Prime Numbers' Hidden Order Revealed

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Wired

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Science

Mathematicians Uncover a New Way to Count Prime Numbers

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A new proof has brought mathematicians one step closer to understanding the hidden order of those “atoms of arithmetic,” the prime numbers.

A better understanding of how the primes are distributed would illuminate vast swaths of the mathematical universe.

The new proof makes use of a set of tools from a very different area of mathematics.

Ben Green and Mehtaab Sawhney proved that there are infinitely many primes that can be written as the sum of squares of actual primes.

They used a tool called a Gowers norm to measure how random or structured a function or set of numbers is.

The result marks a significant breakthrough on a type of problem where progress is usually very rare.

Mathematicians now hope to broaden the scope of the Gowers norm even further—to try using it to solve other problems in number theory beyond counting primes.

“It’s a lot of fun for me to see things I thought about some time ago have unexpected new applications,” Ziegler said.

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