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:
|Description:||(211279 + 1)/3|
|Verification status (*):||PRP|
|Official Comment:||Cyclotomy, generalized Lucas number, Wagstaff|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||PM : Mihailescu|
|Decimal Digits:||3395 (log10 is 3394.84019983932)|
|Rank (*):||84717 (digit rank is 1)|
|Entrance Rank (*):||6068|
|Currently on list? (*):||short|
|Score (*):||29.0853 (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
- Cyclotomy Proof (tolerated *)
- Prime on list: no, rank 112
Subcategory: "Cyclotomy Proof"
(archival tag id 181336, tag last modified 2005-12-06 08:20:23)
- Generalized Lucas Number (archivable *)
- Prime on list: no, rank 92
Subcategory: "Generalized Lucas Number"
(archival tag id 181335, tag last modified 2016-05-02 05:50:25)
- Wagstaff (archivable *)
- Prime on list: yes, rank 5
(archival tag id 181337, tag last modified 2014-09-17 12:50:33)
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 (2^11279+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 5, base 1+sqrt(5) Running N+1 test using discriminant 5, base 2+sqrt(5) Running N+1 test using discriminant 5, base 5+sqrt(5) Running N+1 test using discriminant 5, base 6+sqrt(5) Calling N+1 BLS with factored part 0.82% and helper 0.12% (2.62% proof) (2^11279+1)/3 is Fermat and Lucas PRP! (493.410000 seconds) |
Query times: 0.0006 seconds to select prime, 0.0008 seconds to seek comments.