Currently the implementation of mpz_nextprime is:

void mpz_nextprime(mpz_ptr x, mpz_srcptr y)
{
  gmp_randstate_t rnd;

  gmp_randinit_default(rnd);
  mpz_next_prime_candidate(x, y, rnd);
  gmp_randclear(rnd);
}

This certainly looks like it will return many composites, which is
definitely not what we want.

Bill.

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