24792057 - 22396029 + 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.

Description:24792057 - 22396029 + 1
Verification status (*):Proven
Official Comment (*):Gaussian Mersenne norm 40?, generalized unique
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L3839 : Batalov, EMsieve, LLR
Decimal Digits:1442553   (log10 is 1442552.89793155)
Rank (*):236 (digit rank is 1)
Entrance Rank (*):41
Currently on list? (*):short
Submitted:4/5/2014 11:25:37 CDT
Last modified:8/4/2020 13:21:47 CDT
Database id:117556
Status Flags:TrialDiv
Score (*):47.7569 (normalized score 32.536)

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.
Gaussian Mersenne norm (archivable *)
Prime on list: yes, rank 2
Subcategory: "Gaussian Mersenne norm"
(archival tag id 217666, tag last modified 2020-08-02 20:20:04)
Generalized Unique (archivable *)
Prime on list: yes, rank 11
Subcategory: "Generalized Unique"
(archival tag id 224087, tag last modified 2020-08-04 13:50:04)

User comments about this prime (disclaimer):

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Serge Batalov writes (11 Sep 2014):  (report abuse)
Gaussian Mersenne norms are also Generalized unique primes.
This one can be written as Phi(4, 2^2396029 - 1)/2.

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -t -q"2^4792057-2^2396029+1" 2>&1 PFGW Version [GWNUM 26.5] Primality testing 2^4792057-2^2396029+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Calling Brillhart-Lehmer-Selfridge with factored part 50.00% 2^4792057-2^2396029+1 is prime! (578678.3784s+0.0048s) [Elapsed time: 6.70 days]
modified2020-07-07 17:30:17
created2014-04-05 16:42:03

Query times: 0.0016 seconds to select prime, 0.0007 seconds to seek comments.
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