2 · 43156947 + 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:2 · 43156947 + 1
Verification status (*):Proven
Official Comment:Divides Phi(431^56947,2)
Proof-code(s): (*):g404 : Taniguchi, Proth.exe
Decimal Digits:150026   (log10 is 150025.87813384)
Rank (*):26952 (digit rank is 1)
Entrance Rank (*):1135
Currently on list? (*):no
Submitted:11/13/2007 20:38:43 CDT
Last modified:11/13/2007 21:44:39 CDT
Database id:82994
Status Flags:none
Score (*):40.8035 (normalized score 0.0692)

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.
Divides Phi (archivable *)
Prime on list: no, rank 40
Subcategory: "Divides Phi"
(archival tag id 187402, tag last modified 2014-10-11 22:50:03)

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_id82994
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 2 431 56947 1 2>&1
[Elapsed time: 8.229 seconds]
modified2011-12-27 16:48:48
created2007-11-13 20:52:01
id95105

fieldvalue
prime_id82994
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"2*431^56947+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 2*431^56947+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(65536,20) to FFT(65536,19)
Reduced from FFT(65536,19) to FFT(65536,18)
Reduced from FFT(65536,18) to FFT(65536,17)
Reduced from FFT(65536,17) to FFT(65536,16)
996760 bit request FFT size=(65536,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
2*431^56947+1 is prime! (-1256.8673s+0.0300s)
[Elapsed time: 51.63 minutes]
modified2008-01-03 10:54:43
created2007-11-13 20:53:01
id95106

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.