Subject: 1 Bernoulli and 5 An factorisations Date: Mon, 02 Nov 1998 10:12:34 +0000 From: Allan MacLeod <MACL-MS0@wpmail.paisley.ac.uk> To: kc2h-msm@asahi-net.or.jp Hello, The following results appeared during the weekend. Allan MacLeod (a) The factorisation of the remaining composite of Bernoulli 146 into P32 * P34 * P34 Input number is 269116590632726862241599354298826948271748399014997974494963599274965614871988049574489970791060991 (99 digits) Using B1=3000000, B2=300000000, polynomial x^30, sigma=630597632 Step 1 took 672912ms for 39102834 muls, 3 gcdexts Step 2 took 319175ms for 16480797 muls, 29004 gcdexts ********** Factor found in step 2: 37996324998547740539691528067877 Found probable prime factor of 32 digits: 37996324998547740539691528067877 Composite cofactor 7082700514931714608424383737254089922262631966445989054616137913683 has 67 digits Input number is 7082700514931714608424383737254089922262631966445989054616137913683 (67 digits) Using B1=3000000, B2=300000000, polynomial x^30, sigma=749175733 Step 1 took 337857ms for 39102834 muls, 3 gcdexts Step 2 took 164945ms for 16480797 muls, 29004 gcdexts ********** Factor found in step 2: 4036138055144761320534304068715607 Found probable prime factor of 34 digits: 4036138055144761320534304068715607 Probable prime cofactor 1754821172656266926966923716442469 has 34 digits (b) Factor of A70 = 70! - 69! + 68! - .... Input number is 859078741381485846771480781396806231586766814640923689834377870700001999521248398187 (84 digits) Using B1=3000000, B2=300000000, polynomial x^30, sigma=1822271789 Step 1 took 617197ms for 39102834 muls, 3 gcdexts Step 2 took 239451ms for 13394950 muls, 26969 gcdexts ********** Factor found in step 2: 585030093394485946687838023247 Found probable prime factor of 30 digits: 585030093394485946687838023247 Probable prime cofactor 1468435130228777520806101110144198014434899612807530021 has 55 digits (c) Factor of A77 Input number is 423924430121577093663604665618738428866938776566665245999701885276513297515199 (78 digits) Using B1=3000000, B2=300000000, polynomial x^30, sigma=972015242 Step 1 took 610000ms for 39102834 muls, 3 gcdexts ********** Factor found in step 1: 17591036707326253625414788854031670107 Found probable prime factor of 38 digits: 17591036707326253625414788854031670107 Probable prime cofactor 24098888381321069342745720538599406741357 has 41 digits (d) Factors of A82 into P31 * P29 * P43 Input number is 62937272289325306279305300003450030931627644452080234239146224241178226225750471622048311877940966703 (101 digits) Using B1=3000000, B2=300000000, polynomial x^30, sigma=1620692091 Step 1 took 669175ms for 39102834 muls, 3 gcdexts Step 2 took 316759ms for 16480797 muls, 29004 gcdexts ********** Factor found in step 2: 1361843985381500874962939678969 Found probable prime factor of 31 digits: 1361843985381500874962939678969 Composite cofactor 46214744834882345710554126266356144933371170136427326716235875870435687 has 71 digits Input number is 46214744834882345710554126266356144933371170136427326716235875870435687 (71 digits) Using B1=3000000, B2=300000000, polynomial x^30, sigma=2140987371 Step 1 took 416813ms for 39102834 muls, 3 gcdexts Step 2 took 200274ms for 16480797 muls, 29004 gcdexts ********** Factor found in step 2: 31253997184032546487207810861 Found probable prime factor of 29 digits: 31253997184032546487207810861 Probable prime cofactor 1478682696576588383655163289071530063028067 has 43 digits (e) Factors of A90 Input number is 49877967180978338576246594784518191787007540514926385103788159802480881731335303745593600990648267904551 (104 digits) Using B1=3000000, B2=300000000, polynomial x^30, sigma=1754054057 Step 1 took 671043ms for 39102834 muls, 3 gcdexts Step 2 took 323077ms for 16480797 muls, 29004 gcdexts ********** Factor found in step 2: 55019405240237536315808689741 Found probable prime factor of 29 digits: 55019405240237536315808689741 Probable prime cofactor 906552278476847444160580153565664347318791317572967678202253771246791481411 has 75 digits (f) Factors of A94 Input number is 107745253847603392494772654100857391663112957777817924584621505847263825176047393003652310766916363930287761382063980793761156049285396710361 (141 digits) Using B1=3000000, B2=300000000, polynomial x^30, sigma=491176053 Step 1 took 1402142ms for 39102834 muls, 3 gcdexts Step 2 took 670165ms for 16480797 muls, 29004 gcdexts ********** Factor found in step 2: 16961617771107656498762423 Found probable prime factor of 26 digits: 16961617771107656498762423 Probable prime cofactor 6352298188863574899660125160672761857177312600750424600022590896869845596544818074214778062973059728996047576845807 has 115 digits