primV(86756)

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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:	primV(86756)
Verification status (*):	PRP
Official Comment (*):	Lucas primitive part, ECPP
Proof-code(s): (*):	c74 : Lasher, Dubner, Primo
Decimal Digits:	16920 (log₁₀ is 16919.639354638)
Rank (*):	76589 (digit rank is 1)
Entrance Rank (*):	61592
Currently on list? (*):	yes
Submitted:	1/14/2015 20:26:37 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	119086
Status Flags:	Verify
Score (*):	34.0688 (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.

Lucas primitive part (archivable *)
Prime on list: yes, rank 16
Subcategory: "Lucas primitive part"
(archival tag id 217883, tag last modified 2024-10-11 22:37:11)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 153
Subcategory: "ECPP"
(archival tag id 217884, 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 119086

person_id 9

machine Using: Xeon 4c+4c 3.5GHz

what prp

notes PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 4358676513...3665526401 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 19 Running N-1 test using base 37 Running N+1 test using discriminant 67, base 15+sqrt(67) Calling N-1 BLS with factored part 1.48% and helper 0.00% (4.45% proof) 4358676513...3665526401 is Fermat and Lucas PRP! (27.1360s+0.1449s) [Elapsed time: 27.00 seconds]

modified 2020-07-07 22:30:17

created 2015-01-14 20:31:02

id 164691

field	value
prime_id	119086
person_id	9
machine	Using: Xeon 4c+4c 3.5GHz
what	prp
notes	PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 4358676513...3665526401 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 19 Running N-1 test using base 37 Running N+1 test using discriminant 67, base 15+sqrt(67) Calling N-1 BLS with factored part 1.48% and helper 0.00% (4.45% proof) 4358676513...3665526401 is Fermat and Lucas PRP! (27.1360s+0.1449s) [Elapsed time: 27.00 seconds]
modified	2020-07-07 22:30:17
created	2015-01-14 20:31:02
id	164691

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