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Old 2009-04-06, 16:44   #2
R. Gerbicz
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"Robert Gerbicz"
Oct 2005

2·7·103 Posts

Originally Posted by Bill Bouris View Post
Proth theorem extended:
let Q= k*2^n +1, where n=>3 is a odd natural number & k<= 2^n +1. if for some 'a', a^((Q-1)/4) == +/-1(mod Q), then 'Q' is prime. 'k' doesn't need to be restricted to only 'odd' numbers, either.

When I see such a "theorem" I try to find a counter-example in Pari-Gp. Here it is one:

Q=8355841, so n=15, k=255, and let a=3, the conditions are true.
a^((Q-1)/4)==1 mod Q, but Q is composite: Q=13*41*61*257
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