A preprint of my paper with Michael Filaseta and Hester Graves, "Only finitely many s-Cullen numbers are repunits for a fixed s≥2" has appeared on the math arXiv. This is a sequel to an earlier paper with Hester, which proved that there were only finitely many solutions for all s, subject to the abc conjecture.

This proof is unconditional. I am now working on computations to extend 65536 to a much larger number -- it should be possible to get it into the millions.