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 QAA00356 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 PAA23156; Wed, 30 Jan 2002 15:54:44 -0500 (EST) Date: Wed, 30 Jan 2002 15:54:44 -0500 (EST) Message-Id: <200201302054.PAA23156@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 130 digits - 134 digits ----------------------- As of December 2, 1998 p(14479) Factors: 2 * 5 * 13 * 41 * 1629767213 * 403535482694114075368527747340743003130914765776479 * 315888375201253900734681729031300656181232958456977986754284170677 Date: August 25, 1997 Method: trial division, ecm, ppmpqs (two largest factors) Time: approximately 200 mips years Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: August 25, 1997 --------------------------------------------------------------- p(14489) Factors: 3 * 5 * 13 * 23 * 4371508403 * 2273696030977005519570565402015273771 * 27613720902178557418497803755939119725287056306054926874505136599739231190349649 Date: Feb 23, 1995 Method: TD, ECM (using Lips): p10, p37, restp80 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: February 23, 1995 --------------------------------------------------------------- p(14503) Factors: 2 * 2 * 2 * 2 * 3 * 163 * 16787 * 5198799459937662960498090256961 * 170643781632241953719405424485582201 * 12251951719172747947825890805487332846862116992709680827 Date:December 20, 1992 Method: TD, ECM : p31 , PPMPQS :p36 restp56 (using LIPS) Time: ECM 29 mips days , PPMPQS ca. 4 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: December 20, 1992 --------------------------------------------------------------- p(14519) Factors: 2 * 2 * 3 * 5 * 5 * 19 * 67 * 3626626793197016603921 * PRP103 Date: April 10, 1991 Method: ECM (p22) Time: 4E-3 (1.5 MIP-days) Name: Peter L. Montgomery Recd: April 10, 1991 --------------------------------------------------------------- p(14533) Factors: 2 * 509 * 54083 * 333274195847 * 842619758831 * PRP99 Date: March 22, 1991 Method: ECM (both p12) Time: 8E-4 Name: Peter L. Montgomery Recd: March 22, 1991 --------------------------------------------------------------- p(14537) = 2045267387376149839362021481305998700209870305700437601392318748934384715093661776242581839862986629662209910794053213966352093652 (130 digits) Factors: 2 * 2 * 7 * 7 * 11 * 13 * 43 * 47 * 443 * 167240897077616175771045305339456854660858989586481 * 487355034069563535324043102420569636890465872800533801975518374764813 Date: December 28, 1999 Method: trial division, gnfs (two largest factors, with CWI's NFS code and Arjen's lattice siever) Time: 18 cpudays polyn selection, c. 146 cpudays sieving (SGI workstations, R10000 for line sieving; assorted Pentiums for lattice sieving), 3.75 cpudays matrix ("new" rsa155 filter with merge_8) Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com ------------------------------------------------------------------ p(14543) Factors: 2 * 5 * 397 * 4862822912911 * 121752118805324729663239011426019 * 927110570468325127967892571754596493006711789086048114760073794544514282086470197 Date: July 10, 1993 Method: ecm (c114 = p33*p81, first limit 2*10^6, < 200 curves) Name: Bruce Dodson, Matt Fante Email: bad0@lehigh.edu Recd: June 10, 1993 --------------------------------------------------------------- p(14549) Factors: 2 * 2 * 5 * 5 * 7 * 9661 * 21523 * 5756789 * 651281485665823 * PRP97 Date: March 21, 1991 Method: ECM Time: 2E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(14551) Factors: 3 * 3 * 3 * 3 * 3 * 3 * 7 * 7 * 1783 * 1760151015582143 * 177850750020598026043234998553 * 118936064914036242382668099678805865224813946682971588014990246307665638903913 Date: July 14, 1993 Method: ecm (c107 = p30*p78, first limit 2*10^6, 140th curve) Name: Bruce Dodson, Matt Fante Email: bad0@lehigh.edu Recd: June 14, 1993 --------------------------------------------------------------- p(14557) Factors: 3 * 3 * 7 * 19 * 23 * 47 * 524197 * 2275681 * 92728997 * 97034947781 * 61015478756685630976207 * PRP70 Date: August 8, 1991 Method: Pollard Rho + P-1 (p8, p11), ECM (p23) Time: 0.07 Name: Peter L. Montgomery Recd: August 8, 1991 --------------------------------------------------------------- p(14561) Factors: 3 * 5807065489 * 5735013127104523546495917836490637235369 * 26378589361936627700741732745213664980434541085489975223050785570829015716561569 Date: March 4, 1997 Method: trial division, ecm/fft (p40 with program MIPS.ecm2.3000000.nonshared from Peter Montgomery) Time: under 50 curves on Centre Charles Hermite's R4K-R8K, R10K