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:||(228759 - 1)/226160777|
|Verification status (*):||PRP|
|Official Comment:||Mersenne cofactor, ECPP|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||c60 : Lemsafer, Primo|
|Decimal Digits:||8649 (log10 is 8648.9672280129)|
|Rank (*):||74730 (digit rank is 1)|
|Entrance Rank (*):||62604|
|Currently on list? (*):||short|
|Submitted:||9/24/2012 10:40:16 CDT|
|Last modified:||9/24/2012 11:20:28 CDT|
|Score (*):||31.9901 (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 196
(archival tag id 214529, tag last modified 2018-03-14 05:50:22)
- Mersenne cofactor (archivable *)
- Prime on list: yes, rank 12
Subcategory: "Mersenne cofactor"
(archival tag id 214530, 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||RedHat P4 P4|
|notes||Command: /home/caldwell/client/pfgw -o -f -q"(2^28759-1)/226160777" 2>&1|
PFGW Version 126.96.36.199BIT.20110215.x86_Dev [GWNUM 26.5]
(2^28759-1)/226160777 1/1 mro=0
trial factoring to 2455982
(2^28759-1)/226160777 has no small factor.
[Elapsed time: 1.976 seconds]
|machine||RedHat Virtual STEM Server|
|notes||Command: /home/caldwell/client/pfgw -tc -q"(2^28759-1)/226160777" 2>&1|
PFGW Version 188.8.131.5200405.x86_Stable [GWNUM 25.14]
Primality testing (2^28759-1)/226160777 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N+1 BLS with factored part 0.09% and helper 0.08% (0.37% proof)
(2^28759-1)/226160777 is Fermat and Lucas PRP! (23.8864s+0.0265s)
[Elapsed time: 24.00 seconds]
Query times: 0.0002 seconds to select prime, 0.0001 seconds to seek comments.