(1021328211729 · 2521# · (483 · 2521# + 1) + 2310) · (483 · 2521# - 1)/210 + 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:	(1021328211729 · 2521# · (483 · 2521# + 1) + 2310) · (483 · 2521# - 1)/210 + 1
Verification status (*):	PRP
Official Comment (*):	Consecutive primes arithmetic progression (1,d=6),ECPP
Proof-code(s): (*):	c100 : DavisK, APTreeSieve, NewPGen, OpenPFGW, Primo
Decimal Digits:	3207 (log₁₀ is 3206.1556816723)
Rank (*):	95640 (digit rank is 4)
Entrance Rank (*):	93835
Currently on list? (*):	no
Submitted:	7/2/2023 07:17:42 UTC
Last modified:	7/30/2023 17:37:05 UTC
Database id:	136218
Status Flags:	Verify
Score (*):	28.9074 (normalized score 0)

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.

Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 333
Subcategory: "Arithmetic progression (1,d=*)"
(archival tag id 228739, tag last modified 2023-07-30 17:37:06)
Consecutive Primes in Arithmetic Progression (archivable class *)
Prime on list: no, rank 31
Subcategory: "Consecutive primes in arithmetic progression (1,d=*)"
(archival tag id 228738, tag last modified 2023-07-30 17:37:08)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 719
Subcategory: "ECPP"
(archival tag id 228740, tag last modified 2024-04-24 05:37:26)

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 136218

person_id 9

machine Using: Digital Ocean Droplet

what prp

notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"(1021328211729*2521#*(483*2521#+1)+2310)*(483*2521#-1)/210+1" 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (1021328211729*2521#*(483*2521#+1)+2310)*(483*2521#-1)/210+1 [N-1, Brillhart-Lehmer-Selfridge]
trial

Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 10651-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.25%

(1021328211729*2521#*(483*2521#+1)+2310)*(483*2521#-1)/210+1 is PRP! (0.3317s+0.0017s)
[Elapsed time: 0.00 seconds]

modified 2023-07-02 12:09:02

created 2023-07-02 12:09:02

id 182049

field	value
prime_id	136218
person_id	9
machine	Using: Digital Ocean Droplet
what	prp
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"(10213282117292521#(4832521#+1)+2310)(4832521#-1)/210+1" 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing (10213282117292521#(4832521#+1)+2310)(4832521#-1)/210+1 [N-1, Brillhart-Lehmer-Selfridge] trial Running N-1 test using base 3 Generic modular reduction using generic reduction FMA3 FFT length 1K on A 10651-bit number Calling Brillhart-Lehmer-Selfridge with factored part 0.25% (10213282117292521#(4832521#+1)+2310)(483*2521#-1)/210+1 is PRP! (0.3317s+0.0017s) [Elapsed time: 0.00 seconds]
modified	2023-07-02 12:09:02
created	2023-07-02 12:09:02
id	182049

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