Inefficacious Conditions of the Frobenius Primality Test and Grantham's Problem

Quadratic Frobenius pseudoprimes with respect to $x^{2}+5x+5$

“…Thus, the order of t in (Z/m p Z) × is equal to 2. Therefore, by the approach explained in [1], which uses Chinese remainder theorem and elements of order 2 in (Z/r er Z) × where r is a prime factor of m p and e r is the largest integer such that r er | m p , we can easily compute t if the prime factorization of m p is known. To compute all prime factors of m p for a given p in our experiments, we factorize p − 1 by using the trial division algorithm.…”