20210610, 21:45  #463 
Sep 2010
Weston, Ontario
5·47 Posts 
Since I am no longer using the final column of my Leyland prime indexing chart to indicate intervals, I've added a "P" therein for entries that I know are proven primes. That necessitated removing the "date approximate" for Selevich's L(8656,2929) and adding a "~" in front of that entry's date, which is how I had it originally. The indices of my chart are of course one greater than the indices of the Leyland "Prime Wiki" table because they are a reflection of OEIS A094133 which has a spurious first term.

20210610, 22:16  #464 
"Oliver"
Sep 2017
Porta Westfalica, DE
2×613 Posts 
Looking at that table, there are a lot of results that should be able to be proven in less than a day (at least) on "bigger" systems. Please correct me, if I am wrong here, frequent Primo users!
If correct, I'd like to reserve some of the smaller ones tomorrow for Primo. I will specify them futher then and also double check them on FactorDB. In the list of kar_bon, maybe we should try to certify the "orange" entries, too? 
20210611, 07:14  #465  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2×5,791 Posts 
Quote:
Long ago I pointed out that they seem to have a reasonable density of primes of all sizes, have a very simple algebraic description and have no obvious properties which can be exploited by specialpurpose algorithms. Several have been used to set records for the size of a certified prime. They are frequently used, I believe, to test new implementations of general primality testing algorithms. 

20210614, 16:45  #466  
"Oliver"
Sep 2017
Porta Westfalica, DE
2·613 Posts 
Quote:


20210630, 05:24  #467 
Jan 2020
11 Posts 
I found a new record for largest Leyland PRP
It is 386642 digits long (previous record is 386434 digits) PRP: 81650^54369+54369^81650 
20210706, 13:22  #468 
"Oliver"
Sep 2017
Porta Westfalica, DE
10011001010_{2} Posts 
It took around 1820 h on a 5950X (all cores used). The certificate is uploaded. Who has to be informed to update the table? I guess we can wait with this until the numbers below are finished as well.
I'd like to reserve

20210712, 20:02  #470 
"Oliver"
Sep 2017
Porta Westfalica, DE
2×613 Posts 
My reservations from above are now completed and are currently being processed by FactorDB. Thus, I'd like to reserve:
As a personal side note, the last number in the list above will be my first 10k digit ECPP run. Knowing that this is not something impressive at all by itself, I am still pleased. PS: I just saw FactorDB got a hardware upgrade. They now run:
Last fiddled with by kruoli on 20210712 at 20:11 Reason: Certificates missing. Semantic clarifications. 
20210713, 10:09  #471 
"Norbert"
Jul 2014
Budapest
11^{2} Posts 
Another new PRP:
457^60454+60454^457, 160803 digits. 
20210815, 12:37  #472 
Sep 2010
Weston, Ontario
5·47 Posts 
I'm done. In addition to Anatoly Selevich's L(314738,9), I found 16 new primes. The twoandahalf months was pretty close. So to get up to 305000 decimal digits (which is on my schedule) will take another ten months. But first I want to make sure that there are no primes in the interval between Sergey Batalov's L(328574,15) and Yusuf AttarBashi's L(81650,54369).
Last fiddled with by pxp on 20210815 at 12:41 Reason: missing word 
20210908, 14:52  #473  
Sep 2010
Weston, Ontario
5·47 Posts 
Largest Leyland Prime Hunt
Quote:
<386642> Jun 2021 L(81650,54369) <386561> Aug 2021 L(80565,62824) new <386548> Aug 2021 L(83747,41272) new <386434> May 2014 L(328574,15) This means that these four (currently largest) Leyland PRPs are consecutive. As an informal proof thereof I have saved outputs of the pfgw testing as summarized here. 

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