Hi just wondering if anyone can help me please with this one?

I have a set of prime numbers, i.e. 3,5,7,11,13,17,19,23,19 etc

I would like to use the sum of two square numbers to indicate whether the prime numbers can be written as the sum of those squared numbers?

I know that 29 is a prime number, also I know that 25 and 4 are square numbers, so if I were to add these two numbers together, i.e. 25 + 4 = 29. The two square numbers make up the prime number?

So in the example of say number 3. This prime number has no square number values because only 1 is a square number, and the numbers 2 and 3 are not square numbers?

Is my logic reasonable, am I doing this right???

Thanks for any help