1288726869465789 · 234567 + 1
(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:1288726869465789 · 234567 + 1
Verification status (*):Proven
Official Comment:Triplet (3)
Proof-code(s): (*):p296 : Kaiser1, Srsieve, LLR, OpenPFGW
Decimal Digits:10421   (log10 is 10420.814021)
Rank (*):72594 (digit rank is 1)
Entrance Rank (*):66586
Currently on list? (*):short
Submitted:4/16/2014 14:46:57 CDT
Last modified:4/16/2014 15:52:10 CDT
Database id:117635
Status Flags:TrialDiv
Score (*):32.5678 (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.
Triplet (archivable class *)
Prime on list: yes, rank 3
Subcategory: "Triplet (3)"
(archival tag id 217670, tag last modified 2015-08-31 10:50:38)

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_id117635
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"1288726869465789*2^34567+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 1288726869465789*2^34567+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 99.86%
1288726869465789*2^34567+1 is prime! (12.4968s+0.0004s)
[Elapsed time: 13.00 seconds]
modified2014-06-21 13:36:26
created2014-04-16 15:27:01
id163176

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.