U(9667, 1, 3960) - U(9667, 1, 3959)

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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(9667, 1, 3960) - U(9667, 1, 3959)
Verification status (*):	PRP
Official Comment (*):	Lehmer number, cyclotomy
Proof-code(s): (*):	x25 : Broadhurst, Water, OpenPFGW, Primo
Decimal Digits:	15778 (log₁₀ is 15777.769850587)
Rank (*):	76459 (digit rank is 1)
Entrance Rank (*):	11662
Currently on list? (*):	no
Submitted:	11/16/2002 01:00:49 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	59883
Status Flags:	Verify
Score (*):	33.8525 (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.

Lehmer number (archivable *)
Prime on list: no, rank 24
Subcategory: "Lehmer number"
(archival tag id 192471, tag last modified 2023-03-11 15:53:59)
Cyclotomy Proof (tolerated *)
Prime on list: no, rank 19
Subcategory: "Cyclotomy Proof"
(archival tag id 192470, 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 59883

person_id 9

machine Linux PII 200

what prp

notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality Running N-1 test using base 29 0302111169...3020296801 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 37, base 12+sqrt(37) Calling N-1 BLS with factored part 1.66% and helper 0.59% (5.58% proof) U(9667,1,3960)-U(9667,1,3959) is Fermat and Lucas PRP! (-419.557296 seconds)

modified 2003-03-25 17:21:51

created 2003-01-20 21:31:11

id 66874

field	value
prime_id	59883
person_id	9
machine	Linux PII 200
what	prp
notes	PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality Running N-1 test using base 29 0302111169...3020296801 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 37, base 12+sqrt(37) Calling N-1 BLS with factored part 1.66% and helper 0.59% (5.58% proof) U(9667,1,3960)-U(9667,1,3959) is Fermat and Lucas PRP! (-419.557296 seconds)
modified	2003-03-25 17:21:51
created	2003-01-20 21:31:11
id	66874

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