163221 · 2124601 + 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:163221 · 2124601 + 1
Verification status (*):Proven
Official Comment:Cunningham chain 2nd kind (2p-1)
Proof-code(s): (*):L983 : Wu_T, LLR
Decimal Digits:37514   (log10 is 37513.851265762)
Rank (*):50438 (digit rank is 1)
Entrance Rank (*):27509
Currently on list? (*):short
Submitted:12/8/2009 07:46:14 CDT
Last modified:12/8/2009 08:06:38 CDT
Database id:91116
Status Flags:none
Score (*):36.5301 (normalized score 0.001)

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: yes, rank 4, weight 36.2522899897608
Subcategory: "Cunningham chain 2nd kind (2p-1)"
(archival tag id 212403, tag last modified 2014-07-17 11:51:38)

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_id91116
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 163221 2 124601 1 2>&1
[Elapsed time: 8.816 seconds]
modified2011-12-27 16:48:41
created2009-12-08 07:48:11
id111604

fieldvalue
prime_id91116
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"163221*2^124601+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 163221*2^124601+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(14336,20) to FFT(14336,19)
Reduced from FFT(14336,19) to FFT(14336,18)
249246 bit request FFT size=(14336,18)
Calling Brillhart-Lehmer-Selfridge with factored part 99.99%
163221*2^124601+1 is prime! (65.5000s+0.0000s)
[Elapsed time: 67.00 seconds]
modified2010-03-13 18:56:32
created2009-12-08 08:03:40
id111610

Query times: 0.0005 seconds to select prime, 0.0005 seconds to seek comments.