24750253665536 + 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:24750253665536 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L5739 : Pistorius, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:550082   (log10 is 550081.63615407)
Rank (*):6872 (digit rank is 1)
Entrance Rank (*):4355
Currently on list? (*):no
Submitted:2/26/2023 15:07:32 UTC
Last modified:5/20/2023 20:59:19 UTC
Removed (*):7/30/2023 15:27:05 UTC
Database id:135629
Status Flags:none
Score (*):44.7983 (normalized score 0.7942)

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 1980
Subcategory: "Generalized Fermat"
(archival tag id 227678, tag last modified 2024-07-10 06:37:26)

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: Dual Intel Xeon Gold 5222 CPUs 3.8GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -q"247502536^65536+1" 2>&1
PFGW Version [GWNUM 29.8]
Primality testing 247502536^65536+1 [N-1, Brillhart-Lehmer-Selfridge]
F: 247502536^65536+1 165888/5782994 (trial factor to 209320673)
F: 247502536^65536+1 333824/5782994 (trial factor to 209320673)
F: 247502536^65536+1 501760/5782994 (trial factor to 209320673)
F: 247502536^65536+1 669696/5782994 (trial factor to 209320673)
F: 247502536^65536+1 837632/5782994 (trial factor to 209320673)

Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 89.24%

247502536^65536+1 is prime! (3212.1358s+0.0052s)
[Elapsed time: 53.55 minutes]
modified2023-02-26 16:11:34
created2023-02-26 15:18:01

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