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Topic: Prime numbers and primality tests
Replies: 4   Last Post: Jan 22, 2013 11:18 PM

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Posts: 18
Registered: 11/27/06
Re: Prime numbers and primality tests
Posted: Jan 21, 2013 12:06 AM
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I forgot to say: if a composite N passes the usual probable prime
b^(N-1) = 1 (mod N)
for one base b, then it is more likely than the average number that
size to pass another test, c^(N-1) = 1 (mod N).

For example, N = 341 is a pseudoprime base 2, which means that 2^3401 (mod 341). There are 100 bases b between 1 and 340 such that b^340
= 1 (mod 341).

On the other hand, if b^(N-1) = 1 (mod N), then this N seems
(empirically and heuristically) to be LESS likely than average to pass
a Lucas probable prime test.

That's why I like to do one or more of EACH type of test, which I
think is what PrimeQ does.

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