Simple prime number utilities

Primes.scala

// Simple prime number utilities
object Primes {
  private val buffer = scala.collection.mutable.ArrayBuffer(2)

  // Given the primes ps, check if x is a prime by trial division
  private def check(ps: Traversable[Int])(x: Int) = {
    val limit = math.sqrt(x).ceil.toInt
    ps takeWhile { _ <= limit } forall { x % _ != 0 }
  }

  // Get the i'th prime; store primes found so far in the buffer
  private def get(i: Int) = {
    while (buffer.length <= i) buffer += (Stream.from(buffer.last + 1) find check(buffer) get)
    buffer(i)
  }

  val stream = { def s(i: Int): Stream[Int] = get(i) #:: s(i + 1); s(0) }

  val isPrime: PartialFunction[Int, Boolean] = {
    case 2 => true
    case x if x > 2 => check(stream)(x)
  }

  def factorize(x: Int): Stream[Int] = {
    val factor = {
      val limit = math.sqrt(x).ceil.toInt
      stream takeWhile { _ <= limit } find { x % _ == 0 } getOrElse x
    }

    val rest = x / factor

    factor #:: (if (rest > 1) factorize(rest) else Stream.empty)
  }
}

Primes2.scala

// A shorter version that doesn't contain a mutable buffer
object Primes2 {
  val stream = 2 #:: 3 #:: 5 #:: primesFrom(7)

  def primesFrom(x: Int): Stream[Int] = if (isPrime(x)) x #:: primesFrom(x + 1) else primesFrom(x + 1)

  val isPrime: PartialFunction[Int, Boolean] = {
    case 2 => true
    case x if x > 2 => val limit = math.sqrt(x).ceil.toInt; stream takeWhile { _ <= limit } forall { x % _ != 0 }
  }

  def factorize(x: Int): Stream[Int] = {
    val f = { val limit = math.sqrt(x).ceil.toInt; stream takeWhile { _ <= limit } find { x % _ == 0 } getOrElse x }
    f #:: { val r = x / f; if (r == 1) Stream.empty else factorize(r) }
  }

  def almostPrimes(n: Int): Stream[Int] = Stream.from(4) filter { factorize(_).length == n }
}