primV(112770)

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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(112770)
Verification status (*):	PRP
Official Comment (*):	Lucas primitive part, ECPP
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	c8 : Broadhurst, Water, Primo
Decimal Digits:	10714 (log₁₀ is 10713.543736426)
Rank (*):	82142 (digit rank is 1)
Entrance Rank (*):	67116
Currently on list? (*):	no
Submitted:	8/30/2014 23:31:28 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	118424
Status Flags:	Verify
Score (*):	32.6537 (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: no, rank 36
Subcategory: "Lucas primitive part"
(archival tag id 217802, tag last modified 2023-11-13 17:37:16)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 282
Subcategory: "ECPP"
(archival tag id 217803, tag last modified 2024-04-13 23:37:20)

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)

certificate

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 118424

person_id 9

machine Xeon 4c+4c 3.5GHz

what prp

notes PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 3497328487...9997337601 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 29 Running N-1 test using base 43 Running N-1 test using base 59 Running N-1 test using base 67 Running N-1 test using base 71 Running N-1 test using base 83 Running N+1 test using discriminant 101, base 12+sqrt(101) Calling N-1 BLS with factored part 1.01% and helper 0.00% (3.04% proof) 3497328487...9997337601 is Fermat and Lucas PRP! (17.8023s+0.0033s) [Elapsed time: 18.00 seconds]

modified 2020-07-07 22:30:17

created 2014-08-30 23:41:05

id 164001

field	value
prime_id	118424
person_id	9
machine	Xeon 4c+4c 3.5GHz
what	prp
notes	PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 3497328487...9997337601 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 29 Running N-1 test using base 43 Running N-1 test using base 59 Running N-1 test using base 67 Running N-1 test using base 71 Running N-1 test using base 83 Running N+1 test using discriminant 101, base 12+sqrt(101) Calling N-1 BLS with factored part 1.01% and helper 0.00% (3.04% proof) 3497328487...9997337601 is Fermat and Lucas PRP! (17.8023s+0.0033s) [Elapsed time: 18.00 seconds]
modified	2020-07-07 22:30:17
created	2014-08-30 23:41:05
id	164001

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