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 QAA00331 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 PAA23144; Wed, 30 Jan 2002 15:54:43 -0500 (EST) Date: Wed, 30 Jan 2002 15:54:43 -0500 (EST) Message-Id: <200201302054.PAA23144@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 150 digits - 154 digits ----------------------- As of July 11, 1999 p(19141) = 3324883096583872041953087090862546457240630065051502752489855110289241062143094922965959366528563455483019604067328673788710653669487098672400372229122123 (154 digits) Factors: 227 * 872015655797620097 * 987059802907075010867909 * PRP105 Date: September 22, 1991 Method: ECM (p18, p24 -- first limit 300000) Time: 0.08 Name: Peter L. Montgomery --------------------------------------------------------------- p(19163) Factors: 3 * 436015799 * 5686313916138375287 * 38653779840100019390434577 * 469245693688374201882640399657601853695947 * 908313535368810453818895031787714009716758661085265029 Date: August 5, 1993 Methods: trial division, Pollard rho (p9), ecm (p19, p26), ppmpqs Time: 20 hours on a 16K MasPar for ppmpqs Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: August 5, 1993 --------------------------------------------------------------- p(19181) Factors: 2 * 241 * 89669 * 10178344219709 * 3924177909522130680140783 * p104 Date: December 16, 1992 Method: ecm (16th curve, p25 in 2nd step) Time: 5 CPU hours on RS/6000, model 220 (timing), 340 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 16, 1992 --------------------------------------------------------------- p(19211) Factors: 2 * 618857 * 972302361617 * 13284920224925057 * PRP116 Date: May 2, 1991 Method: ECM (p12, p17) Time: 0.02 Name: Peter L. Montgomery Recd: May 2, 1991 --------------------------------------------------------------- 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: July 11, 1993 --------------------------------------------------------------- p(19219) Factors: 5 * 13 * 167 * 57552893 * 11651604869 * 117754298447494831265724255853 * 7678693415413899366546179359658492673964343 * 31176957079726122377432554692980183578151494723376966659 Date: August 7, 1993 Methods: Rho (p8), ECM (p11, p30), ppmpqs (largest two factors) Time: two days on a 16K MasPar for ppmpqs Name: Paul Leyland, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: August 9, 1993 --------------------------------------------------------------- p(19231) Factors: 11 * 13 * 47 * 191 * 167381 * 19417 * 70919 * 84467 * 1394083 * 6497930409595095756036977592011 * p88 Date: December 16, 1992 Method: ecm (18th curve, p31 at start of 2nd step) Time: < 5 CPU hours on RS/6000, model 220 (timing), 340 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 16, 1992 --------------------------------------------------------------- p(19237) Factors: 2 * 7 * 6899 * 52783 * 6766554737 * PRP130 Method: Pollard Rho Time: 8E-6 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(19249) Factors: 5 * 5 * 5 * 2577101 * 191174164229 * PRP130 Date: March 21, 1991 Method: ECM Time: 4E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(19267) Factors: 2 * 11 * 16823 * 49266617 * 216266497883863425420888323154352589 * 80903470763092057088295598077612241981742428784948421783805294825877734456894915531028264462778123167 Date: November 26, 1998 Method: trial division, ecm, ecm/fft (p36 with program MIPS.ecm2.8000000.shared from Peter Montgomery) Time: 11th 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: November 26, 1998 --------------------------------------------------------------- p(19259) Factors: 2 * 2 * 2 * 3 * 5 * 5 * 11 * 61 * 160885106563 * 18934805776703997351251 * PRP111 Date: October 24, 1991 Method: P-1 (p12), ECM/FFT (p23 - first limit 400000) Time: 0.10 Name: Peter L. Montgomery Recd: October 24, 1991 --------------------------------------------------------------- p(19273) Factors: 3 * 2081 * 8929 * 118263163101798131 * 525012360587328870163724042573 * p95 Date: December 27, 1992 Method: ecm (p30 with first limit 240000 - p18 with 80000) Time: 23 CPU hours on RS/6000, model 220 (timing), 340 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 27, 1992 --------------------------------------------------------------- p(19289) Factors 3 * 5 * 11 * 29 * 577 * 12007 * 765823 * 2255023 * 50515911750223571 * 175415446411313 * 33146353716682986678314621 * 751755062824206466559164195734769 * 30889997382206058951913374726422918651 Date: January 13, 1993 Method: ecm, ppmpqs Time: a few minutes on a 16K MasPar (ppmpqs) Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: January 13, 1993 --------------------------------------------------------------- p(19301) Factors: 19 * 1412858626744447182701791573 * 31606042127035602955460653380119 * 2262716181630393082591799267685215519 * 227088211001307715336837323624173410257952923581386451 Date: December 4, 1998 Method: trial division, ecm, ecm/fft (p32 then p37 