primV(27655, 1, 19926)

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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(27655, 1, 19926)
Verification status (*):	PRP
Official Comment (*):	Generalized Lucas primitive part
Proof-code(s): (*):	x25 : Broadhurst, Water, OpenPFGW, Primo
Decimal Digits:	57566 (log₁₀ is 57565.386662596)
Rank (*):	59045 (digit rank is 1)
Entrance Rank (*):	38890
Currently on list? (*):	yes
Submitted:	3/6/2013 11:02:17 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	111497
Status Flags:	Verify
Score (*):	37.8517 (normalized score 0.0006)

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 2
Subcategory: "Generalized Lucas primitive part"
(archival tag id 215199, tag last modified 2023-03-11 15:53:59)

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 111497

person_id 9

machine Ditto P4 P4

what trial_divided

notes Command: /home/ditto/client/pfgw -o -f -q"primV(27655,1,19926)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] primV(27655,1,19926) 1/1 mro=0 trial factoring to 18883765 primV(27655,1,19926) has no small factor. [Elapsed time: 86.512 seconds]

modified 2020-07-07 22:30:22

created 2013-03-06 11:05:02

id 153316

field	value
prime_id	111497
person_id	9
machine	Ditto P4 P4
what	trial_divided
notes	Command: /home/ditto/client/pfgw -o -f -q"primV(27655,1,19926)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] primV(27655,1,19926) 1/1 mro=0 trial factoring to 18883765 primV(27655,1,19926) has no small factor. [Elapsed time: 86.512 seconds]
modified	2020-07-07 22:30:22
created	2013-03-06 11:05:02
id	153316

field value

prime_id 111497

person_id 9

machine Ditto P4 P4

what prp

notes Command: /home/ditto/client/pfgw -tc -q"primV(27655,1,19926)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing primV(27655,1,19926) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 23 Running N-1 test using base 53 Running N+1 test using discriminant 67, base 18+sqrt(67) Calling N-1 BLS with factored part 0.88% and helper 0.01% (2.64% proof) primV(27655,1,19926) is Fermat and Lucas PRP! (1723.2800s+0.1694s) [Elapsed time: 28.72 minutes]

modified 2020-07-07 22:30:22

created 2013-03-06 11:08:02

id 153317

field	value
prime_id	111497
person_id	9
machine	Ditto P4 P4
what	prp
notes	Command: /home/ditto/client/pfgw -tc -q"primV(27655,1,19926)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing primV(27655,1,19926) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 23 Running N-1 test using base 53 Running N+1 test using discriminant 67, base 18+sqrt(67) Calling N-1 BLS with factored part 0.88% and helper 0.01% (2.64% proof) primV(27655,1,19926) is Fermat and Lucas PRP! (1723.2800s+0.1694s) [Elapsed time: 28.72 minutes]
modified	2020-07-07 22:30:22
created	2013-03-06 11:08:02
id	153317

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