V(64063)/464426465381142115542697818362662865912299

Previous Next Random

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(64063)/464426465381142115542697818362662865912299
Verification status (*):	PRP
Official Comment (*):	Lucas cofactor, ECPP
Proof-code(s): (*):	E1 : Batalov, CM
Decimal Digits:	13347 (log₁₀ is 13346.708280374)
Rank (*):	79833 (digit rank is 2)
Entrance Rank (*):	79478
Currently on list? (*):	yes
Submitted:	8/4/2024 10:25:09 UTC
Last modified:	8/4/2024 11:37:19 UTC
Database id:	138373
Status Flags:	Verify
Score (*):	33.3345 (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.

Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 213
Subcategory: "ECPP"
(archival tag id 229613, tag last modified 2024-10-27 10:37:10)
Lucas cofactor (archivable *)
Prime on list: yes, rank 14
Subcategory: "Lucas cofactor"
(archival tag id 229614, tag last modified 2024-08-04 11:37:22)

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 138373

person_id 9

machine Using: Digital Ocean Droplet

what prp

notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"V(64063)/464426465381142115542697818362662865912299" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing V(64063)/4644264653...2865912299 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial

Running N-1 test using base 11
Generic modular reduction using generic reduction FMA3 FFT length 5K on A 44337-bit number
Running N-1 test using base 13
Generic modular reduction using generic reduction FMA3 FFT length 5K on A 44337-bit number
Running N+1 test using discriminant 19, base 1+sqrt(19)
Generic modular reduction using generic reduction FMA3 FFT length 5K on A 44337-bit number
Calling N-1 BLS with factored part 0.06% and helper 0.04% (0.22% proof)

V(64063)/4644264653...2865912299 is Fermat and Lucas PRP! (12.4717s+0.0060s)
[Elapsed time: 15.00 seconds]

modified 2024-08-04 11:23:04

created 2024-08-04 11:22:49

id 184215

field	value
prime_id	138373
person_id	9
machine	Using: Digital Ocean Droplet
what	prp
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"V(64063)/464426465381142115542697818362662865912299" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing V(64063)/4644264653...2865912299 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial Running N-1 test using base 11 Generic modular reduction using generic reduction FMA3 FFT length 5K on A 44337-bit number Running N-1 test using base 13 Generic modular reduction using generic reduction FMA3 FFT length 5K on A 44337-bit number Running N+1 test using discriminant 19, base 1+sqrt(19) Generic modular reduction using generic reduction FMA3 FFT length 5K on A 44337-bit number Calling N-1 BLS with factored part 0.06% and helper 0.04% (0.22% proof) V(64063)/4644264653...2865912299 is Fermat and Lucas PRP! (12.4717s+0.0060s) [Elapsed time: 15.00 seconds]
modified	2024-08-04 11:23:04
created	2024-08-04 11:22:49
id	184215

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