twin primes conjecture – Quanta Magazine

A New Generation of Mathematicians Pushes Prime Number Barriers

Erica Klarreich — Thu, 26 Oct 2023 15:02:05 +0000

More than 2,000 years ago, the Greek mathematician Eratosthenes came up with a method for finding prime numbers that continues to reverberate through mathematics today. His idea was to identify all the primes up to a given point by gradually “sieving out” the numbers that aren’t prime. His sieve starts by crossing out all the multiples of 2 (except 2 itself), then the multiples of 3 (except 3...

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Teenager Solves Stubborn Riddle About Prime Number Look-Alikes

Jordana Cepelewicz — Thu, 13 Oct 2022 15:05:40 +0000

When Daniel Larsen was in middle school, he started designing crossword puzzles. He had to layer the hobby on top of his other interests: chess, programming, piano, violin. He twice qualified for the Scripps National Spelling Bee near Washington, D.C., after winning his regional competition. “He gets focused on something, and it’s just bang, bang, bang, until he succeeds,” said Larsen’s mother...

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How Do Mathematicians Know Their Proofs Are Correct?

Steven Strogatz — Wed, 13 Jul 2022 20:13:19 +0000

How can anyone speak with certainty about infinity? What can we really know about the mysterious prime numbers without knowing all of them? Just as scientists need data to assess their hypotheses, mathematicians need evidence to prove or disprove conjectures. But what counts as evidence in the intangible realm of number theory? In this episode, Steven Strogatz speaks with Melanie Matchett Wood...

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A Solver of the Hardest Easy Problems About Prime Numbers

Erica Klarreich — Tue, 05 Jul 2022 07:21:31 +0000

In 2013, one of the best — but also one of the worst — things that can happen to a mathematician happened to James Maynard. Fresh out of graduate school, he solved one of the discipline’s oldest and most central problems, about the spacing of prime numbers. It was an achievement that ordinarily would have garnered him fame even beyond the cloistered world of pure math research. There was just one...

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Mathematicians Outwit Hidden Number Conspiracy

Jordana Cepelewicz — Mon, 03 Jan 2022 15:46:20 +0000

A new proof has debunked a conspiracy that mathematicians feared might haunt the number line. In doing so, it has given them another set of tools for understanding arithmetic’s fundamental building blocks, the prime numbers. In a paper posted last March, Harald Helfgott of the University of Göttingen in Germany and Maksym Radziwiłł of the California Institute of Technology presented an improved...

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