12647417865536 + 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:12647417865536 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L4865 : Schmeisser, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:530973   (log10 is 530972.79425464)
Rank (*):3444 (digit rank is 1)
Entrance Rank (*):3083
Currently on list? (*):yes
Submitted:5/25/2021 20:55:09 CDT
Last modified:5/25/2021 23:37:16 CDT
Database id:132346
Status Flags:TrialDiv
Score (*):44.6897 (normalized score 1.2779)

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 655
Subcategory: "Generalized Fermat"
(archival tag id 226124, tag last modified 2021-10-19 21:37:19)

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.
fieldvalue
prime_id132346
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"126474178^65536+1" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 126474178^65536+1 [N-1, Brillhart-Lehmer-Selfridge]
F: 126474178^65536+1 110592/5581655 (trial factor to 201612735)
F: 126474178^65536+1 223232/5581655 (trial factor to 201612735)
F: 126474178^65536+1 333824/5581655 (trial factor to 201612735)
F: 126474178^65536+1 446464/5581655 (trial factor to 201612735)
F: 126474178^65536+1 559104/5581655 (trial factor to 201612735)
F: 126474178^65536+1 671744/5581655 (trial factor to 201612735)
F: 126474178^65536+1 784384/5581655 (trial factor to 201612735)
F: 126474178^65536+1 897024/5581655 (trial factor to 201612735)
F: 126474178^65536+1 1009664/5581655 (trial factor to 201612735)
F: 126474178^65536+1 1120256/5581655 (trial factor to 201612735)
F: 126474178^65536+1 1232896/5581655 (trial factor to 201612735)
F: 126474178^65536+1 1345536/5581655 (trial factor to 201612735)
F: 126474178^65536+1 1458176/5581655 (trial factor to 201612735)
F: 126474178^65536+1 1568768/5581655 (trial factor to 201612735)
F: 126474178^65536+1 1681408/5581655 (trial factor to 201612735)
F: 126474178^65536+1 1794048/5581655 (trial factor to 201612735)




Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 96.28%


126474178^65536+1 is prime! (6566.4969s+0.0054s)
[Elapsed time: 1.82 hours]
modified2021-05-25 22:50:28
created2021-05-25 21:01:02
id178057

Query times: 0.0007 seconds to select prime, 0.0008 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.