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prime numbers

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A teenager wearing a blue polo shirt and glasses.
number theory

Teenager Solves Stubborn Riddle About Prime Number Look-Alikes

By Jordana Cepelewicz
October 13, 2022
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In his senior year of high school, Daniel Larsen proved a key theorem about Carmichael numbers — strange entities that mimic the primes.

number theory

A Numerical Mystery From the 19th Century Finally Gets Solved

By Leila Sloman
August 15, 2022
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Two mathematicians have proven Patterson’s conjecture, which was designed to explain a strange pattern in sums involving prime numbers.

A deltoid and other mathematical shapes.
geometry

A Question About a Rotating Line Helps Reveal What Makes Real Numbers Special

By Kevin Hartnett
July 26, 2022
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The Kakeya conjecture predicts how much room you need to point a line in every direction. In one number system after another — with one important exception — mathematicians have been proving it true.

cartoon of a red-headed woman holding a flashlight that illuminates certain numbers against a dark blue background
Quantized Academy

How Can Infinitely Many Primes Be Infinitely Far Apart?

By Patrick Honner
July 21, 2022
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Mathematicians have been studying the distribution of prime numbers for thousands of years. Recent results about a curious kind of prime offer a new take on how spread out they can be.

The Joy of Why

How Do Mathematicians Know Their Proofs Are Correct?

By Steven Strogatz
July 13, 2022
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What makes a proof stronger than a guess? What does evidence look like in the realm of mathematical abstraction? Hear the mathematician Melanie Matchett Wood explain how probability helps to guide number theorists toward certainty.

2022 Fields and Abacus Medals

A Solver of the Hardest Easy Problems About Prime Numbers

By Erica Klarreich
July 5, 2022
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On his way to winning a Fields Medal, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

number theory

Graduate Student’s Side Project Proves Prime Number Conjecture

By Jordana Cepelewicz
June 6, 2022
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Jared Duker Lichtman, 26, has proved a longstanding conjecture relating prime numbers to a broad class of “primitive” sets. To his adviser, it came as a “complete shock.”

number theory

Mathematicians Clear Hurdle in Quest to Decode Primes

By Kevin Hartnett
January 13, 2022
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Paul Nelson has solved the subconvexity problem, bringing mathematicians one step closer to understanding the Riemann hypothesis and the distribution of prime numbers.

An illustration of a flashlight whose beam illuminates graphs and numbers.
number theory

Mathematicians Outwit Hidden Number Conspiracy

By Jordana Cepelewicz
January 3, 2022
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Decades ago, a mathematician posed a warmup problem for some of the most difficult questions about prime numbers. It turned out to be just as difficult to solve, until now.


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