Monday, March 10, 2008

Shavitian subprime numbers

In honor of the fact that I'm a bit of a nerd, here's interesting class of numbers I discovered: Shavitian subprime numbers. A number is a Shavitian subprime if it's prime, and every number within it is prime. For instance, for the number 1,234 to be a Shavitian subprime, the following numbers would all have to be prime: 1, 2, 3, 4, 12, 23, 34, 123, 234, 1234.

If you're still reading, you probably have too much time on your hands. As a reward, I'll let you in on a little secret: there's only nine such numbers in all of existence: 2, 3, 5, 7, 23, 37, 53, 73 and 373.

Intrigued? You can read more (including as close to a formal proof as I could come up with) on my GooglePages page on Shavitian subprime numbers. That's not meant as linkbait -- I just don't want to bore you with a big ol' copy-paste.