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(19309) Factors: 2 * 2 * 3 * 5 * 29 * 31 * 40662218625443 * 32147857466923152110111 * 1580498413752288335710241 * 40766522755073468445578539 * P60 Date: 25 November 1992 Method: TD, ECM (p14, p23, p25), PPMPQS (p26, p60) Time: 2 Name: Paul C Leyland Recd: November 25, 1992 --------------------------------------------------------------- p(19319) = 514272744644534376828148957223023948168027512673250099447410043590344160963926561420213271953626294634109826582479537060064406266091769548924882070790 (150 digits) Factors: 2 * 5 * 7 * 1904316588491 * 1213078166087 * 86305991628776916901500411414625111465954979 * 36849074517509941617014231351445824702254881499465771065531132013189559675670679 Date: November 21, 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(19333) Factors: 2 * 2 * 3 * 11 * 33937 * PRP144 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(19373) Factors: 2 * 5 * 293 * 1189313 * 3404281653307 * 17307395640990625029640381 * 270802452690257205094049826614169913 * 15176092927529238602460102122144298352450672754546100392104285976323 Date: Feb 13, 1995 Method: TD, ECM (using Lips): p7, p13, p26, p36, restp68 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 13, 1995 --------------------------------------------------------------- p(19379) Factors: 2 * 2 * 5 * 5 * 5 * 5 * 7523 * 4227606137 * 240639888353 * 19104858222562733 * 24706455239629873 * 46883900250534059 * 676316361181306786590981692356771 * 3113059368042824482541138365221562470431 Date: June 19, 1991 Method: ECM (p10, p12, three p17), ppmpqs(p33, p40) Time: 0.05 for ECM; 0.05 for ppmpqs Name: Peter L. Montgomery and Arjen K. Lenstra Recd: 19 June, 1991 --------------------------------------------------------------- p(19381) Factors: 2 * 2 * 2 * 2 * 7 * 127 * PRP146 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(19387) Factors: 2 * 337 * 548616857 * 813708387452646229 * PRP121 Date: February 25, 1992 Method: Pollard Rho (p9), ECM (p18) Time: 0.13 Name: Peter L. Montgomery Recd: February 25, 1992 --------------------------------------------------------------- p(19391) Factors: 2 * 5 * 13 * 113 * 1901 * 88379 * PRP138 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(19417) Factors: 2 * 7 * 2433487050151 * 11790841563629501604914100401 * 11068493351185748319301464185571721 * 11951449120273778530255062880770727 * 23758563706148355647203080467044545723907 Date: Mar 7, 1995 Method: TD, ECM (using Lips): p13, p29, p35, MPQS (ipsc860): p35, p41 Time: ECM 6 mips years, MPQS ca. 6 hours 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: March 7, 1995 --------------------------------------------------------------- p(19421) Factors: 2 * 5 * 11 * 127 * 1847 * 803749 * 598615778448731 * 405885149855034098449 * 5462573495673724186869722747121044083 * 47577088692794978811443787868931182518107516586768775331285588801 Date: October 25, 1993 Method: trial division, ecm (p6, p15, p21), ppmpqs (two largest factors) Time: 57 hours on a 16K MasPar for ppmpqs Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 25, 1993 --------------------------------------------------------------- p(19423) Factors: 2 * 7 * 7 * 137 * 139 * 193 * 269 * 659 * 11048413776665718160704624949883741 * 1890700688031904440700913567648608344700521258286835286793868861223420176189482983454204197128503178497 Date: June 25, 1998 Method: ECM (p35 with first limit 3003464) Time: about 10 curves with first bound at 2*10e6 or 3*10e6 (for p35) Name: Eric Prestemon Email: ecp@io.com Phone: 650-842-6546 Recd: July 9, 1998 --------------------------------------------------------------- p(19427) Factors: 31 * 97931 * 987433 * 20194622241799 * PRP125 Date: March 21, 1991 Method: ECM Time: 3E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(19429) Factors: 2 * 2 * 2 * 2 * 5 * 19 * 1978014008776041151 * PRP129 Date: May 2, 1991 Method: ECM (p19) Time: 0.02 Name: Peter L. Montgomery Recd: May 2, 1991 --------------------------------------------------------------- p(19433) Factors: 23 * 57998339281429695648647923 * p124 Date: December 23, 1992 Method: ecm (p26 with first limit 240000) Time: 32 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(19441) Factors: 5 * 132252773 * PRP142 Method: Pollard Rho Time: 5E-5 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(19447) Factors: 3 * 23 * 3881 * 86839037261 * 36727144924243452839 * 34216682327789217040564498572610429 * 1321081822633001672448747952814464793 * 43030077309667787222076193148627647631132009 Date: September 30, 1996 Method: trial division, ecm (p35 with first step 1400000), magma qs (two largest factors) Name: Bruce Dodson, Arjen K. Lenstra Email: arjen.lenstra@citicorp.com Recd: September 30, 1996 --------------------------------------------------------------- p(19457) Factors: 2 * 7 * 7 * 67 * 26327820737 * 19765775206500229 * PRP120 Date: April 17, 1991 Method: ECM (p11, p17) Time: 