Look, I don't have a page for every number. This has got to stop sometime, why not now?

As long as you're here, though, please take a moment to think about
**Goldbach's Conjecture**, which states (in my
super-elegant rewording):

*
Every non-prime even number is the sum of two primes.
*

This has long been my favorite unproven hypothesis, even since before
Fermat's Last Theorem kicked the bucket. Tell me if you know of any
progress. *I'm* certainly not making any... :-)

While we're on the subject of unproven hypotheses, here are some others I like to think about:

- Are there an infinite number of twin primes? That is, two primes P1 and P2, where P2 - P1 = 2.
- The 3n + 1 conjecture (it has a name, I just can't remember
what it is... the "Collatz Conjecture", that's it): take a number N.
If it's odd, multiply it by three and add 1; if it's even, divide it
by two. Repeat this sequence until it is equal to 1. It is
conjectured that
*every*number eventually reaches 1 this way, but no one has proven it so far. No exceptions have been found, either, of course. :-)

You might also want to see this unsolved problems page.

(Back to Karl Fogel's home page.)