Proth Search Page for Proth--the Windows program by Yves Gallot Yves Gallot wrote an excellent Win95/98/NT4.0 program which makes it easy for anyone to find record size or otherwise interesting primes, but this creates a problem: without a coordinated effort, many of us were be searching the same ranges of numbers for primes! Some spent hundreds of hours checking ranges that were already known ...

Lucas's Primality Test With Factored N-1 Fermat's Little Theorem assures us that if N is a prime then b^(N-1) = 1 (mod N) (1) for every integer b coprime to N. In contrast, if N is composite it is quite rare for the above congruence to be satisfied for ANY b. This fact enables us to test for compositeness quite easily, simply by checking to see if b^(N-1) is congruent to 1 (mod N) for some ...