sgi's, after 2000 curves with first limit 1400000 at Lehigh Univ Address: http://www.loria.fr/CCH (for "Centre Charles Hermite") Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: March 4, 1997 --------------------------------------------------------------- p(14563) Factors: 2 * 7 * 19 * 31 * 485063 * 3347891 * 40022839 * 71284951 * PRP98 Method: Pollard Rho Time: 1E-5 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(14591) Factors: 2252629 * 199057804038492664103651 * 562844142575068848382067737 * 14332520090992239906837627807733155497522531950506827558454145620914994977 Date:November 20, 1992 Method: ECM : p7 p24, PPMPQS :p27 restp74 (using LIPS) Time: ECM ca. 4 mips days , PPMPQS ca. 30 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: November 20, 1992 --------------------------------------------------------------- p(14593) Factors: 7 * 7 * 13664143 * 6704780878361 * 193086581388262069534424038466135579988557 * 4262134406043502038394645514306790903014822732019161186076719622971 Date: August 1, 1994 Method: trial division, ecm, ppmpqs (two largest factors) Time: 80 mips years Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: August 1, 1994 --------------------------------------------------------------- p(14621) Factors: 5 * 7 * 7 * 1153 * 1223 * 1381 * 3891170929 * 60032322890366111 * 76877018396658668603 * 2267793734772282953566769 * PRP48 Date: June 16, 1991 Method: P-1 (p10), ECM (p17), P+-1 (p20), ppmpqs (p25, p48) Time: 0.04 (2 MIP-weeks) for ECM; 0.03 for ppmpqs Name: Peter L. Montgomery and Arjen K. Lenstra Recd: June 16, 1991 --------------------------------------------------------------- p(14627) Factors: 3 * 3 * 43 * 34499 * 1724507 * 62209160249 * 4519536104001698115064149568599489649 * 816737397470754448430174815374491329657378156569699324433378106761667 Date: March 9th, 1993 Method: TD, ECM (even p37 found at p=2803103 in 2nd stage) Time: 53 hours on an HP710 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 9, 1993 --------------------------------------------------------------- p(14629) Factors: 2 * 2 * 2 * 2 * 3 * 5 * 11 * PRP127 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(14633) Factors: 5 * 17 * 73 * 800623 * 15164276104511 * PRP107 Method: P-1 Time: 1E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(14639) Factors: 2 * 2 * 5 * 109 * 653 * 606241 * PRP118 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(14653) Factors 2 * 2 * 5 * 17 * 71 * 9173 * 88120527785971 * 15916743509273964571 * 12979823099237695014154461808633 * 1724588306410909054723044765531865528874149342541875086607 Date: April 30, 1992 Method: ppmpqs Time: approximately 1.5 mips years Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: April 30, 1992 --------------------------------------------------------------- p(14657) Factors: 2 * 89 * 293 * 37200098839 * 31549242748183907 * 183109299706419389353 * P78 Date: 21 April 1992 Method: TD, ECM (p11, p17, p21) Time: 0.1 Name: Paul C Leyland Recd: April 21, 1992 --------------------------------------------------------------- p(14669) Factors: 2 * 2 * 2 * 5 * 11 * 28612158393241 * 2448383193608689 * 169149755719745227463478727 * 5938511462611113321681157672717 * 265725135533398915283316064218615318122591 Date: 3 September 1991 Time: 0.17 Method: TD, ECM (p14, p16, p27), PPMPQS (p31, p42) Name: Paul C Leyland Recd: September 3, 1991 --------------------------------------------------------------- p(14683) Factors: 113 * 137 * 173 * 199 * 7949 * 370175251 * 46700269303843783116652755443861 * P78 Date: 25 November 1992 Method: TD, Rho (p9), ECM (p32) Time: 0.8 Name: Paul C Leyland Recd: November 30, 1992 --------------------------------------------------------------- p(14699) Factors 3 * 5 * 5 * 5 * 23 * 631 * 5261 * 3011581 * 53474507862223833213923 * 27565521028630783895127449590934397842773 * 88738531162377564256015877063629542077311454096491 Date: May 3, 1992 Method: ppmpqs Time: approximately 1.5 mips years Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: May 3, 1992 --------------------------------------------------------------- p(14713) Factors 2 * 11 * 12154103750689 * 3279797686197452330787739 * 382306701140939597075502409 * 38972967469007509075355347324304251091083143030949935295113748093 Date: May 6, 1992 Method: ppmpqs Time: approximately 1.5 mips years Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: May 6, 1992 --------------------------------------------------------------- p(14717) Factors: 2 * 132154140137 * PRP119 Method: P-1 Time: 6E-5 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(14723) Factors: 173 * 90280055795814993159240689 * 204199924470340549780608605500955449 * 4550853606776530204368686390433710915334346545450054493588182108511 Date: August 12, 1993 Method: trial division, ecm (p26), ppmpqs (two largest factors) Time: 2.5 days days on 16K MasPar for ppmpqs Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: August 12, 1993 --------------------------------------------------------------- p(14731) Factors: 11 * 11 * 443392441 * 1425382463085247 * PRP105 Date: April 10, 1991 Method: Pollard Rho (p9), ECM (p16) Time: 4E-3 (1.5 MIP-days) Name: Peter L. Montgomery Recd: April 10, 1991 --------------------------------------------------------------- p(14737) Factors: 2 * 2 * 2 * 38459130352524949 * 25552300249229777561820446303606422807812199 * 2138487368590493951860078693246700241643624053358466192339203781772917 Date: March 10, 1995 Method: trial division, ecm, ppmpqs (two largest factors) Time: approxmately 230 mips years Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: March 10, 1995 --------------------------------------------------------------- p(14741) Factors: 3 * 56713 * 1643845320457 * 269202054525160321 * PRP96 Date: April 10, 1991 Method: P-1 (p13), ECM (p18) Time: 4E-3 (1.5 MIP-days) Name: Peter L. Montgomery Recd: April 10, 1991 --------------------------------------------------------------- p(14747) Factors: 2 * 2 * 2 * 3 * 7 * 7 * 7 * PRP127 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(14753) Factors: 9837527886287 * 45565964161160361228131413781675871180923 * 44363158416663080212726983987117233052442866662301557678329347054366123940939 Date: November 24, 1998 Method: ecm, ecm/fft (p41 with program MIPS.ecm2.30000000.shared from Peter Montgomery) Time: 300th curve with 30000000 ecmfft, on an SGI Octane Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: November 24, 1998 --------------------------------------------------------------- p(14759) Factors: 5 * 13 * 26082036523 * PRP119 Method: P-1 Time: 6E-5 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(14767) Factors: 2 * 2 * 2 * 2 * 3 * 11 * 39130626127 * 333964059047 * 52287867544443975007754152684151708645506129 * 63837063074086955995058252941026662981083644085408395187593911 Date: October 28, 1993 Method: trial division, ecm, ppmpqs (two largest factors) Time: a few secs for trial division and ecm, a month and a half of idle time of 30 workstations for ppmpqs Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: October 28, 1993 --------------------------------------------------------------- p(14771) Factors: 13 * 57033029 * PRP122 Method: P-1 Time: 1E-6 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(14779) Factors: 2 * 2 * 2 * 2 * 2 * 5 * 5 * 11 * 43 * 43 * 4133 * 1314673 * 13924731250219 * 1928113231021758167 * 87643860528786867797 * PRP63 Date: June 5, 1991 Method: ECM (p19 before p14, later p20) Time: 0.04 (2 MIP-weeks) Name: Peter L. Montgomery Recd: June 5, 1991 --------------------------------------------------------------- p(14783) Factors: 2 * 3 * 3 * 35666237 * 2840221361 * 494496007129383881 * 3331735679353152355558038171372582443 * 9066887580939768625148103122868740433536678095973931351503 Date: November 2, 1992 Method: ppmpqs Time: one day on a 16K MasPar Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: November 2, 1992 --------------------------------------------------------------- p(14797) Factors 13 * 19 * 63179 * 484592510577394914343478747 * 24629045582859381320758206983617 * 171677183751368828977816116228301 * 986456563759525123280298090279539 Date: December 17, 1992 Method: ecm, ppmpqs Time: a day and a half on a 16K MasPar (ppmpqs) Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: December 17, 1992 --------------------------------------------------------------- p(14821) Factors 2 * 2 * 3 * 29 * 28355531 * 2228579944333 * 809941810756504979939 * 2009309278027126186279488526630114038679 * 1133151221692870306477057594244511634388406091349 Date: May 8, 1992 Method: ppmpqs Time: approximately 1.2 mips years Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: May 8, 1992 --------------------------------------------------------------- p(14827) Factors: 73 * 64409467 * 59243776913 * 1459337974136881 * 2167171956765002233155632039431 * 49016550353484573840497274146342611472806377289185007234049121523 Date: November 4, 1992 Method: ppmpqs Time: 17 hours on a 16K