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Project Euler Problem 27

November 21, 2011

Project Euler Problem 27 solution reuses the function set for working with primes from Project Euler Problem 10 solution.
Other, than that, the solution is straightforward: for each combination of a and b try building a sequence of primes for sequence of numbers accumulating data about max sequence length and correspondent product of coefficients:

open System

let rec primes = 
    Seq.cache <| seq { yield 2; yield! Seq.unfold nextPrime 3 }
and nextPrime n =
    if isPrime n then Some(n, n + 2) else nextPrime(n + 2)
and isPrime n =
    if n >= 2 then
        primes 
        |> Seq.tryFind (fun x -> n % x = 0 || x * x > n)
        |> fun x -> x.Value * x.Value > n
    else false

let inline form a b n = n * n + a * n + b

let mutable max = 0
let mutable result = 0
let problem027 () =
    for a = -999 to 999 do
        for b = -999 to 999 do
            Seq.unfold
                (fun n -> if isPrime (form a b n) then Some(n, n+1)
                 else None) 0
            |> Seq.length
            |> fun x -> if x > max then max <- x; result <- a * b
    result
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