In [53]:

    

// to find the largest prime factor `N` we'll find all primes up
// to sqrt(N), filter out non factors and find the largest

let limit = 600851475143UL
 
let compositesInRange fromNum toNum =
    [|2 .. toNum/fromNum|]
    |> Array.map (fun x -> fromNum * x)

let primesTo n =
    // start off assuming every number from 0 .. n is prime
    let isPrime = Array.init (1+n) (fun _ -> true)
    
    // simple sieve of eratosthenes - update "primeness" of
    // each number in the isPrime array
    for x in 2 .. int(sqrt(double(n))) do 
        if isPrime.[x] then             
            compositesInRange x n
            |> Array.map (fun i -> isPrime.[i] <- false)
            |> ignore
                
    // now return numbers which are "true" in isPrime array
    [2..n]
    |> List.filter (fun x -> isPrime.[x])

primesTo (int(sqrt(double(limit))))
|> List.filter (fun x -> (limit % uint64(x) = 0UL))
|> List.last


    

    
Out[53]:





6857

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