MasPar Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: November 4, 1992 --------------------------------------------------------------- p(14831) Factors: 2 * 2 * 2 * 2 * 7 * 7 * 7 * 13 * 29 * 5431 * PRP121 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(14843) Factors: 13 * 19 * 61 * 107 * 353 * 90876137468585473171222216629243232031 * 987131284952574855210322170683582224751817063226390784535166910856458433283942100461 Date: June 23, 1997 Method: trial division, ecm/fft (p38 with program MIPS.ecm2.3000000.nonshared from Peter Montgomery) Time: 230 curves on Centre Charles Hermite's R4K-R8K, R10K sgi's, after 1100 curves with first limit 1400000 at Lehigh Univ Address: http://www.loria.fr/CCH (for "Centre Charles Hermite") Name: Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann Email: arjen.lenstra@citicorp.com Recd: June 24, 1997 --------------------------------------------------------------- p(14851) Factors: 3 * 3 * 3 * 3 * 3 * 577 * 1347918542037177301 * 7263191062242087918637524230688428269302713 * 40436505453493769568503803385808807105890440784823378185830513487 Date: August 11, 1994 Method: trial division, ecm, ppmpqs (two largest factors) Time: 80 mips years Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: August 11, 1994 --------------------------------------------------------------- p(14867) Factors: 2 * 5 * 5 * 7 * 11 * 37 * PRP126 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(14869) Factors: 2 * 2 * 2 * 5 * 5 * 5 * 43 * 1301603 * 361482240693795127 * 100281707437283832077 * PRP83 Date: June 5, 1991 Method: ECM (p18, p21) Time: 0.04 (2 MIP-weeks) Name: Peter L. Montgomery Recd: June 5, 1991 --------------------------------------------------------------- p(14891) Factors: 2 * 3 * 5 * 5 * 7 * 8059 * 16333 * 201854437 * 207738259 * 129425049580985916980421042048494147 * 112402364725296943660351941243526861103399302335245796695970769740733 Date: September 1, 1993 Method: ecm (c104 = p36*p69, first limit 2*10^6, 50th curve) Name: Bruce Dodson, Matt Fante Email: bad0@lehigh.edu Recd: September 1, 1993 --------------------------------------------------------------- p(14897) Factors: 73 * 48909835057071803 * 60784308956651397847 * PRP93 Date: June 16, 1991 Method: ECM (p17, p20) Time: 0.05 (2.5 MIP-weeks) Name: Peter L. Montgomery Recd: June 16, 1991 --------------------------------------------------------------- p(14923) Factors: 2 * 23 * 257 * 369825831601 * PRP116 Date: March 21, 1991 Method: ECM Time: 7E-4 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(14929) Factors: 2 * 3 * 5 * 7 * 7 * 48536263 * 89741821162339 * PRP107 Date: April 10, 1991 Method: Pollard Rho (p8), ECM (p14) Time: 4E-3 (1.5 MIP-days) Name: Peter L. Montgomery Recd: April 10, 1991 --------------------------------------------------------------- p(14939) Factors: 2 * 5 * 7 * 11 * 23 * 5167 * 40699 * 4798967269 * 6450008940005138629996386861383 * 21619020266846112847309902300623 * 55824705481562471844284845423294459467575656331 Date: September 21, 1993 Method: trial division, ecm (p31), ppmpqs (two largest factors) Time: six hours for ecm, short for ppmpqs Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: September 21, 1993 --------------------------------------------------------------- p(14947) Factors: 3 * 61 * 3793 * 4861 * PRP122 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(14951) Factors: 401 * 484793360578414451089727 * 10075765167901188327924252162041049502061799473462507 * 80493265441999664609226003034445892819914737214213029 Date: June 7, 1994 Method: TD, ECM : p24 , PPMPQS :p53 restp53 (using LIPS) Time: ECM ca. 7 mips days , PPMPQS 65 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: June 7, 1994 --------------------------------------------------------------- p(14957) Factors: 7 * 4406939 * 2108763496647978603692913892519856162800073 * 2580068244253356715544578475534334283619913400073194367695030362386093093115928151 Date: Feb 27, 1996 Method: TD, ECM (using Lips): p7, p43, restp82 Time: 35 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(14969) Factors: 5 * 17 * 191 * 16921129 * 50188377931059682981333 * 65078234903869234058651531927033 * 211967081412464098288127727570635039228303968145634142802841869761 Date:November 21, 1992 Method: TD, ECM : p8 p32 , PPMPQS :p23 restp66 (using LIPS) Time: ECM ca. 60 mips days , PPMPQS ca. 