module _58

open common

let primeDiagonals =

    let isPrime n =
        let limit = System.Math.Ceiling(sqrt (float n)) |> int
        let rec check i =
            i > n/limit || (n % i <> 0 && check (i + 1))
        check 2

//    let isPrime = isPrimeW [2I;3I]

    let sideLengthPrimeCount l = 1 + (l - 1) * 2

    let sideLengths =
        (2,2) |> Seq.unfold(
            fun (l, r) ->
                match r with
                | 0 -> Some(l, (l + 2, 3))
                | _ -> Some(l, (l, r - 1))
            )
    sideLengths
    |> Seq.scan (fun (c,_) l -> (c + (l), l + 1)) (3,3) 
    |> Seq.scan (fun (p,_) (d,l) -> 
            let r = isPrime (d)
            match r with
            | true -> (p + 1, l)
            | false -> (p, l)
        ) (0,0) |> Seq.skip 1
    |> Seq.skipWhile (fun (p,l) -> (float p)/(float (sideLengthPrimeCount l)) >= 0.1)
    |> Seq.nth 1