New ECPP record (currently: 59,798 digits)

[a1call]

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. 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

Congratulations sir, on your accomplishment on Naw-Ruz 2022.

Let's take that as good omen for a civilized year ahead, void of animalistic wars and bloodshed.

[rudy235]

I love the unique –and dare I say– beautiful decimal representation of the now famous repunit,

409 rows of 120 1’s each and the last row has a solitary 1 in the middle.

111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
[...] 406 rows more
111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111

1

[Dr Sardonicus]

The University of Illinois used to have a post mark commemorating its achievement finding the latest Mersenne prime, proving that

2¹¹²¹³ - 1 IS PRIME

Imagine the possibilities of putting

R₄₉₀₈₁ IS PRIME

on something

[rudy235]

I think that UTM might be a good choice for the MathPost. ( Unless, of course, someone else has a more viable option.)

[paulunderwood]

Originally Posted by rudy235

I love the unique –and dare I say– beautiful decimal representation of the now famous repunit,

409 rows of 120 1’s each and the last row has a solitary 1 in the middle.

Or a single "1" as a picture comprised of "pixels" of the 49081 ones.

[paulunderwood]

Here are the PNGs of the screenshots I captured.

[Dr Sardonicus]

Originally Posted by paulunderwood

Here are the PNGs of the screenshots I captured.

Hmm, 30582157 seconds, almost a year of computer time.

"A man was seen by the road holding a hand-lettered cardboard sign..."

I have set a new prime-proving record

Now my electricity provider is threatening to shut off my power

PLEASE HELP

[sweety439]

Originally Posted by paulunderwood

[5] http://www.ellipsa.eu/public/primo/records.html

The links in http://www.ellipsa.eu/public/primo/records.html are wrong, they should be "ecpp49081.7z.001" instead of "ecpp40000.7z.001", also, the page http://www.ellipsa.eu/public/primo/f...0000-f4.7z.006 is "Error 404"

[paulunderwood]

Originally Posted by sweety439

The links in http://www.ellipsa.eu/public/primo/records.html are wrong, they should be "ecpp49081.7z.001" instead of "ecpp40000.7z.001", also, the page http://www.ellipsa.eu/public/primo/f...0000-f4.7z.006 is "Error 404"

I have emailed Marcel for a fix.

Fixed now

[Uncwilly]

Originally Posted by Dr Sardonicus

I have set a new prime-proving record

Now my electricity provider is threatening to shut off my power

PLEASE HELP

Imagine the Fiasco that would have happened if Aaron had found an MP.

[paulunderwood]

R49081 also tops the top20 Unique primes: https://primes.utm.edu/top20/page.php?id=62

Thanks to Ray Chandler for pointing it out.