In reply to:


Just saying that a factor of P is P and 1 isn't quite what they had in mind. Finding the values of the two prime numbers that make up P is much harder as you know



Well unless the two (prime) numbers that were multiplied to make P were 1 and P, then the resulting number from this multiplication can *never* be prime.

However what you are saying is that the difficulty of finding quickly large prime (or near-prime) numbers is a major cornerstone of modern cryptographic systems.

So, once a quick way is found to find (also called factoring) such large numbers then this cornerstone is severely weakened.

Its this aspect that Gates (and others) have previously commented on.