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prime numbers

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Quantized Academy

What Hot Dogs Can Teach Us About Number Theory

By Patrick Honner
November 18, 2021
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The Chinese remainder theorem is an ancient and powerful extension of the simple math of least common multiples.

A graphic showing that changing any of the digits of 505, 447 turns it into a composite number
prime numbers

Mathematicians Find a New Class of Digitally Delicate Primes

By Steve Nadis
March 30, 2021
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Despite finding no specific examples, researchers have proved the existence of a pervasive kind of prime number so delicate that changing any of its infinite digits renders it composite.

Quantized Academy

The Mysterious Math of Perfection

By Patrick Honner
March 15, 2021
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Enter the world of perfect numbers and explore the mystery mathematicians have spent thousands of years trying to solve.

A comically long “missing persons” poster for an odd perfect number that shows all the restrictions it has to satisfy.
number theory

Mathematicians Open a New Front on an Ancient Number Problem

By Steve Nadis
September 10, 2020
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For millennia, mathematicians have wondered whether odd perfect numbers exist, establishing an extraordinary list of restrictions for the hypothetical objects in the process. Insight on this question could come from studying the next best things.

Visualization of the distribution of prime numbers in the shape of colorful dots in a hexagonal pattern
Abstractions blog

Mathematicians Will Never Stop Proving the Prime Number Theorem

By Susan D'Agostino
July 22, 2020
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Why do mathematicians enjoy proving the same results in different ways?

A photograph of the mathematician James Maynard outside his home in Oxford, England.
profiles

A Number Theorist Who Solves the Hardest Easy Problems

By Erica Klarreich
July 1, 2020
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In his rapid ascent to the top of his field, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

Multimedia

The Map of Mathematics

By Kevin Hartnett
February 13, 2020
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Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

An illustration of a woman sitting in a field embroidering a flower pattern. Around her grow wildflowers that appear to be randomly distributed but whose colors reveal a hidden pattern.
number theory

Mathematicians Catch a Pattern by Figuring Out How to Avoid It

By Kevin Hartnett
November 25, 2019
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We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”

Colored spheres arranged in pairs.
prime numbers

Big Question About Primes Proved in Small Number Systems

By Kevin Hartnett
September 26, 2019
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The twin primes conjecture is one of the most important and difficult questions in mathematics. Two mathematicians have solved a parallel version of the problem for small number systems.


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