primV(111534, 1, 27000)

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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(111534, 1, 27000)
Verification status (*):	PRP
Official Comment (*):	Generalized Lucas primitive part
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	x25 : Broadhurst, Water, OpenPFGW, Primo
Decimal Digits:	72683 (log₁₀ is 72682.664799838)
Rank (*):	55348 (digit rank is 1)
Entrance Rank (*):	38122
Currently on list? (*):	yes
Submitted:	11/15/2013 13:01:15 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	116319
Status Flags:	Verify
Score (*):	38.5708 (normalized score 0.0014)

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.

Generalized Lucas primitive part (archivable *)
Prime on list: yes, rank 1
Subcategory: "Generalized Lucas primitive part"
(archival tag id 217445, tag last modified 2023-03-11 15:53:59)

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)

CHG proof at 72683 digits and 26.29% factorization, with details in http://physics.open.ac.uk/~dbroadhu/cert/b27000.zip and a certificate compressed to 43 MB in http://physics.open.ac.uk/~dbroadhu/cert/b27000_cert.gp.gz. It is notable that no use of ECPP was required for this proof, since the 9692-digit helper primV(111534,1,3600) was proven by BLS. All other helpers had less than 600 digits and were proven by Pari-GP. At time of posting, primV(111534,1,27000) occupied first place at http://physics.open.ac.uk/~dbroadhu/cert/gigantic.

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 116319

person_id 9

machine Ditto P4 P4

what prp

notes Command: /home/ditto/client/pfgw -tc -q"primV(111534,1,27000)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing primV(111534,1,27000) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Running N-1 test using base 41 Running N+1 test using discriminant 59, base 4+sqrt(59) Calling N-1 BLS with factored part 0.81% and helper 0.01% (2.43% proof) primV(111534,1,27000) is Fermat and Lucas PRP! (2843.2577s+0.3164s) [Elapsed time: 47.38 minutes]

modified 2020-07-07 22:30:18

created 2013-11-15 13:08:02

id 161825

field	value
prime_id	116319
person_id	9
machine	Ditto P4 P4
what	prp
notes	Command: /home/ditto/client/pfgw -tc -q"primV(111534,1,27000)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing primV(111534,1,27000) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Running N-1 test using base 41 Running N+1 test using discriminant 59, base 4+sqrt(59) Calling N-1 BLS with factored part 0.81% and helper 0.01% (2.43% proof) primV(111534,1,27000) is Fermat and Lucas PRP! (2843.2577s+0.3164s) [Elapsed time: 47.38 minutes]
modified	2020-07-07 22:30:18
created	2013-11-15 13:08:02
id	161825

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.