Hi! On page 111 of the manual (section 15.7.1, Prime Testing) https://gmplib.org/gmp-man-6.1.2.pdf
you say "For an odd input n, and with n = q2k + 1 where q is odd, this algorithm selects a random base x and tests whether x^q mod n is 1 or -1, or an x^(q2^j) mod n is 1, for 1 <= j <= k. If so then n is probably prime, if not then n is definitely composite." It looks like you're trying to describe the strong probable prime test. However, in a strong probable prime test, the second check should be x^(q2^j) mod n is -1, for 1 <= j < k. If x^q is either 1 or -1 (mod n), and some x^(q2^j) = -1 (mod n) for j = 1...k-1, then n is a strong probable prime base x. See Sam Wagstaff's book, "The Joy of Factoring", or the paper, "The Pseudoprimes to 25*10^9 by Pomerance, Selfridge, and Wagstaff. Yours truly, Robert Baillie _______________________________________________ gmp-bugs mailing list [email protected] https://gmplib.org/mailman/listinfo/gmp-bugs
