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Pieces of Numbers

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

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10:54am, June 14, 2005

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 mathematics graduate student has put what may be the final piece into the picture of one of the most surprising patterns of all.

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