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: November 21, 1992 --------------------------------------------------------------- p(14983) Factors: 5 * 5 * 5925463 * 81116232917 * 3332275891603 * PRP100 Method: P-1 + Pollard Rho Time: 7E-5 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(15013) Factors: 3 * 7 * 7 * 268913 * 3928381 * 753233084467 * 1982547318281401858247 * PRP85 Date: April 25, 1991 Method: ECM (p12, p22) Time: 0.01 Name: Peter L. Montgomery Recd: April 25, 1991 --------------------------------------------------------------- p(15017) Factors: 2 * 2 * 3 * 11 * 16273 * 48465733 * 271800421 * 36508499551384272030769 * PRP87 Date: October 24, 1991 Method: P-1 + Pollard Rho (p8, p9), ECM (p23 - first limit 300000) Time: 0.10 Name: Peter L. Montgomery Recd: October 24, 1991 --------------------------------------------------------------- p(15031) Factors: 13 * 1091 * 4957 * 592639 * 835979 * 33263109751 * 25514689886331989684957131585661383074052438675007 * 12264296564362762910262478911110566664327951900156621 Date: March 16, 1993 Method: TD, ECM : p11 , PPMPQS :p50 restp53 (using LIPS) Time: ECM ca. 22 mips minutes , PPMPQS ca. 40 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 16, 1993 --------------------------------------------------------------- p(15053) Factors: 7 * 13797688963 * 1076250288073 * PRP109 Date: April 10, 1991 Method: ECM (p11, p13) Time: 4E-3 (1.5 MIP-days) Name: Peter L. Montgomery Recd: April 10, 1991 --------------------------------------------------------------- p(15061) Factors : 2 * 2 * 3 * 1801856407944031856899152169 * 22899792148480297726979559220656202260476951255083142606726529845760016094903437805692560979968148263739 Date: Nov 9, 1992 Method: TD, ECM : p28, restp104 (using LIPS) Time: ECM ca. 0.6 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: November 9, 1992 --------------------------------------------------------------- p(15073) Factors: 2 * 3 * 13 * 13 * 13 * 277 * 373 * 83648520289018501225396726782667199 * 4922810367246956432882880997278323284886597419253481157220354791752957683434127906973923 Date: March 1, 1996 Method: trial division, ecm (p35 with first step 1400000) Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: March 1, 1996 --------------------------------------------------------------- p(15077) Factors: 2 * 2 * 2 * 7 * 7 * 7 * 33893 * 467914330161892829 * PRP107 Date: April 25, 1991 Method: ECM (p18) Time: 0.01 Name: Peter L. Montgomery Recd: April 25, 1991 --------------------------------------------------------------- p(15083) Factors: 2 * 5 * 7 * 7 * 7 * 149 * 389 * 499801 * 14152669930737933243950680654260527 * 442435231806519400100611707463881212495949224387802662480628819395869627325847695779 Date: Apr 04, 1995 Method: TD, ECM (using Lips): p35, restp84 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: April 4, 1995 --------------------------------------------------------------- p(15091) Factors: 2 * 3 * 3 * 3 * 7 * 103 * 349 * 99716017850366443887670381532099 * p93 Date: November 29, 1992 Method: ecm (434th curve, first limit up to 240000, p32 in 2nd step) Time: 5.4 CPU days 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: November 29, 1992 --------------------------------------------------------------- p(15101) Factors: 2 * 2 * 3 * 13 * 43 * 83 * 10928282653 * 1491799993278739465215419513 * 82618474784390758356278447933428021260568679015924630902663310642409276090049005557729843 Date: October 27, 1992 Method: ecm (first limit 80000, 13th curve) Time: < 2.4 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: October 27, 1992 --------------------------------------------------------------- p(15107) Factors: 2 * 2 * 71 * 17897751113801981 * PRP114 Date: April 10, 1991 Method: ECM (p17) Time: 4E-3 (1.5 MIP-days) Name: Peter L. Montgomery Recd: April 10, 1991 --------------------------------------------------------------- p(15121) Factors: 5 * 7 * 37 * 37 * 37 * 199 * 402503 * 13633340999 * 201695529273318623 * PRP91 Date: April 25, 1991 Method: ECM (p11, p18) Time: 0.01 Name: Peter L. Montgomery Recd: April 25, 1991 --------------------------------------------------------------- p(15131) Factors: 2 * 11 * 83 * 277 * 419 * 580693 * 12487 * 83341 * 88406915170349 * 76373206686258089022449 * 1183527538906396425987128857439225102157279738022778745533896635028121437 Date: October 27, 1992 Method: ecm (first limit 80000, 15th curve) Time: < 1.7 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: October 27, 1992 --------------------------------------------------------------- p(15137) Factors: 2 * 2 * 7 * 487 * 57811979 * 4776114070289 * 1201636615725926882360587478268298516942727 * 240716309629594428721952497306083756556409722116256815544666110041 Date: August 22, 1994 Method: trial division, ecm, ppmpqs (two largest factors) Time: 80 mips years Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: August 22, 1994 --------------------------------------------------------------- p(15139) Factors: 5 * 7 * 7 * 71 * 479 * 1326791 * 3825348228589 * PRP107 Date: April 10, 1991 Method: ECM (p13) Time: 4E-3 (1.5 MIP-days) Name: Peter L. Montgomery Recd: April 10, 1991 --------------------------------------------------------------- p(15161) Factors: 3 * 11 * 19 * 22037 * PRP126 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(15173) Factors: 3 * 3 * 1427 * 1483 * 247155109480056301 * 22965899278195381721701 * 40111291475554007294344118476157959 * 364574973151314125951985104321331661874166476164589 Date:November 28, 1992 Method: TD, ECM : p18 p23 , PPMPQS :p35 restp51 (using LIPS) Time: ECM ca. 23 mips days , PPMPQS ca. 1 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: November 28, 1992 --------------------------------------------------------------- p(15187) Factors: 2 * 7 * 7 * 7 * 7 * 4799 * 5755559 * 55139190409 * 8837783833537905539 * 3967601749258259638336695829680800828861 * 7125484418635544185938739389124893386213637121109 Date:November 25, 1992 Method: TD, ECM : p7 p11 p19 , PPMPQS :p40 restp49 (using LIPS) Time: ECM 24 mips days , PPMPQS ca. 3 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: November 25, 1992 --------------------------------------------------------------- p(15193) Factors: 11761577 * 846548385475367 * PRP111 Date: April 10, 1991 Method: ECM (p15) Time: 4E-3 (1.5 MIP-days) Name: Peter L. Montgomery Recd: April 10, 1991 --------------------------------------------------------------- p(15199) Factors: 2 * 2 * 2 * 3 * 5 * 5 * 5 * 6067 * 40978414049 * 310361733126619 * 26018177660442684157279 * PRP78 Date: April 25, 1991 Method: P-1 (p11), ECM (p15, p23 - first limit 30000) Time: 0.01 Name: Peter L. Montgomery Recd: April 25, 1991 --------------------------------------------------------------- p(15217) Factors: 5 * 43 * PRP131 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(15227) Factors: 2 * 551300819 * 228824787625354061711 * 5107203396736021703491854752051140919 * 2144055352440091076234355246844021543140634130097445518208176750349 Date: August 24, 1993 Method: ecm (c104 = p37*p67, first limit 2*10^6, 42nd curve) Name: Bruce Dodson, Matt Fante Email: bad0@lehigh.edu Recd: August 25, 1993 --------------------------------------------------------------- p(15233) Factors: 2 * 2 * 3 * 1691369 * PRP126 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(15241) Factors: 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 11 * 11 * 13 * 704863 * 30160189 * PRP113 Method: Pollard Rho Time: 6E-6 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(15259) Factors: 3 * 3 * 3 * 5 * 5 * 5 * 5 * 7 * 101 * 181 * 569 * 1031 * 12967 * 205327 * PRP109 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(15263) Factors: 2 * 2 * 2 * 2 * 5 * 11 * 11 * 787 * 1231 * 1027153 * 16030233176977913 * PRP101 Date: April 10, 1991 Method: ECM (p17) Time: 4E-3 (1.5 MIP-days) Name: Peter L. Montgomery Recd: April 10, 1991 --------------------------------------------------------------- p(15269) Factors: 2 * 2 * 2 * 2 * 3 * 5 * 7237140815489213 * PRP115 Date: April 10, 1991 Method: ECM (p16) Time: 4E-3 (1.5 MIP-days) Name: Peter L. Montgomery Recd: April 10, 1991 --------------------------------------------------------------- p(15271) Factors: 643 * 50224105853 * 1286147310883 * 21294427024624153721 * 34949072661702086460913 * PRP66 Date: April 25, 1991 Method: P-1 (p11, p13), ECM (p20, p23 - first limit 30000) Time: 0.01 Name: Peter L. Montgomery Recd: April 25, 1991 --------------------------------------------------------------- p(15277) Factors: 89 * 21191 * 2047112953845609304743486997 * p100 Date: November 22, 1992 Method: ecm (476th curve, first limit up to 240000, p28 at start of 2nd step) Time: < 6.4 CPU days 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: November 23, 1992 --------------------------------------------------------------- p(15287) Factors: 2 * 2 * 2 * 2 * 3 * 3 * 3 * 683 * 2801 * 403253 * PRP119 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(15289) Factors: 2 * 2 * 3 * 5 * 928226494710947445706151 * 33921091528156915271367281 * PRP82 Date: August 28, 1991 Method: ECM (p24, p26; both with first limit 300000) Time: 0.07 Name: