(1021328211729 · 2521# · (483 · 2521# + 1) + 2310) · (483 · 2521# - 1)/210 + 19

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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 + 19
Verification status (*):	PRP
Official Comment (*):	Consecutive primes arithmetic progression (4,d=6),ECPP
Proof-code(s): (*):	c100 : DavisK, APTreeSieve, NewPGen, OpenPFGW, Primo
Decimal Digits:	3207 (log₁₀ is 3206.1556816723)
Rank (*):	96312 (digit rank is 1)
Entrance Rank (*):	93835
Currently on list? (*):	yes
Submitted:	7/2/2023 07:19:47 UTC
Last modified:	7/2/2023 12:37:18 UTC
Database id:	136221
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.

Consecutive Primes in Arithmetic Progression (archivable class *)
Prime on list: yes, rank 4
Subcategory: "Consecutive primes in arithmetic progression (4,d=*)"
(archival tag id 228667, tag last modified 2024-06-24 15:37:18)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 187, weight 38.185038356552
Subcategory: "Arithmetic progression (4,d=*)"
(archival tag id 228668, tag last modified 2024-06-24 15:37:18)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 740
Subcategory: "ECPP"
(archival tag id 228669, tag last modified 2024-10-27 10:37:10)

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 136221

person_id 9

machine Using: Digital Ocean Droplet

what prp

notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"(1021328211729*2521#*(483*2521#+1)+2310)*(483*2521#-1)/210+19" 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+19 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial

Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 10651-bit number
Running N+1 test using discriminant 7, base 2+sqrt(7)
Generic modular reduction using generic reduction FMA3 FFT length 1K on A 10651-bit number
Calling N+1 BLS with factored part 0.21% and helper 0.03% (0.67% proof)

(1021328211729*2521#*(483*2521#+1)+2310)*(483*2521#-1)/210+19 is Fermat and Lucas PRP! (1.5741s+0.0004s)
[Elapsed time: 1.00 seconds]

modified 2023-07-02 12:09:07

created 2023-07-02 12:09:06

id 182052

field	value
prime_id	136221
person_id	9
machine	Using: Digital Ocean Droplet
what	prp
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"(10213282117292521#(4832521#+1)+2310)(4832521#-1)/210+19" 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing (10213282117292521#(4832521#+1)+2310)(4832521#-1)/210+19 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial Running N-1 test using base 2 Generic modular reduction using generic reduction FMA3 FFT length 1K on A 10651-bit number Running N+1 test using discriminant 7, base 2+sqrt(7) Generic modular reduction using generic reduction FMA3 FFT length 1K on A 10651-bit number Calling N+1 BLS with factored part 0.21% and helper 0.03% (0.67% proof) (10213282117292521#(4832521#+1)+2310)(483*2521#-1)/210+19 is Fermat and Lucas PRP! (1.5741s+0.0004s) [Elapsed time: 1.00 seconds]
modified	2023-07-02 12:09:07
created	2023-07-02 12:09:06
id	182052

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