(22976221 - 1) · (10204068 - 1172064) + 1

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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

This prime's information:

Description:(22976221 - 1) · (10204068 - 1172064) + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p449 : Rodriguez2, OpenPFGW
Decimal Digits:1100000   (log10 is 1099999.794725)
Rank (*):1019 (digit rank is 1)
Entrance Rank (*):975
Currently on list? (*):yes
Submitted:10/7/2024 07:01:42 UTC
Last modified:11/11/2024 15:12:22 UTC
Database id:138625
Status Flags:none
Score (*):46.9254 (normalized score 6.0386)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Ruben Rodriguez Cunillera writes (8 Nov 2024):  (report abuse)
To prove the primality using PFGW, we need to create a helper file named helper.txt containing this line:
2^2976221-1
which is a Mersenne prime and the large factor of n-1.

C:app3>pfgw64 -t -V -hhelper.txt -q"(2^2976221-1)*(10^204068-1172064)+1"
PFGW Version 4.1.3.64BIT.20240114.Win_Dev [GWNUM 30.19]

Primality testing (2^2976221-1)*(10^204068-1172064)+1 [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.txt
Running N-1 test using base 3 5351)
Generic modular reduction using Montgomery reduction AVX-512 FFT length 2x192K, Pass1=3K, Pass2=64, clm=1 on A 3654121-bit number
(2^2976221-1)*(10^204068-1172064)+1 is prime! (12997.0135s+0.0062s)

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions.  We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.
fieldvalue
prime_id138625
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper_138625 -q"(2^2976221-1)*(10^204068-1172064)+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (2^2976221-1)*(10^204068-1172064)+1 [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_138625
trial


Running N-1 test using base 3
Generic modular reduction using generic reduction AVX-512 FFT length 384K, Pass1=1K, Pass2=384, clm=1 on A 3654122-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 81.45%


(2^2976221-1)*(10^204068-1172064)+1 is prime! (48375.7853s+0.0101s)
[Elapsed time: 13.44 hours]


Helper File:
2^2976221-1
modified2024-11-11 15:12:22
created2024-11-11 01:46:02
id184565

fieldvalue
prime_id138625
person_id9
machineUsing: Digital Ocean Droplet
whatprp
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -q"(2^2976221-1)*(10^204068-1172064)+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (2^2976221-1)*(10^204068-1172064)+1 [N-1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 3
Generic modular reduction using generic reduction AVX-512 FFT length 384K, Pass1=1K, Pass2=384, clm=1 on A 3654122-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%


(2^2976221-1)*(10^204068-1172064)+1 is PRP! (22242.8790s+0.0106s)
[Elapsed time: 6.18 hours]
modified2024-10-07 17:05:07
created2024-10-07 10:54:22
id184469

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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