Let's say we want to check whether a number N is a prime number or not. The idea to solve this problem is to iterate through all the numbers starting from 2 to N using a loop and for every number check if it divides N. If you find any number that divides, we conclude that N is not prime (you should break from the loop as you don't need check further for this number). If we did not find any number between 2 and N which divides N then it means that N is prime. But one challenge could arise when you need to know the reason why your loop breaks. Is it because we managed to divide or is it that the loop completed?

I am writing a Python program.    

N = int(input("Enter a number: "))      # prompts user to enter a number

if N > 1:  #if the input number is greater than 1

  for k in range(2,N):   # loop starts which iterates from 2 to input number

      if (N % k) == 0:   # if input number is divisible by value in k

          print(N,"is not a Prime Number")  #displays input no. is not prime

          break   #terminates the loop

  else:   # if input numbers is not divisible by any value in k

      print(N,"is a Prime Number")     # displays that input number is prime

else:   # if the input number is less than or equal to 1

     print(N,"is not greater than 1 and is not a prime number")  

Explanation:

Lets take a value of N to understand the above program.

Suppose the user enters the value 5.

This value is stored in N variable.

If condition checks if the value entered by the user is greater than 1. This condition evaluates to true because 5>1

So the program flow enters the loop. The loop has a range() function is used for the iteration purpose in the loop. It will iterate generating the numbers in the given range which means starting from 2 and ending at N (5 here).

If condition in the loop checks if the input number N which is 5 is completely divisible by any number in the given range i.e. from 2 until it reaches N. Mod operator % is used here because if the N is divisible by any number in the range then its remainder will be 0.  If  this condition evaluates to true this means that N is not a prime number as the prime number is only divisible by 1 and itself. So if this condition is true then the line 5 is not a Prime Number is displayed in the output.

At every iteration the mod of number 5 and each number in the given range is computed and is checked if the result is 0 e.g 5%2 = 1 , 5%3 = 2, 5%4 = 1 and none of the result is equal to 0 so this means 5 is a prime number.

If the condition evaluates to False this means that the number N is prime as it is not divisible by any number in the given range. So the line 5 is a Prime Number is printed on the screen as output.

The last else part is executed when the first outer if condition evaluates to false which means if N is less than 1 and this line 5 is not greater than 1 and is not a prime number is printed as result.

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