6E-3 (2 MIP-days) Name: Peter L. Montgomery Recd: April 16, 1991 --------------------------------------------------------------- p(19463) Factors: 2 * 5 * 17 * 23 * 23 * 9815248771 * 60137503056511 * 574265275232909951 * PRP104 Date: September 30, 1991 Method: P-1 (p10), ECM (p14, p18) Time: 0.08 Name: Peter L. Montgomery Recd: September 30, 1991 --------------------------------------------------------------- p(19469) Factors: 5 * 13 * 19 * 1069129 * 36247584806647 * 5123395062251 * 348745576533151954841851 * p92 Date: December 17, 1992 Method: ecm (46th curve, first limit quickly to 240000, p24 at start of 2nd step) Time: 12 CPU hours on RS/6000, model 220 (timing), 340 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 17, 1992 --------------------------------------------------------------- p(19471) Factors: 2 * 2 * 2 * 2 * 5 * 587 * 371069 * 45593152777603 * 132148389082901977 * 23712567020947410445027872775411 * 12619648296997969119130989804862029383 * 65850875163658086060441363430145873210153 Date: July 27, 1994 Method: TD, ECM (using Lips):p14, p18, p32 MPQS (ipsc860):p38,p41 Time: ECM ca. 3.1 mips years MPQS ca. 7.5 hours 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: August 5, 1994 --------------------------------------------------------------- p(19477) Factors: 743 * 5664157 * 274330031 * 2268722121077 * 668450082333266567 * 3172710255068699727102871 * PRP78 Date: June 5, 1991 Method: Pollard Rho (p9), ECM (p13, p18), P+-1 (p25, first limit 1000000) Time: 0.04 (2 MIP-weeks) Name: Peter L. Montgomery Recd: June 5, 1991 --------------------------------------------------------------- p(19483) Factors: 267224868954787670235319509905141 * 8639355717436681676864706415099009162369520671321141155049174347563758099819481769576112583294204469661126429914026363 Date: October 29, 1997 Method: ecm/fft (p33 with program MIPS.ecm2.3000000.nonshared from Peter Montgomery) Time: under 200 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: October 29, 1997 --------------------------------------------------------------- p(19489) Factors: 2 * 5 * 7 * 29 * 1453 * 4793 * 6657067831607624108570156407164407 * 25912779130000388429070888710396845983897701512462734919943092578665271124543977336373845312518693299785151 Date: May 17, 1993 Method: TD, ECM (using Lips): p34, restp107 Time: ECM ca. 0.36 mips 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: May 17, 1993 --------------------------------------------------------------- p(19507) Factors: 2 * 2 * 2 * 3 * 7 * 41 * 137 * 1279 * 119788909 * 1977453455297285223994434131 * 41373963438466004767305484748247608847119517423271321 * 243015193575898849893088147411078978874992813383364819 Date: August 23,1995 Method: trial division, ecm, ppmpqs (two largest factors) Time: approximately 100 mips years Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 1, 1995 --------------------------------------------------------------- p(19531) Factors: 2 * 2 * 2 * 2 * 2 * 2 * 5 * 5 * 11 * 11486878481543 * PRP134 Date: March 21, 1991 Method: ECM Time: 2E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(19541) Factors: 7 * 23 * 83 * 4639 * 49827299 * 613829703153300774607101444374881 * 2067780871869027334197868061913841570980471357644618810509592205507610273418843029774488616505998590823 Date: January 25, 1999 Method: trial division, ecm, ecm/fft (p33 with program MIPS.ecm2.8000000.shared from Peter Montgomery) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: January 25, 1999 --------------------------------------------------------------- p(19553) Factors: 2 * 2 * 11 * 37751440547 * 6257286301772513484580993 * p114 Date: December 27, 1992 Method: ecm (p25 with first limit 240000) Time: 30 CPU hours on RS/6000, model 220 (timing), 340 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 27, 1992 --------------------------------------------------------------- p(19559) Factors: 2 * 5 * 98346239 * 335627147 * 270742514753 * 2019947273055767553023 * 660134178069418085950094554819891089944745105829 * 38771418303912270114748178607129034658516388546618697 Date: October 18, 1993 Method: trial division, ecm (p8, p9, p12, p22), ppmpqs (two largest factors) Time: 57 hours on a 16K MasPar for ppmpqs Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 18, 1993 --------------------------------------------------------------- p(19571) Factors: 3 * 7432319 * 594107417 * 102435410165639 * PRP121 Date: April 17, 1991 Method: P-1 (p9), ECM (p15) Time: 6E-3 (2 MIP-days) Name: Peter L. Montgomery Recd: April 16, 1991 --------------------------------------------------------------- p(19577) Factors: 2 * 2 * 2 * 3 * 7 * 17 * 19 * 29 * 53 * 5501 * 82301 * 1615040014647154980581 * PRP113 Date: December 31, 1991 Method: ECM (p22) Time: 0.12 Name: Peter L. Montgomery Recd: December 31, 1991 --------------------------------------------------------------- p(19583) Factors: 2 * 2 * 19 * 113328734983683612917 * 16224176646035263 * 13676230387397 * 798657117476570520532272857813 * p70 Date: December 31, 1992 Method: ecm (p30 with first limit 240000 - p17 and p21 with 5000, p14 with 80000) Time: 1.75 CPU days on RS/6000, model 220 (timing), 340 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 31, 1992 --------------------------------------------------------------- p(19597) Factors: 11 * 11 * 1101691 * 84361061885177023036267382453 * 64464555203411652362625537407269706743 * 9011088416823700546174115895691928642072238419156806992836991485473107883229 Date: July 30, 1998 Method: trial division, ecm (p29), ecm/fft (p38 with program MIPS.ecm2.16000000.shared from Peter Montgomery) Time: 229th curve with 16000000 ecm/fft, on an SGI Octane at Lehigh University Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Recd: July 30, 1998 --------------------------------------------------------------- p(19603) Factors: 3 * 3 * 15083 * 1835237547053 * 5479375747904483 * 265152164799887943707 * 10735193747327873806555287339797 * p67 Date: December 27, 1992 Method: ecm (p32 with first limit 240000 - p21 with 120000) Time: 20 CPU hours on RS/6000, model 220 (timing), 340, 580 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 27, 1992 --------------------------------------------------------------- p(19609) Factors: 2 * 3 * 5 * 5 * 2028581 * 11387219371425683647 * 1231420531952989463 * 24515827281780074702548663 * p80 Date: December 18, 1992 Method: ecm (p26 in 1st step, first limit 240000 after 32 curves, p19 with 1200000, p20 with 5000 - timing/curves omitted) Time: 10.5 CPU hours on RS/6000, model 220 (timing), 340 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 18, 1992 --------------------------------------------------------------- p(19661) Factors: 2 * 2 * 7 * 79 * 99892051217717348257 * 53244356129623598201 * 916631015985564788923254409270300423858482722201 * 1084750761329794294959942191807297599030480908094869830281579 Date: September 23, 1995 Method: trial division, ecm, ppmpqs (two largest factors) Time: approximately 80 mips years Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 1, 1995 --------------------------------------------------------------- p(19681) Factors: 3 * 3 * 157 * 5310446279 * 34745428649661146928323 * 7425756749034597413884991373302657261 * 7247530080891277195376900477010497976100259741003566213003035098591289802739731 Date: January 14, 1998 Method: trial division, ecm (p37 with first limit 1400000) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: January 14, 1998 --------------------------------------------------------------- p(19687) Factors: 3 * 3 * 3 * 3 * 5 * 514068733 * 55831321718131 * 495537455080533282811 * PRP106 Date: July 19, 1991 Method: Pollard Rho (p9), ECM (p14, p21) Time: 0.06 Name: Peter L. Montgomery Recd: July 19, 1991 --------------------------------------------------------------- p(19697) Factors: 3 * 5 * 47 * 6745616038979 * 3903352313710043 * PRP120 Date: April 1, 1991 Method: ECM (p13, p16) Time: 8E-4 Name: Peter L. Montgomery Recd: April 1, 1991 --------------------------------------------------------------- p(19699) Factors: 5 * 5 * 5 * 1346091887433977 * 1548999846243037 * 20887357092034499373209737347988379 * 3035544529920830021273172347279901079342136330389375573766963691482644769923400378569 Date: Mar 20, 1995 Method: TD, ECM (using Lips): p16, p16, p35, restp85 Time: 6 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 20, 1995 --------------------------------------------------------------- p(19709) Factors: 2 * 2 * 2 * 2 * 5 * 11 * 5387 * 12911 * 4715496259 * 124022536120932611 * PRP114 Date: May 16, 1991 Method: P+-1 (p18) Time: 0.02 Name: Peter L. Montgomery Recd: May 16, 1991 --------------------------------------------------------------- p(19727) Factors: 2 * 2 * 2 * 2 * 3 * 31 * 431 * 11903 * 213859 * 129051407 * 226936393 * 296454979196627 * PRP106 Date: April 4, 1991 Method: Pollard Rho (first p9), P-1 (second p9), ECM (p15) Time: 8E-4 Name: Peter L. Montgomery Recd: April 4, 1991 --------------------------------------------------------------- p(19751) Factors: 3 * 7 * 11 * 101 * 7066514381 * 93901337 * 1013360840392071920636510964227 * p100 Date: December 27, 1992 Method: ecm (p31 with first limit 240000) Time: 27 CPU hours on RS/6000, model 220 (timing), 340 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 27, 1992 --------------------------------------------------------------- p(19759) = 28495218316133287212437566192000004791027974451425918137274335404685193646239503572524912312831885006036248623396373078791285772039075789343475917617960 (152 digits) Factors: 2 * 2 * 2 * 5 * 7 * 17 * 17 * 349 * 12165059 * 189922678907464260157326893 * 240468354596543712359435516209292406215831162929 * 1816108156001527288879490839232391615097391039302908137485250069 Date: February 21, 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 Email: