PROGRAM PRIMES

      !Program:  Lists all prime numbers from 2 up to an arbitrarily
      !chosen number "N".  Method used: Ancient "Sieve of Eratosthenes"
      !and a well known theorem in number theory that every composite
      !(i.e., not prime) number has a prime number factor less than or
      !equal to the square root of the number itself.  The number
      !"NMAX=10000000" below is arbitrary and may need to be reduced in
      !the program because of your specific computer memory and Fortran
      !compiler limitations.  As a note, the code can be easily
      !re-written to save the numbers in an array and to write that
      !array to a hard disk file.
      !
      !Author:  Dr. Jerry R. Ziemke
      
      PARAMETER (NMAX=10000000)
      REAL Q(NMAX)

      WRITE(*,*) 'Enter N (0 < N <= 10,000,000):'
      READ(*,*) X
      N=IFIX(X)
      WRITE(*,*) 'Prime numbers:'
      DO I=1,N
        Q(I)=1.
      ENDDO
      DO I=2,N
        IF (Q(I).EQ.1.) THEN
          J=1
          DO WHILE ((I*J).LE.N)
            Q(I*J)=0.
            j=j+1
          ENDDO
          WRITE(*,*) I
        ENDIF
      ENDDO

      STOP
      END