Why is a nested loop necessary in this code?

I am having a hard time trying to decipher the usage of multiple loops in this code:

for i=2:100
       for j=2:100
        if(~mod(i,j)) 
            break; % if factor found, not prime
        end 
      end
      if(j > (i/j))
          fprintf('%d is prime\n', i);
      end
end

I don't understand why solely one for loop wouldn't work.

Answer 1

[Mischa Kim]

Ashkhan, the outer (first) loop is used to step through all the numbers that are analyzed. To identify a prime number you need to check if that number is divisible by any other number than itself and 1. To do so you devide each number investigated, let's call it n, by numbers ranging from 2 to n-1. This is done in the inner loop. To make the above code more efficient you would

 for i = 2:100
       for j = 2:(i-1)   % i being the number analyzed
       ...