657 · 21998854 + 1
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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:657 · 21998854 + 1
Verification status (*):Proven
Official Comment:Divides GF(1998852,10)
Proof-code(s): (*):L2520 : Mamanakis, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:601718   (log10 is 601717.8285183)
Rank (*):1958 (digit rank is 1)
Entrance Rank (*):274
Currently on list? (*):short
Submitted:10/29/2013 11:19:05 CDT
Last modified:10/29/2013 16:38:58 CDT
Database id:116132
Status Flags:TrialDiv
Score (*):45.0738 (normalized score 2.4801)

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 8, weight 51.5615321621671
Subcategory: "Divides GF(*,10)"
(archival tag id 217396, tag last modified 2017-08-24 21:20:02)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"657*2^1998854+1" 2>&1
PFGW Version [GWNUM 26.5]
Primality testing 657*2^1998854+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
657*2^1998854+1 is prime! (11724.9821s+0.0014s)
[Elapsed time: 3.26 hours]
modified2014-04-01 17:37:40
created2013-10-29 11:23:01

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