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:||U(31321, 1, 4620) - U(31321, 1, 4619)|
|Verification status (*):||PRP|
|Official Comment:||Lehmer number|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||x25 : Water, Broadhurst, Primo, OpenPFGW|
|Decimal Digits:||20767 (log10 is 20766.264710686)|
|Rank (*):||65281 (digit rank is 1)|
|Entrance Rank (*):||61292|
|Currently on list? (*):||short|
|Submitted:||6/2/2016 12:47:02 CDT|
|Last modified:||6/2/2016 13:20:36 CDT|
|Status Flags:||Verify, TrialDiv|
|Score (*):||34.7025 (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
- Lehmer number (archivable *)
- Prime on list: yes, rank 15
Subcategory: "Lehmer number"
(archival tag id 218340, tag last modified 2019-08-03 12:50:11)
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"lucasU(31321,1,4620)-lucasU(31321,1,4619)" 2>&1|
PFGW Version 22.214.171.124BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing lucasU(31321,1,4620)-lucasU(31321,1,4619) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 17
Running N-1 test using base 19
Running N+1 test using discriminant 37, base 3+sqrt(37)
Calling N-1 BLS with factored part 1.24% and helper 0.49% (4.23% proof)
lucasU(31321,1,4620)-lucasU(31321,1,4619) is Fermat and Lucas PRP! (51.4896s+0.0010s)
[Elapsed time: 51.00 seconds]
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.