After many hours I figure out 1 part of what I have to do with this.

I have to enter a positive integer: 44

then this has to output

44 = 3 + 41

44 = 2 + 5 + 37

First off I have to find out if a positive integer is true for the goldbach conjecture.

Every even number > 2 is a sum of two primes

Every integer > 5 is a sum of three primes

For example

44 = 3 + 41

44 = 2 + 5 + 37

346 = 29 + 317

346 = 2 + 7 + 337

Okay now I figured out how to do the sum of two primes for every number greater than 2 by..

44 % 44 = 1

44 is not prime, 1 is not prime

44 % 41 = 3

41 is prime, 3 is prime

therefore 44 = 3 + 41

Now I don't know how to get

44 = 2 + 5 + 37 which is under the sum of 3 primes rule

I have to do this kind of begginer(ish) wise. lol. I can never think of the right word for that. I appreciate any ideas or suggestions. I would also appreciate if anyone could give me any ideas on an easy way to determine if a number is prime.