
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:  Phi(3, 10^{103182}) + (137 · 10^{103183} + 731 · 10^{66639}) · (10^{36543}  1)/999 
Verification status (*):  PRP 
Official Comment:  Palindrome 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  x29 : Broadhurst, OpenPFGW 
Decimal Digits:  206365 (log_{10} is 206364) 
Rank (*):  21109 (digit rank is 1) 
Entrance Rank (*):  14815 
Currently on list? (*):  short 
Submitted:  1/31/2014 08:49:30 CDT 
Last modified:  1/31/2014 16:20:55 CDT 
Database id:  117033 
Status Flags:  Verify, TrialDiv 
Score (*):  41.7847 (normalized score 0.1421) 

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.
 Palindrome (archivable *)
 Prime on list: yes, rank 20
Subcategory: "Palindrome"
(archival tag id 217596, tag last modified 20160110 02:20:35)
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  117033 
person_id  9 
machine  RedHat P4 P4 
what  prp 
notes  Command: /home/caldwell/client/pfgw tc q"Phi(3,10^103182)+(137*10^103183+731*10^66639)*(10^365431)/999" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing Phi(3,10^103182)+(137*10^103183+731*10^66639)*(10^365431)/999 [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 7 Running N+1 test using discriminant 13, base 8+sqrt(13) Calling N1 BLS with factored part 32.29% and helper 0.00% (96.88% proof) Phi(3,10^103182)+(137*10^103183+731*10^66639)*(10^365431)/999 is Fermat and Lucas PRP! (25257.7512s+0.1102s) [Elapsed time: 7.02 hours]

modified  20140401 17:37:38 
created  20140131 08:53:01 
id  162547 

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
