Project Euler: Problem 46

Euler0046.scala

package euler.zerosum

import euler.zerosum.Prime._
import euler.zerosum.Number._
import euler.zerosum.Divisors._

object Euler0046 {

  private val oddComposites = from(2).filterNot(n => n % 2 == 0 || primes(1, n).contains(n))

  def main(args: Array[String]) {
    println(oddComposites.dropWhile(isGoldbachsConjecture(_)).head)
  }

  private def isGoldbachsConjecture(n: Int): Boolean = {
    val rs = from(1).take(n / 2)
    val twiceSquares = rs.map(r => 2 * r * r).filter(_ < n)

    !twiceSquares.filter(s => isPrime(n - s)).isEmpty
  }

  private def isPrime(n: Int): Boolean = n != 1 && getDivisors(n).filterNot(_ == 1).isEmpty
}