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 QAA00350 for ; Wed, 30 Jan 2002 16:03:23 -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 PAA23145; Wed, 30 Jan 2002 15:54:43 -0500 (EST) Date: Wed, 30 Jan 2002 15:54:43 -0500 (EST) Message-Id: <200201302054.PAA23145@cameos.majordomo.rsasecurity.com> From: challenge-administrator@majordomo.rsasecurity.com (RSA Factoring Challenge Administrator) To: rayo@ontko.com X-IMAPbase: 1128097136 1 Status: RO X-Status: X-Keywords: X-UID: 1 Status/NEWS REPORT ON RSA DATA SECURITY FACTORING CHALLENGE (as of 3/30/00) RSA Challenge List: ------------------ Awards: (2nd Quarter, 1991) RSA-100 Arjen Lenstra and Mark Manasse, $1,000 (2nd Quarter, 1992) RSA-110 Arjen K. Lenstra, $4,429 (2nd Quarter, 1993) RSA-120 Arjen K. Lenstra (45.503%), Bruce Dodson (30.271%), Thomas Denny (22.516%), Mark Manasse (1.658%), Walter Lioen and Herman te Riele (0.049%), $5898 (2nd Quarter, 1994) *** RSA-129 Derek Atkins, Michael Graff, Arjen K. Lenstra, Paul Leyland, and more than 600 volunteers $100 (*** Not part of the RSA Factoring Challenge) (2nd Quarter, 1996) RSA-130 Bruce Dodson, Peter L. Montgomery, Marije Elkenbracht-Huizing, Arjen K. Lenstra, WWW contributors, Matt Fante, Paul Leyland, Damian Weber, Joerg Zayer, sieving code from Bellcore, CWI, Saarbruecken $14,527 (1st Quarter 1999) RSA-140 The 'Cabal' Peter L. Montgomery, Stefania Cavallar, Herman J.J. te Riele, Walter M. Lioen, Paul Leyland, Bruce Dodson, Paul Zimmermann, Arjen K. Lenstra $17,226 (3rd Quarter 1999) RSA-155 Names: Herman J.J. te Riele (CWI Amsterdam, contact person) sites: Karen Aardal (Utrecht University, The Netherlands) Stefania Cavallar, Walter M. Lioen (CWI Amsterdam, The Netherlands) Bruce Dodson (Lehigh University, Bethlehem, PA, USA) Jeff Gilchrist (Entrust Technologies Ltd., Ottawa, Canada) Arjen K. Lenstra (Citibank, Parsippany, NJ, USA and Univ. of Sydney, Australia) Paul Leyland (Microsoft Research, Cambridge, UK) Joel Marchand (Ecole Polytechnique/CNRS, Palaiseau, France) Peter L. Montgomery (Microsoft Research, USA, and CWI) Francois Morain and Gerard Guillerm (Ecole Polytechnique, Palaiseau, France) Alec Muffett (Sun Microsystems Professional Services, Camberley, UK) Brian Murphy (The Australian National University, Canberra) Chris and Craig Putnam (USA) Paul Zimmermann (Inria Lorraine and Loria, Nancy, France) $9383 Totals: 6 numbers factored 6 First Prize awards 0 Second Prize awards 0 Third Prize awards $52,463 cash prizes awarded total Smallest 4 unfactored numbers (at beginning of quarter): RSA-150 (150 digits) RSA-160 (160 digits) RSA-170 (170 digits) RSA-180 (180 digits) Size of award kitty on 09/30/99 will be: $8787 Factorizations: Partition Challenge List: ------------------------ Awards: (2nd Quarter, 1991) p(8681) Arjen Lenstra, $1,000 p(8689) Arjen Lenstra, $500 p(8693) Arjen Lenstra, $250 (3rd Quarter, 1991) 200 points, Arjen K. Lenstra, $699 140 points, Brandon Dixon & Arjen K. Lenstra, $489 72 points, Peter L. Montgomery, $251 35 points, Paul C Leyland, $122 24 points, Lambert E. Bright, $84 18 points, Paul C Leyland & Peter L Montgomery, $63 8 points, Arjen K. Lenstra & Peter Montgomery, $28 4 points, Wolfgang Niebuhr, $14 -------------- 501 points total (4th Quarter, 1991) 131 points, Arjen K. Lenstra, $1,349 27 points, Peter L. Montgomery, $278 4 points, Peter L. Montgomery & Arjen K. Lenstra, $41 4 points, Arjen K. Lenstra & Paul C. Leyland, $41 4 points, Paul C. Leyland, $41 -------------- 170 points total (1st Quarter, 1992) 122 points, Arjen Lenstra, $1,405 12 points, Franz-Dieter Berger, Johannes Buchmann, $138 8 points, Peter L. Montgomery, $92 6 points, Peter L Montgomery & Paul C Leyland, $69 4 points, Lambert E. Bright, $46 -------------- 152 points total (2nd Quarter, 1992) 78 points, Arjen Lenstra, $989 48 points, Franz-Dieter Berger, Thomas Denny, Johannes Buchmann, $609 5 points, Peter L. Montgomery, $63 4 points, Peter L Montgomery & Paul C Leyland, $51 3 points, Paul C Leyland, $38 -------------- 138 points total (3rd Quarter, 1992) 1 point, Heinz-Bernd Eggenstein, $11 84 points, Arjen K. Lenstra, $907 1 point, Paul C Leyland & Arjen K Lenstra, $11 58 points, Franz-Dieter Berger, Thomas Denny, Johannes Buchmann, $626 12 points, Paul C Leyland, $130 2 points, Francois MORAIN, Reynald LERCIER, $22 4 points, FactOregon (Joe Buhler, Peter Montgomery, Robby Robson, Russell Ruby), $43 -------------- 162 points total (4th Quarter, 1992) 79 points, Arjen K. Lenstra, $634 4 points, Paul Leyland, Arjen K. Lenstra, $32 4 points, Bruce Dodson, Arjen K. Lenstra, $32 60 points, Franz-Dieter Berger, Thomas Denny, Johannes Buchmann, $482 6 points, FactOregon (Joe Buhler, Peter Montgomery, Robby Robson, Russell Ruby), $48 52 points, Bruce Dodson, Matt Fante, $418 5 points, Paul C Leyland, $40 3 points, Heinz-Bernd Eggenstein, $24 5 points, Reynald Lercier, Francois Morain, $40 -------------- 218 points total (1st Quarter, 1993) 35 points, Arjen K. Lenstra, $712 13 points, Reynald Lercier, Francois Morain, $265 1 point, Bruce Dodson, Matt Fante, $20 11 points, Bruce Dodson, Arjen K. Lenstra, $224 21 points, Franz-Dieter Berger, Thomas Denny, Johannes Buchmann, $427 5 points, Paul C Leyland, $102 -------------- 86 points total (2nd Quarter, 1993) 12 points, Arjen K. Lenstra, $1000 1 point, Reynald Lercier, Francois Morain, $83 6 points, Franz-Dieter Berger, Thomas Denny, Johannes Buchman, $500 2 points, Paul C. Leyland, $167 -------------- 21 points total (3rd Quarter, 1993) 30 points, Arjen K. Lenstra, $395 4 points, Paul C. Leyland, $53 73 points, Bruce Dodson, Matt Fante, $960 11 points, Franz-Dieter Berger, Thomas Denny, Johannes Buchmann, $145 5 points, Paul Leyland, Arjen K. Lenstra, $66 5 points, Bruce Dodson, Arjen K. Lenstra, $66 1 point, Reynald Lercier, Francois Morain, $13 1 point, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski), Heinz-Bernd Eggenstein, $13 3 points, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski), $39 -------------- 133 points total (4th Quarter, 1993) 7 points, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski), $227 3 points, Bruce Dodson, Matt Fante, $97 26 points, Bruce Dodson, Arjen K. Lenstra, $843 17 points, Arjen K. Lenstra, $551 1 point, Paul C Leyland, $32 -------------- 54 points total (1st Quarter, 1994) 48 points, Bruce Dodson, Arjen K. Lenstra, $1218 19 points, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski), $482 1 point, Paul C Leyland, $25 1 point, Reynald Lercier, Francois Morain, $25 -------------- 69 points total (2nd Quarter, 1994) 30 points, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski), $665 28 points, Bruce Dodson, Arjen K. Lenstra, $620 16 points, Magnus Y Alvestad, Arjen K. Lenstra, $354 4 points, Paul C leyland, $89 1 point, Heinz-Bernd Eggenstein, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski), $22 -------------- 79 points total (3rd Quarter, 1994) 12 points, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski), $328 8 points, Bruce Dodson, Arjen K. Lenstra, Peter L. Montgomery, $219 28 points, Bruce Dodson, Arjen K. Lenstra, $765 8 points, Magnus Y Alvestad, Arjen K. Lenstra, $219 8 points, Michael Graff, Arjen K. Lenstra, Paul Leyland, $219 -------------- 64 points total (4th Quarter, 1994) 18 points, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski), $516 23 points, Bruce Dodson, Arjen K. Lenstra, $660 12 points, Arjen K. Lenstra, $344 8 points, Scott Contini, Bruce Dodson, Arjen K. Lenstra, Peter Montgomery, $230 -------------- 61 points total (1st Quarter, 1995) 14 points, Bruce Dodson, Arjen K. Lenstra, $500 27 points, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski), $964 8 points, Arjen K. Lenstra, $286 0 points, Raymond L. Jerome, $0 ------------- 49 points total (2nd Quarter, 1995) 12 points, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski), $656 20 points, Bruce Dodson, Arjen K. Lenstra, $1094 ------------- 32 points total (3rd Quarter, 1995) 1 point, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski), $17 115 points, Bruce Dodson, Arjen K. Lenstra, $1733 --------------- 116 points total (4th Quarter, 1995) 11 points, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski), $664 18 points, Bruce Dodson, Arjen K. Lenstra, $1086 --------------- 29 points total (1st Quarter, 1996) 31 points, Bruce Dodson, Arjen K. Lenstra, $1233 13 points, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski), $517 --------------- 44 points total (2nd Quarter, 1996) 22 points, Bruce Dodson, Arjen K. Lenstra, $1604 2 points, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski), $146 --------------- 24 points total (3rd Quarter, 1996) 2 points, Bruce Dodson, Arjen K. Lenstra, $583 4 points, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski), $1167 --------------- 6 points total (4th Quarter, 1996) 4 points, Bruce Dodson, Arjen K. Lenstra, $583 8 points, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski), $1167 --------------- 12 points total (1st Quarter, 1997) 4 points, Bruce Dodson, Arjen K. Lenstra, $206 3 points, Factoring Factory Buchmann (Franz-Dieter Berger, Johannes Buchmann, Thomas F. Denny, Andreas M"uller, Thomas Sosnowski), $154 21 points, Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann, $1081 6 points, Paul Zimmermann, $309 --------------- 34 points total (2nd Quarter, 1997) 8 points, Bruce Dodson, Arjen K. Lenstra, $333 34 points, Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann, $1417 --------------- 42 points total (3rd Quarter, 1997) 34 points, Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann, --------------- 34 points total (4th Quarter, 1997) 11 points, Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann, --------------- 11 points total (1st Quarter, 1998) 17 points, Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann, --------------- 17 points total (2nd Quarter, 1998) 12 points, Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann ---------------- 12 points total (3rd Quarter, 1998) 70 points, Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann 7 points, Eric Prestemon ---------------- 77 points total (4th Quarter, 1998) 51 points, Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann ---------------- 51 points total (1st Quarter, 1999) 33 points, Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann ---------------- 33 points total (2nd Quarter, 1999) 12 points, Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann ---------------- 12 points total (3rd Quarter, 1999) 62 points, Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann --------------------- 62 points total (4th Quarter, 1999) 62 points, Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann --------------------- 62 points total (1st Quarter, 2000) 26 points, Bruce Dodson, Arjen K. Lenstra, Paul Zimmermann --------------------- 26 points total Totals: 1640 partition numbers factored Smallest Unfactored Number at Beginning of Quarter: 131 Digits - p(14813) Factorizations and Points: (See Challenge Rules for Explanation) Status of partition Numbers: (X indicates factorization completed) Length 100 digits: (closed) 8681.X. 8689.X. 8693.X. 8699.X. 8707.X. 8713.X. 8719.X. 8731.X. 8737.X. 8741.X. 8747.X. 8753.X. 8761.X. 8779.X. 8783.X. 8803.X. 8807.X. 8819.X. 8821.X. 8831.X. 8837.X. 8839.X. Length 101 digits: (closed) 8849.X. 8861.X. 8863.X. 8867.X. 8887.X. 8893.X. 8923.X. 8929.X. 8933.X. 8941.X. 8951.X. 8963.X. 8969.X. 8971.X. 8999.X. 9001.X. 9007.X. 9011.X. 9013.X. Length 102 digits: (closed) 9029.X. 9041.X. 9043.X. 9049.X. 9059.X. 9067.X. 9091.X. 9103.X. 9109.X. 9127.X. 9133.X. 9137.X. 9151.X. 9157.X. 9161.X. 9173.X. 9181.X. 9187.X. Length 103 digits: (closed) 9199.X. 9203.X. 9209.X. 9221.X. 9227.X. 9239.X. 9241.X. 9257.X. 9277.X. 9281.X. 9283.X. 9293.X. 9311.X. 9319.X. 9323.X. 9337.X. 9341.X. 9343.X. 9349.X. Length 104 digits: (closed) 9371.X. 9377.X. 9391.X. 9397.X. 9403.X. 9413.X. 9419.X. 9421.X. 9431.X. 9433.X. 9437.X. 9439.X. 9461.X. 9463.X. 9467.X. 9473.X. 9479.X. 9491.X. 9497.X. 9511.X. 9521.X. 9533.X. 9539.X. Length 105 digits: (closed) 9547.X. 9551.X. 9587.X. 9601.X. 9613.X. 9619.X. 9623.X. 9629.X. 9631.X. 9643.X. 9649.X. 9661.X. 9677.X. 9679.X. 9689.X. 9697.X. 9719.X. Length 106 digits: (closed) 9721.X. 9733.X. 9739.X. 9743.X. 9749.X. 9767.X. 9769.X. 9781.X. 9787.X. 9791.X. 9803.X. 9811.X. 9817.X. 9829.X. 9833.X. 9839.X. 9851.X. 9857.X. 9859.X. 9871.X. 9883.X. 9887.X. Length 107 digits: (closed) 