U(5797, - 5798, 4201)

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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:	U(5797, - 5798, 4201)
Verification status (*):	PRP
Official Comment (*):	Generalized Lucas number, cyclotomy
Unofficial Comments:	This prime has 2 user comments below.
Proof-code(s): (*):	CH11 : Wang3, OpenPFGW, Primo, CHG
Decimal Digits:	15806 (log₁₀ is 15805.768411382)
Rank (*):	76480 (digit rank is 1)
Entrance Rank (*):	67684
Currently on list? (*):	no
Submitted:	11/1/2018 15:05:41 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	125746
Status Flags:	Verify
Score (*):	33.858 (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.

Cyclotomy Proof (tolerated *)
Prime on list: no, rank 18
Subcategory: "Cyclotomy Proof"
(archival tag id 219957, tag last modified 2023-03-11 15:53:59)
Generalized Lucas Number (archivable *)
Prime on list: no, rank 25
Subcategory: "Generalized Lucas Number"
(archival tag id 219956, tag last modified 2023-10-24 02:37:13)

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.

Serge Batalov writes (6 Nov 2018): (report abuse)

Also can be written as (5798^4201+1)/5799. The N-1 is factored at 28.09% so CHG was likely used.

Anonymous Person(s) writes (1 May 2019): (report abuse)

U(5797,-5798,4201) 28.097% Factorization of N-1, along with Primo certificate of a P1740 factor, can be found at http://factordb.com/index.php?id=1100000001174685072 CHG input/output files available at https://www.mat.univie.ac.at/~chen/5798_4201.in and https://www.mat.univie.ac.at/~chen/5798_4201.out

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 125746

person_id 9

machine Using: Xeon 4c+4c 3.5GHz

what prp

notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"(5798^4201+1)/5799" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing (5798^4201+1)/5799 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N-1 test using base 11 Running N+1 test using discriminant 23, base 2+sqrt(23) Calling N-1 BLS with factored part 1.29% and helper 0.08% (3.96% proof) (5798^4201+1)/5799 is Fermat and Lucas PRP! (24.4422s+0.0005s) [Elapsed time: 24.00 seconds]

modified 2020-07-07 22:30:14

created 2018-11-01 15:11:02

id 171423

field	value
prime_id	125746
person_id	9
machine	Using: Xeon 4c+4c 3.5GHz
what	prp
notes	Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"(5798^4201+1)/5799" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing (5798^4201+1)/5799 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N-1 test using base 11 Running N+1 test using discriminant 23, base 2+sqrt(23) Calling N-1 BLS with factored part 1.29% and helper 0.08% (3.96% proof) (5798^4201+1)/5799 is Fermat and Lucas PRP! (24.4422s+0.0005s) [Elapsed time: 24.00 seconds]
modified	2020-07-07 22:30:14
created	2018-11-01 15:11:02
id	171423

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