# 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 Proven Divides GF(10829343,3), GF(10829345,5) This prime has 2 user comments below. L3770 : Tang, Srsieve, PrimeGrid, LLR 3259959   (log10 is 3259958.456545) 96 (digit rank is 1) 12 short 1/17/2014 15:35:15 UTC 3/11/2023 15:54:10 UTC 116922 Verify, TrialDiv 50.2557 (normalized score 242.1404)

#### 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)"
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 3, weight 51.354370959703
Subcategory: "Divides GF(*,5)"

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)
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#### 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_id116922
person_id9
machineExternal
whatprime
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
id162431

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