9901.X. 9907.X. 9923.X. 9929.X. 9931.X. 9941.X. 9949.X. 9967.X. 9973.X. 10007.X. 10009.X. 10037.X. 10039.X. 10061.X. 10067.X. 10069.X. 10079.X. Length 108 digits: (closed) 10091.X. 10093.X. 10099.X. 10103.X. 10111.X. 10133.X. 10139.X. 10141.X. 10151.X. 10159.X. 10163.X. 10169.X. 10177.X. 10181.X. 10193.X. 10211.X. 10223.X. 10243.X. 10247.X. 10253.X. 10259.X. Length 109 digits: (closed) 10267.X. 10271.X. 10273.X. 10289.X. 10301.X. 10303.X. 10313.X. 10321.X. 10331.X. 10333.X. 10337.X. 10343.X. 10357.X. 10369.X. 10391.X. 10399.X. 10427.X. 10429.X. 10433.X. Length 110 digits: (closed) 10453.X. 10457.X. 10459.X. 10463.X. 10477.X. 10487.X. 10499.X. 10501.X. 10513.X. 10529.X. 10531.X. 10559.X. 10567.X. 10589.X. 10597.X. 10601.X. 10607.X. 10613.X. 10627.X. 10631.X. Length 111 digits: (closed) 10639.X. 10651.X. 10657.X. 10663.X. 10667.X. 10687.X. 10691.X. 10709.X. 10711.X. 10723.X. 10729.X. 10733.X. 10739.X. 10753.X. 10771.X. 10781.X. 10789.X. 10799.X. Length 112 digits: (closed) 10831.X. 10837.X. 10847.X. 10853.X. 10859.X. 10861.X. 10867.X. 10883.X. 10889.X. 10891.X. 10903.X. 10909.X. 10937.X. 10939.X. 10949.X. 10957.X. 10973.X. 10979.X. 10987.X. 10993.X. 11003.X. Length 113 digits: (closed) 11027.X. 11047.X. 11057.X. 11059.X. 11069.X. 11071.X. 11083.X. 11087.X. 11093.X. 11113.X. 11117.X. 11119.X. 11131.X. 11149.X. 11159.X. 11161.X. 11171.X. 11173.X. 11177.X. 11197.X. Length 114 digits: (closed) 11213.X. 11239.X. 11243.X. 11251.X. 11257.X. 11261.X. 11273.X. 11279.X. 11287.X. 11299.X. 11311.X. 11317.X. 11321.X. 11329.X. 11351.X. 11353.X. 11369.X. 11383.X. Length 115 digits: (closed) 11393.X. 11399.X. 11411.X. 11423.X. 11437.X. 11443.X. 11447.X. 11467.X. 11471.X. 11483.X. 11489.X. 11491.X. 11497.X. 11503.X. 11519.X. 11527.X. 11549.X. 11551.X. 11579.X. Length 116 digits: (closed) 11587.X. 11593.X. 11597.X. 11617.X. 11621.X. 11633.X. 11657.X. 11677.X. 11681.X. 11689.X. 11699.X. 11701.X. 11717.X. 11719.X. 11731.X. 11743.X. 11777.X. 11779.X. Length 117 digits: (closed) 11783.X. 11789.X. 11801.X. 11807.X. 11813.X. 11821.X. 11827.X. 11831.X. 11833.X. 11839.X. 11863.X. 11867.X. 11887.X. 11897.X. 11903.X. 11909.X. 11923.X. 11927.X. 11933.X. 11939.X. 11941.X. 11953.X. 11959.X. 11969.X. 11971.X. Length 118 digits: (closed) 11981.X. 11987.X. 12007.X. 12011.X. 12037.X. 12041.X. 12043.X. 12049.X. 12071.X. 12073.X. 12097.X. 12101.X. 12107.X. 12109.X. 12113.X. 12119.X. 12143.X. 12149.X. 12157.X. 12161.X. 12163.X. Length 119 digits: (closed) 12197.X. 12203.X. 12211.X. 12227.X. 12239.X. 12241.X. 12251.X. 12253.X. 12263.X. 12269.X. 12277.X. 12281.X. 12289.X. 12301.X. 12323.X. 12329.X. 12343.X. 12347.X. 12373.X. Length 120 digits: (closed) 12377.X. 12379.X. 12391.X. 12401.X. 12409.X. 12413.X. 12421.X. 12433.X. 12437.X. 12451.X. 12457.X. 12473.X. 12479.X. 12487.X. 12491.X. 12497.X. 12503.X. 12511.X. 12517.X. 12527.X. 12539.X. 12541.X. 12547.X. 12553.X. 12569.X. 12577.X. Length 121 digits: (closed) 12583.X. 12589.X. 12601.X. 12611.X. 12613.X. 12619.X. 12637.X. 12641.X. 12647.X. 12653.X. 12659.X. 12671.X. 12689.X. 12697.X. 12703.X. 12713.X. 12721.X. 12739.X. 12743.X. 12757.X. 12763.X. 12781.X. Length 122 digits: (closed) 12791.X. 12799.X. 12809.X. 12821.X. 12823.X. 12829.X. 12841.X. 12853.X. 12889.X. 12893.X. 12899.X. 12907.X. 12911.X. 12917.X. 12919.X. 12923.X. 12941.X. 12953.X. 12959.X. 12967.X. 12973.X. 12979.X. 12983.X. Length 123 digits: (closed) 13001.X. 13003.X. 13007.X. 13009.X. 13033.X. 13037.X. 13043.X. 13049.X. 13063.X. 13093.X. 13099.X. 13103.X. 13109.X. 13121.X. 13127.X. 13147.X. 13151.X. 13159.X. 13163.X. 13171.X. 13177.X. 13183.X. 13187.X. Length 124 digits: (closed) 13217.X. 13219.X. 13229.X. 13241.X. 13249.X. 13259.X. 13267.X. 13291.X. 13297.X. 13309.X. 13313.X. 13327.X. 13331.X. 13337.X. 13339.X. 13367.X. 13381.X. 13397.X. 13399.X. Length 125 digits: (closed) 13411.X. 13417.X. 13421.X. 13441.X. 13451.X. 13457.X. 13463.X. 13469.X. 13477.X. 13487.X. 13499.X. 13513.X. 13523.X. 13537.X. 13553.X. 13567.X. 13577.X. 13591.X. 13597.X. Length 126 digits: (closed) 13613.X. 13619.X. 13627.X. 13633.X. 13649.X. 13669.X. 13679.X. 13681.X. 13687.X. 13691.X. 13693.X. 13697.X. 13709.X. 13711.X. 13721.X. 