41676 · 7875197 - 1

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:41676 · 7875197 - 1
Verification status (*):Proven
Official Comment (*):Generalized Woodall
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L2777 : Ritschel, Gcwsieve, TOPS, LLR
Decimal Digits:739632   (log10 is 739631.88921239)
Rank (*):3782 (digit rank is 1)
Entrance Rank (*):87
Currently on list? (*):short
Submitted:3/18/2012 18:01:44 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:105684
Status Flags:none
Score (*):45.7074 (normalized score 2.0961)

Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper.  Such primes are tracked with archival tags.
Generalized Woodall (archivable *)
Prime on list: yes, rank 20
Subcategory: "Generalized Woodall"
(archival tag id 214239, tag last modified 2024-02-26 15:37:18)

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.

Thomas Ritschel writes (11 Sep 2014):  (report abuse)
291732*343^291732-1

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_id105684
person_id9
machineRedHat Virtual STEM Server
whatprime
notesCommand: /home/caldwell/client/pfgw -tp -q"41676*7^875197-1" 2>&1 PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing 41676*7^875197-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 11, base 2+sqrt(11) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 41676*7^875197-1 is prime! (73877.5416s+0.0979s) [Elapsed time: 20.52 hours]
modified2020-07-07 22:30:27
created2012-03-18 18:03:41
id140957

fieldvalue
prime_id105684
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 41676 7 875197 -1 2>&1 [Elapsed time: 10.410 seconds]
modified2020-07-07 22:30:27
created2012-03-18 18:05:01
id140958

Query times: 0.0005 seconds to select prime, 0.0005 seconds to seek comments.
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