In number theory, integer factorization is the process of breaking down a composite number into smaller non-trivial divisors, which when multiplied together equal the original integer.
When the numbers are very large, no efficient integer factorization algorithm is publicly known; a recent effort which factored a 200-digit number (RSA-200) took eighteen months and used over half a century of computer time. The presumed difficulty of this problem is at the heart of certain algorithms in cryptography such as RSA. Many areas of mathematics and computer science have been brought to bear on the problem, including elliptic curves, algebraic number theory, and quantum computing.
Not all numbers of a given length are equally hard to factor. The hardest instances of these problems (for currently known techniques) are semiprimes, i.e. the product of two distinct prime numbers. When they are both large, randomly chosen, and about the same size (but not too close), even the fastest prime factorization algorithms on the fastest computers can take enough time to make the search impractical.
Reference:
http://en.wikipedia.org/wiki/Integer_factorization
