V(202667)

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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:	V(202667)
Verification status (*):	PRP
Official Comment (*):	Lucas number, ECPP
Proof-code(s): (*):	E4 : Childers, CM
Decimal Digits:	42355 (log₁₀ is 42354.898086542)
Rank (*):	63498 (digit rank is 1)
Entrance Rank (*):	62130
Currently on list? (*):	short
Submitted:	11/9/2023 22:02:04 UTC
Last modified:	11/9/2023 22:37:14 UTC
Database id:	136636
Status Flags:	Verify
Score (*):	36.9049 (normalized score 0.0003)

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.

Elliptic Curve Primality Proof (archivable *)
Prime on list: yes, rank 9
Subcategory: "ECPP"
(archival tag id 228942, tag last modified 2023-11-09 22:37:15)
Lucas Number (archivable *)
Prime on list: yes, rank 1
Subcategory: "Lucas Number"
(archival tag id 228943, tag last modified 2023-11-09 22:37:16)

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 136636

person_id 9

machine Using: Digital Ocean Droplet

what prp

notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"V(202667)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing V(202667) [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial

Running N-1 test using base 3
Generic modular reduction using generic reduction AVX-512 FFT length 16K on A 140700-bit number
Running N+1 test using discriminant 17, base 1+sqrt(17)
Generic modular reduction using generic reduction AVX-512 FFT length 16K on A 140700-bit number
Calling N+1 BLS with factored part 0.04% and helper 0.01% (0.15% proof)

V(202667) is Fermat and Lucas PRP! (98.2383s+0.0088s)
[Elapsed time: 1.67 minutes]

modified 2023-11-09 22:04:41

created 2023-11-09 22:03:01

id 182471

field	value
prime_id	136636
person_id	9
machine	Using: Digital Ocean Droplet
what	prp
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"V(202667)" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing V(202667) [N-1/N+1, Brillhart-Lehmer-Selfridge] trial Running N-1 test using base 3 Generic modular reduction using generic reduction AVX-512 FFT length 16K on A 140700-bit number Running N+1 test using discriminant 17, base 1+sqrt(17) Generic modular reduction using generic reduction AVX-512 FFT length 16K on A 140700-bit number Calling N+1 BLS with factored part 0.04% and helper 0.01% (0.15% proof) V(202667) is Fermat and Lucas PRP! (98.2383s+0.0088s) [Elapsed time: 1.67 minutes]
modified	2023-11-09 22:04:41
created	2023-11-09 22:03:01
id	182471

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.