U(51031)/95846689435051369

Previous Next Random

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(51031)/95846689435051369
Verification status (*):	PRP
Official Comment (*):	Fibonacci cofactor, ECPP
Proof-code(s): (*):	c8 : Broadhurst, Water, Primo
Decimal Digits:	10648 (log₁₀ is 10647.517207478)
Rank (*):	82189 (digit rank is 1)
Entrance Rank (*):	67203
Currently on list? (*):	short
Submitted:	9/11/2014 17:59:39 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	118483
Status Flags:	Verify
Score (*):	32.6345 (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 285
Subcategory: "ECPP"
(archival tag id 217813, tag last modified 2024-04-19 02:37:11)
Fibonacci cofactor (archivable *)
Prime on list: yes, rank 14
Subcategory: "Fibonacci cofactor"
(archival tag id 217814, tag last modified 2024-04-19 02:37:11)

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 118483

person_id 9

machine Using: Xeon 4c+4c 3.5GHz

what prp

notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"U(51031)/95846689435051369" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing U(51031)/95846689435051369 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 17 Running N-1 test using base 23 Running N-1 test using base 31 Running N-1 test using base 41 Running N+1 test using discriminant 53, base 6+sqrt(53) Calling N-1 BLS with factored part 0.16% and helper 0.01% (0.50% proof) U(51031)/95846689435051369 is Fermat and Lucas PRP! (15.9680s+0.0008s) [Elapsed time: 16.00 seconds]

modified 2020-07-07 22:30:17

created 2014-09-11 18:01:01

id 164061

field	value
prime_id	118483
person_id	9
machine	Using: Xeon 4c+4c 3.5GHz
what	prp
notes	Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"U(51031)/95846689435051369" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing U(51031)/95846689435051369 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 17 Running N-1 test using base 23 Running N-1 test using base 31 Running N-1 test using base 41 Running N+1 test using discriminant 53, base 6+sqrt(53) Calling N-1 BLS with factored part 0.16% and helper 0.01% (0.50% proof) U(51031)/95846689435051369 is Fermat and Lucas PRP! (15.9680s+0.0008s) [Elapsed time: 16.00 seconds]
modified	2020-07-07 22:30:17
created	2014-09-11 18:01:01
id	164061

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