5586416131072 + 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:5586416131072 + 1
Verification status (*):Proven
Official Comment:Generalized Fermat
Proof-code(s): (*):L4454 : Clark5, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:884361   (log10 is 884360.252344679)
Rank (*):387 (digit rank is 1)
Entrance Rank (*):263
Currently on list? (*):short
Submitted:9/24/2016 14:39:18 CDT
Last modified:9/24/2016 19:20:45 CDT
Database id:122248
Status Flags:TrialDiv
Score (*):46.2559 (normalized score 12.3678)

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 (archivable *)
Prime on list: no, rank 57
Subcategory: "Generalized Fermat"
(archival tag id 218428, tag last modified 2017-09-15 04:50:18)

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_id122248
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"5586416^131072+1" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 5586416^131072+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 66.72%


5586416^131072+1 is prime! (16322.5467s+0.0229s)
[Elapsed time: 4.53 hours]
modified2017-01-27 05:57:11
created2016-09-24 14:41:01
id167887

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