
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:  (V(45366, 1, 4857) + 1)/(V(45366, 1, 3) + 1) 
Verification status (*):  PRP 
Official Comment:  Lehmer primitive part 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  x25 : Water, Broadhurst, Primo, OpenPFGW 
Decimal Digits:  22604 (log_{10} is 22603.769789892) 
Rank (*):  62963 (digit rank is 1) 
Entrance Rank (*):  52666 
Currently on list? (*):  short 
Submitted:  2/5/2013 16:45:44 CDT 
Last modified:  2/5/2013 17:20:25 CDT 
Database id:  111121 
Status Flags:  Verify 
Score (*):  34.9647 (normalized score 0.0001) 

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 primitive part (archivable *)
 Prime on list: yes, rank 5
Subcategory: "Lehmer primitive part"
(archival tag id 215067, tag last modified 20160614 19:50:41)
User comments about this prime (disclaimer):
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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  111121 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  Command: /home/caldwell/client/pfgw o f q"(lucasV(45366,1,4857)+1)/(lucasV(45366,1,3)+1)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] (lucasV(45366,1,....sV(45366,1,3)+1) 1/1 mro=0
trial factoring to 6923599 (lucasV(45366,1,4857)+1)/(lucasV(45366,1,3)+1) has no small factor. [Elapsed time: 13.265 seconds]

modified  20130216 12:06:20 
created  20130205 16:48:01 
id  152516 

field  value 
prime_id  111121 
person_id  9 
machine  RedHat P4 P4 
what  prp 
notes  Command: /home/caldwell/client/pfgw tc q"(lucasV(45366,1,4857)+1)/(lucasV(45366,1,3)+1)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing (lucasV(45366,1,4857)+1)/(lucasV(45366,1,3)+1) [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 29 Running N+1 test using discriminant 47, base 18+sqrt(47) Calling N1 BLS with factored part 0.97% and helper 0.03% (2.93% proof) (lucasV(45366,1,4857)+1)/(lucasV(45366,1,3)+1) is Fermat and Lucas PRP! (200.7965s+0.0039s) [Elapsed time: 3.33 minutes]

modified  20130216 12:06:20 
created  20130205 16:53:01 
id  152517 

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
