Integer factorisation is the problem of finding a non-trivial factor of a given number. A factor of n is a number that divides n, and non-trivial means neither 1 nor n.

For example, a non-trivial factor of 11111 is 41, whereas trivial factors are 1, -1, 11111 and -11111.

If n is prime then it has no non-trivial factors. There are techniques for identifying non-primes that do not explicitly exhibit a factor, so the question of finding a factor is interesting.

The RSA public key cryptosystem uses numbers that are hard to factor, and if a way could be found to factor numbers quickly then that would effectively break it.

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