This is because 65 is not prime. Note that 12+25 and 32+22=13 are both primes (of the form 4n+1, so the factors you find are indeed prime.
You may find the Wikipedia article helpful.
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This is because 65 is not prime. Note that 12+25 and 32+22=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.