
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:
field (help)  value 
Description:  U(21412, 1, 4620)  U(21412, 1, 4619) 
Verification status (*):  PRP 
Official Comment:  Lehmer number 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  x25 : Water, Broadhurst, Primo, OpenPFGW 
Decimal Digits:  20004 (log_{10} is 20003.305742473) 
Rank (*):  65483 (digit rank is 2) 
Entrance Rank (*):  61578 
Currently on list? (*):  short 
Submitted:  6/8/2016 19:49:28 CDT 
Last modified:  6/8/2016 20:20:37 CDT 
Database id:  121751 
Status Flags:  Verify, TrialDiv 
Score (*):  34.5868 (normalized score 0) 

Archival tags:
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
tags.
 Lehmer number (archivable *)
 Prime on list: yes, rank 17
Subcategory: "Lehmer number"
(archival tag id 218346, tag last modified 20190803 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.
Verification data:
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.
field  value 
prime_id  121751 
person_id  9 
machine  Using: Xeon 4c+4c 3.5GHz 
what  prp 
notes  Command: /home/caldwell/client/pfgw/pfgw64 tc q"lucasU(21412,1,4620)lucasU(21412,1,4619)" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing lucasU(21412,1,4620)lucasU(21412,1,4619) [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 37 Running N1 test using base 59 Running N+1 test using discriminant 67, base 15+sqrt(67) Calling N1 BLS with factored part 1.16% and helper 0.53% (4.00% proof)
lucasU(21412,1,4620)lucasU(21412,1,4619) is Fermat and Lucas PRP! (42.7255s+0.0028s) [Elapsed time: 43.00 seconds]

modified  20170127 05:57:11 
created  20160608 19:51:01 
id  167389 

Query times: 0.0005 seconds to select prime, 0.0009 seconds to seek comments.