13723.X. 13729.X. 13751.X. 13757.X. 13759.X. 13763.X. 13781.X. 13789.X. 13799.X. 13807.X. Length 127 digits: (closed) 13829.X. 13831.X. 13841.X. 13859.X. 13873.X. 13877.X. 13879.X. 13883.X. 13901.X. 13903.X. 13907.X. 13913.X. 13921.X. 13931.X. 13933.X. 13963.X. 13967.X. 13997.X. 13999.X. 14009.X. 14011.X. 14029.X. 14033.X. Length 128 digits: (closed) 14051.X. 14057.X. 14071.X. 14081.X. 14083.X. 14087.X. 14107.X. 14143.X. 14149.X. 14153.X. 14159.X. 14173.X. 14177.X. 14197.X. 14207.X. 14221.X. 14243.X. 14249.X. 14251.X. Length 129 digits: (closed) 14281.X. 14293.X. 14303.X. 14321.X. 14323.X. 14327.X. 14341.X. 14347.X. 14369.X. 14387.X. 14389.X. 14401.X. 14407.X. 14411.X. 14419.X. 14423.X. 14431.X. 14437.X. 14447.X. 14449.X. 14461.X. Length 130 digits: (closed) 14479.X. 14489.X. 14503.X. 14519.X. 14533.X. 14537.X. 14543.X. 14549.X. 14551.X. 14557.X. 14561.X. 14563.X. 14591.X. 14593.X. 14621.X. 14627.X. 14629.X. 14633.X. 14639.X. 14653.X. 14657.X. 14669.X. 14683.X. Length 131 digits: 8 points each 14699.X. 14713.X. 14717.X. 14723.X. 14731.X. 14737.X. 14741.X. 14747.X. 14753.X. 14759.X. 14767.X. 14771.X. 14779.X. 14783.X. 14797.X. 14813... 14821.X. 14827.X. 14831.X. 14843.X. 14851.X. 14867.X. 14869.X. 14879... 14887... 14891.X. 14897.X. Length 132 digits: (closed) 14923.X. 14929.X. 14939.X. 14947.X. 14951.X. 14957.X. 14969.X. 14983.X. 15013.X. 15017.X. 15031.X. 15053.X. 15061.X. 15073.X. 15077.X. 15083.X. 15091.X. 15101.X. 15107.X. 15121.X. Length 133 digits: 8 points each 15131.X. 15137.X. 15139.X. 15149... 15161.X. 15173.X. 15187.X. 15193.X. 15199.X. 15217.X. 15227.X. 15233.X. 15241.X. 15259.X. 15263.X. 15269.X. 15271.X. 15277.X. 15287.X. 15289.X. 15299.X. 15307.X. 15313.X. 15319.X. 15329.X. 15331.X. 15349.X. Length 134 digits: 8 points each (closed) 15359.X. 15361.X. 15373.X. 15377.X. 15383.X. 15391.X. 15401.X. 15413.X. 15427.X. 15439.X. 15443.X. 15451.X. 15461.X. 15467.X. 15473.X. 15493.X. 15497.X. 15511.X. 15527.X. 15541.X. 15551.X. 15559.X. 15569.X. Length 135 digits: 8 points each 15581.X. 15583.X. 15601.X. 15607.X. 15619.X. 15629.X. 15641.X. 15643.X. 15647.X. 15649.X. 15661.X. 15667.X. 15671.X. 15679.X. 15683.X. 15727.X. 15731... 15733.X. 15737.X. 15739.X. 15749.X. 15761.X. 15767.X. 15773.X. 15787.X. 15791.X. 15797.X. Length 136 digits: 8 points each 15803.X. 15809... 15817.X. 15823.X. 15859.X. 15877.X. 15881.X. 15887.X. 15889.X. 15901.X. 15907.X. 15913.X. 15919.X. 15923.X. 15937.X. 15959.X. 15971... 15973.X. 15991.X. 16001.X. 16007.X. Length 137 digits: 8 points each 16033... 16057.X. 16061.X. 16063.X. 16067.X. 16069.X. 16073.X. 16087.X. 16091.X. 16097... 16103.X. 16111.X. 16127.X. 16139.X. 16141... 16183.X. 16187.X. 16189.X. 16193.X. 16217.X. 16223... 16229.X. 16231.X. 16249.X. 16253.X. Length 138 digits: 8 points each 16267... 16273.X. 16301.X. 16319.X. 16333.X. 16339.X. 16349.X. 16361... 16363.X. 16369.X. 16381.X. 16411.X. 16417.X. 16421.X. 16427.X. 16433.X. 16447.X. 16451.X. 16453.X. 16477... 16481.X. 16487.X. Length 139 digits: 8 points each 16493.X. 16519.X. 16529.X. 16547.X. 16553.X. 16561.X. 16567.X. 16573... 16603.X. 16607.X. 16619.X. 16631.X. 16633.X. 16649.X. 16651.X. 16657.X. 16661.X. 16673.X. 16691.X. 16693.X. 16699.X. 16703.X. Length 140 digits: 8 points each 16729.X. 16741.X. 16747.X. 16759.X. 16763.X. 16787.X. 16811... 16823.X. 16829.X. 16831.X. 16843.X. 16871.X. 16879.X. 16883.X. 16889.X. 16901.X. 16903.X. 16921.X. 16927.X. 16931.X. 16937... 16943.X. Length 141 digits: 4 points each 16963.X. 16979.X. 16981.X. 16987... 16993.X. 17011.X. 17021.X. 17027.X. 17029.X. 17033.X. 17041.X. 17047.X. 17053.X. 17077.X. 17093... 17099.X. 17107.X. 17117.X. 17123.X. 17137.X. 17159.X. 17167.X. 17183.X. 17189.X. 17191.X. Length 142 digits: 4 points each 17203... 17207.X. 17209... 17231.X. 17239.X. 17257.X. 17291.X. 17293.X. 17299.X. 17317.X. 17321.X. 17327.X. 17333.X. 17341... 17351.X. 17359... 17377.X. 17383... 17387... 17389.X. 17393.X. 17401.X. 17417.X. 17419.X. 17431.X. Length 143 digits: 4 points each 17443.X. 17449.X. 17467.X. 17471.X. 17477.X. 17483.X. 17489... 17491.Xp. 17497.X. 17509... 17519.X. 17539.X. 17551.X. 17569.X. 17573.X. 17579.X. 17581... 17597.X. 17599... 