The theorem says that every positive integer greater than 1 can be written as a product of prime numbers ( or the integer is itself a prime number ) . Thus Theorem 1 of takes the form , `` Every positive integer , except 1 , is a product of one or more primes , '' and Theorem 2 ( their `` Fundamental '' ) asserts uniqueness . By convention , the number 1 is not itself prime , but since it is the product of no numbers , it is often convenient to include it in the theorem by the empty product rule .