9145334 · 39145334 + 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:9145334 · 39145334 + 1
Verification status (*):Proven
Official Comment (*):Generalized Cullen
Proof-code(s): (*):A6 : Propper, Gcwsieve, PRST
Decimal Digits:4363441   (log10 is 4363440.19411)
Rank (*):58 (digit rank is 1)
Entrance Rank (*):50
Currently on list? (*):short
Submitted:12/25/2023 00:41:28 UTC
Last modified:12/29/2023 19:37:12 UTC
Database id:136811
Status Flags:none
Score (*):51.1486 (normalized score 458.2255)

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 Cullen (archivable *)
Prime on list: yes, rank 2
Subcategory: "Generalized Cullen"
(archival tag id 229096, tag last modified 2023-12-29 19:37:13)

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_id136811
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -q"9145334*3^9145334+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 9145334*3^9145334+1 [N-1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 3
Special modular reduction using zero-padded FMA3 FFT length 1536K, Pass1=384, Pass2=4K, clm=2 on 9145334*3^9145334+1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


9145334*3^9145334+1 is prime! (216694.6106s+0.0471s)
[Elapsed time: 2.51 days]
modified2023-12-29 18:58:36
created2023-12-27 06:47:01
id182652

fieldvalue
prime_id136811
person_id9
machineUsing: Digital Ocean Droplet
whatrequested
notesN-1: 9145334*3^9145334+1 8450000/14495035 mro=0
modified2023-12-26 06:28:15
created2023-12-25 00:42:01
id182650

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