e58.scala

def isPrime(n: Int): Boolean = (2 to math.sqrt(n).toInt).forall(n % _ != 0)

def nextCorner(st: Stream[Int]) = st.zip(st.tail).map( n => n._2 + (n._2 - n._1 + 8) )
val upperRight: Stream[Int] = 1 #:: 3 #:: nextCorner(upperRight)
val upperLeft:  Stream[Int] = 1 #:: 5 #:: nextCorner(upperLeft)
val lowerLeft:  Stream[Int] = 1 #:: 7 #:: nextCorner(lowerLeft)
val lowerRight: Stream[Int] = 1 #:: 9 #:: nextCorner(lowerRight)
val zipped: Stream[List[Int]] = Stream.from(1).map( idx =>
  List(upperRight(idx), upperLeft(idx), lowerLeft(idx), lowerRight(idx)) )

@annotation.tailrec
def calc58(numSize: Int, primeSize: Int, zipped: Stream[List[Int]]): Int = {
  val (ns, ps) = (numSize + 4, primeSize + zipped.head.count(isPrime))
  if ( (ps.toDouble / ns) < 0.1 ) return math.sqrt(zipped.head(3)).toInt
  calc58(ns, ps, zipped.tail)
}

println(calc58(1, 0, zipped)) // => 226241