New ECPP record (currently: 59,798 digits)

[Puzzle-Peter]

What a monster. Congrats!

[paulunderwood]

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

[kar_bon]

The link to H.Dubners article at AMS in your PrimePages comment is cut off (as the link given in the previous post here with "20...01-01319-9.pdf").

[paulunderwood]

Originally Posted by kar_bon

The link to H.Dubners article at AMS in your PrimePages comment is cut off (as the link given in the previous post here with "20...01-01319-9.pdf").

Thanks for pointing that out. It is fixed now.

[rudy235]

Congratulations! I been following this repunit since about 10 years and thought it would be eventually be proven by BLS, KP or CHG but the factorized part of N-1 never exceeded 17.79%.

So the only other possibility was PRIMO but with over 49000 digits it seemed impossible to surmount.

I want to believe Harvey Dubner would have been immensely happy to see that his R(49081) was finally proven prime. The next one R(86453) will probably have to wait until most of us here are gone.

[Dr Sardonicus]

Originally Posted by paulunderwood

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.
<snip>

Hooray! What a beast! At long last... Christmas came and went. New Year's came and went. But it did finish right about on New Year's notwithstanding. (Feed "Nowruz" to your favorite search engine.)

That doesn't just break your previous PRIMO record - it shatters it!





I don't anticipate that record being broken any time soon, but a sanity check on that is in order: Are there any larger Primo or other ECPP jobs in the pipeline?

[paulunderwood]

Originally Posted by Dr Sardonicus

I don't anticipate that record being broken any time soon, but a sanity check on that is in order: Are there any larger Primo or other ECPP jobs in the pipeline?

None larger. I have 5 proofs in the pipeline, but none are getting any electricity until the fall.

[sweety439]

Can you upload its certificate to factordb?

[Cybertronic]

Hello Paul, Big big big congratulations for this great job !!!


Norman

[pinhodecarlos]

Congrats Paul!

[paulunderwood]

Originally Posted by sweety439

Can you upload its certificate to factordb?

Uploaded all 114,314,839 bytes. "Processing". If it is single core it will take ~1 month.