Fundamental theorem of arithmetic
So, now see what happens when somebody says that he/she knows a positive integer, greater than 1, which can not be written as a product of primes. In that case we ask him/her to mention all the numbers, greater than 1, that can not be written as a product of primes. One of these numbers must be the smallest: let's call it n. Of course, this number n cannot be 1. Further, it cannot be a prime number, because a prime number is a 'product' of a single prime: itself. So it must be a product of numbers. Thus-