arjen.lenstra@citicorp.com ----------------------------------------------------------------- p(19763) Factors: 554137 * 969431 * 3593270324580333838356450338143 * 1774922901204630392800454483871041 * p76 Date: December 30, 1992 Method: ecm (p31 and p34! with first limit 240000) Time: 2.85 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(19777) Factors: 2 * 2 * 2063 * 87351416011 * 1017786606872201 * 6613909310970647095979 * 5204101949883146848822780179208157 * 1328608752033054442919837786233538405858172481286180501796854133857 Date: Spetember 24, 1993 Method: ECM (p11, p16, p22), ppmpqs, primality with ECPP Time: Felix qui potuit rerum cognoscere causas Name: Reynald Lercier, Francois Morain Address: LIX. Ecole Polytechnique, F-91128 Palaiseau Cedex FRANCE Email: lercier@polytechnique.fr or morain@polytechnique.fr Recd: September 24, 1993 --------------------------------------------------------------- p(19801) Factors: 2 * 7 * 1702080037081 * 14226700012621 * 1432301114783734963 * 29907746432587663187456462368125124399 * 2871840620571284654905371191307735726025684059982823372943056389241383 Date: September 5, 1995 Method: trial division, ecm, ppmpqs (two largest factors) Time: approximately 70 mips years Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 1, 1995 --------------------------------------------------------------- p(19819) Factors: 2 * 3 * 5 * 7 * 71 * 51789756752145843671 * PRP128 Date: May 16, 1991 Method: ECM (p20) Time: 0.02 Name: Peter L. Montgomery Recd: May 16, 1991 --------------------------------------------------------------- p(19841) Factors: 2 * 11 * 295524819119 * 11939104362460492197425501531 * p111 Date: December 18, 1992 Method: ecm (36th curve, first limit quickly to 240000, p29 in 2nd step) Time: 15.6 CPU hours on RS/6000, model 220 (timing), 340 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 18, 1992 --------------------------------------------------------------- p(19843) Factors: 2 * 3 * 7 * 7 * 389 * 268292077 * PRP139 Method: P-1 Time: 2E-5 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(19853) Factors: 2 * 2 * 2 * 23 * 4093 * 7879 * 52489 * 3844541 * 577986032073058787 * PRP113 Date: April 21, 1991 Method: ECM (p18) Time: 8E-3 (3 MIP days) Name: Peter L. Montgomery Recd: April 21, 1991 --------------------------------------------------------------- p(19867) Factors: 2 * 2 * 11 * 251 * 14897 * 340307086705891 * PRP130 Date: April 1, 1991 Method: ECM (p15) Time: 8E-4 Name: Peter L. Montgomery Recd: April 1, 1991 --------------------------------------------------------------- p(19889) Factors: 5 * 5 * 1493 * 163017860053 * 21357291336531605791061339 * 444486903456659144459286227609391037 * 1601684190522162675169204187354554745617133666937521145184252996941172489499 Date: April 3, 1996 Method: trial division, ecm (p26; then p36 with first step 1400000) Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 3, 1996 --------------------------------------------------------------- p(19891) Factors: 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 113 * 1237393 * 4990313 * PRP135 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(19913) Factors: 3 * 3 * 5 * 7 * 7 * 149 * PRP147 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(19919) Factors: 2 * 2 * 5 * 5065351 * 8408092202010452325921299561 * p117 Date: December 23, 1992 Method: ecm (p28 with first limit 240000) Time: 1.5 CPU days on RS/6000, model 220 (timing), 340 Name: Bruce Dodson, Matt Fante Email: bad0@ns1.cc.lehigh.edu Recd: December 23, 1992 --------------------------------------------------------------- p(19927) Factors: 3 * 3 * 3 * 5 * 7 * 7 * 11 * 103 * 2063 * 1361801639998390799617662775001 * 97064415967976115091419081244189 * 4161127933621889881765494631712287201157 * 15337629277188614159007458487010758081821 Date: Oct 02, 1995 Method: TD, ECM (using Lips): p31, p32, PPMPQS : p40, restp41 Time: ECM 1 mips year, PPMPQS ca. 12 hours on 8 nodes IPSC860 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 2, 1995 --------------------------------------------------------------- p(19937) Factors: 19 * 19 * 909854055636626408199347 * 313605128081801835411855721326898063069139 * 1386040217295182685261434800076717570155302773658425249756220682508714773687421822951 Date: March 13, 1999 Method: trial division, ecm, ecm (p42 with first limit 3000000, GMP-ECM version 3a, by P. Zimmermann (Inria)) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: March 13, 1999 --------------------------------------------------------------- p(19949) = 159113816332451634775862644248551974316602319375011817616431954355138165617235123430855766135053823037414224098903837608197827827740061798820841036686000 (153 digits) Factors: 2 * 2 * 2 * 2 * 5 * 5 * 5 * 7 * 7 * 11 * 67 * 71 * 40163 * 72167 * 387436118189177832367525221032721002602513 * 27630648506202383044239169450957258236038573435524129225763757892993337266843377802787815517 Date: