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Cybertronic 2022-02-13 08:42

Paul, and even I thought, your post is: Certification done ! :smile:

sweety439 2022-02-13 21:53

[QUOTE=Cybertronic;599965]Paul, and even I thought, your post is: Certification done ! :smile:[/QUOTE]

(10^49081-1)/9 is now proven prime??? You can upload the certificate to [URL="http://factordb.com/index.php?id=1100000000013937242"]factordb[/URL], and also [URL="https://stdkmd.net/nrr/repunit/prpfactors.htm"]this page[/URL] should be updated.

paulunderwood 2022-02-14 00:13

[QUOTE=sweety439;600003](10^49081-1)/9 is now proven prime??? You can upload the certificate to [URL="http://factordb.com/index.php?id=1100000000013937242"]factordb[/URL], and also [URL="https://stdkmd.net/nrr/repunit/prpfactors.htm"]this page[/URL] should be updated.[/QUOTE]

No. It will be done by mid-May.

paulunderwood 2022-02-26 08:42

[QUOTE=paulunderwood;599964] The first phase 2 number involved 3 weeks of factoring a degree 206 polynomial at ~49k digits. It nice to see that one finally cracked.[/QUOTE]

No doubt caused by diggers on this gloriously sunny morning, I had a power cut/outage. This reset the first test back from cracking degree 91 back to degree 206. :cry: The cut should, however, only delay certification by 1 week. I need about 6 weeks of uninterrupted power supply -- a case for UPS.

Cybertronic 2022-02-26 09:07

Hello Paul !
>I need about 6 weeks of uninterrupted power supply

This is very hard at the moment. I hope not the best....maybe we get an attack to the power grid here in europe.

Maybe you find unsers which work for you on other Phase_2 points.


:cry:

I have also reduce my prime k-tuplet calculations.

sweety439 2022-03-06 15:58

Suggest to reserve these numbers:

* (64*10^10906+53)/9 (10907 digits), this prime is the smallest prime of the form 7111...1117, thus currently there is no known [I]proven[/I] prime of the form 7111...1117

* (6^10613-1)/5 (8258 digits), a generalized repunit PRP, an "a little" smaller generalized repunit prime (5^10949-1)/4 was proven prime in 2018

* 8*13^32020+183 (35670 digits), the smallest prime of the form 8000...000111 in base 13, if you prove the primality of this prime, you will full-prove the "[URL="https://primes.utm.edu/glossary/xpage/MinimalPrime.html"]minimal prime[/URL] problem base 13", see [URL="https://raw.githubusercontent.com/xayahrainie4793/mepn-data/master/data/minimal.13.txt"]this data[/URL] and [URL="https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf"]this article[/URL]

* (23*7^9235-11)/6 (7806 digits), the smallest prime of the form 3555...5554 in base 7, proving the primality of this prime will complete the proof of the "[URL="https://docs.google.com/document/d/e/2PACX-1vQct6Hx-IkJd5-iIuDuOKkKdw2teGmmHW-P75MPaxqBXB37u0odFBml5rx0PoLa0odTyuW67N_vn96J/pub"]quasi-minimal prime problem[/URL] base 7", although this prime is not a quasi-minimal prime in base 7 (the "quasi-minimal prime problem base 7" is in fact already be proven, there are 71 quasi-minimal primes in base 7 and the largest of which has only 17 digits in base 7, but the proof of the "quasi-minimal prime problem base 7" include the large PRP (23*7^9235-11)/6

* 5^50669+31712 (35417 digits), if you prove the primality of this prime, you will full-prove the "mixed Sierpinski conjecture base 5", see [URL="http://www.kurims.kyoto-u.ac.jp/EMIS/journals/INTEGERS/papers/i61/i61.pdf"]http://www.kurims.kyoto-u.ac.jp/EMIS/journals/INTEGERS/papers/i61/i61.pdf[/URL] for the base 2 version, and there is 30 k < 159986 without known prime of the form k*5^n+1 with n>=1: {6436, 7528, 10918, 26798, 29914, 31712, 36412, 41738, 44348, 44738, 45748, 51208, 58642, 60394, 62698, 64258, 67612, 67748, 71492, 74632, 76724, 83936, 84284, 90056, 92906, 93484, 105464, 126134, 139196, 152588}, see [URL="http://www.primegrid.com/forum_thread.php?id=5087"]http://www.primegrid.com/forum_thread.php?id=5087[/URL] and [URL="http://www.noprimeleftbehind.net/crus/Sierp-conjecture-base5-reserve.htm"]http://www.noprimeleftbehind.net/crus/Sierp-conjecture-base5-reserve.htm[/URL], and we have these primes in the dual form (5^n+k):

