16869987339975 · 2171960 + 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:16869987339975 · 2171960 + 1
Verification status (*):Proven
Official Comment:Twin (p+2)
Proof-code(s): (*):x24 : Jarai_Z, Farkas, Csajbok, Kasza, Jarai, Unknown
Decimal Digits:51779   (log10 is 51778.3451691349)
Rank (*):51706 (digit rank is 1)
Entrance Rank (*):8233
Currently on list? (*):short
Submitted:9/8/2005 03:46:06 CDT
Last modified:9/8/2005 09:38:09 CDT
Database id:75543
Status Flags:none
Score (*):37.5249 (normalized score 0.0017)

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.
Twin Primes (archivable *)
Prime on list: yes, rank 12
Subcategory: "Twin (p+2)"
(archival tag id 189943, tag last modified 2017-07-04 19:20:06)

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.
machineLinux P4 2.8GHz
notesCommand: /home/caldwell/client/pfgw -f -t -q"16869987339975*2^171960+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 16869987339975*2^171960+1 [N-1, Brillhart-Lehmer-Selfridge]
trial factoring to 16857726
Running N-1 test using base 17
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(24576,20) to FFT(24576,19)
Reduced from FFT(24576,19) to FFT(24576,18)
Reduced from FFT(24576,18) to FFT(24576,17)
Reduced from FFT(24576,17) to FFT(24576,16)
344016 bit request FFT size=(24576,16)
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%
16869987339975*2^171960+1 is prime! (879.6136s+0.0004s)
[Elapsed time: 880 seconds]
modified2005-09-23 12:19:27
created2005-09-08 04:03:33

Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.