Vivek from UWCSEA showed a very clear understanding of what the flow chart does:

The numbers that lead to an output quickly have very small
prime factors.

The numbers that don't, have very large prime factors.

The numbers that don't, have very large prime factors.

The values of D that divide exactly into M are all prime
numbers.

The value of N is the number of prime factors that the number
has (e.g. 12 can be expressed as the product of 3 prime factors - 2
x 2 x 3 and the output when M = 12 is 3).

The flow chart helps you determine whether M is prime because
if M is prime, the output is always 1: M can only be divided by D
when D is the prime number itself. This makes it go around in a
continuous loop without adding anything to N until M is divided by
D (which equals to M), so N is always 1 when M is prime.