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:||(241681 - 1)/1052945423 / 16647332713153 / 2853686272534246492102086015457|
|Verification status (*):||PRP|
|Official Comment:||Mersenne cofactor, ECPP|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||c77 : Batalov, Primo|
|Decimal Digits:||12495 (log10 is 12494.532092524)|
|Rank (*):||70370 (digit rank is 1)|
|Entrance Rank (*):||66447|
|Currently on list? (*):||short|
|Submitted:||4/25/2015 22:24:12 CDT|
|Last modified:||4/25/2015 22:50:24 CDT|
|Status Flags:||Verify, TrialDiv|
|Score (*):||33.1301 (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
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 79
(archival tag id 217994, tag last modified 2017-11-16 23:50:19)
- Mersenne cofactor (archivable *)
- Prime on list: yes, rank 5
Subcategory: "Mersenne cofactor"
(archival tag id 217995, tag last modified 2017-03-08 12:50:38)
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||Using: Xeon 4c+4c 3.5GHz|
|notes||Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"(2^41681-1)/1052945423/16647332713153/2853686272534246492102086015457" 2>&1|
PFGW Version 18.104.22.168BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing (2^41681-1)/1052945423/16647332713153/2853686272...2086015457 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.17% and helper 0.01% (0.52% proof)
(2^41681-1)/1052945423/16647332713153/2853686272...2086015457 is Fermat and Lucas PRP! (10.0084s+0.0003s)
[Elapsed time: 10.00 seconds]
Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.