# 3 · 22291610 + 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 · 22291610 + 1 Proven Divides GF(2291607,3), GF(2291609,5) This prime has 1 user comment below. L753 : Wolfram, Srsieve, PrimeGrid, LLR 689844   (log10 is 689843.82548479) 3305 (digit rank is 1) 40 short 8/20/2008 14:57:52 UTC 3/11/2023 15:54:10 UTC 85438 none 45.4934 (normalized score 2.0693)

#### 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 10, weight 46.592108765078
Subcategory: "Divides GF(*,5)"
(archival tag id 187028, tag last modified 2023-03-11 15:53:59)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 14, weight 46.592108765078
Subcategory: "Divides GF(*,3)"
(archival tag id 187027, tag last modified 2023-03-11 15:53:59)

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PrimeGrid writes (11 Sep 2014):  (report abuse)
 3*2^2291610+1 is a Factor of GF(2291607,3) 3*2^2291610+1 is a Factor of GF(2291609,5) 3*2^2291610+1 is a Factor of xGF(2291609,5,3) 3*2^2291610+1 is a Factor of xGF(2291607,7,4) 3*2^2291610+1 is a Factor of GF(2291608,8) 3*2^2291610+1 is a Factor of xGF(2291608,8,3) 3*2^2291610+1 is a Factor of xGF(2291609,8,5) 3*2^2291610+1 is a Factor of xGF(2291609,9,5) 3*2^2291610+1 is a Factor of xGF(2291608,9,8) 3*2^2291610+1 is a Factor of GF(2291608,11) 3*2^2291610+1 is a Factor of xGF(2291608,11,3) 3*2^2291610+1 is a Factor of xGF(2291609,11,5) 3*2^2291610+1 is a Factor of xGF(2291607,11,8) 3*2^2291610+1 is a Factor of xGF(2291608,11,9) 3*2^2291610+1 is a Factor of xGF(2291604,12,7)

#### 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_id85438
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 3 2 2291610 1 2>&1 [Elapsed time: 10.743 seconds]
modified2020-07-07 22:30:39
created2008-08-20 15:05:01
id100343

fieldvalue
prime_id85438
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"3*2^2291610+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3*2^2291610+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(327680,19) to FFT(327680,18) Reduced from FFT(327680,18) to FFT(327680,17) Reduced from FFT(327680,17) to FFT(327680,16) 4583232 bit request FFT size=(327680,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3*2^2291610+1 is prime! (-350.7503s+0.0000s) [Elapsed time: 13.57 hours]
modified2020-07-07 22:30:39
created2008-08-20 15:08:02
id100344

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.