Prime numbers

The Pythagoreans developed many of the ideas related to numbers that have become so familiar to us, including even and odd numbers, square numbers, triangular numbers, and so on. They also discovered that some integers cannot be decomposed into factors. These are called prime numbers and they constitute the building blocks of all the other integers, called composite. This chapter deals with the prime numbers in a general non-technical way, since much of the writing about them is quite specialized. The prime numbers have remarkable properties, many of which are still resistant to being proved. Prime numbers matter deeply to mathematics, not to mention to the progress of human knowledge generally. Pythagoras believed that prime numbers were part of a secret code which, if deciphered, would allow us to unlock the mysteries of the cosmos itself.