Date: 6 Feb 1998 13:12:40 -0000 From: yamasaki@kusm.kyoto-u.ac.jp To: kc2h-msm@asahi-net.or.jp 三島 久典 様 素因数分解表で未分解の数を6個楕円曲線法で分解したので報告します。 いずれも残っていた合成数を二つの素数に分解しました。 使用プログラムは GMP-ECM です。 三島さんのプロジェクトで百桁以下の合成数がすべて分解されれば、私はしばらく 森本先生のプロジェクトである円分数の素因数分解をしようと思っています。 http://www.kusm.kyoto-u.ac.jp/~yamasaki/a3c.html に関連したことを書きましたので見てみてください。 //ΠPn+NextPrime 51 13493024686066671935841713459 * 329446976396810289693682264296234880400006844018360207487177135951 //ΠPn-NextPrime 53 2671 * 74902801005813938752367 * 17830107318957390571898260197107 * 71776765011163291715821210979395271083021 //An 63 41017 * 15413989571329785465607280049103 * 3086883601795255126191490501671315469050469136457731 //Kn 65 3 * 3 * 11 * 1427427733176073 * 28126844765989039793177072537 * 2107438713765429151613128978549232192805991987 //Euler 76 5 * 145007 * 3460859370585503071 * 581662827280863723239564386159 * 2046494332840854220697501265093364699008503 //Bernoulli 110 5 * 157 * 76493 * 150235116317549231 * 36944818874116823428357691 * 22941274567094524465398178713033734927421643 GMP-ECM のログを次に示します。 Input number is 4445236185272185438169240794291312557432222642727183809026451438704160103479600800432029464509 Using B1=1000000 and sigma=2048806548 A=3306228343696868749141498868768837546585369153779767308015549737158621498625109721267861165744 starting point: x=91706440553337944921328540277564263894030640925630526493942506457726265415022360144870908998 Step 1 took 1249956ms for 13872253 multiplications start step 2 with B1=1000000, B2=100000000, D=7072 x=3048802610787472199293570424666150127267128875159909349493750976231910340713002588745919083764 initialization of Step 2 took 20053ms last interval is 21675681..21689825 ********** Factor found during step 2: 13493024686066671935841713459 Found probable prime factor: 13493024686066671935841713459 Input number is 1279787423156627357418277206580017568537457726669274292313689140821020247 Using B1=1000000 and sigma=1047639601 A=128035017219656631203087593536580728800134077959148130946614074375836080 starting point: x=559892929289010451491565718864078348130807717247352626049417708568848633 Step 1 took 1059777ms for 13872253 multiplications start step 2 with B1=1000000, B2=100000000, D=7072 x=1001009502958249826423392466888552079377855793020181372723290159496350314 initialization of Step 2 took 22591ms last interval is 5084769..5098913 ********** Factor found during step 2: 17830107318957390571898260197107 Found probable prime factor: 17830107318957390571898260197107 Input number is 47581191645980988738293449413565377115917643404375058150569834644653151889163965293 Using B1=1000000 and sigma=101614767 A=46342211018684447482528371876849645223282297633667858181883301850192895015623986616 starting point: x=5821243165953571822851861285056277510619397819965282397883961324576653089143486064 Step 1 took 1530313ms for 13872253 multiplications start step 2 with B1=1000000, B2=100000000, D=7072 x=36178122818474770307341317096228068742017878723311507074721351337518901930981403237 initialization of Step 2 took 25330ms last interval is 5424225..5438369 ********** Factor found during step 2: 15413989571329785465607280049103 Found probable prime factor: 15413989571329785465607280049103 Input number is 59275601555915835120624043933863344860791214819204603582764368840939761019 Using B1=1000000 and sigma=662328827 A=5127405350566240598288916688383590533900571266475438754943739700147094205 starting point: x=4087012557495137300669919942733821343074010203485970901505816893628971677 Step 1 took 1284540ms for 13872253 multiplications start step 2 with B1=1000000, B2=100000000, D=7072 x=44295748844266156433149778474461725164173190752054034068678014345476568996 initialization of Step 2 took 23652ms last interval is 65253345..65267489 ********** Factor found during step 2: 28126844765989039793177072537 Found probable prime factor: 28126844765989039793177072537 Input number is 1190369679654476225016141139240538267897223507375501409178560817116509977 Using B1=1000000 and sigma=146636738 A=728809913144353100754676536271262381425304297804877646433179993112958365 starting point: x=809696209210069209879654361604608038455804749353021493558139915734926860 Step 1 took 1241560ms for 13872253 multiplications start step 2 with B1=1000000, B2=100000000, D=7072 x=551014077569663891631549464542273453562222506987551895459448756292267426 initialization of Step 2 took 20531ms last interval is 39992161..40006305 ********** Factor found during step 2: 581662827280863723239564386159 Found probable prime factor: 581662827280863723239564386159 Input number is 847561233622690045157120478631770050118086105598398459216576578906313 Using B1=1000000 and sigma=680747766 A=426257479657392931652401639366209713746346887611759203912093226257105 starting point: x=367451174251534895285111932759325192699041460429117958385072744581626 Step 1 took 992996ms for 13872253 multiplications start step 2 with B1=1000000, B2=100000000, D=7072 x=423757878741100013480201658566691393066271543633970689772895434887276 initialization of Step 2 took 16503ms last interval is 2284257..2298401 ********** Factor found during step 2: 36944818874116823428357691 Found probable prime factor: 36944818874116823428357691 yamasaki@kusm.kyoto-u.ac.jp URL: http://www.kusm.kyoto-u.ac.jp 京都大学大学院理学研究科 数学教室助手 山崎愛一