"6994339275...(15032 other digits)...6277935111"

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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:	"6994339275...(15032 other digits)...6277935111"
Verification status (*):	PRP
Official Comment (*):	Cyclotomy
Proof-code(s): (*):	PM : Mihailescu
Decimal Digits:	15053 (log₁₀ is 15052.8447467)
Rank (*):	78318 (digit rank is 1)
Entrance Rank (*):	199
Currently on list? (*):	no
Submitted:	3/1998
Last modified:	3/11/2023 15:54:10 UTC
Removed (*):	9/2/2000 05:17:44 UTC
Database id:	12806
Blob database id:	14
Status Flags:	Verify
Score (*):	33.7069 (normalized score 0)

Description: (from blob table id=14)

This 15,053 (decimal) digit prime (69943...35111) does not have a nice short description! Preda Mihailescu formed it by computing a sequence of primes p_i where prime is a "random" number times twice the proceeding prime plus one (see \cite{Mihailescu94}) and our pages on proving primality). A primality certificate is available.

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.

Cyclotomy Proof (tolerated *)
Prime on list: no, rank 22
Subcategory: "Cyclotomy Proof"
(archival tag id 192529, 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 12806

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 7 8725864215...6277935111 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 41, base 1+sqrt(41) Running N+1 test using discriminant 41, base 2+sqrt(41) Running N+1 test using discriminant 41, base 3+sqrt(41) Running N+1 test using discriminant 41, base 4+sqrt(41) Calling N-1 BLS with factored part 0.12% and helper 0.02% (0.37% proof) 6994339275...6277935111 is Fermat and Lucas PRP! (-1500.701888 seconds)

modified 2003-03-25 17:21:43

created 2003-02-02 16:05:01

id 68093

field	value
prime_id	12806
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 7 8725864215...6277935111 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 41, base 1+sqrt(41) Running N+1 test using discriminant 41, base 2+sqrt(41) Running N+1 test using discriminant 41, base 3+sqrt(41) Running N+1 test using discriminant 41, base 4+sqrt(41) Calling N-1 BLS with factored part 0.12% and helper 0.02% (0.37% proof) 6994339275...6277935111 is Fermat and Lucas PRP! (-1500.701888 seconds)
modified	2003-03-25 17:21:43
created	2003-02-02 16:05:01
id	68093

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