How find a twin prime number from a range determin

Question

I want to make a program that finds twin prime numbers in a certain range, from n to m. Here it is what I have so far:

             program twin
                 implicit none
                 integer  i, count1, n, m, count2, j, k, pri1, pri2
                 count1 = 0
                 count2 = 0
                 read(5,*)n
                 read(5,*)m
                 do i = 1,m
                    do j = n,m
                    if (mod(j,i) ==0) then
                         count1 = count1 +1
                    else
                         count1 = count1
                         if(count1 ==0) then
                            pri1 = j
                            do k=j,m
                            if (mod(k,i)==0) then
                               count2 = count2 +1
                            else
                               count2 = count2
                               if(count2 ==0) then
                                 pri2 = k
                                 if (pri2-pri1 == 2) then
                                     write(*,*)j,k
                                 end if
                               end if
                            end if
                            end do
                         end if
                     end if
                     end do
                 end do
             end program twin

I tried n = 4 and m = 8, expecting to get 5 and 7, the n = 70 and m = 74, wanting 71 and 73, but in both cases it doesn't return nothing, why is that?

Answer 1

I decided to rewrite your code using a function call. I always try to use functions and subroutines as much as possible when there is repeated code. In this case, the check to see if the integer was a prime is an obvious choice.

I also reduced the loops to only look at numbers between m and n (I swapped them round because I'm funny like that) and once a prime has been found between that number and n.

program twin

  implicit none

  integer :: m, n, i, j, prime1, prime2

  read(*,*)m
  read(*,*)n

  do i = m, n 
     if (is_prime(i)) then
        prime1 = i
        do j = i, n
           if (is_prime(j)) then
              prime2 = j
              if (prime2-prime1 == 2) then
                 write(*,*)i, j
              end if
           end if
        end do
     end if
  end do

contains

  function is_prime(num) result(output)
    implicit none
    integer, intent(in) :: num
    logical :: output
    integer :: i
    integer :: count

    count = 0

    if (num > 1) then
       do i = 2, num-1
          if (mod(num, i) == 0) then
             count = count + 1
          end if
       end do
    else
       count = count + 1
    end if

    if (count .eq. 0) then
       output = .true.
    else
       output = .false.
    end if

  end function is_prime

end program twin

There are several issues with the original code, the count variables are not reinitialized for each loop. Once this is fixed, there are problems when checking for a prime number. I have found it impossible, thus far, to maintain the original structure and return only genuine prime numbers. Problems arise from the mod(j, i) check. When i > j, the code returns j as a prime. When all i are not common factors of j, it returns a prime.

program twin
  implicit none
  integer  i, count1, n, m, count2, j, k, pri1, pri2
  count1 = 0
  count2 = 0
  pri1 = 0
  pri2 = 0
  read(5,*)n
  read(5,*)m
  do i = n, m
     count1 = 0
     do j = 2, i - 1
        if (mod(i, j) == 0) then
           count1 = count1 + 1
        else
           count1 = count1
        end if
     end do
     if (count1 == 0) then
        pri1 = i
        do k = i, m
           count2 = 0
           do j = 2, k - 1
              if (mod(k, j) == 0) then
                 count2 = count2 + 1
              else
                 count2 = count2
              end if
           end do
           if (count2 == 0) then
              pri2 = k
              if (pri2 - pri1 == 2) then
                 write(*,*) pri1, pri2
              end if
           end if
        end do
     end if
  end do

end program twin