The crisp new dollar bill that I have just taken from my wallet bears the serial number 24598176. It’s easy to tell that the number is exactly divisible by 2 but not by 5. Is it divisible by 3? by 4?

Three and five are prime numbers — that is, they are divisible only by one and by themselves. So are five and seven. And 11 and 13. And for each of these pairs of prime numbers, the difference is two.

The world belongs to the mathematicians and the physicists. We lay people may pump our minds with Discovery Channel specials, but they’re the ones who get to understand how it all really works–how the ...