25123941665536 + 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:25123941665536 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L5520 : Bennett1, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:550509   (log10 is 550508.15243722)
Rank (*):4566 (digit rank is 1)
Entrance Rank (*):4350
Currently on list? (*):yes
Submitted:2/27/2023 18:31:35 UTC
Last modified:3/11/2023 16:02:25 UTC
Database id:135654
Status Flags:TrialDiv
Score (*):44.8006 (normalized score 1.0289)

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 1066
Subcategory: "Generalized Fermat"
(archival tag id 227650, tag last modified 2023-04-01 22:37:48)

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_id135654
person_id9
machineUsing: Dual Intel Xeon Gold 5222 CPUs 3.8GHz
whatprime
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -q"251239416^65536+1" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 251239416^65536+1 [N-1, Brillhart-Lehmer-Selfridge]
F: 251239416^65536+1 163840/5787526 (trial factor to 209492913)
F: 251239416^65536+1 329728/5787526 (trial factor to 209492913)




Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 83.57%


251239416^65536+1 is prime! (3265.1595s+0.0040s)
[Elapsed time: 54.42 minutes]
modified2023-02-27 19:42:26
created2023-02-27 18:48:01
id181434

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.