1341174 · 531341174 + 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:1341174 · 531341174 + 1
Verification status (*):Proven
Official Comment (*):Generalized Cullen
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L4668 : Okazaki, Gcwsieve, MultiSieve, PrimeGrid, LLR
Decimal Digits:2312561   (log10 is 2312560.0926211)
Rank (*):110 (digit rank is 1)
Entrance Rank (*):30
Currently on list? (*):short
Submitted:8/22/2017 17:13:20 CDT
Last modified:8/23/2017 07:50:09 CDT
Database id:123862
Status Flags:TrialDiv
Score (*):49.2037 (normalized score 115.3261)

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 Cullen (archivable *)
Prime on list: yes, rank 6
Subcategory: "Generalized Cullen"
(archival tag id 218863, tag last modified 2021-09-01 15:37:16)

User comments about this prime (disclaimer):

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PrimeGrid writes (11 Mar 2018):  (report abuse)
This is the first known Generalized Cullen prime for base 53. For more details, please see the official announcement.

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"1341174*53^1341174+1" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 1341174*53^1341174+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 1341174*53^1341174+1 is prime! (51274.9367s+0.0329s) [Elapsed time: 14.24 hours]
modified2020-07-07 17:30:15
created2017-08-22 17:21:01

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