P41.scala

package arithmetic

// P41 (**) A list of Goldbach compositions.
//     Given a range of integers by its lower and upper limit, print a list of
//     all even numbers and their Goldbach composition.
//
//     scala> printGoldbachList(9 to 20)
//     10 = 3 + 7
//     12 = 5 + 7
//     14 = 3 + 11
//     16 = 3 + 13
//     18 = 5 + 13
//     20 = 3 + 17
//
//     In most cases, if an even number is written as the sum of two prime
//     numbers, one of them is very small.  Very rarely, the primes are both
//     bigger than, say, 50.  Try to find out how many such cases there are in
//     the range 2..3000.
//
//     Example (minimum value of 50 for the primes):
//     scala> printGoldbachListLimited(1 to 2000, 50)
//     992 = 73 + 919
//     1382 = 61 + 1321
//     1856 = 67 + 1789
//     1928 = 61 + 1867

object P41:
  // This implementation isn't very efficient because the primes are generated
  // eagerly. It works much better in Haskell where list is lazy.
  def goldbachList(a: Int, b: Int): Map[Int, (Int, Int)] =
    (a to b)
      .collect:
        case x if x % 2 == 0 => (x, P40.goldbach(x))
      .toMap