The existence of a 4-chromatic unit distance graph (e.g., [the Moser spindle](https://en.wikipedia.org/wiki/Moser_spindle)) establishes a lower bound of 4 for the chromatic number of the plane (see the [Nelson-Hadwiger problem](https://en.wikipedia.org/wiki/Hadwiger%E2%80%93Nelson_problem)).


Obviously, it would be nice to have an example of a *5-chromatic* unit distance graph. To the best of my knowledge, the existence of such a graph is open. Has there been any (documented) attempt to find such a graph through a computer search? For instance, has every $n$-vertex possibility been checked up to some $n$?



Has there been a computer search for a 5-chromatic unit distance graph?
As of this morning [there is a paper on the ArXiv](https://arxiv.org/pdf/1804.02385) claiming to show that there exists a 5-chromatic unit distance graph with $1567$ vertices. The paper is written by non-mathematician Aubrey De Grey (of anti-aging fame), but it appears to be a serious paper. Time will tell if it holds up to scrutiny.


EDIT: in fact, it must be the one with 1585 vertices, according to checkers, see <https://dustingmixon.wordpress.com/2018/04/10/the-chromatic-number-of-the-plane-is-at-least-5/>


