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(15631, 1, 5040) - U(15631, 1, 5039)|
|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:||21134 (log10 is 21133.4992624487)|
|Rank (*):||63714 (digit rank is 2)|
|Entrance Rank (*):||10499|
|Currently on list? (*):||short|
|Submitted:||4/23/2003 07:08:03 CDT|
|Last modified:||4/23/2003 07:08:03 CDT|
|Score (*):||34.7568 (normalized score 0.0001)|
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 8
Subcategory: "Lehmer number"
(archival tag id 192134, tag last modified 2017-06-28 15:50:31)
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||Linux P4 2.8GHz|
|notes||PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor')|
Running N-1 test using base 59
6413180756...7639097601 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 61
Running N+1 test using discriminant 83, base 12+sqrt(83)
Calling N-1 BLS with factored part 1.25% and helper 0.20% (3.96% proof)
3156911801...7639097601 is Fermat and Lucas PRP! (562.690000 seconds)
Query times: 0.0005 seconds to select prime, 0.0003 seconds to seek comments.