124080788131072 + 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:124080788131072 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L5639 : Cavecchia, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:1060859   (log10 is 1060858.0418455)
Rank (*):1434 (digit rank is 1)
Entrance Rank (*):660
Currently on list? (*):short
Submitted:1/5/2023 00:33:21 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:134742
Status Flags:none
Score (*):46.8142 (normalized score 6.2856)

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 615
Subcategory: "Generalized Fermat"
(archival tag id 227595, tag last modified 2024-04-10 08:37:14)

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_id134742
person_id9
machineUsing: Dual Intel Xeon Gold 5222 CPUs 3.8GHz
whatprime
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -q"124080788^131072+1" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 124080788^131072+1 [N-1, Brillhart-Lehmer-Selfridge]
F: 124080788^131072+1 86016/11169438 (trial factor to 419886333)




Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 78.80%


124080788^131072+1 is prime! (12355.5667s+0.0086s)
[Elapsed time: 3.43 hours]
modified2023-01-05 03:59:56
created2023-01-05 00:34:01
id180522

Query times: 0.0004 seconds to select prime, 0.0045 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.