17609.X. 17623.X. 17627.X. 17657.X. 17659.X. 17669.X. Length 144 digits: 4 points each 17681.X. 17683... 17707.X. 17713.X. 17729.X. 17737.X. 17747.X. 17749.X. 17761.X. 17783.X. 17789.X. 17791.X. 17807... 17827.X. 17837.X. 17839... 17851.X. 17863.X. 17881.X. 17891.X. 17903... 17909.X. 17911... Length 145 digits: 4 points each 17921.X. 17923.X. 17929.X. 17939.X. 17957.X. 17959.X. 17971.X. 17977.X. 17981... 17987.X. 17989.X. 18013.X. 18041.X. 18043.X. 18047.X. 18049.X. 18059.X. 18061.X. 18077.X. 18089.X. 18097.X. 18119.X. 18121... 18127.X. 18131.X. 18133.X. 18143.X. 18149.X. Length 146 digits: 4 points each 18169.X. 18181... 18191.X. 18199.X. 18211.X. 18217... 18223.X. 18229... 18233.X. 18251.X. 18253.X. 18257.X. 18269.X. 18287.X. 18289.X. 18301.X. 18307... 18311.X. 18313.X. 18329.X. 18341.X. 18353... 18367.X. 18371.X. 18379.X. 18397.X. Length 147 digits: 4 points each 18401... 18413... 18427.X. 18433.X. 18439.X. 18443.X. 18451.X. 18457.X. 18461.X. 18481.X. 18493.X. 18503.X. 18517... 18521.X. 18523.X. 18539.X. 18541.X. 18553.X. 18583.X. 18587.X. 18593.X. 18617.X. 18637.X. Length 148 digits: 4 points each 18661.X. 18671.X. 18679.X. 18691.X. 18701.X. 18713.X. 18719.X. 18731.X. 18743.X. 18749.X. 18757.X. 18773.X. 18787.X. 18793.X. 18797.X. 18803... 18839.X. 18859.X. 18869.X. Length 149 digits: 4 point each 18899.X. 18911.X. 18913.X. 18917.X. 18919... 18947.X. 18959.X. 18973.X. 18979.X. 19001.X. 19009.X. 19013.X. 19031.X. 19037.X. 19051.X. 19069.X. 19073.X. 19079.X. 19081... 19087.X. 19121.X. 19139... Length 150 digits: 4 point each 19141.X. 19157... 19163.X. 19181.X. 19183... 19207... 19211.X. 19213.X. 19219.X. 19231.X. 19237.X. 19249.X. 19259.X. 19267.X. 19273.X. 19289.X. 19301.X. 19309.X. 19319.X. 19333.X. 19373.X. 19379.X. 19381.X. 19387.X. 19391.X. Length 151 digits: 2 point each 19403... 19417.X. 19421.X. 19423.X. 19427.X. 19429.X. 19433.X. 19441.X. 19447.X. 19457.X. 19463.X. 19469.X. 19471.X. 19477.X. 19483.X. 19489.X. 19501... 19507.X. 19531.X. 19541.X. 19543... 19553.X. 19559.X. 19571.X. 19577.X. 19583.X. 19597.X. 19603.X. 19609.X. Length 152 digits: 2 point each 19661.X. 19681.X. 19687.X. 19697.X. 19699.X. 19709.X. 19717... 19727.X. 19739... 19751.X. 19753... 19759.X. 19763.X. 19777.X. 19793... 19801.X. 19813... 19819.X. 19841.X. 19843.X. 19853.X. 19861... 19867.X. 19889.X. 19891.X. Length 153 digits: 2 point each 19913.X. 19919.X. 19927.X. 19937.X. 19949.X. 19961... v 19963... 19973.X. 19979.X. 19991.X. 19993.X. 19997.X. 20011... 20021.X. 20023.X. 20029... 20047.X. 20051... 20063... 20071.X. 20089.X. 20101.X. 20107.X. 20113.X. 20117.X. 20123... 20129.X. 20143.X. 20147.X. 20149.X. Length 154 digits: 2 point each 20161... 20173.X. 20177.X. 20183.X. 20201.X. 20219.X. 20231.X. 20233.X. 20249.X. 20261.X. 20269.X. 20287.X. 20297.X. 20323.X. 20327... 20333.X. 20341.X. 20347.X. 20353.X. 20357.X. 20359.X. 20369.X. 20389.X. 20393.X. 20399.X. 20407.X. Length 155 digits: 2 point each v 20411.X. 20431.X. 20441.X. 20443.X. 20477.X. 20479.X. 20483... 20507.X. 20509.X. 20521... 20533.X. 20543.X. 20549.X. 20551.X. 20563.X. 20593.X. 20599.X. 20611.X. 20627.X. 20639.X. 20641.X. 20663.X. Length 156 digits: 2 point each 20681.X. 20693... 20707.X. 20717.X. 20719.X. 20731.X. 20743... 20747.X. 20749... 20753.X. 20759.X. 20771.X. 20773.X. 20789.X. 20807.X. 20809.X. 20849.X. 20857.X. 20873.X. 20879... 20887.X. 20897.X. 20899.X. 20903... 20921.X. 20929.X. Length 157 digits: 2 point each 20939.X. 20947.X. 20959.X. 20963.X. 20981.X. 20983... 21001.X. 21011.X. 21013.X. 21017.X. 21019.X. 21023... 21031.X. 21059.X. 21061... 21067.X. 21089.X. 21101... 21107... 21121... 21139.X. 21143.X. 21149... 21157.X. 21163.X. 21169.X. 21179... 21187.X. 21191.X. Length 158 digits: 2 points each 21193.X. 21211.X. 21221... 21227.X. 21247.X. 21269... 21277... 21283.X. 21313.X. 21317.X. 21319.X. 21323.X. 21341.X. 21347... 21377.X. 21379... 21383.X. 21391.X. 21397.X. 21401.X. 21407.X. 21419... 21433... Length 159 digits: 2 point each 21467.X. 21481.X. 21487... 21491.X. 21493.X. 21499.X. 21503... 21517.X. 21521.X. 21523... 21529.X. 21557... 21559.X. 21563.X. 21569... 21577.X. 21587.X. 21589.X. 21599.X. 21601.X. 21611.X. 21613.X. 21617... 