1:  #The prime factors of 13195 are 5, 7, 13 and 29.
   2:  #What is the largest prime factor of the number 600851475143 ?
   3:   
   4:  function getPrimes { #sieve of eratosthenes, http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
   5:      param ($target)
   6:      $nums = @(2..$target)
   7:      $curPrime = 2
   8:      for ($i = 0; [math]::pow($curPrime, 2) -le $target; $i ++) {
   9:          if ($nums[$i] -ne -1) {
  10:              $curPrime = $nums[$i]
  11:              write-debug "Prime`t`t$curPrime"
  12:              for ($x = [math]::pow($curPrime, 2); $x -le $target; $x = $x + $curPrime) {
  13:                  $curNum = $nums[$x - 2];
  14:                  if($curNum -ne -1) {
  15:                      write-debug ("Composite`t{0}" -f $nums[$x - 2])
  16:                      $nums[$x - 2] = -1
  17:                  }
  18:              }
  19:          }
  20:      }
  21:      return ($nums | where { $_ -ne -1 })
  22:  }
  23:   
  24:  function factorPrime {
  25:      param($target,$primes)
  26:      foreach($prime in $primes) {
  27:          do {
  28:              $r = $target / $prime
  29:              $c = ($r -eq [long]$r)
  30:              if ($c) {
  31:                  $prime
  32:                  $target = $r
  33:              }
  34:          }
  35:          while ($c)
  36:          if ($prime -ge $target) {
  37:              return
  38:          }
  39:      }
  40:      throw "not enough primes"
  41:  }
  42:   
  43:  $primes = getPrimes 10000
  44:  factorPrime 600851475143 $primes