Plateau and Depression (PR)Primes

Batalov · 2023-01-22, 18:22

Plateau and Depression (PR)Primes

From: PRP Top Automailer <prptop@primenumbers.net>
To: Ryan Propper + Sergey Batalov
Sent: Sunday, January 22, 2023 at 09:49:38 AM PST
Subject: Submitted PRPs to the PRP Top

You have submitted the following probable prime(s) to the PRP Top queue :
(67*10^1116676+23)/9, 1'116'677 (digits)

Comments : A depression PRP of 74444..44447 kind.

Discoverer : Ryan Propper + Sergey Batalov

Also: a list on M.Kamada's site

Tyler Busby · 2023-01-27, 18:21

Huge find! Not sure if you've talked about it anywhere else, but how exactly do y'all select which near-repdigit-related sequences to push hard into? Since it's the two of you, I wouldn't be surprised if there was some TOP500 time involved. But aside from that, my best guess is that you optimize some property of these sequences for ease of sieving or testing.

From a distance, it doesn't seem like you're minimizing Kamada's "difficulty" metric, and I'm unsure if the general trend of near-repdigits and PDPs being searched more extensively than quasi-repdigits is a function of popularity or some other "ease" explanatory variable that I've missed.

Or maybe you just pick randomly, ha!

Regardless, nice work! I'm assuming this search isn't over, as Kamada doesn't have a "range of search" entry covering this yet. But I'd be interested to hear any extra details of y'all's process that you'd be willing to divulge :)

Batalov · 2023-01-28, 01:25

There are 23 series in all. (one would expect 25 from using simple divisors, but no - two more series are eliminated by covering sets.)

So I sieved for all 23 series and then merged and sorted by exponent and then LLR tests were run, from a randomly chosen starting point of 1M decimal digits and up.
I sieved up to 5,000,000 but it is too expensive to LLR-test, so we are satisfied with this find and moved on to another project ... one prime to rule the world... well, rather, - "today, - an 11+ million digit prime, tomorrow, the world :-)"

Tyler Busby · 2023-01-28, 06:50

Ah, interesting technique!! I guess that means all the PDPs have been searched from 1,000,000-1,116,676 digits then! Hah.

After getting bored of manually sieving and setting up llr runs for PDPs and other near-repdigit-related series, I wrote a primitive tooling system to sieve and test ranges of near-repdigit-related series individually with one command (even going as far as implementing testing while sieving, with llr and srsieve informing the each other of progress periodically). But I hadn't thought of merging multiple to make the search rewards more "consistent"! Completing a single range up to 200k digits seems to really drag with one cpu thread sometimes (and more threads doesn't seem to really help), so I can imagine "trawling" multiple similar series at slowly increasing difficulty makes the search a bit more bearable.

I tried to sllrCUDA test (67*10^1116676+23)/9 on WSL just to see what would happen and my computer immediately locked up, so I think I'll stick to the <200,000 range for now :)

2023-01-22, 18:22	#1
Batalov "Serge" Mar 2008 San Diego, Calif. 3×3,469 Posts	Plateau and Depression (PR)Primes Plateau and Depression (PR)Primes From: PRP Top Automailer <prptop@primenumbers.net> To: Ryan Propper + Sergey Batalov Sent: Sunday, January 22, 2023 at 09:49:38 AM PST Subject: Submitted PRPs to the PRP Top You have submitted the following probable prime(s) to the PRP Top queue : *(6710^1116676+23)/9**, 1'116'677 (digits) Comments : A depression PRP of 74444..44447 kind. Discoverer : Ryan Propper + Sergey Batalov Also: a list on M.Kamada's site

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2023-01-27, 18:21	#2
Tyler Busby Jan 2023 3²×7 Posts	Huge find! Not sure if you've talked about it anywhere else, but how exactly do y'all select which near-repdigit-related sequences to push hard into? Since it's the two of you, I wouldn't be surprised if there was some TOP500 time involved. But aside from that, my best guess is that you optimize some property of these sequences for ease of sieving or testing. From a distance, it doesn't seem like you're minimizing Kamada's "difficulty" metric, and I'm unsure if the general trend of near-repdigits and PDPs being searched more extensively than quasi-repdigits is a function of popularity or some other "ease" explanatory variable that I've missed. Or maybe you just pick randomly, ha! Regardless, nice work! I'm assuming this search isn't over, as Kamada doesn't have a "range of search" entry covering this yet. But I'd be interested to hear any extra details of y'all's process that you'd be willing to divulge :)

2023-01-28, 01:25	#3
Batalov "Serge" Mar 2008 San Diego, Calif. 3×3,469 Posts	There are 23 series in all. (one would expect 25 from using simple divisors, but no - two more series are eliminated by covering sets.) So I sieved for all 23 series and then merged and sorted by exponent and then LLR tests were run, from a randomly chosen starting point of 1M decimal digits and up. I sieved up to 5,000,000 but it is too expensive to LLR-test, so we are satisfied with this find and moved on to another project ... one prime to rule the world... well, rather, - "today, - an 11+ million digit prime, tomorrow, the world :-)"

2023-01-28, 06:50	#4
Tyler Busby Jan 2023 3F₁₆ Posts	Ah, interesting technique!! I guess that means all the PDPs have been searched from 1,000,000-1,116,676 digits then! Hah. After getting bored of manually sieving and setting up llr runs for PDPs and other near-repdigit-related series, I wrote a primitive tooling system to sieve and test ranges of near-repdigit-related series individually with one command (even going as far as implementing testing while sieving, with llr and srsieve informing the each other of progress periodically). But I hadn't thought of merging multiple to make the search rewards more "consistent"! Completing a single range up to 200k digits seems to really drag with one cpu thread sometimes (and more threads doesn't seem to really help), so I can imagine "trawling" multiple similar series at slowly increasing difficulty makes the search a bit more bearable. I tried to sllrCUDA test (67*10^1116676+23)/9 on WSL just to see what would happen and my computer immediately locked up, so I think I'll stick to the <200,000 range for now :)