mersenneforum.org New ECPP record (currently: 73,269 digits)
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2023-02-21, 22:45   #78
paulunderwood

Sep 2002
Database er0rr

4,549 Posts

Quote:
 Originally Posted by frmky I am aware this will soon be exceeded, but 104824^5+5^104824, at 73,269 digits, is prime. Stage 1 took 32 days on 20 24-core computers using GWNUM. Stage 2 took 27 days on 8 20-core computers. A few steps with large prime factors of h took most of the time in stage 2. I will explore the effects of further limiting the largest prime factor of h. Thanks again to Andreas for creating CM and Paul for adding support for GWNUM.
Quote:
 Originally Posted by xilman Nice work! Any estimate when the first 100K digit prime will be proven?
Congrats Greg!

R109297 should be doable with 4x the resources Greg used

Last fiddled with by paulunderwood on 2023-02-21 at 22:56

 2023-02-24, 22:57 #79 rudy235     Jun 2015 Vallejo, CA/. 2×577 Posts So now we have a 73,269 digit proven via ECPP. this is a Leyland Prime. One that cannot be proven by specifically tailored methods. The prime in question is 5104824 + 1048245 73269 digits. A couple of things are worth noting: The โgapโ in digits to the next ECPP primes is notable. Over 23000 digits more than the one just discovered only 2 months ago. The largest 8 ECPP primes have been discovered in the past 52 weeks. We can only assume that R86453 will be proven prime in the fairly near future as it is only twice as hard as this one just discovered. Huge congratulation to Greg Childers. Last fiddled with by rudy235 on 2023-02-24 at 22:58 Reason: typo
2023-02-25, 17:12   #80
kruoli

"Oliver"
Sep 2017
Porta Westfalica, DE

25·32·5 Posts

Quote:
 Originally Posted by xilman Any estimate when the first 100K digit prime will be proven?
Do you mean the smallest number with 100,000 decimal digits that is prime or with at least 100,000 decimal digits? In the latter case, it is February 17, 1992, when M756,839 was discovered.

In the former, that should be 1099,999+309,403, if my quick calculations are correct.

Last fiddled with by kruoli on 2023-02-25 at 17:38 Reason: Corrected as pointed out by xilman.

2023-02-25, 17:35   #81
xilman
Bamboozled!

"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across

1171910 Posts

Quote:
 Originally Posted by kruoli Do you mean the smallest number with 100,000 decimal digits that is prime or with at least 100,000 decimal digits? In the latter case, it is February 17, 1992, when M756,839 was discovered. In the former, thed should be 1099,999+10^99999+309403, if my quick calculations are correct.
Fixing a minor tyypo: I believe you mean

In the former, that should be 1099,999+309403, if my quick calculations are correct.

 2023-02-25, 17:37 #82 kruoli     "Oliver" Sep 2017 Porta Westfalica, DE 5A016 Posts Wow, I have no clue how that happened. :D 1068
 2023-02-25, 20:09 #83 paulunderwood     Sep 2002 Database er0rr 4,549 Posts Comparing total CPU hours for Greg's recent proof with Andreas's expected proof of R86453, the minimal 100k digit number and R109297: Code: ? (86453/73269.)^4 1.9383813225131506029336873744208292121 ? (100000/73269.)^4 3.4699158544965667114008777645966191866 ? (109297/73269.)^4 4.9516724586074826088662323174646459749 But I wonder if Andreas uses GWNUM, which will skew the stats. Last fiddled with by paulunderwood on 2023-02-25 at 20:52
2023-03-04, 13:45   #84
JeppeSN

"Jeppe"
Jan 2016
Denmark

22·47 Posts

Quote:
 Originally Posted by kruoli Do you mean the smallest number with 100,000 decimal digits that is prime or with at least 100,000 decimal digits? In the latter case, it is February 17, 1992, when M756,839 was discovered. In the former, that should be 1099,999+309,403, if my quick calculations are correct.
The smallest PRP with 100'000 digits is registered but not proven prime (I think). The first prime with exactly 100'000 digits that was proven (but not with ECPP) could be 593573509*2^332162+1 from 16 August 2000.

However, given the context of the thread, it is virtually certain xilman meant the first prime with at least 100'000 digits proven prime with the ECPP method.

/JeppeSN

2023-03-04, 18:46   #85
xilman
Bamboozled!

"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across

11,719 Posts

Quote:
 Originally Posted by JeppeSN However, given the context of the thread, it is virtually certain xilman meant the first prime with at least 100'000 digits proven prime with the ECPP method.
Correct.

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