Direct Search Factorization -- from Wolfram MathWorld

Direct search factorization is the simplest (and most simple-minded) prime factorization algorithm. It consists of searching for factors of a number by systematically performing trial divisions, usually using a sequence of increasing numbers. Multiples of small primes are commonly excluded to reduce the number of trial divisors, but just including them is sometimes faster than the time required to exclude them. Direct search factorization is very inefficient, and can be used only with fairly...