QUOTE(azninvasion @ Dec 5 2005, 06:58 PM)

found an article that describes a new method of finding primes.
might be an interesting read for some of you math majors. maybe you could improve the algorith so we can crack taht private key

Uh, no.
Finding primes has never been the problem. It's very easy to find a prime. It was unknown until recently whether proving primality is in P, the set of all problems which can be solved in polynomial time. But that didn't really matter... proof of primality wasn't a problem. The general algorithm for finding a large prime is this: pick a large random number. Run a primality test that will certainly succeed if the number is prime, but may either fail or succeed if the number is composite. If the test fails, throw out the number and start over. If the test succeeds, run another primality test. Keep running primality tests... if the number passes several hundred of them, the odds of it being composite are negligible and the number can be safely assumed prime.
This algorithm is
not in P, because it would theoretically take an infinite amount of time to
prove primality using it... but again, for cryptographic purposes, 99.999999999999999999% certainty is plenty good enough. Agrawal, Kayal, and Saxena, on the other hand, found an algorithm for testing primality that
is in P. It's a tremendous breakthrough, of which they should be very proud. But from a practical standpoint it matters little, and it doesn't make it even a tiny bit easier to factor large composite numbers, which is what would be involved in breaking RSA.
And as I said in a different post, if and when somebody finally
does solve the problem of factoring large composite numbers, we'll wish they hadn't. Hooray, you can play with your $400 computer, yippee! Also, Internet security will go bye-bye, secret military communications will be open to our enemies, digital signatures will be trivially forged, and an awful lot of things we take for granted will be no more. Worth the tradeoff?