5256037# + 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:5256037# + 1
Verification status (*):Proven
Official Comment (*):Primorial
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p444 : Kadowaki, MultiSieve, PrimeGrid, PRST, OpenPFGW
Decimal Digits:2281955   (log10 is 2281954.8287246)
Rank (*):239 (digit rank is 1)
Entrance Rank (*):210
Currently on list? (*):yes
Submitted:8/9/2024 23:02:22 UTC
Last modified:8/31/2024 23:37:16 UTC
Database id:138394
Status Flags:none
Score (*):49.1629 (normalized score 55.6283)

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.
Primorial (archivable *)
Prime on list: yes, rank 4
Subcategory: "Primorial"
(archival tag id 229630, tag last modified 2024-11-08 16:37:12)

User comments about this prime (disclaimer):

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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_id138394
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -q"5256037#+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 5256037#+1 [N-1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 768K, Pass1=384, Pass2=2K, clm=2 on A 7580490-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 7737246/50354430 ERROR: ROUND OFF 0.4636>0.45
(Test aborted, try again using the -a1 switch)
Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 800K, Pass1=320, Pass2=2560, clm=2 on A 7580490-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.33%


5256037#+1 is prime! (1872278.6805s+11.5610s)
[Elapsed time: 21.67 days]
modified2024-08-31 23:33:42
created2024-08-10 07:28:51
id184236

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.
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