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
Date: 16 Oct 92 14:24:00 GMT
Organization: DPMMS University of Cambridge

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
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Newsgroups: sci.math