Posts Tagged ‘conjecture’

Programming Praxis – Goldbach’s Conjecture

March 2, 2010

In today’s Programming Praxis problem we have to test Golbach’s conjecture that every even number greater than 2 can be written as the sum of two primes. Let’s get started.

A quick import (note that both the Numbers and primes packages define this module, but only Numbers contains the isPrime function we’re using):

import Data.Numbers.Primes

The function for testing Goldbach’s conjecture is pretty simple: just look at all the primes p less than n and check if n – p is prime.

goldbach :: Integer -> (Integer, Integer)
goldbach n = head [(p, n - p) | p <- takeWhile (< n) primes, isPrime (n - p)]

A quick test reveals everything’s working correctly.

main :: IO ()
main = do print $ goldbach 28
          print $ goldbach 986332

The Scheme solution implements two versions, citing speed as a reason. I also implemented his second version, but the speed was nearly identical to the algorithm above (about 11 seconds to determine that 532 is indeed the highest first prime in the first one million numbers), and given the choice I’d much rather have one line than thirteen.