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prime numbers

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prime numbers

Big Question About Primes Proved in Small Number Systems

September 26, 2019

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.

A dartboard with pi at its center.
number theory

New Proof Settles How to Approximate Numbers Like Pi

August 14, 2019

The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer.

Illustration of lock with polynomials surrounding it
Abstractions blog

Mathematicians Seal Back Door to Breaking RSA Encryption

December 17, 2018

Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work.

Art for "In the Universe of Equations, Virtually All Are Prime"
number theory

In the Universe of Equations, Virtually All Are Prime

December 10, 2018

Equations, like numbers, cannot always be split into simpler elements.

Art for "The Universal Pattern Popping Up in Math, Physics and Biology"
In Theory

The Universal Pattern Popping Up in Math, Physics and Biology

August 23, 2018

Quanta’s In Theory video series returns with an exploration of a mysterious mathematical pattern found throughout nature.

Crystal diffraction art for "A Chemist Shines Light on a Surprising Prime Number Pattern"
prime numbers

A Chemist Shines Light on a Surprising Prime Number Pattern

May 14, 2018

When a crystallographer treated prime numbers as a system of particles, the resulting diffraction pattern created a new view of existing conjectures in number theory.

Photo of Ziegler's chalkboard
Abstractions blog

The Infinite Primes and Museum Guard Proofs, Explained

March 26, 2018

A simple, step-by-step breakdown of two “perfect” math proofs.

520px photo of Robert Langlands
Abstractions blog

Robert Langlands, Mathematical Visionary, Wins the Abel Prize

March 20, 2018

Generations of researchers have pursued his “Langlands program,” which seeks to create a grand unified theory of mathematics.

Snake
insights puzzle

Solution: ‘The Prime Rib Problem’

September 8, 2017

Pradeep Mutalik and Quanta readers explore an open question about prime numbers: What is the lowest valued, longest consecutive sequence of integers that are divisible by a set of prime numbers?