21647.X. 21649.X. 21661.X. 21673.X. 21683.X. 21701.X. 21713.X. Length 160 digits: 2 point each 21727.X. 21737... 21739.X. 21751... 21757.X. 21767.X. 21773.X. 21787.X. 21799.X. 21803... 21817.X. 21821.X. 21839.X. 21841... 21851.X. 21859... 21863.X. 21871... 21881.X. 21893.X. 21911... 21929... 21937.X. 21943... 21961... 21977... Length 161 digits: 1 point each 21991... 21997.X. 22003... 22013... 22027.X. 22031.X. 22037... 22039... 22051.X. 22063.X. 22067.X. 22073.X. 22079.X. 22091.X. 22093.X. 22109.X. 22111.X. 22123... 22129.X. 22133.X. 22147... 22153... 22157.X. 22159.X. 22171.X. 22189.X. 22193... 22229.X. 22247... Length 162 digits: 1 point each 22259.X. 22271.X. 22273.X. 22277... 22279.X. 22283... 22291... 22303.X. 22307.X. 22343.X. 22349.X. 22367.X. 22369... 22381.X. 22391... 22397... 22409... 22433.X. 22441... 22447... 22453... 22469.X. 22481... 22483.X. 22501.X. 22511... Length 163 digits: 1 point each 22531... 22541.X. 22543.X. 22549.X. 22567.X. 22571.X. 22573... 22613.X. 22619.X. 22621.X. 22637... 22639.X. 22643... 22651... 22669.X. 22679.X. 22691.X. 22697.X. 22699.X. 22709... 22717.X. 22721... 22727.X. 22739.X. 22741.X. 22751... 22769.X. 22777.X. 22783.X. 22787.X. Length 164 digits: 1 point each 22807.X. 22811.X. 22817.X. 22853.X. 22859.X. 22861.X. 22871.X. 22877... 22901.X. 22907.X. 22921.X. 22937.X. 22943... 22961.X. 22963... 22973... 22993.X. 23003.X. 23011.X. 23017.X. 23021.X. 23027.X. 23029.X. 23039.X. 23041.X. 23053.X. 23057... 23059.X. 23063... Length 165 digits: 1 point each 23071.X. 23081.X. 23087.X. 23099.X. 23117.X. 23131.X. 23143.X. 23159.X. 23167... 23173... 23189... 23197.X. 23201... 23203.X. 23209.X. 23227... 23251... 23269.X. 23279.X. 23291... 23293.X. 23297.X. 23311... 23321... 23327.X. 23333.X. 23339... Length 166 digits: 1 point each 23357.X. 23369.X. 23371.X. 23399.X. 23417... 23431... 23447... 23459.X. 23473.X. 23497.X. 23509.X. 23531... 23537.X. 23539.X. 23549.X. 23557... 23561... 23563... 23567.X. 23581.X. 23593.X. 23599.X. 23603... 23609... Length 167 digits: 1 point each 23623... 23627.X. 23629... 23633.X. 23663.X. 23669.X. 23671... 23677.X. 23687... 23689... 23719.X. 23741.X. 23743.X. 23747... 23753... 23761.X. 23767.X. 23773.X. 23789... 23801... 23813... 23819... 23827... 23831... 23833.X. 23857... 23869.X. 23873.X. 23879.X. 23887.X. 23893.X. 23899.X. Length 168 digits: 1 point each 23909.X. 23911... 23917... 23929.X. 23957... 23971.X. 23977.X. 23981.X. 23993... 24001... 24007.X. 24019.X. 24023.X. 24029.X. 24043.X. 24049.X. 24061.X. 24071.X. 24077.X. 24083... 24091.X. 24097... 24103.X. 24107.X. 24109.X. 24113.X. 24121... 24133.X. 24137.X. 24151.X. 24169.X. 24179... Length 169 digits: 1 point each 24181.X. 24197.X. 24203... 24223.X. 24229.X. 24239.X. 24247... 24251.X. 24281... 24317.X. 24329... 24337... 24359.X. 24371.X. 24373... 24379.X. 24391.X. 24407... 24413... 24419.X. 24421.X. 24439.X. 24443... Length 170 digits: 1 point each 24469... 24473.X. 24481... 24499... 24509... 24517... 24527.X. 24533.X. 24547.X. 24551.X. 24571.X. 24593.X. 24611.X. 24623... 24631.X. 24659... 24671... 24677... 24683.X. 24691.X. 24697.X. 24709.X. 24733... Length 171 digits: 1 point each 24749.X. 24763.X. 24767.X. 24781.X. 24793.X. 24799.X. 24809.X. 24821.X. 24841... 24847.X. 24851... 24859.X. 24877... 24889.X. 24907.X. 24917.X. 24919... 24923.X. 24943.X. 24953... 24967.X. 24971.X. 24977... 24979... 24989... 25013.X. Length 172 digits: 1 point each 25031.X. 25033... 25037.X. 25057... 25073... 25087... 25097.X. 25111.X. 25117.X. 25121... 25127... 25147... 25153.X. 25163.X. 25169.X. 25171.X. 25183.X. 25189.X. 25219... 25229... 25237.X. 25243... 25247.X. 25253.X. 25261.X. 25301.X. 25303.X. 25307.X. 25309.X. Length 173 digits: 1 point each 25321... 25339.X. 25343... 25349.X. 25357.X. 25367.X. 25373... 25391.X. 25409.X. 25411... 25423... 25439.X. 25447... 25453.X. 25457... 25463.X. 25469... 25471.X. 25523... 25537.X. 25541.X. 25561... 25577.X. 25579.X. 25583.X. 25589.X. 25601.X. Length 174 digits: 1 point each 25603... 25609.X. 25621... 25633... 25639.X. 25643.X. 25657.X. 25667... 25673.X. 25679.X. 25693... 25703.X. 25717.X. 25733.X. 25741... 