404221232768 + 1
(Another of the Prime Pages' resources)
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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:404221232768 + 1
Verification status (*):Proven
Official Comment:Generalized Fermat
Proof-code(s): (*):p316 : Yama, GeneFer, AthGFNSieve, PrimeGrid, OpenPFGW
Decimal Digits:216486   (log10 is 216485.69424334)
Rank (*):22746 (digit rank is 1)
Entrance Rank (*):2861
Currently on list? (*):no
Submitted:9/6/2011 06:45:09 CDT
Last modified:9/6/2011 08:20:36 CDT
Removed (*):3/10/2012 04:07:17 CDT
Database id:101829
Status Flags:none
Score (*):41.932 (normalized score 0.107)

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 1397
Subcategory: "Generalized Fermat"
(archival tag id 213414, tag last modified 2020-04-02 03:20:21)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 1 4042212 32768 1 2>&1
[Elapsed time: 7.636 seconds]
modified2011-12-27 16:48:29
created2011-09-06 06:48:02

machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -t -q"4042212^32768+1" 2>&1
PFGW Version [GWNUM 25.14]
Primality testing 4042212^32768+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 64.31%
4042212^32768+1 is prime! (3528.6122s+0.0341s)
[Elapsed time: 58.82 minutes]
modified2011-12-27 16:48:29
created2011-09-06 06:52:46

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