V(51169)

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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(51169)
Verification status (*):	PRP
Official Comment (*):	Lucas number
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	p54 : Broadhurst, Water, OpenPFGW
Decimal Digits:	10694 (log₁₀ is 10693.688563951)
Rank (*):	82172 (digit rank is 1)
Entrance Rank (*):	12081
Currently on list? (*):	short
Submitted:	4/26/2001 17:59:06 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	17060
Status Flags:	Verify
Score (*):	32.6479 (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 Number (archivable *)
Prime on list: yes, rank 11
Subcategory: "Lucas Number"
(archival tag id 194185, tag last modified 2023-12-16 03:37:32)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

David Broadhurst writes (11 Sep 2014): (report abuse)

notes

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 17060

person_id 9

machine Linux PII 200

what prp

notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality testing 4881619792...1689057678 Running N-1 test using base 11 5462215855...7431182401 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 17, base 6+sqrt(17) Running N+1 test using discriminant 17, base 10+sqrt(17) Calling N-1 BLS with factored part 1.26% and helper 0.93% (4.71% proof) V(51169) is Fermat and Lucas PRP! (-1537.347296 seconds)

modified 2003-03-25 17:22:40

created 2003-01-09 16:04:25

id 64864

field	value
prime_id	17060
person_id	9
machine	Linux PII 200
what	prp
notes	PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality testing 4881619792...1689057678 Running N-1 test using base 11 5462215855...7431182401 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 17, base 6+sqrt(17) Running N+1 test using discriminant 17, base 10+sqrt(17) Calling N-1 BLS with factored part 1.26% and helper 0.93% (4.71% proof) V(51169) is Fermat and Lucas PRP! (-1537.347296 seconds)
modified	2003-03-25 17:22:40
created	2003-01-09 16:04:25
id	64864

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.