Prime numbers

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Revision as of 10:13, 6 February 2007 by MathematicalOrchid (talk | contribs) (Corrected numerous outright bugs in the code (!))

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The following is an elegant (and highly inefficient) way to generate a list of all the prime numbers in the universe:

  primes = sieve [2..] where
    sieve (p:xs) = p : sieve (filter (\x -> x `mod` p > 0) xs)

With this definition made, a few other useful (??) functions can be added:

  is_prime n = n `elem` (takeWhile (n >=) primes)

  factors n = filter (\p -> n `mod` p == 0) primes

  factorise 1 = []
  factorise n =
    let f = head $ factors n
    in  f : factorise (n `div` f)

(Note the use of takeWhile to prevent the infinite list of primes requiring an infinite amount of CPU time and RAM to process!)