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This is because 65 is not prime. Note that $1^2+2^5$ and $3^2+2^2=13$ are both primes (of the form $4n+1$, so the factors you find are indeed prime.

You may find the Wikipedia article helpful.

This is because 65 is not prime. Note that $1^2+2^5$ and $3^2+2^2=13$ are both primes (of the form $4n+1$, so the factors you find are indeed prime.(Gaussian) primes.

You may find the Wikipedia article helpful.