It shouldn't be nor standardized nor hard-coded because someone with the funds (e.g. NSA) would need to break the encryption using this 'standardized' number on

It shouldn't be nor standardized nor hard-coded because someone with the funds (e.g. NSA) would need to break the encryption using this 'standardized' number only once. If everyone used a random very large prime (spec suggests so) then NSA would have to break with every prime number possible which currently is not possible