82659189 · 226997 + 1
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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:82659189 · 226997 + 1
Verification status (*):Proven
Official Comment:Cunningham chain 2nd kind (p)
Proof-code(s): (*):L983 : Wu_T, LLR
Decimal Digits:8135   (log10 is 8134.8240840805)
Rank (*):70032 (digit rank is 1)
Entrance Rank (*):47392
Currently on list? (*):no
Submitted:3/22/2010 00:13:26 CDT
Last modified:3/22/2010 00:50:47 CDT
Database id:92219
Status Flags:none
Score (*):31.8 (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.
Cunningham Chains (2nd kind) (archivable class *)
Prime on list: no, rank 21, weight 21.9621302067784
Subcategory: "Cunningham chain 2nd kind (p)"
(archival tag id 212440, tag last modified 2014-07-18 20:21:43)

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_id92219
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 82659189 2 26997 1 2>&1
[Elapsed time: 8.184 seconds]
modified2011-12-27 16:48:40
created2010-03-22 00:19:04
id113808

fieldvalue
prime_id92219
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"82659189*2^26997+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 82659189*2^26997+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(3584,21) to FFT(3584,20)
Reduced from FFT(3584,20) to FFT(3584,19)
Reduced from FFT(3584,19) to FFT(3584,18)
Reduced from FFT(3584,18) to FFT(3584,17)
Reduced from FFT(3584,17) to FFT(3584,16)
54056 bit request FFT size=(3584,16)
Calling Brillhart-Lehmer-Selfridge with factored part 99.90%
82659189*2^26997+1 is prime! (3.5800s+0.0000s)
[Elapsed time: 4.00 seconds]
modified2010-10-13 12:41:39
created2010-03-22 00:38:10
id113819

Query times: 0.0004 seconds to select prime, 0.0008 seconds to seek comments.