documentation bug

paul zimmermann Paul.Zimmermann at
Tue Jun 6 10:38:05 UTC 2017

reported to me by Bob Baillie (through Sam Wagstaff):

>Anyway, on page 111 of the manual (section 15.7.1, Prime Testing)
>where it describes the algorithm for “mpz_probab_prime_p”, it says,
>"For an odd input n, and with n = q*2^k + 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 they are 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.
>The manual is wrong, right? Do you know if the code is correctly written?

Paul Zimmermann

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