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Old 2021-09-08, 04:27   #1970
rudy235
 
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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
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Old 2021-09-08, 05:06   #1971
kar_bon
 
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Quote:
Originally Posted by rudy235 View Post
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.
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Old 2021-09-29, 09:48   #1972
manrus
 
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3317*2^2415998-1 is prime! (727292 decimal digits)
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Old 2021-10-15, 15:41   #1973
rudy235
 
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Quote:
Originally Posted by rudy235 View Post
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)
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Old 2021-10-20, 13:23   #1974
manrus
 
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3317*2^3117162-1 is prime! (938363 decimal digits)
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Old 2021-10-27, 16:10   #1975
manrus
 
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3317*2^2523366-1 is prime! (759613 decimal digits)
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Old 2021-11-19, 12:46   #1976
Trilo
 
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Aug 2013
81*2^2797443-1

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81*2^2375447-1 is prime! (715083 digits)
81*2^2797443-1 is prime! (842117 digits) (New personal record )
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Old 2021-11-20, 19:21   #1977
Thomas11
 
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233*2^2846392-1 (856852 digits)
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Old 2021-12-04, 19:27   #1978
andyhedges
 
Mar 2016

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1005·2^3,349,046-1 (1,008,167 digits)
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