446513232768 + 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:446513232768 + 1
Verification status (*):Proven
Official Comment:Generalized Fermat
Proof-code(s): (*):p340 : Smith8, GeneFer, AthGFNSieve, PrimeGrid, OpenPFGW
Decimal Digits:217902   (log10 is 217901.77041448)
Rank (*):22602 (digit rank is 1)
Entrance Rank (*):3980
Currently on list? (*):no
Submitted:2/1/2012 12:24:49 CDT
Last modified:2/1/2012 13:50:24 CDT
Removed (*):3/15/2012 11:38:51 CDT
Database id:104160
Status Flags:none
Score (*):41.952 (normalized score 0.1091)

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 1391
Subcategory: "Generalized Fermat"
(archival tag id 213813, tag last modified 2020-04-05 17:50:21)

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.
machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -t -q"4465132^32768+1" 2>&1
PFGW Version [GWNUM 25.14]
Primality testing 4465132^32768+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 78.24%
4465132^32768+1 is prime! (3080.4770s+0.0637s)
[Elapsed time: 51.42 minutes]
modified2012-02-19 19:07:47
created2012-02-01 12:31:15

machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 1 4465132 32768 1 2>&1
[Elapsed time: 7.559 seconds]
modified2012-02-19 19:07:47
created2012-02-01 12:35:01

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