5256037# + 1

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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 (*):	238 (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 56.5795)

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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PrimeGrid writes (2 Nov 2024): (report abuse)

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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.

field value

prime_id 138394

person_id 9

machine Using: Digital Ocean Droplet

what prime

notes Command: /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]

modified 2024-08-31 23:33:42

created 2024-08-10 07:28:51

id 184236

field	value
prime_id	138394
person_id	9
machine	Using: Digital Ocean Droplet
what	prime
notes	Command: /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]
modified	2024-08-31 23:33:42
created	2024-08-10 07:28:51
id	184236

Query times: 0.0002 seconds to select prime, 0.0005 seconds to seek comments.