Solution

    PROGRAM Prime_Numbers
     IMPLICIT NONE
     INTEGER, ALLOCATABLE, DIMENSION(:) :: Prime
     INTEGER :: N_elts, i

      PRINT*, "Type in the size of the array"
      READ*, N_elts

      ALLOCATE(Prime(N_elts),STAT=i)

      IF (i .NE. 0) THEN
       PRINT*, "Allocation request failed"
      ELSE

       Prime = (/ (i, i = 1,N_elts) /)
       i = 2

       outa: DO
        WHERE (MOD(Prime(i+1:),i) .EQ. 0) Prime(i+1:) = 0
        DO
         i = i + 1
         IF (i .EQ. N_elts) EXIT outa
         IF (Prime(i) .NE. 0) EXIT
        END DO
       END DO outa

       PRINT*, PACK(Prime,Prime/=0)

      !DO i = 1, N_elts
      ! IF (Prime(i) .NE. 0) PRINT*, Prime(i)
      !END DO

       DEALLOCATE(Prime)

      END IF

    END PROGRAM Prime_Numbers