Henrik a écrit :
Probably all of them.
> While searching for Baillie-PSW I found a few variants:
> A. n = 2 or 3 (mod 5); base-2 pseudoprime (Fermat); Fibonacci
> B. strong pseudoprime to base 2; passes Lucas test A.
> C. base-2 strong pseudoprime; in the sequence 5, -7, 9, -11, 13,...
> D. base-2 pseudoprime; Lucas test; n = 2 (mod 5); Lucas pseudoprime
> Now some questions:
Personally, for Primo I use the variant C (except the test is a Lucas
strong pseudoprime test, i.e., not just a Lucas pseudoprime test).
> 2. My sources are old. Are there counter-examples to the Baillie-PSWAFAIK, none. Not only none was found but nobody succeeded in building
> test today?
Primo is used since now more than 3 years and, for each primality
certificate it produces, all intermediate 'primes' are checked with
this test. If one was composite, the certification would necessarily
have failed. This never occurred. In fact, it is presumably that no
composite less than, say, 10000 digits can fool this test.
BTW, in my docs, I don't use "Baillie-PSW" to refer to this test but
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