Interesting take on encryption.  Since how to factor large prime numbers extremely rapidly has been common knowledge ever since prime numbers were first defined, well over 2000 years ago, you must think that no encryption does anything useful at all (a prime number is a number greater than 1 whose only factor greater than 1 is itself).  But in fact no encryption ever used has depended on inability to factor large prime numbers.

Some modern encryption techniques do depend on inability to factor a large number which is not a square and has exactly two distinct factors other than 1, which by definition is not a prime number; if we find a quick way of doing that several asymmetric encryption algorithms will become effectively broken since it will be possible to compute the private key given the public key and vice versa.  Of course if neither key is disclosed that will do no harm but it does effectively destroy some very popular asymmetric key methods in their most common use.   But no symmetric encryption algorithm will be impacted at all.