507935832768 + 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:507935832768 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):p343 : Brown1, GeneFer, AthGFNSieve, PrimeGrid, OpenPFGW
Decimal Digits:219736   (log10 is 219735.94353068)
Rank (*):22896 (digit rank is 1)
Entrance Rank (*):4989
Currently on list? (*):no
Submitted:3/22/2012 18:12:27 CDT
Last modified:3/22/2012 20:20:23 CDT
Removed (*):3/24/2012 07:33:46 CDT
Database id:105778
Status Flags:none
Score (*):41.9778 (normalized score 0.1041)

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 1494
Subcategory: "Generalized Fermat"
(archival tag id 214243, tag last modified 2020-10-21 20:20:21)

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 5079358 32768 1 2>&1 [Elapsed time: 7.548 seconds]
modified2020-07-07 17:30:27
created2012-03-22 18:18:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"5079358^32768+1" 2>&1 PFGW Version [GWNUM 26.5] Primality testing 5079358^32768+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 57.06% 5079358^32768+1 is prime! (5497.1082s+0.0137s) [Elapsed time: 1.53 hours]
modified2020-07-07 17:30:27
created2012-03-22 18:23:02

Query times: 0.0004 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.