400462032768 + 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: 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:

Description:400462032768 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):p316 : Yama, GeneFer, AthGFNSieve, PrimeGrid, OpenPFGW
Decimal Digits:216353   (log10 is 216352.72907154)
Rank (*):27444 (digit rank is 1)
Entrance Rank (*):2779
Currently on list? (*):no
Submitted:7/30/2011 04:16:35 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):3/8/2012 10:36:20 UTC
Database id:100944
Status Flags:none
Score (*):41.9301 (normalized score 0.0586)

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 3594
Subcategory: "Generalized Fermat"
(archival tag id 213336, tag last modified 2023-03-21 09:37:35)

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 4004620 32768 1 2>&1 [Elapsed time: 7.606 seconds]
modified2020-07-07 22:30:31
created2011-07-30 04:18:01

machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -t -q"4004620^32768+1" 2>&1 PFGW Version [GWNUM 25.14] Primality testing 4004620^32768+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 80.30% 4004620^32768+1 is prime! (3043.5153s+0.0358s) [Elapsed time: 50.73 minutes]
modified2020-07-07 22:30:31
created2011-07-30 04:20:39

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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