Yesterday Aubrey D.N.J. de Grey posted to the arXiv a new preprint that announces the first improvement since 1961 on the lower bound on the Hadwiger-Nelson problem (chromatic number of the plane):

Aubrey D.N.J. de Grey: The chromatic number of the plane is at least 5. arXiv:1804.02385 

The abstract reads:

We present a family of finite unit-distance graphs in the plane that are not 4-colourable, thereby improving the lower bound of the Hadwiger-Nelson problem. The smallest such graph that we have so far discovered has 1567 vertices. 

Proposed Polymath problem:

Reduce the number of vertices (currently $1567$) of the smallest known unit-distance graph in the plane that is not 4-colorable.

Yesterday Aubrey D.N.J. de Grey posted to the arXiv a new preprint that announces the first improvement since 1961 on the lower bound on the Hadwiger-Nelson problem (chromatic number of the plane):

Aubrey D.N.J. de Grey: The chromatic number of the plane is at least 5. arXiv:1804.02385 

The abstract reads:

We present a family of finite unit-distance graphs in the plane that are not 4-colourable, thereby improving the lower bound of the Hadwiger-Nelson problem. The smallest such graph that we have so far discovered has 1567 vertices. 

(Note: 1567 was later corrected to 1585.)

Proposed Polymath problem:

Reduce the number of vertices (currently $1585$) of the smallest known unit-distance graph in the plane that is not 4-colorable.