Tag Archives: sieve

Project Euler Problem 7 in F#

In the continuing series of solving Project Euler problems with F#, here is 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?

  1. Generate primes using Sieve of Eratosthenes.
  2. Skip the first ten thousand primes and take the next one.

type public PrimesGenerator() =

member this.PrimesInfinite () =

let rec nextPrime n p primes =

if primes |> Map.containsKey n then

nextPrime (n + p) p primes

else

primes.Add(n, p)

let rec prime n primes =

seq {

if primes |> Map.containsKey n then

let p = primes.Item n

yield! prime (n + 1) (nextPrime (n + p) p (primes.Remove n))

else

yield n

yield! prime (n + 1) (primes.Add(n * n, n))

}

prime 2 Map.empty

member this.Problem7() =

let primes = new PrimesGenerator()

primes.PrimesInfinite() |> Seq.skip 10000 |> Seq.take 1 |> Seq.head

Download the source code with unit tests.