410867232768 + 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:410867232768 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):p329 : Cholt, GeneFer, AthGFNSieve, PrimeGrid, OpenPFGW
Decimal Digits:216718   (log10 is 216717.76984822)
Rank (*):23302 (digit rank is 1)
Entrance Rank (*):3068
Currently on list? (*):no
Submitted:10/13/2011 17:30:34 CDT
Last modified:10/13/2011 19:20:24 CDT
Removed (*):3/10/2012 06:00:08 CDT
Database id:102441
Status Flags:none
Score (*):41.9353 (normalized score 0.0987)

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 1530
Subcategory: "Generalized Fermat"
(archival tag id 213540, tag last modified 2020-11-27 00:50:24)

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 4108672 32768 1 2>&1 [Elapsed time: 7.570 seconds]
modified2020-07-07 17:30:30
created2011-10-13 17:35:01

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -t -q"4108672^32768+1" 2>&1 PFGW Version [GWNUM 26.5] Primality testing 4108672^32768+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 68.14% 4108672^32768+1 is prime! (5287.1193s+0.0089s) [Elapsed time: 88.13 minutes]
modified2020-07-07 17:30:30
created2011-10-13 17:38:01

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.