The late Harvey Dubner found the Rep-unit R49081 to be a probable prime in 1999 and made a report of it in his paper [1]. Today I finished the elliptic curve primailty proving (ECPP) certification and a full verification of it using the most excellent program Primo authored by Marcel Martin. The certification took 20 months on an AMD 3990x computer (64 cores); and verification took about 13 hours. It is the first proof of a Rep-unit prime since that of R1031 in 1985 (Williams and Dubner) [2] ran on a Dubner Cruncher [3]. The new proof exceeds my previous top ECPP record at 40,000 digits [4]. The certificate of R49081 will be available at Marcel's Ellipsa site [5].
There are now 6 Rep-unit primes and 5 known Rep-unit probable primes; The smallest unproven one is R86453 (Baxter, 2000) [2].
[1]
https://www.ams.org/journals/mcom/20...01-01319-9.pdf
[2]
https://primes.utm.edu/top20/page.php?id=57
[3]
https://primes.utm.edu/bios/page.php?id=579
[4]
https://primes.utm.edu/top20/page.php?id=27
[5]
http://www.ellipsa.eu/public/primo/records.html