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 2021-09-08, 04:27 #1970 rudy235     Jun 2015 Vallejo, CA/. 3×383 Posts Both forms of numbers exist, The 3*2k - 1 are called Thabit primes and there are 64 of them known. https://oeis.org/A002235/b002235.txt Those of the Form 3*2k + 1 are called Thabit of the second kind and 50 of them are known https://oeis.org/A002253/b002253.txt
2021-09-08, 05:06   #1971
kar_bon

Mar 2006
Germany

2,999 Posts

Quote:
 Originally Posted by rudy235 It is a 3 2 1 Prime i.e. 3*2k-1
Should read "321 Prime Search i.e. 3*2k±1" so the PrimeGrid Prime Search for both forms.

 2021-09-29, 09:48 #1972 manrus   "Dmitrii" Mar 2021 St.Petersburg,Russia 11 Posts 3317*2^2415998-1 is prime! (727292 decimal digits)
2021-10-15, 15:41   #1973
rudy235

Jun 2015
Vallejo, CA/.

47D16 Posts

Quote:
 Originally Posted by rudy235 Both forms of numbers exist, The 3*2k - 1 are called Thabit primes and there are 64 of them known. https://oeis.org/A002235/b002235.txt Those of the Form 3*2k + 1 are called Thabit of the second kind and 50 of them are known https://oeis.org/A002253/b002253.txt

.....................
HERE IS THE OFFICIAL ANNOUNCEMENT

PrimeGrid’s
321 Prime Search

On 6 September 2021, 07:16:28 UTC, PrimeGrid’s 321 Prime Search found another Mega Prime:

3*217748034-1

The prime is 5,342,692 digits long and will enter Chris Caldwell's “The Largest Known Primes
Database” (http://primes.utm.edu/primes) ranked 18th overall. This is the largest known prime for
the 3*2^n-1 form.

The discovery was made by Marc Wiseler of Ireland using an AMD Ryzen 9 5900X 12-Core
Processor with 16GB RAM, running Microsoft Windows 10 Professional x64 Edition. This
computer took about 2 hours, 45 minutes to complete the primality test using LLR. Marc Wiseler
is a member of Storm.

The prime was verified on 6 September 2021, 11:47 UTC, by an Intel(R) Core(TM) i7-9800X CPU
@ 3.80GHz with 32GB of RAM, running CentOS. This computer took 2 hours and 41 minutes to
complete the primality test using LLR2.
Credits for the discovery are as follows:

1. Marc Wiseler (Ireland), discoverer
2. PrimeGrid, et al.
3. Srsieve, sieving program developed by Geoff Reynolds
4. PSieve, sieving program developed by Ken Brazier and Geoff Reynolds
5. LLR, primality program developed by Jean Penné
6. LLR2, primality program developed by Pavel Atnashev

Entry in “The Largest Know Primes Database” can be found here:
https://primes.utm.edu/primes/page.php?id=132678

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

Last fiddled with by Dr Sardonicus on 2021-10-15 at 16:02 Reason: formatting (superscript exponent)

 2021-10-20, 13:23 #1974 manrus   "Dmitrii" Mar 2021 St.Petersburg,Russia 11 Posts 3317*2^3117162-1 is prime! (938363 decimal digits)
 2021-10-27, 16:10 #1975 manrus   "Dmitrii" Mar 2021 St.Petersburg,Russia 11 Posts 3317*2^2523366-1 is prime! (759613 decimal digits)
 2021-11-19, 12:46 #1976 Trilo     "W. Byerly" Aug 2013 81*2^3174353-1 7×19 Posts 81*2^2375447-1 is prime! (715083 digits) 81*2^2797443-1 is prime! (842117 digits) (New personal record )
 2021-11-20, 19:21 #1977 Thomas11     Feb 2003 27×3×5 Posts 233*2^2846392-1 (856852 digits)
 2021-12-04, 19:27 #1978 andyhedges   Mar 2016 22 Posts 1005·2^3,349,046-1 (1,008,167 digits)
 2022-03-26, 15:02 #1979 rudy235     Jun 2015 Vallejo, CA/. 100011111012 Posts New 321 prime record 3 *2 18924898- 1 5,696,990 Digits L5530 Mar 2022 (Unverified because InProcess) Congratulations to FMatillek Last fiddled with by rudy235 on 2022-03-26 at 15:18 Reason: Typo
 2022-03-31, 09:20 #1980 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 32×1,117 Posts Just for kicks and giggles I tested a little bit of k=1965 (which happens to be my year) and found unlikely quickly 1965 · 23322579 - 1 (1,000,200 digits) and 1965 · 23325639 - 1 (1,001,121 digits). Just a curiosity.

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