1213436745 · 16301# + 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:1213436745 · 16301# + 1
Verification status (*):Proven
Official Comment:Arithmetic progression (5,d=42986923*16301#)
Proof-code(s): (*):p155 : DavisK, NewPGen, OpenPFGW
Decimal Digits:7035   (log10 is 7034.8705313718)
Rank (*):76821 (digit rank is 2)
Entrance Rank (*):76646
Currently on list? (*):short
Submitted:7/9/2017 00:24:38 CDT
Last modified:7/9/2017 00:50:22 CDT
Database id:123719
Status Flags:TrialDiv
Score (*):31.3493 (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.
Arithmetic Progressions of Primes (archivable class *)
Prime on list: yes, rank 5, weight 46.2163955227247
Subcategory: "Arithmetic progression (5,d=*)"
(archival tag id 218828, tag last modified 2017-07-14 09:13:23)

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_id123719
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"1213436745*16301#+1" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 1213436745*16301#+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 33.34%


1213436745*16301#+1 is prime! (4.8832s+0.0042s)
[Elapsed time: 5.00 seconds]
modified2017-08-07 13:02:22
created2017-07-09 00:31:02
id169367

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