## Faster Rabin Miller Test in Haskell

I wrote this program to learn IO in Haskell and its bit faster then mine previous implementation [Technically that implementation is not fully owned by me. A lot of code was borrowed from Haskell site]. The Rabin Miller test can be written as pure function i but i rather prefer impurity😛. You can use filterM isProbable [k1..k2] to get primes in the range [k1,k2]. Remember filterM is not lazy. You can also have a look here.

import Random helpMod::Integer->Integer->Integer->Integer helpMod a d n= fun a d where fun a 1 = mod a n fun a 2 = mod (a^2) n fun a d = let p=fun (mod (a^2) n) (div d 2) q=if odd d then mod (a*p) n else p in mod q n isProbable::Integer->IO Bool isProbable n |n<=1 = return False |n==2 = return True |even n = return False |otherwise = do let d=until (\x->mod x 2/=0) (`div` 2) (n-1) --(n-1=2^s*d) s=until (\x->d*2^x==pred n) (+1) 0 --counts the power rabinMiller 0 n s d rabinMiller::Integer->Integer->Integer->Integer->IO Bool rabinMiller cnt n s d | cnt>=5= return True | otherwise = do a<-getStdRandom $ randomR (2,n-2) let x=helpMod a d n --let l="s= "++ show s ++" d= "++ show d ++" a= "++ show a ++" x= "++ show x --putStrLn l case x==1 of True -> rabinMiller (cnt+1) n s d _ -> if any ( ==pred n) $ take (fromIntegral s) $ iterate (\e->mod (e^2) n) x then rabinMiller (cnt+1) n s d else return False main = do l<-getLine let n=read l k<-isProbable n print k