7678556865536 + 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:7678556865536 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L5007 : Faith, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:516770   (log10 is 516769.68394366)
Rank (*):4170 (digit rank is 1)
Entrance Rank (*):2553
Currently on list? (*):yes
Submitted:2/6/2020 17:50:58 CDT
Last modified:2/6/2020 23:50:17 CDT
Database id:130398
Status Flags:TrialDiv
Score (*):44.6064 (normalized score 1.1634)

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 1196
Subcategory: "Generalized Fermat"
(archival tag id 223734, tag last modified 2021-11-26 12:37:19)

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.
machineUsing: Xeon (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/4/pfgw64 -t -q"76785568^65536+1" 2>&1 PFGW Version [GWNUM 29.8] Primality testing 76785568^65536+1 [N-1, Brillhart-Lehmer-Selfridge] F: 76785568^65536+1 34816/5432129 (trial factor to 195893900) F: 76785568^65536+1 71680/5432129 (trial factor to 195893900) Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 80.91% 76785568^65536+1 is prime! (18197.3895s+0.0278s) [Elapsed time: 5.06 hours]
modified2020-07-07 17:30:10
created2020-02-06 18:23:02

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.