25747.X. 25759.X. 25763... 25771.X. 25793.X. 25799.X. 25801... 25819.X. 25841.X. 25847.X. 25849.X. 25867.X. 25873... 25889... Length 175 digits: 1 point each 25903.X. 25913.X. 25919.X. 25931... 25933.X. 25939.X. 25943.X. 25951.X. 25969... 25981.X. 25997... 25999.X. 26003.X. 26017.X. 26021.X. 26029... 26041... 26053.X. 26083.X. 26099... 26107... 26111... 26113.X. 26119.X. 26141... 26153.X. 26161... 26171... 26177.X. 26183.X. Length 176 digits: 1 point each 26189.X. 26203... 26209.X. 26227... 26237.X. 26249.X. 26251... 26261.X. 26263... 26267.X. 26293... 26297.X. 26309... 26317.X. 26321... 26339.X. 26347.X. 26357... 26371... 26387... 26393... 26399.X. 26407.X. 26417... 26423.X. 26431.X. 26437.X. 26449... 26459... Length 177 digits: 1 point each 26479... 26489.X. 26497... 26501.X. 26513.X. 26539.X. 26557.X. 26561... 26573.X. 26591.X. 26597... 26627.X. 26633... 26641... 26647.X. 26669.X. 26681... 26683... 26687... 26693.X. 26699.X. 26701... 26711.X. 26713.X. 26717... 26723... 26729... 26731.X. 26737... 26759... Length 178 digits: 1 points each 26777.X. 26783.X. 26801... 26813.X. 26821.X. 26833.X. 26839.X. 26849.X. 26861... 26863... 26879.X. 26881... 26891... 26893... 26903.X. 26921... 26927.X. 26947.X. 26951.X. 26953.X. 26959.X. 26981... 26987.X. 26993... 27011.X. 27017.X. 27031... 27043.X. 27059... 27061... Length 179 digits: 1 points each 27067.X. 27073... 27077.X. 27091... 27103... 27107.X. 27109.X. 27127.X. 27143.X. 27179... 27191... 27197... 27211.X. 27239.X. 27241... 27253... 27259... 27271... 27277... 27281.X. 27283... 27299.X. 27329... 27337... 27361.X. Length 180 digits: 1 points each 27367.X. 27397... 27407... 27409.X. 27427... 27431... 27437.X. 27449.X. 27457... 27479... 27481.X. 27487... 27509... 27527... 27529... 27539... 27541... 27551.X. 27581... 27583.X. 27611.X. 27617.X. 27631.X. 27647... 27653... Length 181 digits: 1 points each 27673... 27689... 27691... 27697... 27701... 27733... 27737... 27739.X. 27743.X. 27749... 27751... 27763... 27767.X. 27773... 27779.X. 27791... 27793... 27799.X. 27803.X. 27809.X. 27817.X. 27823... 27827... 27847... 27851... 27883.X. 27893.X. 27901... 27917... 27919... 27941... 27943.X. 27947... 27953... 27961... Length 182 digits: 0 points each 27967... 27983... 27997... 28001... 28019... 28027... 28031... 28051... 28057... 28069... 28081... 28087... 28097... 28099... 28109... 28111... 28123... 28151... 28163... 28181... 28183... 28201... 28211... 28219... 28229... Length 183 digits: 0 points each 28277... 28279... 28283... 28289... 28297... 28307... 28309... 28319... 28349... 28351... 28387... 28393... 28403... 28409... 28411... 28429... 28433... 28439... 28447... 28463... 28477... 28493... 28499... 28513... 28517... 28537... 28541... 28547... 28549... 28559... Length 184 digits: 0 points each 28571... 28573... 28579... 28591... 28597... 28603... 28607... 28619... 28621... 28627... 28631... 28643... 28649... 28657... 28661... 28663... 28669... 28687... 28697... 28703... 28711... 28723... 28729... 28751... 28753... 28759... 28771... 28789... 28793... 28807... 28813... 28817... 28837... 28843... 28859... 28867... 28871... Length 185 digits: 0 points each 28879... 28901... 28909... 28921... 28927... 28933... 28949... 28961... 28979... 29009... 29017... 29021... 29023... 29027... 29033... 29059... 29063... 29077... 29101... 29123... 29129... 29131... 29137... 29147... 29153... 29167... 29173... 29179... Length 186 digits: 0 points each 29191... 29201... 29207... 29209... 29221... 29231... 29243... 29251... 29269... 29287... 29297... 29303... 29311... 29327... 29333... 29339... 29347... 29363... 29383... 29387... 29389... 29399... 29401... 29411... 29423... 29429... 29437... 29443... 29453... 29473... 29483... Length 187 digits: 0 points each 29501... 29527... 29531... 29537... 29567... 29569... 29573... 29581... 29587... 29599... 29611... 29629... 29633... 29641... 29663... 29669... 29671... 29683... 29717... 29723... 29741... 29753... 29759... 29761... 29789... Length 188 digits: 0 points each 29803... 29819... 29833... 29837... 29851... 29863... 29867... 29873... 29879... 29881... 29917... 29921... 29927... 29947... 29959... 29983... 29989...