Is there a simple algorithm that can determine if X is prime?

Question

I have been trying to work my way through Project Euler, and have noticed a handful of problems ask for you to determine a prime number as part of it.

1. I kno

Answer 1

I am working thru the Project Euler problems as well and in fact just finished #3 (by id) which is the search for the highest prime factor of a composite number (the number in the ? is 600851475143).

I looked at all of the info on primes (the sieve techniques already mentioned here), and on integer factorization on wikipedia and came up with a brute force trial division algorithm that I decided would do.

So as I am doing the euler problems to learn ruby I was looking into coding my algorithm and stumbled across the mathn library which has a Prime class and an Integer class with a prime_division method. how cool is that. i was able to get the correct answer to the problem with this ruby snippet:

require "mathn.rb"
puts 600851475143.prime_division.last.first

this snippet outputs the correct answer to the console. of course i ended up doing a ton of reading and learning before i stumbled upon this little beauty, i just thought i would share it with everyone...