object Problem111 {
  def main(args: Array[String]) {
       println(sumOfSFunctions(10))
  }

  def countRepeatedDigits(number: Int, digit: Int): Int = number.toString.count(_ == (digit + 48).toChar)

  def mFunction(primeLength: Int, digit: Int) = getMapOfPrimesWithMaxDigitsNumber(primeLength, digit)._1

  def nFunction(primeLength: Int, digit: Int): Int = getMapOfPrimesWithMaxDigitsNumber(primeLength, digit)._2.size

  def sFunction(primeLength: Int, digit: Int): BigInt = getMapOfPrimesWithMaxDigitsNumber(primeLength, digit)._2.sum

  def getMapOfPrimesWithMaxDigitsNumber(primeLength: Int, digit: Int): (Int, List[Int]) = {
    getListOfPrimesWithLength(primeLength).groupBy(x => countRepeatedDigits(x, digit)).maxBy(_._1)
  }

  def sumOfSFunctions(primeLength: Int): BigInt = (0 to 9).map(x => sFunction(primeLength, x)).sum

  def getListOfPrimesWithLength(length: Int): List[Int] = sieveOfEratosthenes(math.pow(10, length).toInt).filter(x => x >= math.pow(10, length - 1)).toList

  def sieveOfEratosthenes(nTo: Int) = {
    val primes = collection.mutable.BitSet.empty.par ++ (2 to nTo)
    for {
      candidate <- 2 to Math.sqrt(nTo).toInt
      if primes contains candidate
    } primes --= candidate * candidate to nTo by candidate
    primes
  }