763795 · 64582771 + 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:763795 · 64582771 + 1
Verification status (*):Proven
Official Comment (*):Generalized Cullen
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):A6 : Propper, Gcwsieve, PRST
Decimal Digits:3566095   (log10 is 3566094.8668487)
Rank (*):89 (digit rank is 1)
Entrance Rank (*):78
Currently on list? (*):short
Submitted:12/11/2023 14:01:38 UTC
Last modified:12/14/2023 04:37:19 UTC
Database id:136749
Status Flags:none
Score (*):50.5306 (normalized score 248.1274)

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 5
Subcategory: "Generalized Cullen"
(archival tag id 229035, 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.

Ryan Propper writes (11 Dec 2023):  (report abuse)
= 4582770*6^4582770+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_id136749
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -q"763795*6^4582771+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 763795*6^4582771+1 [N-1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 11
Special modular reduction using zero-padded FMA3 FFT length 1344K, Pass1=448, Pass2=3K, clm=2 on 763795*6^4582771+1
Calling Brillhart-Lehmer-Selfridge with factored part 61.31%


763795*6^4582771+1 is prime! (156554.3166s+0.0298s)
[Elapsed time: 1.81 days]
modified2023-12-14 04:08:53
created2023-12-12 08:39:36
id182584

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