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.

This prime's information:

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 (*):191 (digit rank is 1)
Entrance Rank (*):30
Currently on list? (*):short
Submitted:8/22/2017 22:13:20 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:123862
Status Flags:none
Score (*):49.2037 (normalized score 69.7773)

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 10
Subcategory: "Generalized Cullen"
(archival tag id 218863, tag last modified 2023-12-29 19:37:13)

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.

PrimeGrid writes (12 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.
fieldvalue
prime_id123862
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"1341174*53^1341174+1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [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 22:30:15
created2017-08-22 22:21:01
id169516

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