194772106074315 · 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:194772106074315 · 2171960 + 1
Verification status (*):Proven
Official Comment:Twin (p+2)
Proof-code(s): (*):x24 : Jarai_Z, Farkas, Csajbok, Kasza, Jarai, Unknown
Decimal Digits:51780   (log10 is 51779.407581139)
Rank (*):51701 (digit rank is 2)
Entrance Rank (*):13432
Currently on list? (*):short
Submitted:6/20/2007 10:37:51 CDT
Last modified:6/22/2007 07:20:03 CDT
Database id:81185
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 10
Subcategory: "Twin (p+2)"
(archival tag id 189938, 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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 194772106074315 2 171960 1 2>&1
[Elapsed time: 9.303 seconds]
modified2007-09-12 06:50:19
created2007-06-20 10:52:10

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"194772106074315*2^171960+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 194772106074315*2^171960+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 19
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)
344024 bit request FFT size=(24576,16)
Calling Brillhart-Lehmer-Selfridge with factored part 99.97%
194772106074315*2^171960+1 is prime! (314.1900s+0.0000s)
[Elapsed time: 315 seconds]
modified2007-09-12 06:50:19
created2007-06-20 10:57:22

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