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?

In the realm of mathematics, it’s hard to imagine anything more basic than the counting numbers: 1, 2, 3, and so on. Yet this set of mathematical objects abounds with beautiful and unexpected patterns ...