691869865536 + 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:691869865536 + 1
Verification status (*):Proven
Official Comment:Generalized Fermat
Proof-code(s): (*):L4302 : VanRangelrooij, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:448268   (log10 is 448267.837383401)
Rank (*):2518 (digit rank is 1)
Entrance Rank (*):1843
Currently on list? (*):yes
Submitted:2/5/2016 16:14:05 CDT
Last modified:2/5/2016 17:50:13 CDT
Database id:121054
Status Flags:TrialDiv
Score (*):44.1696 (normalized score 1.5358)

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 312
Subcategory: "Generalized Fermat"
(archival tag id 218189, tag last modified 2017-10-06 04:20:21)

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_id121054
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"6918698^65536+1" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 6918698^65536+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 44.56%


6918698^65536+1 is prime! (4191.1298s+0.0129s)
[Elapsed time: 69.85 minutes]
modified2016-04-08 12:40:26
created2016-02-05 16:19:21
id166685

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