“You don’t have to believe in God, but you have to believe in The Book,” the Hungarian mathematician Paul Erdős once said. The Book, which only exists in theory, contains the most elegant proofs of ...

Prime numbers are one of the most basic topics of study in the branch of mathematics called number theory. Primes are numbers that can only be evenly divided by themselves and 1. For example, 7 is a ...

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Visit NAP.edu/10766 to get more information about this book, to buy it in print, or to download it as a free PDF.

Last week, Yitang “Tom” Zhang, a popular math professor at the University of New Hampshire, stunned the world of pure mathematics when he announced that he had proven the “bounded gaps” conjecture ...

Prime numbers are positive integers greater than 1 that can only be divided evenly by 1 and themselves. These numbers are important in many areas of mathematics, including number theory, cryptography, ...

Prime numbers are all the rage these days. I can tell something’s up when random people start asking me about the randomness of primes—without even knowing that I’m a mathematician! In the past couple ...

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