3 · 216408818 + 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:3 · 216408818 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(16408814,3), GF(16408817,5)
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):L5171 : Brown1, LLR2, Srsieve, PrimeGrid, LLR
Decimal Digits:4939547   (log10 is 4939546.8885123)
Rank (*):42 (digit rank is 1)
Entrance Rank (*):21
Currently on list? (*):short
Submitted:10/28/2020 20:19:37 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:131362
Status Flags:none
Score (*):51.5283 (normalized score 664.9133)

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 Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 1, weight 52.626959098855
Subcategory: "Divides GF(*,3)"
(archival tag id 225700, tag last modified 2023-03-11 15:53:59)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 1, weight 52.626959098855
Subcategory: "Divides GF(*,5)"
(archival tag id 225701, tag last modified 2023-03-11 15:53:59)

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 (28 Oct 2020):  (report abuse)
Also divides xGF(16408817,5,3), xGF(16408816,7,4), GF(16408815,8), xGF(16408815,8,3), xGF(16408817,8,5), xGF(16408817,9,5), xGF(16408815,9,8), xGF(16408817,11,4), xGF(16408817,11,7), xGF(16408816,12,7), and xGF(16408817,12,11).

PrimeGrid writes (31 Oct 2020):  (report abuse)
For more information, 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 (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -q"3*2^16408818+1" 2>&1 PFGW Version [GWNUM 29.8] Primality testing 3*2^16408818+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3*2^16408818+1 is prime! (99856.0989s+0.0083s) [Elapsed time: 27.74 hours]
modified2021-04-20 22:39:26
created2020-10-28 20:21:02

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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