It would be great to have a way for many volunteers to work on calculating record numbers of digits of the MRB constant. I have a program, originally written by the late Richard Crandall (a chief scientist), that I have optimized for recent versions of Mathematica, that I have tried, with little success to enable many users to collaborate their efforts on.
I would be enthused if anyone could work on it in such a way to get it so others could join me in my efforts. Various versions of the code, some brief expositions, and reasons why (or examples of how) it is so hard to compute are found in my post, Try to Break these MRB Constant Records -- http://community.wolfram.com/groups/-/m/t/366628 .
The MRB is a key fundamental constant according to Crandall -- http://marvinrayburns.com/UniversalTOC25.pdf
. It is also a Google Scholar subject -- https://scholar.google.com/scholar?q=%22MRB+constant%22
.