17 is the favorite number of David Kelly, a mathematician and professor of Hampshire College. He loves it for a very large number of reasons. He was instrumental in creating a summer camp at Hampshire which has trained many young brilliant mathematical minds. (Including Vi Hart). Thus it has spread.
Following the links from that link, I find wikipedia for 17 says, "Carl Friedrich Gauss (1777–1855) showed that two regular "heptadecagons" (17-sided polygons) could be constructed with ruler and compasses."
(I learned it as straightedge and compass.) Wikipedia did not mention the story that Gauss has a regular heptadecagon inscribed on his tombstone.
You can find such "collections" for numbers like 7, 8, or 13, even ignoring the integers 0-4, and 42 is obviously a reference to Hitchhikers guide, a work of fiction. Am I missing something?
http://www.vinc17.net/yp17/index.en.html