Is There a Formula for Prime Number Factorization?

[MathJakob]

I've been looking into prime number factorisation and was wondering does a formula actually exist or is it thought to be impossible to factor primes using a formula and they need to be factored using brute force?
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RSA Algorithm

 

[SteamKing]

Maybe the OP is talking about taking an arbitrarily large number N and finding all of its prime factors. I think the terminology 'prime number factorisation' is somewhat confusing.

For instance, 12 = 2*2*3

 

[MathJakob]

Yes that is what I'm talking about, sorry for the confusion

"The most difficult integers to factor in practice using existing algorithms are those that are products of two large primes of similar size, and for this reason these are the integers used in cryptographic applications."

http://en.wikipedia.org/wiki/Integer_factorization

 

[micromass]

Yes, algorithms for factoring numbers into primes exist. But they're not very fast. Currently, it is much easier (=faster) to check if something is prime or not than to actually find a primal decomposition.