What is the fastest integer factorization algorithm?

Question

I\'ve written a program that attempts to find Amicable Pairs. This requires finding the sums of the proper divisors of numbers.

Here is my current sumOfDiviso

Answer 1

Depends how big your numbers are. If you're searching for amicable pairs you're doing a lot of factorisations, so the key may not be to factor as quickly as possible, but to share as much work as possible between different calls. To speed up trial division you could look at memoization, and/or precalculating primes up to the square root of the biggest number you care about. It's quicker to get the prime factorisation, then calculate the sum of all factors from that, than it is to loop all the way up to sqrt(n) for every number.

If you're looking for really big amicable pairs, say bigger than 2^64, then on a small number of machines you can't do it by factorising every single number no matter how fast your factorisation is. The short-cuts which you're using to find candidates might help you factor them.