1 | initial version |

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.

2 | No.2 Revision |

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.

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.