Is 1 Prime, and Does It Matter?

If you ask a person on the street whether 1 is a prime number, they’ll probably pause, try to remember what they were taught, and say “no” (or “yes” or “I don’t remember”). Or maybe they’ll cross the street in a hurry. On the other hand, if you ask a mathematician, there’s a good chance they’ll say “That’s an excellent question” or “It’s kind of an interesting story…” Some people treat the non-primeness of 1 as a mathematical fact and nothing more, but those people are missing out on something important about the nature of mathematics. THE PREHISTORY OF PRIMES In early days, 1 wasn’t universally regarded as a number at all. For the Pythagoreans, the first counting number was 2; 1 was the Unit from which all the numbers (2, 3, etc.) were built. So 1, not being a number, was certainly not a prime number. Euclid, although not a member of the Pythagorean Order, agreed that the first prime number was 2. But Greek thought wasn’t homogeneous. Plato’s nephew Speussippus, for instance, thou ... Read full article.