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:
|Verification status (*):||PRP|
|Official Comment:||Lucas number, cyclotomy, APR-CL assisted|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||x25 : Water, Broadhurst, Primo, OpenPFGW|
|Decimal Digits:||4069 (log10 is 4068.78036802684)|
|Rank (*):||84686 (digit rank is 1)|
|Entrance Rank (*):||24886|
|Currently on list? (*):||short|
|Submitted:||1/8/2002 10:16:41 CDT|
|Last modified:||1/8/2002 10:16:41 CDT|
|Score (*):||29.6486 (normalized score 0)|
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
- Lucas Number (archivable *)
- Prime on list: yes, rank 11
Subcategory: "Lucas Number"
(archival tag id 195587, tag last modified 2015-09-23 10:50:29)
- Cyclotomy Proof (tolerated *)
- Prime on list: no, rank 112
Subcategory: "Cyclotomy Proof"
(archival tag id 195586, tag last modified 2018-11-12 02:50:16)
- APR-CL assisted (tolerated *)
- Prime on list: no, rank 4
Subcategory: "APR-CL assisted"
(archival tag id 195585, tag last modified 2009-02-12 20:01:27)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
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.
|machine||Linux PII 200|
|notes||PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Primality testing V(19469) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 13, base 1+sqrt(13) Running N+1 test using discriminant 13, base 2+sqrt(13) Calling N-1 BLS with factored part 2.41% and helper 1.59% (8.83% proof) V(19469) is Fermat and Lucas PRP! (334.720000 seconds) |
Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.