 * 2 * 3 * 12906403 * 5153222579849570967452464547 * 882331116843386482224971560806750510104249324575837 * 7886142582166000123281516312134559785492912706991021333 Date: January 19, 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: January 19, 1995 --------------------------------------------------------------- p(17449) Factors: 2 * 3 * 5 * 5 * 5 * 7 * 7 * 7 * 11 * 14284067373180931 * 14679516144990318341 * 608499255451102365932746540764549063229 * 32596662264146122322507640811177065946915809105268218740761879 Date: September 21, 1993 Method: TD, ECM : p17 p20 , PPMPQS :p39 restp62 (using LIPS) Time: ECM 9 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: September 21, 1993 --------------------------------------------------------------- p(17467) Factors: 2 * 3 * 7 * 3089 * 129634761341685178552045820809343 * 6650330053908672060483993073091915350829071061 * 125183510030524108803191150898104684280175783019544333716297 Date: July 17, 1998 Method: trial division, ecm (p33 with first limit 1400000), ppmpqs (two largest factors) Time: approximately 50 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: July 12, 1998 --------------------------------------------------------------- p(17471) Factors: 3 * 3 * 7 * 7 * 7 * 7 * 17 * 19 * 43 * 93089571827761 * 2522480413762117 * 5082708716361006636647305947694528456153511199719 * 40626291395025087623103406186441480409595739927256740163 Date: January 27, 1995 Method: trial division, ecm, ppmpqs (two largest factors) Time: approximately 45 mips years Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: January 30, 1995 --------------------------------------------------------------- p(17477) Factors: 2 * 7 * 7 * 2427383381 * 310707406843 * 132315470715740863277 * PRP100 Date: April 1, 1991 Method: P-1 (p10, p12), ECM (p21) Time: 8E-4 Name: Peter L. Montgomery Recd: April 1, 1991 --------------------------------------------------------------- p(17483) Factors: 71 * 21013 * 194971210731828026439479 * 178519994099263665863134277 * PRP87 Date: October 15, 1991 Method: ECM (p27 - first limit 200000; p24 as step 1 near 300000) Time: 0.09 Name: Peter L. Montgomery Recd: October 15, 1991 -------------------------------------------------------------- p(17491) Factors: 7 * 7 * 13 * 13417425143 * PRP130 Method: Pollard Rho Time: 9E-5 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(17497) Factors: 10460699941016290658464823033 * 1965747791813662647853744409824247719823 * 909343911538751692434695763841451105892238245213848270391013762269988680863 Date: August 30, 1998 Method: ecm (p29), ecm/fft (p40 with program MIPS.ecm2.16000000.shared from Peter Montgomery) Time: 875th curve with 16000000 ecm/fft, found on Lehigh's Origin2000 Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: August 31, 1998 --------------------------------------------------------------- p(17519) Factors: 2 * 2 * 3 * 3 * 3 * 3 * 5 * 7 * 13 * 1667461 * 800407 * 66157189926260089527699785884493 * 1775754681271847793107353869514193684090662365412447212414972640849206728083608613902048178969 Date: July 2, 1995 Method: trial division, ecm (p32 with first step limit 1400000) Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: July 1, 1995 --------------------------------------------------------------- p(17539) Factors: 2 * 2 * 2 * 2 * 3 * 5 * 17 * 21553794072381027007 * 10371459993091350976658527 * 30725995769553363717786728306606398584326968872004617231235987484137194965252331997219351385719 Date: Feb 27, 1993 Method: TD, ECM (using Lips): p20, p26, restp95 Time: ECM ca. 0.7 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: February 27, 1993 --------------------------------------------------------------- p(17551) Factors: 2 * 2 * 11 * 29 * 541534484198022219052433865458563 * 45521678594173095130950480965843379665029884570552163178516429802927742439531244681711967022465550052497983 Date: June 4, 1994 Method: trial division, ecm (p33 with 500000) Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: June 4, 1994 --------------------------------------------------------------- p(17569) Factors: 2 * 2 * 2 * 5 * 7 * 17 * 3221631172079 * 4340329964387358924110981 * 1651418165824566402255580253987917 * 340289450360215942045040727294343112035653924497582055865699495670021 Date: July 21, 1995 Method: trial division, ecm, ppmpqs (two largest factors) Time: approximately 25 mips years Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: July 21, 1995 --------------------------------------------------------------- p(17573) Factors: 2 * 2 * 2 * 2 * 3 * 3 * 5 * 11 * 23 * 631 * 1949 * 61757 * PRP127 