185688291 · 2161617 + 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:185688291 · 2161617 + 1
Verification status (*):Proven
Official Comment:Cunningham chain 2nd kind (2p-1)
Proof-code(s): (*):p282 : Rajala, NewPGen, OpenPFGW
Decimal Digits:48660   (log10 is 48659.833593745)
Rank (*):52510 (digit rank is 3)
Entrance Rank (*):47985
Currently on list? (*):short
Submitted:1/7/2015 23:10:57 CDT
Last modified:1/7/2015 23:20:33 CDT
Database id:119064
Status Flags:TrialDiv
Score (*):37.3332 (normalized score 0.0016)

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.
Cunningham Chains (2nd kind) (archivable class *)
Prime on list: yes, rank 4, weight 37.0553499519556
Subcategory: "Cunningham chain 2nd kind (2p-1)"
(archival tag id 217880, tag last modified 2016-07-12 03:50:40)

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_id119064
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"185688291*2^161617+1" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 185688291*2^161617+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%


185688291*2^161617+1 is prime! (13.4244s+0.0003s)
[Elapsed time: 13.00 seconds]
modified2015-04-20 07:32:10
created2015-01-07 23:11:02
id164667

Query times: 0.0006 seconds to select prime, 0.0004 seconds to seek comments.