814659265536 + 1
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help

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:814659265536 + 1
Verification status (*):Proven
Official Comment:Generalized Fermat
Proof-code(s): (*):L4318 : Marshall1, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:452918   (log10 is 452917.720933478)
Rank (*):2440 (digit rank is 1)
Entrance Rank (*):1804
Currently on list? (*):yes
Submitted:2/13/2016 17:44:24 CDT
Last modified:2/13/2016 19:20:34 CDT
Database id:121147
Status Flags:TrialDiv
Score (*):44.2013 (normalized score 1.5853)

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 297
Subcategory: "Generalized Fermat"
(archival tag id 218205, 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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"8146592^65536+1" 2>&1
PFGW Version [GWNUM 27.11]
Primality testing 8146592^65536+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 59.72%

8146592^65536+1 is prime! (4086.0613s+0.0103s)
[Elapsed time: 68.10 minutes]
modified2016-04-08 12:40:26
created2016-02-13 17:51:02

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