Hi Will, I had previously tested the Melissa O'Neil prime function (using the primes 0.1.1 package) and found it to be fast (for a functional approach), but with high memory use. To fully test a prime function, I think you should: 1. Test for more than the first 10^6 primes. Generating all primes to 10^6 is quite easy for modern computers. Most prime generating functions will run in less than 1 sec and look fast. Try generating all primes to 10^7 and 10^8 then you will see how 'fast' these lazy functional methods really are. 2. Measure memory use. As you move above 10^6 and test primes up to 10^7, 10^8, and 10^9, memory use becomes very important. A prime function with excessive memory use will soon consume all of the system's memory. Here's another primes function which performs quite well. primes :: [Int] primes = 2 : filter (isPrime primes) [3,5..] where isPrime (p:ps) n | mod n p == 0 = False | p*p > n = True | otherwise = isPrime ps n isPrime [] _ = False -- never used, but avoids compiler warning Here's some results from my PC, for generating primes to 10^8. 10**6 10**7 10**8 secs MiB secs MiB secs MiB ------------------------------- 1 0.01 0 0.1 2 2 14 2 0.56 7 11.1 43 270 306 3 0.61 7 11.8 44 260 342 4 0.43 36 5.4 345 900 not finished 1 using a Haskell ST Array 2 your primes function 3 my primes function, listed above 4 Melissa O'Neil method from primes 0.1.1 package To summarise the results from the tests I've run: - if you want fast functional primes, forget it, its not possible. - if you just want fast primes, then use C, or a Haskell array. - if performance does not matter and slow primes are acceptable, then use the purely functional approach. Regards, Steve