G'day all. This one is pretty elegant. A Pritchard sieve is actually an Eratosthenes sieve with the loops reversed. Unfortunately, it's a bit slower. Maybe someone else can speed it up a bit. mergeRemove :: [Integer] -> [Integer] -> [Integer] mergeRemove [] ys = [] mergeRemove xs [] = xs mergeRemove xs'@(x:xs) ys'@(y:ys) = case compare x y of LT -> x : mergeRemove xs ys' EQ -> mergeRemove xs ys GT -> mergeRemove xs' ys pritchardSieve :: Integer -> [Integer] pritchardSieve n | n <= 16 = takeWhile (<=n) [2,3,5,7,11,13] | otherwise = removeComposites [2..n] (sieve [2..n`div`2]) where removeComposites ps [] = ps removeComposites ps (cs@(c:_):css) = removeComposites' ps where removeComposites' [] = [] removeComposites' (p:ps) | p < c = p : removeComposites' ps | otherwise = removeComposites (mergeRemove ps cs) css pjs = pritchardSieve sn sn = isqrt n sieve [] = [] sieve (f:fs) = composites pjs : sieve fs where composites [] = [] composites (p:ps) | pf > n || f `mod` p == 0 = [pf] | otherwise = pf : composites ps where pf = p*f Cheers, Andrew Bromage