Phi(3, 10104279) + (137 · 10104280 + 731 · 1093395) · (1010884 - 1)/999
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help
 

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, 10104279) + (137 · 10104280 + 731 · 1093395) · (1010884 - 1)/999
Verification status (*):Proven
Official Comment:Palindrome
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p44 : Broadhurst, OpenPFGW
Decimal Digits:208559   (log10 is 208558)
Rank (*):20865 (digit rank is 1)
Entrance Rank (*):14807
Currently on list? (*):short
Submitted:2/27/2014 18:15:21 CDT
Last modified:2/28/2014 04:22:10 CDT
Database id:117318
Status Flags:TrialDiv
Score (*):41.8172 (normalized score 0.1461)

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 15
Subcategory: "Palindrome"
(archival tag id 217634, tag last modified 2016-01-10 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.

David Broadhurst writes (11 Sep 2014): 
1 (0)_{93394} (137)_{3628} 1 (731)_{3628} (0)_{93394} 1

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.
fieldvalue
prime_id117318
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -tc -q"Phi(3,10^104279)+(137*10^104280+731*10^93395)*(10^10884-1)/999" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing Phi(3,10^104279)+(137*10^104280+731*10^93395)*(10^10884-1)/999 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 6+sqrt(13)
Calling N-1 BLS with factored part 44.78% and helper 0.00% (134.36% proof)
Phi(3,10^104279)+(137*10^104280+731*10^93395)*(10^10884-1)/999 is prime! (31577.2267s+0.2123s)
[Elapsed time: 8.77 hours]
modified2014-04-01 17:37:38
created2014-02-27 19:13:09
id162837

Query times: 0.0003 seconds to select prime, 0.0006 seconds to seek comments.