The ternary Goldbach Problem

Snapshots of modern mathematics from Oberwolfach

The ternary Goldbach Problem

Leonhard Euler (1707–1783) – one of the greatest mathematicians of the eighteenth century and of all times – often corresponded with a friend of his, Christian Goldbach (1690–1764), an amateur and polymath who lived and worked in Russia, just like Euler himself. In a letter written in June 1742, Goldbach made a conjecture – that is, an educated guess – on prime numbers:

“Es scheinet wenigstens, dass eine jede Zahl, die größer ist als 2, ein aggregatum trium numerorum primorum sey.”

“It seems [ … ] that every positive integer greater than 2 can be written as the sum of three prime numbers.”

In this snapshot, we will describe to what extent the mathematical community has resolved Goldbach’s conjecture, with some emphasis on recent progress.

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Mathematical subjects

Algebra and Number Theory

Connections to other fields

Computer Science


Harald Helfgott
Senior Editor:
Carla Cederbaum
Junior Editor:
Lea Renner


DOI (Digital Object Identifier)


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snapshots: overview

Mathematical subjects

Algebra and Number Theory
Didactics and Education
Discrete Mathematics and Foundations
Geometry and Topology
Numerics and Scientific Computing
Probability Theory and Statistics

Connections to other fields

Chemistry and Earth Science
Computer Science
Engineering and Technology
Humanities and Social Sciences
Life Science
Reflections on Mathematics

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