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When a crystallographer treated prime numbers as a system of particles, the resulting diffraction pattern created a new view of existing conjectures in number theory.

A simple, step-by-step breakdown of two “perfect” math proofs.

Generations of researchers have pursued his “Langlands program,” which seeks to create a grand unified theory of mathematics.

Pradeep Mutalik and Quanta readers explore an open question about prime numbers: What is the lowest valued, longest consecutive sequence of integers that are divisible by a set of prime numbers?

Prime numbers are endlessly fascinating to number theorists and math enthusiasts. This month’s puzzle explores primes by cooking up a whimsical dish of grilled snake ribs.

Kaisa Matomäki has proved that properties of prime numbers over long intervals hold over short intervals as well. The techniques she uses have transformed the study of these elusive numbers.

An obscure number theorist who became an overnight sensation with a major proof about the gaps between prime numbers now finds quiet inspiration walking along the Pacific Coast.

Physicists are attempting to map the distribution of the prime numbers to the energy levels of a particular quantum system.

19th-century mathematicians thought the “roots of unity” were the key to solving Fermat’s Last Theorem. Then they discovered a fatal flaw.

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