
At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:
field (help)  value 
Description:  3 · 2^{2291610} + 1 
Verification status (*):  Proven 
Official Comment:  Divides GF(2291607,3), GF(2291609,5) 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  L753 : Wolfram, Srsieve, PrimeGrid, LLR 
Decimal Digits:  689844 (log_{10} is 689843.82548479) 
Rank (*):  659 (digit rank is 1) 
Entrance Rank (*):  40 
Currently on list? (*):  short 
Submitted:  8/20/2008 09:57:52 CDT 
Last modified:  3/18/2009 09:45:55 CDT 
Database id:  85438 
Status Flags:  none 
Score (*):  45.4934 (normalized score 5.8405) 

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 46.5921087650778
Subcategory: "Divides GF(*,5)"
(archival tag id 187028, tag last modified 20160315 13:57:15)  Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
 Prime on list: yes, rank 8, weight 46.5921087650778
Subcategory: "Divides GF(*,3)"
(archival tag id 187027, tag last modified 20160315 13:57:15)
User comments about this prime (disclaimer):
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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.
field  value 
prime_id  85438 
person_id  9 
machine  Ditto P4 P4 
what  trial_divided 
notes  Command: /home/ditto/client/TrialDiv/TrialDiv q 3 2 2291610 1 2>&1 [Elapsed time: 10.743 seconds]

modified  20111227 16:48:46 
created  20080820 10:05:01 
id  100343 

field  value 
prime_id  85438 
person_id  9 
machine  Ditto P4 P4 
what  prime 
notes  Command: /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 [N1, BrillhartLehmerSelfridge] Running N1 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 BrillhartLehmerSelfridge with factored part 100.00% 3*2^2291610+1 is prime! (350.7503s+0.0000s) [Elapsed time: 13.57 hours]

modified  20080912 14:12:35 
created  20080820 10:08:02 
id  100344 

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
