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:
|Verification status (*):||PRP|
|Official Comment (*):||Euler irregular, ECPP|
|Proof-code(s): (*):||c8 : Broadhurst, Water, Primo|
|Decimal Digits:||6011 (log10 is 6010.9671549975)|
|Rank (*):||85803 (digit rank is 1)|
|Entrance Rank (*):||68220|
|Currently on list? (*):||short|
|Submitted:||2/16/2013 05:29:34 CDT|
|Last modified:||2/16/2013 05:50:53 CDT|
|Blob database id:||289|
|Score (*):||30.8611 (normalized score 0)|
Description: (from blob table id=289)
[This prime has a pre-calculated decimal expansion (linked blob)]
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.
- Euler Irregular primes (archivable *)
- Prime on list: yes, rank 6
Subcategory: "Euler Irregular primes"
(archival tag id 215073, tag last modified 2022-08-26 14:30:32)
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 466
(archival tag id 215074, tag last modified 2022-11-14 11:36:29)
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 111251 person_id 9 machine Ditto P4 P4 what trial_divided notes PFGW Version 220.127.116.11BIT.20110215.x86_Dev [GWNUM 26.5] 9271606631946363....4612780099166521 1/1 mro=0 trial factoring to 1656050 9271606631...0099166521 has no small factor. [Elapsed time: 3.990 seconds] modified 2020-07-07 17:30:23 created 2013-02-16 05:35:02 id 152772
field value prime_id 111251 person_id 9 machine Ditto P4 P4 what prp notes PFGW Version 18.104.22.168BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 9271606631...0099166521 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N+1 test using discriminant 13, base 6+sqrt(13) Calling N+1 BLS with factored part 0.37% and helper 0.06% (1.16% proof) 9271606631...0099166521 is Fermat and Lucas PRP! (11.9787s+0.0017s) [Elapsed time: 12.00 seconds] modified 2020-07-07 17:30:23 created 2013-02-16 05:45:55 id 152774