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-- 10001st prime
-- Problem 7
-- By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13,
-- we can see that the 6th prime is 13.
-- What is the 10 001st prime number?
main = do
print ([x | x <- [1..150000], is_prime x] !! 10000) -- ugly and inefficient
print (eratos_sieve [2..150000] !! 10000) -- still ugly and inefficient due
-- to the arbirary range
print (nth_prime 10000) -- better but meh since we're testing every divisor each time,
-- should keep a list of them
-- print (primes !! 10000) -- from the haskell website, stream of numbers (takes forever)
nth_prime :: Int -> Int
nth_prime n = nth_check n 0
where nth_check n x
| is_prime x = if n == 0 then x else nth_check (n - 1) (x + 1)
| otherwise = nth_check n (x + 1)
eratos_sieve :: [Int] -> [Int]
eratos_sieve [] = []
eratos_sieve (x:xs)
| x * x > last xs = x:xs
| otherwise = x:eratos_sieve [n | n <- xs, n `mod` x /= 0]
is_prime :: Int -> Bool
is_prime 0 = False
is_prime 1 = False
is_prime 2 = True
is_prime 3 = True
is_prime x
| x `mod` 2 == 0 || x `mod` 3 == 0 = False
| otherwise = trial_div 5
where trial_div d
| d * d > x = True
| x `mod` d == 0 || x `mod` (d + 2) == 0 = False
| otherwise = trial_div (d + 6)
primes :: [Int]
primes = filterPrimes [2..]
where filterPrimes (p:xs) = p : filterPrimes [x | x <- xs, x `mod` p /= 0]
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