primU(43359)

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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.

Description:	primU(43359)
Verification status (*):	PRP
Official Comment (*):	Fibonacci primitive part, ECPP
Proof-code(s): (*):	c8 : Broadhurst, Water, Primo
Decimal Digits:	5939 (log₁₀ is 5938.4758400585)
Rank (*):	84106 (digit rank is 2)
Entrance Rank (*):	68772
Currently on list? (*):	short
Submitted:	3/24/2013 06:38:33 CDT
Last modified:	3/24/2013 07:20:36 CDT
Database id:	111800
Status Flags:	Verify
Score (*):	30.8234 (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 395
Subcategory: "ECPP"
(archival tag id 215219, tag last modified 2021-08-03 03:37:33)
Fibonacci Primitive Part (archivable *)
Prime on list: yes, rank 20
Subcategory: "Fibonacci Primitive Part"
(archival tag id 215220, tag last modified 2019-03-30 15:20:27)

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 111800

person_id 9

machine RedHat P4 P4

what trial_divided

notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 2991162851944353....3160207078384001 1/1 mro=0 trial factoring to 1634386 2991162851...7078384001 has no small factor. [Elapsed time: 4.423 seconds]

modified 2020-07-07 17:30:22

created 2013-03-24 06:48:17

id 153939

field	value
prime_id	111800
person_id	9
machine	RedHat P4 P4
what	trial_divided
notes	PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 2991162851944353....3160207078384001 1/1 mro=0 trial factoring to 1634386 2991162851...7078384001 has no small factor. [Elapsed time: 4.423 seconds]
modified	2020-07-07 17:30:22
created	2013-03-24 06:48:17
id	153939

field value

prime_id 111800

person_id 9

machine RedHat P4 P4

what prp

notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 2991162851...7078384001 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Running N-1 test using base 19 Running N-1 test using base 37 Running N+1 test using discriminant 43, base 3+sqrt(43) Calling N-1 BLS with factored part 1.15% and helper 0.04% (3.50% proof) 2991162851...7078384001 is Fermat and Lucas PRP! (17.0916s+0.0017s) [Elapsed time: 17.00 seconds]

modified 2020-07-07 17:30:22

created 2013-03-24 06:54:48

id 153959

field	value
prime_id	111800
person_id	9
machine	RedHat P4 P4
what	prp
notes	PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 2991162851...7078384001 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Running N-1 test using base 19 Running N-1 test using base 37 Running N+1 test using discriminant 43, base 3+sqrt(43) Calling N-1 BLS with factored part 1.15% and helper 0.04% (3.50% proof) 2991162851...7078384001 is Fermat and Lucas PRP! (17.0916s+0.0017s) [Elapsed time: 17.00 seconds]
modified	2020-07-07 17:30:22
created	2013-03-24 06:54:48
id	153959

Query times: 0.0003 seconds to select prime, 0.0008 seconds to seek comments.