30941436262144 + 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:30941436262144 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L4362 : Mochizuki, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:1963601   (log10 is 1963600.239801)
Rank (*):309 (digit rank is 1)
Entrance Rank (*):259
Currently on list? (*):short
Submitted:1/9/2024 22:49:08 UTC
Last modified:1/12/2024 23:37:26 UTC
Database id:136870
Status Flags:none
Score (*):48.7024 (normalized score 39.2205)

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 62
Subcategory: "Generalized Fermat"
(archival tag id 229143, tag last modified 2024-06-30 09:37:11)

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 -f -t -q"30941436^262144+1" >command_output 2>&1
PFGW Version [GWNUM 30.11]
Primality testing 30941436^262144+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 5
Special modular reduction using generic reduction FMA3 FFT length 672K, Pass1=448, Pass2=1536, clm=4 on 30941436^262144+1
Calling Brillhart-Lehmer-Selfridge with factored part 85.59%

30941436^262144+1 is prime! (124733.2711s+0.0202s)
[Elapsed time: 34.65 hours]
modified2024-01-12 23:32:10
created2024-01-11 12:53:13

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