R(49081)

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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:	R(49081)
Verification status (*):	External
Official Comment (*):	Repunit, unique, ECPP
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	c70 : Underwood, Dubner, Primo
Decimal Digits:	49081 (log₁₀ is 49080.04575749)
Rank (*):	62653 (digit rank is 1)
Entrance Rank (*):	57918
Currently on list? (*):	yes
Submitted:	3/21/2022 12:15:00 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	133761
Status Flags:	Verify
Score (*):	37.3597 (normalized score 0.0004)

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.

Unique (archivable *)
Prime on list: yes, rank 2
Subcategory: "Unique"
(archival tag id 226974, tag last modified 2023-05-15 15:37:15)
Repunit (archivable *)
Prime on list: yes, rank 2
Subcategory: "Repunit"
(archival tag id 226973, tag last modified 2023-05-15 15:37:15)
Elliptic Curve Primality Proof (archivable *)
Prime on list: yes, rank 8
Subcategory: "ECPP"
(archival tag id 226972, tag last modified 2023-10-16 19:37:14)

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.

Paul Underwood writes (21 Mar 2022): (report abuse)

PRP found by Harvey Dubner: his paper. Proven prime by Paul Underwood. Announcement here. Certificate sited here.

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 133761

person_id 9

machine Using: Dual Intel Xeon Gold 5222 CPUs 3.8GHz

what prp

notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"R(49081)" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing R(49081) [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 17, base 1+sqrt(17) Calling N-1 BLS with factored part 0.31% and helper 0.01% (0.95% proof) R(49081) is Fermat and Lucas PRP! (89.2909s+0.0003s) [Elapsed time: 89.00 seconds]

modified 2022-07-11 18:21:45

created 2022-03-21 12:16:02

id 179483

field	value
prime_id	133761
person_id	9
machine	Using: Dual Intel Xeon Gold 5222 CPUs 3.8GHz
what	prp
notes	Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"R(49081)" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing R(49081) [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 17, base 1+sqrt(17) Calling N-1 BLS with factored part 0.31% and helper 0.01% (0.95% proof) R(49081) is Fermat and Lucas PRP! (89.2909s+0.0003s) [Elapsed time: 89.00 seconds]
modified	2022-07-11 18:21:45
created	2022-03-21 12:16:02
id	179483

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