(9236524691 - 1)/92364

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:(9236524691 - 1)/92364
Verification status (*):PRP
Official Comment (*):Generalized repunit
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):CH14 : Wu_T, CM, OpenPFGW, CHG
Decimal Digits:122599   (log10 is 122598.37856424)
Rank (*):45084 (digit rank is 1)
Entrance Rank (*):44282
Currently on list? (*):short
Submitted:2/3/2024 22:22:10 UTC
Last modified:2/4/2024 02:37:18 UTC
Database id:137137
Status Flags:Verify
Score (*):40.1818 (normalized score 0.0082)

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 Repunit (archivable *)
Prime on list: yes, rank 1
Subcategory: "Generalized Repunit"
(archival tag id 229268, tag last modified 2024-02-04 02:37:20)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Jeppe Stig Nielsen writes (4 Feb 2024):  (report abuse)
More info from the finder at xenon.stanford.edu/~tjw/pp.

Tom Wu writes (4 Feb 2024):  (report abuse)
CHG proof with 26.87% of N-1 factored is available here.
The largest helper prime at 32630 digits was proven in 3 weeks with CM-ECPP.

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_id137137
person_id9
machineUsing: Digital Ocean Droplet
whatprp
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -tc -q"(92365^24691-1)/92364" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (92365^24691-1)/92364 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 40K, Pass1=640, Pass2=64, clm=2 on A 407263-bit number
Running N-1 test using base 7
Generic modular reduction using generic reduction FMA3 FFT length 40K, Pass1=640, Pass2=64, clm=2 on A 407263-bit number
Running N+1 test using discriminant 23, base 2+sqrt(23)
Generic modular reduction using generic reduction FMA3 FFT length 40K, Pass1=640, Pass2=64, clm=2 on A 407263-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 36/407284 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 23, base 2+sqrt(23)
Generic modular reduction using generic reduction FMA3 FFT length 48K, Pass1=768, Pass2=64, clm=2 on A 407263-bit number
Calling N-1 BLS with factored part 0.05% and helper 0.00% (0.15% proof)


(92365^24691-1)/92364 is Fermat and Lucas PRP! (1424.9318s+0.0013s)
[Elapsed time: 23.77 minutes]
modified2024-02-04 01:53:29
created2024-02-04 01:29:43
id182975

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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