prime numbers – Quanta Magazine

‘Sensational’ Proof Delivers New Insights Into Prime Numbers

Jordana Cepelewicz — Mon, 15 Jul 2024 13:55:18 +0000

Sometimes mathematicians try to tackle a problem head on, and sometimes they come at it sideways. That’s especially true when the mathematical stakes are high, as with the Riemann hypothesis, whose solution comes with a $1 million reward from the Clay Mathematics Institute. Its proof would give mathematicians much deeper certainty about how prime numbers are distributed, while also implying a host...

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What Makes for ‘Good’ Mathematics?

Steven Strogatz — Thu, 01 Feb 2024 14:03:12 +0000

We tend to think of mathematics as purely logical, but the teaching of math, its values, its usefulness and its workings are packed with nuance. So what is “good” mathematics? In 2007, the mathematician Terence Tao wrote an essay for the Bulletin of the American Mathematical Society that sought to answer this question. Today, as the recipient of a Fields Medal, a Breakthrough Prize in Mathematics...

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Pierre de Fermat’s Link to a High School Student’s Prime Math Proof

Patrick Honner — Wed, 22 Nov 2023 13:30:00 +0000

Like many math students, I had dreams of mathematical greatness. I thought I was close once. A difficult algebra problem in college kept me working late into the night. After hours of struggle, I felt a breakthrough coming. I deftly manipulated expressions. I factored, multiplied and simplified, until my discovery finally revealed itself: $latex 1 + 1 = 2$. I couldn’t help but laugh.

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The Hidden Connection That Changed Number Theory

Max G. Levy — Wed, 01 Nov 2023 14:37:03 +0000

There are three kinds of prime numbers. The first is a solitary outlier: 2, the only even prime. After that, half the primes leave a remainder of 1 when divided by 4. The other half leave a remainder of 3. (5 and 13 fall in the first camp, 7 and 11 in the second.) There is no obvious reason that remainder-1 primes and remainder-3 primes should behave in fundamentally different ways. But they do.

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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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