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 2004-10-19, 16:56 #1 JuanTutors     Mar 2004 3·163 Posts P-1 question of curiosity This is more a question of curiosity than anything else: What happens if, say, EVERY prime factor of a specific composite Mersenne number was "very smooth" for P-1 testing? I.e. what if for some specific M_p, Prime95 sets the first bound B1, and it just so happens that every prime q dividing M_p is B1-smooth? Would the P-1 test detect that? Would it somehow fail to detect that? Would your computer blow up?
 2004-10-19, 17:46 #2 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts Every prime factor of M_p would appear in the output, that means P-1 would simply report M_p itself as the factor found. Alex
 2004-10-19, 17:48 #3 dave_dm   May 2004 24×5 Posts I don't know what Prime95 itself does but the p-1 algorithm can detect this, yes. Let the gcd at the end be d = gcd(a^X-1, n), where n is the number to be factored and X is the product of all prime powers < B1. When d=1 we fail to find a factor; when 1
 2004-10-20, 04:37 #4 Olympia   13·431 Posts Hi. Could you please Help? Suppose that p>3 is an odd prime and that a is not equal to 1 mod p. Prove that if a^3 congruences 1 mod p, then p congruences 1 mod 3. Hint: what happens if you divide p-1 by 3? What does Fermat's little theorem says all about this? Thank so much. Olympia Last fiddled with by Olympia on 2004-10-20 at 04:39

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