# Prime numbers

From HaskellWiki

Revision as of 16:33, 5 February 2007 by MathematicalOrchid (talk | contribs) (I hope this amuses somebody...)

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

(Note the repeated use of `takeWhile`

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