V(145193)/38621339

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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(145193)/38621339
Verification status (*):	PRP
Official Comment (*):	Lucas cofactor, ECPP
Proof-code(s): (*):	E4 : Childers, CM
Decimal Digits:	30336 (log₁₀ is 30335.955623488)
Rank (*):	68918 (digit rank is 1)
Entrance Rank (*):	66889
Currently on list? (*):	yes
Submitted:	11/13/2023 17:21:19 UTC
Last modified:	11/13/2023 17:37:14 UTC
Database id:	136656
Status Flags:	Verify
Score (*):	35.8741 (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 38
Subcategory: "ECPP"
(archival tag id 228959, tag last modified 2024-10-27 10:37:10)
Lucas cofactor (archivable *)
Prime on list: yes, rank 2
Subcategory: "Lucas cofactor"
(archival tag id 228960, tag last modified 2023-11-19 12:37:21)

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 136656

person_id 9

machine Using: Digital Ocean Droplet

what prp

notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"V(145193)/38621339" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing V(145193)/38621339 [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 10K on A 100774-bit number
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction AVX-512 FFT length 10K on A 100774-bit number
Calling N-1 BLS with factored part 0.04% and helper 0.03% (0.16% proof)

V(145193)/38621339 is Fermat and Lucas PRP! (44.3888s+0.0097s)
[Elapsed time: 45.00 seconds]

modified 2023-11-13 17:22:46

created 2023-11-13 17:22:01

id 182491

field	value
prime_id	136656
person_id	9
machine	Using: Digital Ocean Droplet
what	prp
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"V(145193)/38621339" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing V(145193)/38621339 [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 10K on A 100774-bit number Running N+1 test using discriminant 7, base 1+sqrt(7) Generic modular reduction using generic reduction AVX-512 FFT length 10K on A 100774-bit number Calling N-1 BLS with factored part 0.04% and helper 0.03% (0.16% proof) V(145193)/38621339 is Fermat and Lucas PRP! (44.3888s+0.0097s) [Elapsed time: 45.00 seconds]
modified	2023-11-13 17:22:46
created	2023-11-13 17:22:01
id	182491

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