23704053 + 21852027 + 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:23704053 + 21852027 + 1
Verification status (*):Proven
Official Comment (*):Gaussian Mersenne norm 39?, generalized unique
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L3839 : Batalov, EMsieve, LLR
Decimal Digits:1115032   (log10 is 1115031.0585292)
Rank (*):362 (digit rank is 1)
Entrance Rank (*):73
Currently on list? (*):short
Submitted:9/6/2014 11:22:12 CDT
Last modified:8/4/2020 13:21:47 CDT
Database id:118452
Status Flags:TrialDiv
Score (*):46.967 (normalized score 13.1946)

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 3
Subcategory: "Gaussian Mersenne norm"
(archival tag id 217810, tag last modified 2020-08-02 20:20:04)
Generalized Unique (archivable *)
Prime on list: yes, rank 18
Subcategory: "Generalized Unique"
(archival tag id 224094, tag last modified 2020-08-04 13:50:04)

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.

Serge Batalov writes (11 Sep 2014):  (report abuse)
Gaussian Mersenne norms are also Generalized unique primes.
This one can be written as Phi(4, 2^1852027 + 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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"2^3704053+2^1852027+1" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 2^3704053+2^1852027+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 50.00% 2^3704053+2^1852027+1 is prime! (27993.8014s+0.0014s) [Elapsed time: 7.78 hours]
modified2020-07-07 17:30:17
created2014-09-06 11:31:01

Query times: 0.0008 seconds to select prime, 0.0012 seconds to seek comments.
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