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:||1043085905 · 235000 + 18197|
|Verification status (*):||PRP|
|Official Comment:||ECPP, consecutive primes arithmetic progression (3,d=18198)|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||c4 : Broadhurst, Primo|
|Decimal Digits:||10546 (log10 is 10545.068168316)|
|Rank (*):||72952 (digit rank is 4)|
|Entrance Rank (*):||66090|
|Currently on list? (*):||short|
|Submitted:||2/21/2014 12:43:37 CDT|
|Last modified:||2/21/2014 13:22:31 CDT|
|Status Flags:||Verify, TrialDiv|
|Score (*):||32.6046 (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
- Consecutive Primes in Arithmetic Progression (archivable class *)
- Prime on list: yes, rank 2
Subcategory: "Consecutive primes in arithmetic progression (3,d=*)"
(archival tag id 217621, tag last modified 2014-03-19 14:52:09)
- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: no, rank 119, weight 38.2075522696631
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 217622, tag last modified 2017-02-02 09:20:09)
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 132
(archival tag id 217623, tag last modified 2018-03-14 05:50:22)
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||Ditto P4 P4|
|notes||Command: /home/ditto/client/pfgw -tc -q"1043085905*2^35000+18197" 2>&1|
PFGW Version 220.127.116.11BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 1043085905*2^35000+18197 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 3+sqrt(11)
Calling N+1 BLS with factored part 0.03% and helper 0.02% (0.11% proof)
1043085905*2^35000+18197 is Fermat and Lucas PRP! (31.1955s+0.0003s)
[Elapsed time: 32.00 seconds]
Query times: 0.0006 seconds to select prime, 0.0003 seconds to seek comments.