NetNews Usenet Archive 1992 #23

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Internet Message Format | 1992-10-16 | 5.3 KB

Path: sparky!uunet!mcsun!uknet!pavo.csi.cam.ac.uk!emu.pmms.cam.ac.uk!rgep From: rgep@emu.pmms.cam.ac.uk (Richard Pinch) Newsgroups: sci.math Subject: Even pseudoprimes up to 10^12 Summary: There are 155 even pseudoprimes up to 10^12 Keywords: Pseudoprime Message-ID: <1992Oct16.142400.13541@infodev.cam.ac.uk> Date: 16 Oct 92 14:24:00 GMT Sender: R.G.E.Pinch@pmms.cam.ac.uk Organization: DPMMS University of Cambridge Lines: 169 Nntp-Posting-Host: emu.pmms.cam.ac.uk Even pseudoprimes up to 10^12 The list of pseudoprimes up to 10^12 which I announced in June were those satisfying 2^N-1 == 1 modulo N. Some people use the definition 2^N == 2 modulo N, which allows the possiblity of even N. There are 155 even pseudoprimes up to 10^12. The list follows. Richard Pinch Dept of Pure Mathematics and Mathematical Statistics University of Cambridge 161038 2 73 1103 215326 2 23 31 151 2568226 2 23 31 1801 3020626 2 7 359 601 7866046 2 23 271 631 9115426 2 31 233 631 49699666 2 311 79903 143742226 2 23 31 100801 161292286 2 127 199 3191 196116194 2 127 599 1289 209665666 2 7 89 191 881 213388066 2 23 31 151 991 293974066 2 73 631 3191 336408382 2 73 1103 2089 377994926 2 23 89 127 727 410857426 2 7 191 153649 665387746 2 23 3463 4177 667363522 2 7 5471 8713 672655726 2 73 1103 4177 760569694 2 1319 288313 1066079026 2 23 31 151 4951 1105826338 2 23 73 127 2593 1423998226 2 7 79 271 4751 1451887438 2 79 89 223 463 1610063326 2 73 2089 5279 2001038066 2 47 311 68449 2138882626 2 73 3191 4591 2952654706 2 31 71 631 1063 3220041826 2 73 103 233 919 3434672242 2 727 911 2593 4338249646 2 4721 459463 4783964626 2 7 23 73 271 751 5269424734 2 7 1433 262657 5820708466 2 79 3257 11311 6182224786 2 23 31 151 28711 6381449614 2 73 199 239 919 8356926046 2 7 79 7555991 8419609486 2 31 2441 55633 9548385826 2 7 31 89 247201 9895191538 2 127 1289 30223 10504379326 2 7 31 89 151 1801 11675882626 2 151 2143 18041 14184805006 2 71 127 151 5209 14731729666 2 31 4271 55633 14965276226 2 31 223 601 1801 14973142786 2 7 31 151 228479 15369282226 2 23 151 199 11119 15660993826 2 73 601 178481 16667060194 2 47 5209 34039 16732427362 2 7 79 1847 8191 18411253246 2 71 89 127 11471 18661908574 2 89 127 463 1783 19252624546 2 71 1103 122921 23360021026 2 151 383 201961 23494981966 2 127 1289 71761 26429263246 2 23 73 89 191 463 27355580686 2 7 73 103 151 1721 28087608418 2 23 15241 40063 29712533746 2 7 1823 1164193 30789370162 2 73 167 487 2593 30910262626 2 23 31 151 143551 34439472946 2 73 271 870431 35239366306 2 1063 3511 4721 35921441746 2 127 2143 65993 37130195614 2 47 337 479 2447 38523731842 2 73 103 2561759 43487454286 2 23 31 151 201961 44849716066 2 47 89 1289 4159 45436160386 2 199 743 153649 48930395086 2 23 23311 45631 74562118786 2 199 337 631 881 77404107886 2 7 31 79 151 14951 79204064626 2 71 337 919 1801 81473324626 2 23 1801 983431 82284719986 2 7 31 79 2399951 83720640862 2 73 89 199 32377 85898088046 2 31 71 127 153649 95553085486 2 89 4423 121369 98730252226 2 23 31 601 115201 100320423886 2 31 73 89 271 919 104987373454 2 73 1567 458897 105990932734 2 239 2143 103471 107427982366 2 23 31 233 367 881 116344653886 2 73 271 2940521 126217792286 2 431 1103 132751 131282477602 2 89 19471 37879 134744844466 2 31 463 1471 3191 136767694402 2 79 1087 796337 141144077746 2 7 31 89 631 5791 154550451826 2 23 31 151 717751 155783377198 2 167 2089 223273 161097973246 2 7 199 3191 18121 173299248046 2 73 191 991 6271 178830663166 2 89 127 271 29191 183689075122 2 7 647 2143 9463 188481991006 2 31 151 223 90281 193205875006 2 47 73 151 199 937 198503648066 2 31 2441 1311623 205641055918 2 73 89 103 153649 211108982498 2 239 6361 69431 211641323986 2 127 599 1391041 215470719934 2 127 13367 63463 222461530066 2 151 1721 428023 224981223886 2 199 367 631 2441 233069077726 2 23 31 151 601 1801 261712995886 2 31 233 631 28711 264326824126 2 31 367 2441 4759 266213783122 2 7 45137 421279 273322367806 2 151 431 2099863 278007622606 2 7 31 271 1103 2143 281928253426 2 151 4663 200201 291328299406 2 73 631 991 3191 297876680146 2 31 151 3257 9769 315554044786 2 71 127 151 115879 335141132866 2 31 71 127 599479 351542853586 2 463 2591 146521 352188388018 2 73 233 10353001 354716524306 2 31 881 991 6553 356788708046 2 2927 6271 9719 357647681422 2 1087 164511353 365187556126 2 31 71 73 631 1801 387932434066 2 31 89 4177 16831 398842105186 2 7 47 73 631 13159 423429752866 2 31 47 9719 14951 434671442206 2 31 337 1871 11119 442366889966 2 23 89 127 850807 443624282494 2 239 18127 51199 468713690974 2 89 14633 179951 484454279566 2 631 1103 348031 487199621746 2 631 6719 57457 514377881326 2 127 199 881 11551 543726705026 2 71 127 239 126151 547551530002 2 40433 6771097 553588254766 2 191 337 967 4447 569903252626 2 151 39551 47713 587924453326 2 7 31 89 151 100801 591379183822 2 7 47 103 2089 4177 600030498926 2 23 31 420778751 601335417266 2 23 31 3191 132151 605339739346 2 23 31 151 881 3191 635501599426 2 73 199 919 23801 650537257294 2 23 73 2089 92737 652746157966 2 7 89 991 528631 689380287058 2 89 337 11492353 738239981326 2 31 463 881 29191 754907532226 2 103 337 881 12343 775619881726 2 2351 2551 64663 778581406786 2 839 3823 121369 851011808626 2 7 89 601 631 1801 860026430158 2 7 55633 1104209 861969666286 2 31 79 151 631 1847 880365757426 2 23 127 239 337 1871 902678572846 2 73 127 359 135607 957191716174 2 23 103 337 599479 979053260626 2 7 31 89 751 33751 ------------