let divides divisor number =
    divisor <> number && number % divisor = 0

let rec sieve multiples potential_primes =
    match multiples with
    | first :: rest -> sieve rest (List.filter ((divides first) >> not) potential_primes)
    | [] -> potential_primes

let primesUpTo n =
    let upper_bound = int (sqrt (float n))
    let candidates = 2::[3 .. 2 .. n]
    sieve (List.takeWhile (fun n -> n < upper_bound) candidates) candidates

let calculate_sums (numbers: list<int>) max_sum n =
    Seq.windowed n numbers |> Seq.map Seq.sum |> Seq.takeWhile (fun sum -> sum <= max_sum) |> Set.ofSeq

let solve windows upper_bound =
    let primes = primesUpTo upper_bound
    let max_prime = List.rev primes |> List.head
    let sums = windows |> Seq.map (calculate_sums primes max_prime)
    Set.intersectMany sums |> Set.minElement

solve [7; 17; 41; 541] 10000000