Strong prime

Even using algorithms more advanced than trial division, these numbers would be difficult to factor by hand.

For a modern computer algebra system, these numbers can be factored almost instantaneously.

Some people suggest that in the key generation process in RSA cryptosystems, the modulus n should be chosen as the product of two strong primes.

For this reason, strong primes are required by the ANSI X9.31 standard for use in generating RSA keys for digital signatures.

[1] It is shown by Stephen Pohlig and Martin Hellman in 1978 that if all the factors of p − 1 are less than logc p, then the problem of solving discrete logarithm modulo p is in P. Therefore, for cryptosystems based on discrete logarithm, such as DSA, it is required that p − 1 have at least one large prime factor.