Prime numbers

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.

Two years ago, Yitang Zhang was virtually unknown. Now his surprise solution to a major problem in number theory has catapulted him to mathematical stardom. Where does he go from here?

A year after tackling how close together prime number pairs can stay, mathematicians have now made the first major advance in 76 years in understanding how far apart primes can be.