Consolidated function is much slower

Question

I wrote an isPrime function. It checks whether the given number is prime or not. The last "simple" list is listed separately.

prime :: [Integer]
prime = 2 : filter isPrime [3..]
isPrime :: Integer -> Bool
isPrime n | n < 2 = False
isPrime n = all (\p -> n `mod` p /= 0) . takeWhile ((<=n) . (^2)) $ prime

I thought it was always better to combine two functions into one, if possible. I consolidated isPrime and ran isPrime2 in one function. But the performance of isPrime2 is very poor.

isPrime2 :: Integer -> Bool
isPrime2 n | n < 2 = False
isPrime2 n = all (\p -> n `mod` p /= 0) . takeWhile ((<=n) . (^2)) $ 2 : filter isPrime2 [3..]

isPrime 40000000000000000001

=> 0.5 seconds

isPrime2 40000000000000000001

=> 19.8 seconds

My machine is Ubuntu 17.10 x86-64. I am using ghc 8.2.1. Does anyone know why?

Answer 1

The first fragment will save only one list primein memory.

prime n^2 , isPrime2. . isPrime2 , .

:

isPrime2 :: Integer -> Bool
isPrime2 m = isPrime m
   where
   prime :: [Integer]
   prime = 2 : filter isPrime [3..]
   isPrime :: Integer -> Bool
   isPrime n | n < 2 = False
   isPrime n = all (\p -> n `mod` p /= 0) . takeWhile ((<=n) . (^2)) $ prime

prime isPrime2, , isPrime prime s.