"Every even integer greater than 2 can be written as the sum of two primes."

Come up with a list of even integers. For these integers, brainstorm 2 prime numbers that add to it. Is there more than one set of primes that add to it? Then, create a simple python program that allows a user to input an even integer and it outputs all the prime pairs that add to it. 

"Every odd integer greater than 5 can be written as the sum of three primes."

Come up with a list of odd integers. For these integers, brainstorm 3 prime numbers that add to it. Is there more than one set of primes that add to it? Then, create a simple python program that allows a user to input an odd integer and it outputs all the prime triplets that add to it.