I'm trying to write a prime number generator and utilizing MillerRabin formula check whether or not the number is prime before it returns the number back into me. Here is my code below:

```
primegen :: Int -> IO Integer
primegen bits =
fix $ \again -> do
x <- fmap (.|. 1) $ randomRIO (2^(bits - 1), 2^bits - 1)
if primecheck x then return x else again
primesTo100 = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]
powerMod :: (Integral a, Integral b) => a -> a -> b -> a
powerMod m _ 0 = 1
powerMod m x n | n > 0 = join (flip f (n - 1)) x `rem` m where
f _ 0 y = y
f a d y = g a d where
g b i | even i = g (b*b `rem` m) (i `quot` 2)
| otherwise = f b (i-1) (b*y `rem` m)
witns :: (Num a, Ord a, Random a) => Int -> a -> IO [a]
witns x y = do
g <- newStdGen
let r = [9080191, 4759123141, 2152302898747, 3474749600383, 341550071728321]
fs = [[31,73],[2,7,61],[2,3,5,7,11],[2,3,5,7,11,13],[2,3,5,7,11,13,17]]
if y >= 341550071728321
then return $ take x $ randomRs (2,y-1) g
else return $ snd.head.dropWhile ((<= y).fst) $ zip r fs
primecheck :: Integer -> IO Bool
primecheck n | n `elem` primesTo100 = return True
| otherwise = do
let pn = pred n
e = uncurry (++) . second(take 1) . span even . iterate (`div` 2) $ pn
try = return . all (\a -> let c = map (powerMod n a) e in
pn `elem` c || last c == 1)
witns 100 n >>= try
```

I don't understand whats going on with the IO Bool. And I'm getting the following error...

```
Couldn't match expected type `Bool' with actual type `IO Bool'
In the return type of a call of `primecheck'
In the expression: primecheck x
In a stmt of a 'do' block: if primecheck x then return x else again
```

If I change the IO Bool to just a normal Bool, they will give me this:

```
Couldn't match expected type `Bool' with actual type `m0 a0'
```

Thanks for the help guys! I appreciate it.

`MonadRandom`

instead of`IO`

.