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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 t…
Even in the twentieth century, the mathematician G. H. Hardy, coauthor of the first great work on number theory written in the English language, classified 1 as a prime in his early writings. They were doing what good mathematicians always do: maintaining a flexible attitude toward terminology, and keeping in mind that sometimes the right way to define things only comes into focus when you’ve played with several variants. The numerical facts asserted by the Law of Quadratic Reciprocity are equally true for Christian Goldbach and Carl Friedrich Gauss and Nicomachus of Gerasa and you and me, even if we might initially use different definitions of the word “prime” when we’re talking about them.
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