Project Euler - Problem 03 - What is the largest prime factor of the number 600851475143 ?

Problem03.scala

// http://projecteuler.net/problem=3

//The prime factors of 13195 are 5, 7, 13 and 29.

//What is the largest prime factor of the number 600851475143 ?

object Problem03 {
  def main(args: Array[String]) {
    //val number = 13195
    val number = 600851475143L
    println(maxPrimeFactor(number))
  }

  def maxPrimeFactor(value: Long) = 
    value match {
      case _ if (value < 2) => throw new IllegalArgumentException
      case _ => factors(value).sortWith(_ > _).filter(isPrime).max
    }

  def isPrime(value: Long) : Boolean =
    if (value == 2) true else primeTest(value, math.sqrt(value).toLong)

  def primeTest(value: Long, attempt: Long): Boolean = 
    attempt match {
      case 1 => true
      case _ if (value % attempt == 0) => false
      case _ => primeTest(value, attempt - 1)
    }

  def factors(value: Long): List[Long] = {
    val factorLimit = math.max(math.sqrt(value).toInt, 2)
    val smallFactors = (2 to factorLimit).toList.filter(value % _ == 0).map(_.toLong)
    val largeFactors = smallFactors.map(value / _)
    smallFactors ::: largeFactors
  }
}