183 · 24894125 + 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:183 · 24894125 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(4894123,3), GF(4894124,5)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L5961 : Carlier, LLR2, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:1473281   (log10 is 1473280.6899801)
Rank (*):517 (digit rank is 1)
Entrance Rank (*):476
Currently on list? (*):short
Submitted:3/21/2024 21:27:40 UTC
Last modified:3/22/2024 08:37:10 UTC
Database id:137862
Status Flags:none
Score (*):47.8216 (normalized score 16.4626)

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 Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 9, weight 53.031106327276
Subcategory: "Divides GF(*,3)"
(archival tag id 229450, tag last modified 2024-03-22 08:37:12)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 7, weight 53.031106327276
Subcategory: "Divides GF(*,5)"
(archival tag id 229451, tag last modified 2024-03-22 08:37:12)

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.

PrimeGrid writes (21 Mar 2024):  (report abuse)
Also divides xGF(4894124,5,3) and xGF(4894124,9,5).

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_id137862
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -q"183*2^4894125+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 183*2^4894125+1 [N-1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 5
Special modular reduction using all-complex AVX-512 FFT length 320K, Pass1=640, Pass2=512, clm=2 on 183*2^4894125+1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


183*2^4894125+1 is prime! (8903.4259s+0.0037s)
[Elapsed time: 2.47 hours]
modified2024-03-22 08:05:12
created2024-03-22 05:36:46
id183704

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