V(50989)/69818796119453411

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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(50989)/69818796119453411
Verification status (*):	PRP
Official Comment (*):	Lucas cofactor, ECPP
Proof-code(s): (*):	c8 : Broadhurst, Water, Primo
Decimal Digits:	10640 (log₁₀ is 10639.22681635)
Rank (*):	82936 (digit rank is 2)
Entrance Rank (*):	67117
Currently on list? (*):	yes
Submitted:	8/23/2014 01:39:26 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	118387
Status Flags:	Verify
Score (*):	32.6321 (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 307
Subcategory: "ECPP"
(archival tag id 217797, tag last modified 2024-10-27 10:37:10)
Lucas cofactor (archivable *)
Prime on list: yes, rank 20
Subcategory: "Lucas cofactor"
(archival tag id 217798, 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 118387

person_id 9

machine Xeon 4c+4c 3.5GHz

what prp

notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"V(50989)/69818796119453411" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing V(50989)/69818796119453411 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 11, base 2+sqrt(11) Calling N-1 BLS with factored part 0.14% and helper 0.06% (0.47% proof) V(50989)/69818796119453411 is Fermat and Lucas PRP! (8.1840s+0.1379s) [Elapsed time: 9.00 seconds]

modified 2020-07-07 22:30:17

created 2014-08-23 01:41:02

id 163963

field	value
prime_id	118387
person_id	9
machine	Xeon 4c+4c 3.5GHz
what	prp
notes	Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"V(50989)/69818796119453411" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing V(50989)/69818796119453411 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 11, base 2+sqrt(11) Calling N-1 BLS with factored part 0.14% and helper 0.06% (0.47% proof) V(50989)/69818796119453411 is Fermat and Lucas PRP! (8.1840s+0.1379s) [Elapsed time: 9.00 seconds]
modified	2020-07-07 22:30:17
created	2014-08-23 01:41:02
id	163963

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