User:A()/A()'s Square Prime conjecture

User:A()’s Square Prime conjecture states that the following is true:

1. There are infinite square numbers
2. There are infinite prime numbers
3. For any square number n where n > 4, there must at least one set of primes that when summed together equal n
4. Said set of primes cannot have duplicates (i.e {2,2,3} is invalid)

• 9 -> {2,7}
• 16 -> {3, 13}
• 25 -> {5, 7, 13}
• 36 -> {13, 23}
• 49 -> {7, 11, 31}

… etc

How to find prime candidates

1. Take an integer X
2. Take a prime P which is the biggest prime smaller than X
3. Take the difference of X and P

• If the difference of X and P is prime, stop
• Else, substitute X for the difference and repeat steps 2-3
• If the difference is 1, go back to step 2 and choose a smaller prime number P