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(17579) Factors: 2 * 2 * 3 * 5 * 41 * 77141 * 8783046037 * 1755110663634339175521968773760597 * 14077033471174531191468602882508382840389428490794210196897921218931780095816089803096293011 Date: August 17, 1998 Method: trial division, ecm, ecm/fft (p34 with program MIPS.ecm2.16000000.shared from Peter Montgomery, found in step 1) Time: 1st curve with 16000000 ecm/fft, on Lehigh's Origin2000 Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: August 17, 1998 ------------------------------------------------------------------------------ p(17597) Factors: 2 * 2 * 3 * 3 * 31 * 1291 * 117689353 * 9239637814934209 * 263294269010180285841011149208131337853689 * 118689874928462418196806389171548863906057915449818190519279777664062611 Date: December 4, 1996 Method: trial division, ecm, ppmpqs (two largest factors) Time: approximately 150 mips years Name: Bruce Dodson, Arjen K. Lenstra Email: arjen.lenstra@citicorp.com Recd: December 4, 1996 --------------------------------------------------------------- p(17609) Factors: 5 * 7 * 71 * 76213 * 4106854641247224216527877563 * 70640853054351812727187545047296948148941363241842353400361573317685315516543831454405974626799371068825637 Date: Mar 3, 1993 Method: TD, ECM (using Lips): p28, restp107 Time: ECM ca. 1 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 3, 1993 --------------------------------------------------------------- p(17623) Factors: 197 * 46021731999596983126893506921519174267 * 6932667225601305380242086133843967989825243446144099269679175871252814726943076177526267805144825052869 Date: September 7, 1997 Method: trial division, ecm (p38 with first limit 1400000) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: September 6, 1997 --------------------------------------------------------------- p(17627) Factors: 2 * 3824089 * 830983883 * 156158914624813 * PRP113 Date: April 17, 1991 Method: Pollard Rho (p9), ECM (p15) Time: 6E-3 (2 MIP-days) Name: Peter L. Montgomery Recd: April 16, 1991 --------------------------------------------------------------- p(17657) Factors: 7 * PRP143 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(17659) Factors: 3 * 5 * 7 * 7 * 17 * 16127 * 150041053 * 16026352337 * PRP117 Method: Pollard Rho + P-1 Time: 1E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(17669) Factors: 5 * 11 * 19 * 23 * 23 * 473165221675194346693 * 50460962409041 * 79729643098321331235798319912667 * p71 Date: December 12, 1992 Method: ecm (30th curve, first limit quickly up to 240000, p32 at start of 2nd step. p21 with 80000) Time: 9 hours on RS/6000, model 220 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 12, 1992 --------------------------------------------------------------- p(17681) Factors: 2 * 2 * 7 * 7 * 574839191608182658738670793330932819 * 973332348738563920036077664099926864869717272725639809653236950582079436118184853187431324389363859140319 Date: February 14, 1997 Method: trial division, ecm/fft (p36 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(17707) = 140701647583237686465414613520671581748927253487083779252421984147235825465061995024938851818710108828209959522577273909228508598409302547078497 (144 digits) Factors: 3 * 3 * 3 * 2131 * 922619 * 1400733203 * 13759687518601963775341906981869033247787 * 137519910341941926576308032152646218018411211915336838360828188839613346124401731459 Date: July 3, 1999 Method: trial division, ecm, ecm/fft (p41 with program MIPS.ecm2.30000000.shared from Peter Montgomery) Time: 274th curve with 30000000 ecmfft, on an SGI Octane Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com --------------------------------------------------------------- p(17713) Factors: 2 * 11 * 2129 * PRP139 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(17729) Factors: 2 * 5 * 5 * 5 * 7 * 7 * 13 * 83 * 458456939 * 1394980842199159 * 171934650114054953127187 * 20171811616717594572605051 * P64 Date: June 16, 1991 Method: P-1 (p9), ECM (p16, p26 - first limit 70000), ECM/FFT (p24) Time: 0.05 (2.5 MIP-weeks) Name: Peter L. Montgomery Recd: June 16, 1991 --------------------------------------------------------------- p(17737) Factors: 2 * 2 * 3 * 103 * 263 * 3733 * 2035349 * 736393933524047 * 752826697843852452403544267 * PRP87 Date: October 24, 1991 Method: ECM (p15), ECM/FFT (p27 - first limit 400000) Time 0.10 Name: Peter L. Montgomery Recd: October 24, 1991 --------------------------------------------------------------- p(17747) Factors: 19 * 59669115943 * PRP132 Method: P-1 Time: 1E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(17749) Factors: 2 * 2 * 2 * 2 * 2 * 5 * 5 * 5 * 11 * 2063 * 4787 * 1420433527 * PRP123 Method: ECM Time: 1E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(17761) Factors: 11 * 23 * 23 * 61 * 830990959 * 114726013469 * PRP118 Method: P-1 (p9), ECM (p12) Time: 1E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(17783) Factors: 2 * 3 * 3 * 1499 * 1514611841923 * 15001845486607241912753059267426795793 * 18161942605656278279988226960798080424519 * 26154444606461925644691353390152373085361240310401 Date: January 22, 1999 Method: trial division, ecm, ecm/fft (p38 with program MIPS.ecm2.16000000.shared from Peter Montgomery), MAGMA ppmpqs (two largest factors) Time: approx 90 cpuhours for ppmpqs on an sgi Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: January 22, 1999 --------------------------------------------------------------- p(17789) Factors: 2 * 2 * 5 * 43 * 10091 * PRP137 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(17791) Factors: 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 7948822326310927279 * 89663858056723792323038321329 * 205217829310198446977207481372471520481 * 8395939427121392711149714622542694922422647041608825677 Date: April 28, 1993 Method: ECM (p19, p29), ppmpqs; primality with ECPP Time: less than usual Name: Reynald Lercier, Francois Morain Address: LIX. Ecole Polytechnique, F-91128 Palaiseau Cedex FRANCE Email: lercier@polytechnique.fr or morain@polytechnique.fr Recd: April 28, 1993 --------------------------------------------------------------- p(17827) = 443432390923041004112278331038303769605643271595673776789669461949204326075951300120691737930716836084613156537684717668356577596159191077096833 (144 digits) Factors: 3 * 3 * 7 * 7 * 9689 * 8130665021502455801097613 * 7732299004174156327084484103959400772706897698327 * 1650726637967867642711573233285744117539273196912523778963560467 Date: April 4, 1997 (found); December 30, 1999 (sent) Method: trial division, ecm, ppmpqs (two largest factors) Time: approximately 150 mips years Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com ---------------------------------------------------------------- p(17837) Factors: 2 * 11 * 89 * 8867 * 110651 * 1142311 * 39546084852027572671 * 153884412634428535426716125488903829913118804970771 * 36531609706683476865711142114808379706728577720939801367 Date: February 7, 1995 Method: trial division, ecm, ppmpqs (two largest factors) Time: approximately 60 mips years Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: February 7, 1995 --------------------------------------------------------------- p(17851) Factors: 2 * 7 * 48235193 * 34318795566116891 * 405083531556202016209 * PRP98 Date: September 8, 1991 Method: P-1 (p8), ECM (p17, p21) Time: 0.08 Name: Peter L. Montgomery Recd: September 8, 1991 --------------------------------------------------------------- p(17863) Factors: 5 * 19 * 2707 * 11213 * 16301017 * 50383301280218213 * 59581426310366071226149 * PRP88 Date: August 8, 1991 Method: P-1 (p8), ECM (p17, p23) Time: 0.07 Name: Peter L. Montgomery Recd: August 8, 1991 --------------------------------------------------------------- p(17881) Factors: 3 * 5 * 11 * 67 * 46069513468603 * 291126084226369632701803 * PRP103 Date: May 2, 1991 Method: ECM (p14, p24 - first limit 30000) Time: 0.02 Name: Peter L. Montgomery Recd: May 2, 1991 --------------------------------------------------------------- p(17891) Factors: 2 * 41 * 107 * 62590318469979511 * 1003806192832640371 * PRP106 Date: May 2, 1991 Method: ECM (p17, p19) Time: 0.02 Name: Peter L. Montgomery Recd: May 2, 1991 --------------------------------------------------------------- p(17909) Factors: 2 * 2 * 3 * 5 * 193 * 12577 * 19421 * 122040326372493073 * 17778182321031996411516589736509 * 157972560663024962242620991978283330965767533032229498429264846197052288224717407889 Date: Jun 18, 1993 Method: TD, ECM (using Lips): p18, p32, restp84 Time: ECM ca. 0.78 mips-years Name: Franz-Dieter Berger, Thomas Denny, Johannes Buchmann Recd: June 21, 1993 p(17921) = 1086868973768159176727104694218827114975268680504706789208689546959985658262490261469815673684264268418381829969402316814082280835613317526446718 (145 digits) Factors: 2 * 2543 * 66638051 * 49805998651 * 2638807870553 * 23010459204174861995957830577063466683351684587 * 1060385645660948970469098485886838753320144241590892784414185883 Date: July 30, 1995 (found); December 30, 1999 (sent) Method: trial division, ecm, ppmpqs (two largest factors) Time: approximately 200 mips years Name: Bruce Dodson, Arjen K. Lenstra Email: arjen.lenstra@citicorp.com (was: lenstra@bellcore.com) -----------------------------------------------------------------------