TITLE: Has there been a computer search for a 5-chromatic unit distance graph?
QUESTION [29 upvotes]: The existence of a 4-chromatic unit distance graph (e.g., the Moser spindle) establishes a lower bound of 4 for the chromatic number of the plane (see the Nelson-Hadwiger 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 $n$?

REPLY [43 votes]: As of this morning there is a paper on the ArXiv 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/