*Please see my wiki for a comprehensible version of this post.*
I was pretty pleased that I factored a recent

Composite of the day entirely in the complex plane.

The number was 9509, which I noticed immediately is 97²+10². Since I know

Fermat's little theorem,
and I know that the Composite of the day is composite, I knew there
should be another way to write it as the sum of two squares. A little
bit of counting (100+193+191) showed that it is also equal to 95²+22².

For some reason, I know that if I use those two summations to write
complex integers with modulus 9509, their greatest common factor will
also divide 9509.

So I said, (97+10i) - (95+22i) = 2-12i. The modulus of that is
2²+12²=148. The factors of 2 must be irrelevant (since the Cotd is odd),
so

**37 **should be the number we're looking for.

Similarly, (97-10i) - (95+22i) = 2-32i. The modulus of that is 1048.
Again, discarding factors of 2, we're left with the prime

**257**.

And the number is now factored, by finding complex
integers with the right modulus and manuipulating them in the complex
plane.

Pretty wild, huh?