These are live demonstrations, not theory.

This demoed randomly generated RSA compliant moduli at certain bit length.

This demonstrates random gen of verified RSA moduli using Miller-Rabin at 4096 and 9192 bit length with primes of 2048 and 4096 bit-length, respectively.

Then, I demonstrate markedly quicker results when only input is N.W no reference to prior params used to random gen RSA compluant Public Mod N.

Welcome to the new cryptography.