25695584465536 + 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.

This prime's information:

Description:25695584465536 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L5070 : Millerick, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:551149   (log10 is 551148.48661556)
Rank (*):4516 (digit rank is 2)
Entrance Rank (*):4381
Currently on list? (*):yes
Submitted:3/8/2023 03:34:00 UTC
Last modified:3/11/2023 16:02:25 UTC
Database id:135736
Status Flags:TrialDiv
Score (*):44.8042 (normalized score 1.0331)

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 1019
Subcategory: "Generalized Fermat"
(archival tag id 227610, tag last modified 2023-03-30 23:37:17)

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"256955844^65536+1" 2>&1
PFGW Version [GWNUM 29.8]
Primality testing 256955844^65536+1 [N-1, Brillhart-Lehmer-Selfridge]
F: 256955844^65536+1 104448/5794327 (trial factor to 209751470)
F: 256955844^65536+1 217088/5794327 (trial factor to 209751470)
F: 256955844^65536+1 329728/5794327 (trial factor to 209751470)
F: 256955844^65536+1 442368/5794327 (trial factor to 209751470)
F: 256955844^65536+1 548864/5794327 (trial factor to 209751470)
F: 256955844^65536+1 661504/5794327 (trial factor to 209751470)

Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 87.17%

256955844^65536+1 is prime! (6512.7117s+0.0053s)
[Elapsed time: 1.81 hours]
modified2023-03-08 05:23:34
created2023-03-08 03:35:01

Query times: 0.0004 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.