13 and 31 are known as the Signature of G-d in some Rabbinic circles. They are the only prime numbers that are transpositions of each other that also transpositions of the square of each. 13 squared is 169, and 31 squared is 961.
Shows up in certain mystical contexts I believe, but I certainly wouldn't call it occultic in the demonic sense.
Yes - I agree with what you say about the good signifcances of the number 13. Yet at the same time, it has tremendous occult signifcance.
"Both sides" use it. Similar to 33, which is a "sacred" occult number. Yet it is also the number of years of Christ's life.........and is the number of buttons on a priest's cassock.