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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.

For centuries, mathematicians tried to solve problems by adding new values to the usual numbers. Now they’re investigating the unintended consequences of that tinkering.

A previously unnoticed property of prime numbers seems to violate a long-standing assumption about how they behave.

Using crowd-sourced and traditional mathematics research, Terence Tao has devised a solution to a long-standing problem posed by the legendary Paul Erdős.

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