Pieces of Numbers

A proof brings closure to a dramatic tale of partitions and primes

By Erica Klarreich, 15:52 PM April 15, 2008

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. For example, pick any number and double it. You'll always find a prime number—a number divisible only by itself and by 1—between that number and its double. As another case in point, primes that leave a remainder of 1 when divided by 4 can always be expressed as the sum of two squares. Now, a ...

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