I'll give a simple (and-incorrect, as it does not involve prime numbers) example to show what I mean. 500 squared=250,000. Notice that the product has six digits and the square root three. SO...if we are dealing with 1024 bit keys, why not simply have a supercomputer multiply all possible prime 512 bit keys together sequentially?? Probable primacy is relatively simple. The number can't end in an even digit, or five, and it's digits can't add up to a number divisible by three. You could further divide it by small primes like seven, eleven and thirteen. Even if that calculation is wrong, you merely end up with too many numbers. You'd need a lot of storage space, of course, but, then, you just look up the public key in the computer, and you have the prime (private) key-NO??