Phi(6685, - 10)

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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:	Phi(6685, - 10)
Verification status (*):	PRP
Official Comment (*):	Unique, ECPP
Proof-code(s): (*):	c8 : Broadhurst, Water, Primo
Decimal Digits:	4560 (log₁₀ is 4559.9586117012)
Rank (*):	92704 (digit rank is 1)
Entrance Rank (*):	28211
Currently on list? (*):	no
Submitted:	3/31/2003 12:34:52 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	64262
Status Flags:	Verify
Score (*):	30.0029 (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.

Unique (archivable *)
Prime on list: no, rank 27
Subcategory: "Unique"
(archival tag id 210380, tag last modified 2023-05-15 15:37:15)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 582
Subcategory: "ECPP"
(archival tag id 210379, tag last modified 2024-04-13 23:37:20)

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 64262

person_id 9

machine Linux P4 2.8GHz

what prp

notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Primality testing Phi(6685,-10) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Calling Brillhart-Lehmer-Selfridge with factored part 1.02% Phi(6685,-10) is PRP! (13.180000 seconds)

modified 2020-07-07 22:30:48

created 2003-03-31 17:59:26

id 69130

field	value
prime_id	64262
person_id	9
machine	Linux P4 2.8GHz
what	prp
notes	PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Primality testing Phi(6685,-10) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Calling Brillhart-Lehmer-Selfridge with factored part 1.02% Phi(6685,-10) is PRP! (13.180000 seconds)
modified	2020-07-07 22:30:48
created	2003-03-31 17:59:26
id	69130

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