Trial Division : Improvements and Implementations

Abstract: Trial division is possibly the simplest algorithm for factoring numbers.The problem with Trial division is that it is slow and wastes computationaltime on unnecessary tests of division. How can this simple algorithms besped up while still being serial? How does this algorithm behave whenparallelized? Can a superior serial and a parallel version be combined intoan even more powerful algorithm?To answer these questions the basics of trial divisions where researchedand improvements where suggested. These improvements where later im-plemented and tested by measuring the time it took to factorize a givennumber.A version using a list of primes and multiple threads turned out to bethe fastest for numbers larger than 10 10 , but was beaten when factoringlower numbers by its serial counterpart. A problem was detected thatcaused the parallel versions to have long allocation times which slowedthem down, but this did not hinder them much.