Proth primes

[kar_bon]

...but it's a Proth-type prime, not Riesel, false thread.

Moderator note: Previous post moved from Riesel thread and parked in this one

[rudy235]

Thanks

[Batalov]

It is one of the Extended Sierpinski Project.

(That is, proving the next Sierpinski constant, while proving the first one is still on the 'eliminate last five k values' stage.)

[rudy235]

Originally Posted by rudy235

13 202705 · 2^21320516 + 1 6418121 L5181 Dec 2021
(Unverified because InProcess)

Congratulations to Pavel Atnashev and PrimeGrid

OFFICIAL ANNOUNCEMENt IS HERE

PrimeGrid’s
Extended Sierpinski Problem Prime Search

On 25 November 2021, 03:19:26 UTC, PrimeGrid's Extended Sierpinski Problem found the
Mega Prime:

202705*2^21320516+1

The prime is 6,418,121 digits long and will enter Chris Caldwell's “The Largest Known Primes
Database” (http://primes.utm.edu/primes) ranked 13th overall. This find eliminates k=202705; 8
k's remain in the Extended Sierpinski Problem.
The discovery was made by Pavel Atnashev of Russia using an Intel(R) Xeon(R) E5-2695 v2
CPU @ 2.40GHz with 16GB RAM running Tiny Core Linux. This computer took about 10 hours,
59 minutes to complete the primality test using LLR2. Pavel Atnashev is a member of Ural
Federal University.
Credits for the discovery are as follows:

1. Pavel Atnashev (Russia), discoverer
2. PrimeGrid, et al.
3. Srsieve, sieving program developed by Geoff Reynolds
4. LLR, primality program developed by Jean Penné
5. LLR2, primality program developed by Pavel Atnashev
6. OpenPFGW, a primality program developed by Chris Nash & Jim Fougeron with maintenance and improvements by Mark Rodenkirch

Entry in "The Largest Known Primes Database" can be found here:

https://primes.utm.edu/primes/page.php?id=133011

OpenPFGW, a primality program developed by Chris Nash & Jim Fougeron, was used to check
for Fermat Number divisibility (including generalized and extended). For more information
about Fermat and generalized Fermat Number divisors, please see Wilfrid Keller's sites:

• http://www.prothsearch.com/fermat.html
• http://www.prothsearch.com/GFNfacs.html

No generalized and extended generalized Fermat number divisors were discovered with this
prime find.

Using a single PC would have taken years to find this prime. So this timely discovery would not
have been possible without the thousands of volunteers who contributed their spare CPU
cycles. A special thanks to everyone who contributed their advice and/or computing power to
the search - especially all the sievers who work behind the scenes to make a find like this
possible.

The Extended Sierpinski Problem Prime Search will continue to seek even larger primes. To join
the search please visit PrimeGrid: http://www.primegrid.com

[rudy235]

37 ·2^14166940 + 1

Fourth largest prime of the year. 4.26 million digits Rank 36

Congratulations!