It's currently unknown if this program will ever halt. http://en.wikipedia.org/wiki/Goldbach's_conjecture http://en.wikipedia.org/wiki/Halting_problem

goldbach_conjecture.rb

require 'prime'

primes = Prime.lazy
n = 4

loop do
  n += 2
  prime1 = primes.next
  prime2 = n - 1
  prime2 -= 2 until prime2.prime?
  while n != prime1 + prime2
    prime1 = primes.next
    if prime1 + prime2 > n
      prime1 = primes.rewind.next
      prime2 -= 2
      prime2 -= 2 until prime2.prime?
      abort "The Goldbach Conjecture is false!" if prime2 < n/2
    end
  end
  puts "#{n} = #{prime1} + #{prime2}"
end