309567465536 + 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:309567465536 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):p343 : Brown1, GeneFer, AthGFNSieve, PrimeGrid, OpenPFGW
Decimal Digits:425379   (log10 is 425378.13407358)
Rank (*):6526 (digit rank is 1)
Entrance Rank (*):953
Currently on list? (*):no
Submitted:6/12/2013 12:13:50 CDT
Last modified:6/12/2013 20:20:26 CDT
Removed (*):6/29/2019 21:42:00 CDT
Database id:114388
Status Flags:none
Score (*):44.0085 (normalized score 0.7933)

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 1368
Subcategory: "Generalized Fermat"
(archival tag id 217183, 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 3095674 65536 1 2>&1 [Elapsed time: 7.859 seconds]
modified2020-07-07 17:30:19
created2013-06-12 12:18:02

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"3095674^65536+1" 2>&1 PFGW Version [GWNUM 26.5] Primality testing 3095674^65536+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 95.36% 3095674^65536+1 is prime! (27828.8784s+0.0294s) [Elapsed time: 7.73 hours]
modified2020-07-07 17:30:19
created2013-06-12 12:23:02

Query times: 0.0006 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.