Project Euler – Problem 41 Solution

Problem

We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.

What is the largest n-digit pandigital prime that exists?

Solution

let rec distribute e = function
    | [] -> [[e]]
    | x::xs' as xs -> (e::xs)::[for xs in distribute e xs' -> x::xs]
let rec permute = function
    | [] -> [[]]
    | e::xs -> List.collect (distribute e) (permute xs)

let hasDivisor(n) =
    let upperBound = int64(sqrt(double(n)))
    [2L..upperBound] |> Seq.exists (fun x -> n % x = 0L)
let isPrime(n) = if n = 1L then false else not(hasDivisor(n))

let answer =
    [1..9]
    |> List.collect (fun m -> [1..m] |> permute)
    |> List.map (fun l -> l |> List.map string |> List.reduce (fun acc item -> acc + item))
    |> List.map int64
    |> List.filter isPrime
    |> List.max

This is a simple brute force solution which for n = 1..9 generates all permutations of 1..n, for each permutation the digits are merged into a number, e.g. [1; 4; 8; 7] –> 1487, and the max prime number is returned.

  • Vinícius Manjabosco

    Use this method to check for primes, is 10 times faster.

    let isPrime n =
    if n float |> sqrt |> int
    let rec check i = i > maximumDivisor || (n % i 0 && check (i + 1))
    check 2

  • Yan Cui

    Check out some of the later answers, I started to use a siev which was able to generate 1 million primes in well under a second on my machine. (didn’t know what a siev is when I put this answer together unfortunately…)