Listing 1.

!==================  Seive  ===========
program Sieve_Of_Eratosthenes

!  Find prime numbers using array processing.
!
!  Strike the Twos and strike the Threes
!  The Sieve of Eratosthenes!
!  When the multiplies sublime
!  The numbers that are left, are prime.
!  From:  Drunkard's Walk, by Frederik Pohl

  integer              :: last_number
  integer, dimension(:), allocatable :: numbers
  integer              :: i, number_of_primes, ac

   do
      print *, "What is the last number you "&
   "want to check?"
      read *, last_number
      select case (last_number)
       case (0)
          exit   !   zero ends the testing
       case (:-1, 1, 2)
          print *, "That's not possible, "&
      "try again"
       case (3:100000)
          allocate (numbers(last_number))
          !  Initialize numbers array to 0, 2, 3,
     !  ..., last_number
          !  Zero instead of 1 because 1 is a
     !  special case for primes.
          numbers = (/ 0, (ac, ac = 2, &
      last_number) /)
          do i = 2, last_number
             ! if this number is prime, eliminate
        ! all multiples
             if (numbers(i) /= 0) then
                numbers(2*i : last_number : i) = 0
             endif
          enddo

          !  Count the primes.
          number_of_primes = count (numbers /= 0)

          !  Gather them into the front of the
     !  array.
          numbers(1:number_of_primes) = &
      pack(numbers, numbers /= 0)

          !  Print them
          print *, "There are ",number_of_primes,&
      " prime numbers less than or equal to",&
      last_number
          print "(5i7)",&
       numbers(1:number_of_primes)

          deallocate (numbers)

       case default
          print *, "That's too large a value "&
      "to try"
      end select
   end do
!  Sample output:
! There are  25 prime numbers less than or equal
! to 100
!     2      3      5      7     11
!    13     17     19     23     29
!    31     37     41     43     47
!    53     59     61     67     71
!    73     79     83     89     97
end program Sieve_Of_Eratosthenes