78439440131072 + 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:78439440131072 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L5051 : Veit, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:1034753   (log10 is 1034752.42394755)
Rank (*):435 (digit rank is 1)
Entrance Rank (*):427
Currently on list? (*):short
Submitted:10/3/2020 20:47:40 CDT
Last modified:10/4/2020 03:50:20 CDT
Database id:131294
Status Flags:TrialDiv
Score (*):46.7378 (normalized score 12.1424)

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 74
Subcategory: "Generalized Fermat"
(archival tag id 225675, tag last modified 2020-10-25 04:50:19)

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/1/pfgw64 -t -q"78439440^131072+1" 2>&1
PFGW Version [GWNUM 29.8]
Primality testing 78439440^131072+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Calling Brillhart-Lehmer-Selfridge with factored part 69.85%

78439440^131072+1 is prime! (24843.7316s+0.0285s)
[Elapsed time: 6.90 hours]
modified2020-10-04 03:45:05
created2020-10-03 20:51:01

Query times: 0.0019 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.