347 · 2544887 + 1
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

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:347 · 2544887 + 1
Verification status (*):Proven
Official Comment:Divides GF(544886,5)
Proof-code(s): (*):L679 : Foody, Srsieve, PrimeGrid, LLR
Decimal Digits:164030   (log10 is 164029.87157683)
Rank (*):31185 (digit rank is 1)
Entrance Rank (*):1612
Currently on list? (*):no
Submitted:2/23/2009 03:11:33 CDT
Last modified:2/23/2009 03:50:20 CDT
Database id:86845
Status Flags:none
Score (*):41.0782 (normalized score 0.0545)

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.
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 30, weight 46.9275419180723
Subcategory: "Divides GF(*,5)"
(archival tag id 208921, tag last modified 2016-03-15 13:57:15)

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_id86845
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 347 2 544887 1 2>&1
[Elapsed time: 9.727 seconds]
modified2011-12-27 16:48:45
created2009-02-23 03:18:01
id103061

fieldvalue
prime_id86845
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"347*2^544887+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 347*2^544887+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
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)
1089800 bit request FFT size=(65536,17)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
347*2^544887+1 is prime! (1456.4600s+0.0000s)
[Elapsed time: 24.40 minutes]
modified2009-03-24 13:31:30
created2009-02-23 03:23:01
id103062

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.