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:||Phi(3, 31118781 + 1)/3|
|Verification status (*):||Proven|
|Official Comment:||Generalized unique|
|Unofficial Comments:||This prime has 2 user comments below.|
|Proof-code(s): (*):||L3839 : Batalov, EMsieve, LLR|
|Decimal Digits:||1067588 (log10 is 1067587.91183178)|
|Rank (*):||91 (digit rank is 1)|
|Entrance Rank (*):||63|
|Currently on list? (*):||short|
|Submitted:||3/29/2014 04:39:12 CDT|
|Last modified:||8/22/2014 08:37:26 CDT|
|Score (*):||46.8336 (normalized score 27.3116)|
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
- Generalized Unique (archivable *)
- Prime on list: yes, rank 1
Subcategory: "Generalized Unique"
(archival tag id 217791, tag last modified 2014-08-18 06:50:07)
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||Xeon 4c+4c 3.5GHz|
|notes||Command: ./pfgw64 -tc -q"Phi(3,3^1118781+1)/3" 2>&1|
PFGW Version 18.104.22.168BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing Phi(3,3^1118781+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N-1 test using base 13
Running N-1 test using base 17
Running N-1 test using base 59
Running N-1 test using base 61
Running N+1 test using discriminant 97, base 3+sqrt(97)
Calling N-1 BLS with factored part 50.00% and helper 0.00% (150.01% proof)
Phi(3,3^1118781+1)/3 is prime! (255252.0424s+0.3649s)
[Elapsed time: 2.95 days]
Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.