Thread: New ECPP record
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Old 2022-03-21, 12:15   #35
paulunderwood
 
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Sep 2002
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Default R49081 is prime!

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
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