[CODE]
5^24+6436
5^36+7528
5^144+10918
5^1505+26798
5^4+29914
5^50669+31712
5^458+36412
5^3+41738
5^9+44348
5^485+44738
5^12+45748
5^12+51208
5^46+58642
5^12+60394
5^2+62698
5^2+64258
5^10+67612
5^41+67748
5^13+71492
5^74+74632
5^7+76724
5^3+83936
5^21+84284
5^181+90056
5^23+92906
5^4+93484
5^11+105464
5^11+126134
5^1+139196
5^15+152588
[/CODE]

all of them except 5^50669+31712 are proven primes, thus if you prove the primality of 5^50669+31712, you will prove the "mixed Sierpinski conjecture base 5", i.e. the "mixed Sierpinski conjecture base 5" will become a theorem, like the base 2 case, when the primality of 2^16389+67607 was proven, the "mixed Sierpinski conjecture" become a theorem.

Gelly 2022-04-18 20:30

[QUOTE=Gelly;594054]looks like no one claimed it, and i've de-crufted my machine and set up, so i'm working on this candidate again!![/QUOTE]

done! took way longer than it should have for a variety of reasons (love my IceGiant cooler, but the fans fall apart LOUDLY), but we have another ECPP prime with 30k+ digits! currently working its way through the digestive system of factordb and, once it's independently verified, will send it over to primo and T5K.

will be taking a break on this machine while I move apartments.

paulunderwood 2022-04-19 03:22

[QUOTE=Gelly;604238]done! took way longer than it should have for a variety of reasons (love my IceGiant cooler, but the fans fall apart LOUDLY), but we have another ECPP prime with 30k+ digits! currently working its way through the digestive system of factordb and, once it's independently verified, will send it over to primo and T5K.

will be taking a break on this machine while I move apartments.[/QUOTE]

Marcel Martin can download the certificate from factorDB :smile:

Congrats on your 30k+'er, the largest proven Mersenne co-factor. :toot:

paulunderwood 2022-04-20 11:50

[QUOTE=paulunderwood;604247]Marcel Martin can download the certificate from factorDB :smile:
[/QUOTE]

It seems Marcel only displays [URL="http://www.ellipsa.eu/public/primo/records.html"]record-breakers now[/URL] -- no longer the top 20 Primo proofs.

Gelly 2022-04-26 02:38

[QUOTE=paulunderwood;604247]Marcel Martin can download the certificate from factorDB :smile:

Congrats on your 30k+'er, the largest proven Mersenne co-factor. :toot:[/QUOTE]

factordb seems to agree that it's prime, but the forward facing certificate doesn't appear to be available. not entirely sure what's going on there, as it says it's proven prime, but doesn't have an ECPP cert attached or anything.

i'll still attach the factordb entry to a t5k post but i'm still slightly unsure.

and yeah, i don't blame marcel for no longer posting all top 20s. seems to get updated a lot haha.

paulunderwood 2022-04-27 16:13

[QUOTE=Gelly;604793]factordb seems to agree that it's prime, but the forward facing certificate doesn't appear to be available. not entirely sure what's going on there, as it says it's proven prime, but doesn't have an ECPP cert attached or anything.

i'll still attach the factordb entry to a t5k post but i'm still slightly unsure.
[/QUOTE]

I'd say go ahead and report it to The Prime Pages at UTM and be assured in the knowledge that factorDB successfully verified the certificate.

ps. Do you fancy proving the [URL="https://www.mersenne.ca/exponent/78737"]co-factor of M78737[/URL]?


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