
At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:
field (help)  value 
Description:  "6994339275...(15032 other digits)...6277935111" 
Verification status (*):  PRP 
Official Comment:  Cyclotomy 
Proofcode(s): (*):  PM : Mihailescu 
Decimal Digits:  15053 (log_{10} is 15052.8447467) 
Rank (*):  68601 (digit rank is 1) 
Entrance Rank (*):  199 
Currently on list? (*):  no 
Submitted:  3/1998 
Last modified:  3/1998 
Removed (*):  9/2/2000 00:17:44 CDT 
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 12
Subcategory: "Cyclotomy Proof"
(archival tag id 192529, tag last modified 20090212 20:01:27)
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 N1 test using base 7 8725864215...6277935111 [N1/N+1, BrillhartLehmerSelfridge] 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 N1 BLS with factored part 0.12% and helper 0.02% (0.37% proof) 6994339275...6277935111 is Fermat and Lucas PRP! (1500.701888 seconds) 
modified  20030325 11:21:43 
created  20030202 10:05:01 
id  68093 

Query times: 0.0006 seconds to select prime, 0.0005 seconds to seek comments.
