163214942131072 + 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:163214942131072 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L4933 : Jacques, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:1076463   (log10 is 1076462.8675822)
Rank (*):1303 (digit rank is 1)
Entrance Rank (*):693
Currently on list? (*):short
Submitted:4/16/2023 15:06:11 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:135956
Status Flags:none
Score (*):46.859 (normalized score 6.2073)

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 504
Subcategory: "Generalized Fermat"
(archival tag id 228497, tag last modified 2024-07-23 06:37:17)

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: Digital Ocean Droplet
notesCommand: /var/www/clientpool/1/pfgw64 -V -t -q"163214942^131072+1" 2>&1
PFGW Version [GWNUM 30.11]
Primality testing 163214942^131072+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Special modular reduction using generic reduction FMA3 FFT length 384K, Pass1=384, Pass2=1K, clm=4 on 163214942^131072+1
Calling Brillhart-Lehmer-Selfridge with factored part 61.11%

163214942^131072+1 is prime! (28982.4492s+0.0092s)
[Elapsed time: 8.05 hours]
modified2023-04-17 10:24:54
created2023-04-17 02:21:51

Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.