Loading problem…
Status
On this page
Status
Topics
Problem 508
What is the chromatic number of the plane? That is, what is the smallest number of colours required to colour such that no two points of the same colour are distance apart?
Source: erdosproblems.com/508
- Geometry
- Ramsey theory
Status
OpenNo claim settles this problem.
Open. The site labels the problem OPEN (page last edited 22 January 2026) and records the bounds in its remarks; the claim pages record de Grey's refereed lower bound, a later result on the lower bound, and a rejected announcement of the value.