3 · 210829346 + 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 · 210829346 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(10829343,3), GF(10829345,5)
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):L3770 : Tang, Srsieve, PrimeGrid, LLR
Decimal Digits:3259959   (log10 is 3259958.456545)
Rank (*):124 (digit rank is 1)
Entrance Rank (*):12
Currently on list? (*):short
Submitted:1/17/2014 15:35:15 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:116922
Status Flags:Verify
Score (*):50.2557 (normalized score 187.6308)

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 4, weight 51.354370959703
Subcategory: "Divides GF(*,3)"
(archival tag id 217592, tag last modified 2023-03-11 15:53:59)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 3, weight 51.354370959703
Subcategory: "Divides GF(*,5)"
(archival tag id 217593, 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.

Serge Batalov writes (11 Sep 2014):  (report abuse)
PrimeGrid reports that 3*2^10829346+1 Divides GF(10829343,3), GF(10829345,5), GF(10829344,8), and GF(10829345,11), as well as xGF(10829345,5,3), xGF(10829342,7,4), xGF(10829344,8,3), xGF(10829345,8,5), xGF(10829345,9,5), xGF(10829344,9,8), xGF(10829345,11,3), xGF(10829344,11,5), xGF(10829345,11,8) xGF(10829345,11,9), and xGF(10829343,12,7)

PrimeGrid writes (27 Nov 2016):  (report abuse)
For more details, 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.
notesPrimality testing 3*2^10829346+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Special modular reduction using all-complex AVX FFT length 576K, Pass1=128, Pass2=4608 on 3*2^10829346+1 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3*2^10829346+1 is prime! (42686.3529s+0.0169s) Primality testing 3*2^10829346+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 3*2^10829346+1 is prime! (46223.9576s+0.0026s)
modified2020-07-07 22:30:18
created2014-01-17 15:37:05

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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