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A classic problem (as I recall from those university days a few years ago) in 'higher level' mathematics was determining if 'very large' numbers were in fact "prime" or not.
Meaning, divisible only by themselves and 1, instead of being broken down to 2*3 = 6, for example, so it is not prime, but 5 is, etc.
Thing is, a lot of the search engine research piled on my desk next to me starts to touch on those classic problems. A friend of mine a few years ago called it, 'building an efficient lever' which I more or less understand the idea :)
So my question to my fellow WebmasterWorld FOO-ites, is this: has there been any research (outside the search engine arena) on 'large prime number factorization' and short cuts to those large calculations?
Also, their has been no proof to say that it is impossible, however the mechanics of the proof of fermats last theorm, may lead to proving that there is no shortcut to factor large prime numbers.
If you could find an efficient way to factor large primes, then all encryption mechanisms would be rendered useless. But before you published your results, you would probably be visted by the NSA with an offer, than you couldn't refuse (litteraly) :)
If they prove the theory it would be a step in the right direction. Until then, mathematicians will be salivating over the possibility that quantum computers [theregister.co.uk] will be developed.
[cse.iitk.ac.in...]
Abstract
We present a deterministic polynomial-time algorithm that determines whether an input number
n is prime or composite.
