All primes except 2 is an odd number(Think about it. Why?). When p > 2, it must be an odd number.
Sum of the squares of 2 odd numbers is an even number. Therefore sum of the squares of 2, and 2 prime numbers is also an even number, not a prime number.
I tested a few combinations which involves p = 5 and I don't know why the results are always divisible by 3.
Tested a few combinations which involves p = 7 and I don't know why the results still are always divisible by 3.
I assume that all combinations involving p \(\geq\) 5 will always divisible by 3.
Therefore only 1 value is possible for p.
Why on Earth is everything divisble by 3? lol