That makes me wonder if that means the product of two illegal prime numbers is an illegal number, or if it would be contingent on the computational feasibility of a third party factoring the product.
And if it's generally not feasible to do the factoring, what if you distribute the product of an illegal prime number and a non-illegal prime number? The product itself cannot be illegal, as nobody other than its creator could even detect an illegal prime was there, let alone determine its value. That is, unless you made the non-illegal prime number public... which would result in the illegal prime number being public, so it's illegal! You just made a non-illegal prime number illegal by multiplying it by an illegal prime number! How many primes can we illegalise this way?
And if it's generally not feasible to do the factoring, what if you distribute the product of an illegal prime number and a non-illegal prime number? The product itself cannot be illegal, as nobody other than its creator could even detect an illegal prime was there, let alone determine its value. That is, unless you made the non-illegal prime number public... which would result in the illegal prime number being public, so it's illegal! You just made a non-illegal prime number illegal by multiplying it by an illegal prime number! How many primes can we illegalise this way?