No joke — there's a semi-serious proof involved here. We're looking for the smallest number that could easily be mistaken for
prime but in fact is not. How do we find it? Well, since it's not prime, let's look for its
prime factors.
- The number can't be a multiple of two — even numbers are too easy to spot.
- The number can't be a multiple of three — there's an easy test for that.
- The number can't be a multiple of five — thanks to our base ten number system, it's too easy to find those.
- Seven? Sure, why not? Multiples of seven don't look special at all. But we need more than one prime factor -- everybody knows that 49 is seven squared.
- The other factor can't be eleven — 7 x 11 = 77, obviously not prime. Multiples of 11, especially low ones, are fairly obvious.
- But what about thirteen? 7 x 13 = 91. That...looks prime.
So there you have it. A
rigorous proof that the smallest number that looks prime but isn't is
91. Use this to impress your friends and shame your enemies at
cocktail parties.
But what about the smallest number that can't be described in fewer than 15 words?