282912265536 + 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.

Description:282912265536 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):p343 : Brown1, GeneFer, AthGFNSieve, PrimeGrid, OpenPFGW
Decimal Digits:422816   (log10 is 422815.44423222)
Rank (*):7624 (digit rank is 1)
Entrance Rank (*):511
Currently on list? (*):no
Submitted:9/10/2012 20:02:16 CDT
Last modified:9/11/2012 03:50:45 CDT
Removed (*):5/6/2019 10:16:32 CDT
Database id:109211
Status Flags:none
Score (*):43.99 (normalized score 0.6733)

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 1753
Subcategory: "Generalized Fermat"
(archival tag id 214524, tag last modified 2021-06-11 23:37:18)

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 1 2829122 65536 1 2>&1 [Elapsed time: 7.859 seconds]
modified2020-07-07 17:30:24
created2012-09-10 20:05:02

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -t -q"2829122^65536+1" 2>&1 PFGW Version [GWNUM 26.5] Primality testing 2829122^65536+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 72.22% 2829122^65536+1 is prime! (27201.4825s+0.0312s) [Elapsed time: 7.56 hours]
modified2020-07-07 17:30:24
created2012-09-10 20:08:01

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.