Phi(3817, 2)

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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(3817, 2)
Verification status (*):	PRP
Official Comment (*):	Generalized unique
Proof-code(s): (*):	c5 : Carmody, Primo
Decimal Digits:	1042 (log₁₀ is 1041.2629671114)
Rank (*):	130508 (digit rank is 14)
Entrance Rank (*):	48609
Currently on list? (*):	no
Submitted:	3/6/2001 17:27:56 UTC
Last modified:	9/2/2026 15:32:29 UTC
Database id:	55407
Status Flags:	Verify
Score (*):	25.3994 (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.

Generalized Unique (archivable *)
Prime on list: no, rank 1583
Subcategory: "Generalized Unique"
(archival tag id 225628, tag last modified 2026-09-02 01:37:06)

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 55407

person_id 9

machine Linux PII 200

what prp

notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 3 Primality testing Phi(3817,2) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N-1 test using base 11 Running N+1 test using discriminant 19, base 1+sqrt(19) Calling N+1 BLS with factored part 1.76% and helper 0.90% (6.24% proof) Phi(3817,2) is Fermat and Lucas PRP! (12.530000 seconds)

modified 2003-03-25 17:23:04

created 2003-01-04 05:41:46

id 60726

field	value
prime_id	55407
person_id	9
machine	Linux PII 200
what	prp
notes	PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 3 Primality testing Phi(3817,2) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N-1 test using base 11 Running N+1 test using discriminant 19, base 1+sqrt(19) Calling N+1 BLS with factored part 1.76% and helper 0.90% (6.24% proof) Phi(3817,2) is Fermat and Lucas PRP! (12.530000 seconds)
modified	2003-03-25 17:23:04
created	2003-01-04 05:41:46
id	60726

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.