October 25, 1999 Method: trial division, ecm (p42 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 Makeithappen@msn.com Wed Oct 27 03:44:10 PDT 1999 p(19973) Factors: 2 * 87277 * PRP148 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(19979) Factors: 5 * 13 * 29 * 67 * 29830291433 * PRP137 Date: March 21, 1991 Method: ECM Time: 6E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(19991) Factors: 2 * 11828270633 * 12985153108535292747573770515621 * 756734763108910720120665422720086851412359268679144844157922791016965683666096268052949071009042152313331570197 Date: June 3, 1995 Method: trial division, ecm (p32 with first step 1000000) Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: June 3, 1995 --------------------------------------------------------------- p(19993) Factors: 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3 * 5 * 11 * 3480605473 * 20437646814253 * 10986349091671 * 75663330608158981003364047 * p86 Date: December 23, 1992 Method: ecm (p26 with first limit 240000) Time: 17 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(19997) Factors: 7 * 11 * 29 * 41 * 101 * 3467 * 4373 * 5688864305048653702791752405107044435136231 * 307676463687420127640751726892888612989087807131663754847420499403556959129090099202190924197349 Date: Mar 20, 1993 Method: TD, ECM (using Lips): p43, restp96 (using parameters for 27 digits!!) Time: ECM ca. 1 mips 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 20, 1993 --------------------------------------------------------------- p(20021) Factors: 2 * 2 * 11 * 12601 * 19571 * 1138895931687955179929821 * 9555995853692841446761237 * 20706638957631650023610875293499 * 124592591713471063073228327361538076297724067751319898828704307 Date: March 18, 1993 Method: TD, ECM : p25 p25 , PPMPQS :p32 restp63 (using LIPS) Time: ECM 270 mips days , PPMPQS 6 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: March 18, 1993 --------------------------------------------------------------- p(20023) Factors: 2 * 2 * 2 * 2 * 2 * 3 * 29 * 405763 * 38285011 * 12751271935805687 * 431380881879701257821539933371472923 * 1303999024902175591917556445839549147923263012115991465245461180850401123780023010741 Date: August 24, 1997 Method: trial division, ecm (p36 with first limit 1400000) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: August 24, 1997 --------------------------------------------------------------- p(20047) Factors: 2 * 3 * 5 * 19 * 643 * 23833 * 296074447 * 758618677 * 11716163737 * 121696672529 * 351580093007335980599062234531 * 391570032473697985000096022762842422767782208636755928712631234719315571747 Date: Mar 13, 1993 Method: TD, ECM (using Lips): p9, p9, p11, p12, p30, restp75 Time: ECM ca. 0.6 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 13, 1993 --------------------------------------------------------------- p(20071) Factors: 2 * 2 * 3 * 3 * 5 * 5 * 5 * 1093 * PRP146 Date: November 12, 1991 Name: Peter L. Montgomery Recd: November 12, 1991 --------------------------------------------------------------- p(20089) = 562109229922556429413944726575121753428316751186008466254374827627176972828278718913069505586843067504471816903217740461706881609609717865652192029305395 (153 digits) Factors: 5 * 13 * 13 * 13 * 37 * 443 * 62280676231978561444991 * 53655137415225665349240011907122836230593 * 934223040786161778828792069908177056690428513590729697731566666747668212762392979 Date: November 28, 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(20101) Factors: 11 * 384017087 * 9116834772492833 * PRP128 Date: November 12, 1991 Method: P-1 (p9), ECM (p15) Name: Peter L. Montgomery Recd: November 12, 1991 --------------------------------------------------------------- p(20107) Factors: 384301 * 9456480577 * 6707291773303397 * PRP122 Date: November 12, 1991 Method: P-1 (p9), ECM/FFT (p16) Time: 0.02 Name: Peter L. Montgomery Recd: November 12, 1991 --------------------------------------------------------------- p(20113) Factors: 2 * 3 * 7 * 53 * 419 * 1451 * 143562241 * PRP136 Date: November 12, 1991 Method: P-1 (p9) Name: Peter L. Montgomery Recd: November 12, 1991 --------------------------------------------------------------- p(20117) Factors: 2 * 2 * 2 * 139 * 421 * 9807431 * 1250438266121627615503 * 11245767024228244105990867 * 67287706182763100399165924351522136433 * 166450809937672877244227689170528470310584604907882213693 Date: September 20, 1993 Method: trial division, ecm, ppmpqs (two largest factors) Time: four days on idle time of ~30 workstations (ppmpqs) Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: September 20, 1993 --------------------------------------------------------------- p(20129) Factors: 5 * 109 * 16266734939964211 * PRP134 Date: November 12, 1991 Method: ECM (p17) Name: Peter L. Montgomery Recd: November 12, 1991 --------------------------------------------------------------- p(20143) Factors: 2 * 11 * 733 * 2976209 * 7465313 * 342346057843 * PRP124 Date: November 12, 1991 Method: ECM (p12) Name: Peter L. Montgomery Recd: November 12, 1991 --------------------------------------------------------------- p(20147) Factors: 2 * 11 * 101 * 25171 * 1925681 * 69524729 * 143209132312677550324161776033742836438567 * 234678404902562731903819147822905218744779997 * 3762940988267706639377826153093520449642223019 Date: December 18, 1998 Method: trial division, ecm, ecm/fft (p42 then p46=376... with program MIPS.ecm2.16000000.shared from Peter Montgomery; cofactor p45=143...) Time: p42 on 46th curve then p46 on 55th curve Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: December 18, 1998 --------------------------------------------------------------- p(20149) Factors: 2 * 2 * 2 * 3 * 5 * 5 * 7 * 4099 * PRP146 Date: November 12, 1991 Name: Peter L. Montgomery Recd: November 12, 1991 --------------------------------------------------------------- p(20173) Factors: 34077721 * 1280726137 * 2104934447779871 * 4283821743752636249 * 40824362885542423166548753 * 74449335602117082653372699317171421926685032005253460085570557937616432126633 Date: November 29, 1992 Method: ECM (p=1372331 in 2nd step), primality of the factors established with ECPP Time: 56105s 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: December 1, 1992 --------------------------------------------------------------- p(20177) = 1239872528671349088701055564588287667991398580728215582680396510152709359879728566645168559173585958231653808838329654909370562668177506775837242713231092 (154 digits) Factors: 2 * 2 * 3 * 3 * 11 * 70487 * 135532203175771 * 20468467089804204456843972351185537 * 16011978843586066258559579730282837071369813609000958979915828044412529082453947521302733710886523 Date: September 3, 1999 Method: trial division, ecm (p35 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 Sun Sep 5 04:09:01 PDT 1999 p(20183) Factors: 2 * 13 * 23 * 97441 * 363567289 * 42872103651659 * 43542503131247 * PRP110 Date: January 1, 1992 Method: Pollard Rho (p9), ECM (two p14) Name: Peter L. Montgomery Recd: January 1, 1992 --------------------------------------------------------------- p(20201) Factors: 2 * 2 * 3597127 * 617724938867 * 534535384162189 * PRP120 Date: January 1, 1992 Method: P-1 (p12), ECM (p15) Name: Peter L. Montgomery Recd: January 1, 1992 --------------------------------------------------------------- p(20219) Factors: 2 * 2 * 2 * 2 * 2 * 2 * 2 * 5 * 1163 * 2369903677883851 * 595580447139800838293908535595226727082115962317 * 1720495773353296469160903745540751583289932127406867843818860545433055041386924423093 Date: December 6, 1998 Method: trial division, ecm, ecm/fft (p48 with program MIPS.ecm2.8000000.shared from Peter Montgomery) Time: 81st 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: December 6, 1998 --------------------------------------------------------------- p(20231) Factors: 2 * 2 * 3 * 3 * 7 * 160420152901 * 10376308291382148508216526022919509924529 * 4798710669864230948822176791979571729707987891075030533931296978627723854447761546051282060147029109 Date: December 28, 1998 Method: trial division, ecm, ecm/fft (p41 with program MIPS.ecm2.8000000.shared from Peter Montgomery) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: December 28, 1998 --------------------------------------------------------------- p(20233) Factors: 2 * 2 * 7 * 173 * 541 * 31510891 * 6372346031279519471 * 2984691837300859537643687023673 * 1304833322717556232915126925390955147518168341857012745567636229527290336405789620890471667 Date: Feb 27, 1996 Method: TD, ECM (using Lips): p8, p19, p31, restp91 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 27, 1996 --------------------------------------------------------------- p(20249) Factors 3 * 5 * 5 * 5 * 7 * 1162937 * 2218786327 * 349231806842878540722006604323486376681399732992458736982855956028701763756433611620833914342257126985495699818222356122639488161345507 Date: January 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@flash.bellcore.com Recd: January 1, 1992 --------------------------------------------------------------- p(20269) = 2829787684179707450866353575624121563903201697707700206423103384240443569891236942408443963773189742441739685822583287381679447634055842355650147934715740 (154 digits) Factors: 2 * 2 * 5 * 118543907717472583831 * 36525005825846135707 * 3759186334128803371531769119784822720005645115749216621 * 8692815658740896472511234891979988847313200251281546027891 Date: February 10, 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(20287) Factors: 3 * 11 * 239 * 8081939630832044636077389931027 * 52161363713374422604626033673134615002818622759735721364153809702725641690365292159407846655570119993556760659429571527 Date: August 29, 1993 Method: ecm (1st step 500K, 9th curve, C150 = p31*p119) Name: Bruce Dodson, Matt Fante Recd: August 29, 1993 --------------------------------------------------------------- p(20297) Factors 3 * 31 * 653 * 13299651643690387531 * 4502233758190156653243204071085750523946210375853622114464177639858358228720944466215850444260103114098577820751620636090192911993 Date: January 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@flash.bellcore.com Recd: January 1, 1992 --------------------------------------------------------------- p(20323) Factors 2 * 11 * 11 * 17 * 251 * 2347 * 587341 * 7041523 * 113512799 * 4033443371433148738859302122386675490245367991958243323141417281600955210138667919540861958858086826304656416761703625776893 Date: January 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@flash.bellcore.com Recd: January 1, 1992 --------------------------------------------------------------- p(20333) Factors 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3 * 7 * 7 * 7 * 13 * 13127 * 99235236715982751129453653753656816839855977896501781646211467566276490665378796768698304887036144036349127531186650426918275909980198389329741 Date: January 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@flash.bellcore.com Recd: January 1, 1992 --------------------------------------------------------------- p(20341) Factors: 37 * 150323023 * 167996085755004767837 * P124 Date: September 30, 1992 Method: Pollard Rho (p9), ECM (p21) Time: 0.16 MIP year Name: FactOregon (Joe Buhler, Peter Montgomery, Robby Robson, Russell Ruby) Recd: September 30, 1992 --------------------------------------------------------------- p(20347) Factors 5 * 5 * 7 * 19 * 137 * 77797 * 178066703513 * 2018664923027 * 446518996698596564701243866205552665233816379085451636338449770511371624689644798237377456822152129768958679881840717527 Date: January 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@flash.bellcore.com Recd: January 1, 1992 --------------------------------------------------------------- p(20353) Factors: 148633 * 240157954899677509 * 13202223491248661085858518341 * 12735101275466253644020795179004048032253790936560403183901630905642013479346605969159799505054381140919 Date: September 4, 1993 Method: ecm (1st step 500K, one of several 31st curves, C132 = p29*p104) Name: Bruce Dodson, Matt Fante Recd: September 4, 1993 --------------------------------------------------------------- p(20357) Factors: 2 * 3 * 3 * 5707847771 * 50754344107441201819 * 53353290889857655967 * 69194522639933256048060392047917209 * 323103699105409872917408991597193026567603732446428840919021549667101 Date: March 8, 1995 Method: trial division, ecm (p35 with first step limit 1400000) Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: March 8, 1995 --------------------------------------------------------------- p(20359) Factors: 3 * 5 * 636917 * 1576372190276789 * 67350428704143001763777443 * 6242877317517942403769267243486310501707179215056103937618187204674988414845731894701804353038945914718259 Date: Jul 16, 1996 Method: TD, ECM (using Lips): p16, p26, restp106 Time: 40 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 22, 1996 --------------------------------------------------------------- p(20369) Factors 3 * 5 * 13 * 41 * 241 * 601 * 298714542059 * 20017567674282835058212147091508633863983953002404937752452070557998173319566351051078905186065421314704404693378499772366268541188443 Date: January 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@flash.bellcore.com Recd: January 1, 1992 --------------------------------------------------------------- p(20389) Factors: 2 * 5 * 5 * 7 * 11 * 1777 * 17903 * 150853510453453 * 2505110794953579107000515980553775593299067 * 178867795015678291733534643134100308989560295210123872776243091489232723972103503158949 Date: March 18, 1999 Method: trial division, ecm, ecm/fft (p43 with program MIPS.ecm2.16000000.shared from Peter Montgomery) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: March 18, 1999 --------------------------------------------------------------- p(20393) Factors: 199 * 6151 * 16631 * 140611 * 1367383 * 167784426213294467 * 888059266223177465807107 * 5245443473205561844082631271 * P64 Date: August 16 1993 Method: TD, Rho (p7), ECM (p18, p24), PPMPQS (p28, p64) Time: 0.3 ECM, 4.5 PPMPQS Name: Paul C Leyland Recd: August 18, 1993 --------------------------------------------------------------- p(20399) Factors 2 * 2 * 5 * 5 * 7 * 7 * 61 * 609533 * 28854073 * 1722064583015991153084939696192221833995913182649300080260505312323870190375367849093212096133670821496829259313131139995206375167159783 Date: January 1, 1992 Method: ecm Time: short Name: Arjen K. Lenstra Email: lenstra@flash.bellcore.com Recd: January 1, 1992 --------------------------------------------------------------- p(20407) Factors: 2 * 2 * 3 * 3 * 7 * 11 * 64661 * 9373073 * 5006205628379147333 * PRP121 Date: January 1, 1992 Method: ECM (p19) Time: One hour Name: Peter L. Montgomery Recd: January 1, 1992 ---------------------------------------------------------------