Peter L. Montgomery Recd: August 28, 1991 --------------------------------------------------------------- p(15299) Factors 2 * 5 * 5 * 5 * 7 * 173 * 23279 * 21091951416697110877993050169 * 1202002443372830425970359672367 * 32496931548677531557312535398302475583006982462355458043090061639 Date: December 20, 1992 Method: ecm, ppmpqs Time: less than a day on a 16K MasPar (ppmpqs) Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: December 20, 1992 --------------------------------------------------------------- p(15307) Factors: 2 * 7 * 7 * 11 * 4243 * 47005494400790227 * 816481772335766947 * PRP92 Date: April 21, 1991 Method: ECM (p17, p18) Time: 8E-3 (3 MIP days) Name: Peter L. Montgomery Recd: April 21, 1991 --------------------------------------------------------------- p(15313) Factors: 7 * 11 * 37 * 53 * 311 * 108627591757453629425008712106407 * 1314857782978797201002693795375173770365096289074547341108549094798700140220469353436113854101 Date: July 1, 1995 Method: trial division, ecm (p33 with first step limit 1400000) Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: July 1, 1995 --------------------------------------------------------------- p(15319) Factors: 5 * 191 * 2797 * 58065397455503 * 601380499456501 * PRP98 Date: April 10, 1991 Method: P-1 (p15), ECM (p14) Time: 4E-3 (1.5 MIP-days) Name: Peter L. Montgomery Recd: April 10, 1991 --------------------------------------------------------------- p(15329) Factors: 5 * 11 * 31 * 90793 * 2222565653301339313658936859608420497867 * 22986030515069968854359608430336264079748172959347774909821524536374965482372156740761 Date: Jun 30, 1994 Method: TD, ECM (using Lips): p40, 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: July 5, 1994 --------------------------------------------------------------- p(15331) Factors: 7 * 23 * 1069 * 1290529759 * 7309617612102220163101553680020539 * 4972444168859388903191603243524421466526310358856962217135945973180460389657541322579 Date: Nov 26, 1992 Method: TD, ECM (using LIPS): p10, p34, restp85 Time: ca. 1.2 mip 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: November 26, 1992 --------------------------------------------------------------- p(15349) Factors: 5 * 5 * 5 * 7 * 71 * 23459 * 34159 * 23957990153 * 8212703596711 * PRP96 Method: P-1 Time: 4E-5 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(15359) Factors: 2 * 2 * 2 * 2 * 3 * 3 * 5 * 13 * 9973 * PRP126 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(15361) Factors: 7 * 61 * 984701 * 10207466743 * 4631938708337 * 252654681725359 * PRP88 Date: March 22, 1991 Method: P-1 (p11), ECM (p13, p15) Time: 8E-4 Name: Peter L. Montgomery Recd: March 22, 1991 --------------------------------------------------------------- p(15373) Factors: 11 * 13 * 12832511 * 6822010109 * 67810781 * 11867359717644792381488147 * 1234376021229939593586525164599218919924571306408223084754249549773303080753999947 Date: October 28, 1992 Method: ecm (first limit 80000, 20th curve) Time: < 2.6 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: October 28, 1992 --------------------------------------------------------------- p(15377) Factors: 7 * 7 * PRP132 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(15383) Factors: 97 * 163 * 29921 * 6259081 * 1492000231 * 418478751563262840055676238637522802430271880288623 * 7454301066628311239141933392907741146855591333433989713857 Date: December 3, 1994 Method: trial division, ecm, ppmpqs (two largest factors) Time: 90 mips years Name: Bruce Dodson, Arjen K. Lenstra Email: lenstra@bellcore.com Recd: December 3, 1994 --------------------------------------------------------------- p(15391) Factors: 2 * 2 * 7 * PRP132 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(15401) Factors: 5 * 5 * 5 * 109 * 509 * 21892097 * 1193509727 * 44302232382185131 * 8648749292377864447 * 100239279611536100383 * 474198355572455092501129 * 5024087412238620523464766748807 Date: 29 August 1991 Time: 0.2 Method: TD, Pollard Rho (p8, p10), ECM (p17, p19), PPMPQS (p21, p24, p31) Name: Paul C Leyland Recd: August 29, 1991 --------------------------------------------------------------- p(15413) Factors: 2 * 3 * 3 * 3 * 3 * 17 * 3623948500657107269917 * PRP109 Date: February 10, 1992 Method: ECM (p22) Time: 0.13 Name: Peter L. Montgomery Recd: February 10, 1992 --------------------------------------------------------------- p(15427) Factors: 2 * 2 * 5 * 43 * 47 * PRP129 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(15439) Factors: 3 * 5 * 7 * 7 * 11 * 307 * 430811 * 15201747122720983271317379 * PRP97 Date: August 18, 1991 Method: ECM (p26 - first limit 300000) Time: 0.07 Name: Peter L. Montgomery Recd: August 18, 1991 --------------------------------------------------------------- p(15443) Factors: 2 * 2 * 2 * 2 * 2 * 29 * 859 * 32487043 * 1967678154115126314582259208807 * p90 Date: November 22, 1992 Method: ecm (451st curve, first limit up to 240000, p31 in 2nd step) Time: < 91 hrs 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: November 22, 1992 --------------------------------------------------------------- p(15451) Factors: 20113 * 343529 * PRP124 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(15461) Factors: 5 * 7 * 7 * 11 * 11 * 17 * 311 * 93307098374124113202539861425790061962795219659 * 2098351373773042428957406516110265106549559469011856680449010338518894259518861 Date: July 12, 1998 Method: trial division, ecm/fft (p47 with program MIPS.ecm2.16000000.shared from Peter Montgomery) Time: 21st 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: July 12, 1998 --------------------------------------------------------------- p(15467) Factors: 2 * 2063771 * 19956869 * 44890319737 * 30978410228434861 * PRP93 Date: April 10, 1991 Method: P-1 (p8, p11), ECM (p17) Time: 4E-3 (1.5 MIP-days) Name: Peter L. Montgomery Recd: April 10, 1991 --------------------------------------------------------------- p(15473) Factors: 2 * 2 * 2 * 2 * 7 * 13 * 23 * 2927 * 24473 * 165144218410020043297 * 4405290766189461355494478702337 * p71 Date: November 29, 1992 Method: ecm (470th curve, first limit up to 480000, p31 in 2nd step - p21 with first step 80000) Time: 5.5 CPU days on RS/6000, model 220, 340 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: November 29, 1992 --------------------------------------------------------------- p(15493) Factors: 2 * 23 * 547 * 757 * 3253 * 13691003399 * 4378505586019109 * 9743906409375070947229741 * 1176823176650984910068428292487925238492809886349871303046340506531675807 Date: July 3, 1992 Method: TD, ECM (using LIPS): p11, p16, p25, restp73 Time: 0.5 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: July 3, 1992 --------------------------------------------------------------- p(15497) Factors: 7 * 11 * 62633 * 78301504548541 * 249427749358342063 * 32075879872121966402052073 * 2561427177203883189246183329 * 5733872589116204973164599616221969929974293 Date:June 29, 1992 Method: TD, ECM : p14 p18 p28 , PPMPQS : p26, restp43 (using LIPS) Time: ECM ca. 12 mips hours , PMPQS ca. 14,5 mips days 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: June 29, 1992 --------------------------------------------------------------- p(15511) Factors: 2 * PRP134 Name: Peter L. Montgomery Recd: March 21, 1991 --------------------------------------------------------------- p(15527) Factors: 11 * 159170513 * 218466533 * 15413152177 * 219830974277440829 * PRP89 Date: April 10, 1991 Method: Pollard Rho + P-1 (two p9, p11), ECM (p18) Time: 4E-3 (1.5 MIP-days) Name: Peter L. Montgomery Recd: April 10, 1991 --------------------------------------------------------------- p(15541) Factors: 11 * 149 * 151 * 26012148002227 * PRP116 Date: April 10, 1991 Method: ECM (p14) Time: 4E-3 (1.5 MIP-days) Name: Peter L. Montgomery Recd: April 10, 1991 --------------------------------------------------------------- p(15551) Factors: 3 * 3 * 983331940458523 * 1644040256241809 * 14833707927072276910981409 * p78 Date: November 30, 1992 Method: ecm (471st curve, first limit up to 480000, late-ish p26 at start of 2nd step) Time: < 5.4 CPU days 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: November 30, 1992 --------------------------------------------------------------- p(15559) Factors: 2 * 2 * 2 * 2 * 3 * 5 * 7 * 7 * 822599 * 589870783 * 22290809311 * 336920136080257 * 5207988439103384612702006569 * 7333961412309857178212778817 * 51110309413991458118191559499846691 Date: November 2, 1992 Method: ppmpqs Time: six hours on a 16K MasPar Name: Arjen K. Lenstra Email: lenstra@bellcore.com Recd: November 2, 1992 --------------------------------------------------------------- p(15569) Factors: 5 * 163 * 4057 * 136991 * 3183455879 * 10977499607939756355888010351 * p85 Date: November 15, 1992 Method: ecm (238th curve, first limit up to 180000, p29 at start of 2nd step) Time: 2 days (48 hours CPU time) 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: November 17, 1992 ---------------------------------------------------------------