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:||Euler irregular, ECPP|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||c55 : Gramolin, Primo|
|Decimal Digits:||5412 (log10 is 5411.3600318736)|
|Rank (*):||81983 (digit rank is 1)|
|Entrance Rank (*):||58539|
|Currently on list? (*):||short|
|Submitted:||3/26/2011 06:04:24 CDT|
|Last modified:||3/26/2011 23:14:05 CDT|
|Blob database id:||251|
|Score (*):||30.5347 (normalized score 0)|
(from blob table id=251)
For the primality proof certificate see: http://factordb.com/index.php?showid=1100000000293541437.
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
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 395
(archival tag id 213180, tag last modified 2019-06-02 14:20:07)
- Euler Irregular primes (archivable *)
- Prime on list: yes, rank 6
Subcategory: "Euler Irregular primes"
(archival tag id 213179, 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||RedHat P4 P4|
|notes||PFGW Version 184.108.40.206BIT.20110215.x86_Dev [GWNUM 26.5]|
Primality testing 2291035789...0963774693 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 5+sqrt(5)
Calling N+1 BLS with factored part 0.20% and helper 0.18% (0.80% proof)
2291035789...0963774693 is Fermat and Lucas PRP! (10.0634s+0.0016s)
[Elapsed time: 10.00 seconds]
Query times: 0.0004 seconds to select prime, 0.0008 seconds to seek comments.