Fortran code to compute prime numbers.

prime_numbers.f95

!****************************************************
! 素数一覧
! : 入力値以下の素数を全て出力する
!
! date          name            version
! 2017.04.20    mk-mode.com     1.00 新規作成
!
! Copyright(C) 2017 mk-mode.com All Rights Reserved.
!****************************************************
!
program prime_numbers
  implicit none
  integer i, j, n
  logical is_prime
  print *, "自然数を入力してください N:"
  read *, n
  do i = 2, n
    is_prime = .true.
    do j = 2, int(sqrt(dble(i)))
      if (mod(i,j) == 0) then
        is_prime = .false.     ! 割り切れるので素数ではない
        exit
      end if
    end do
    if (is_prime) print *, i   ! もし素数ならば出力
  end do
end program

If you ask me what you should do,
I'm very sorry, but I can only say that you should refer to this 'prime_numbers.f95' code.

It could be a little better/more efficient/faster. The program doesn't have to check all numbers from 2 to n , only the odd ones.

                ...
                ! *** New lines block. ***
		If (n .GE. 2) Then 
			Write(*,*) 2                          ! Two is a prime.
		Else
			Return
		End If
                ! *** End of new lines block. ***

		Do i = 3, n, 2                                !<--- Change here.
			is_prime = .TRUE.
			Do j = 3, Int(Sqrt(Dble(i))), 2       !<--- Change here.
                        ...