3 · 25082306 + 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:3 · 25082306 + 1
Verification status (*):Proven
Official Comment:Divides GF(5082303,3), GF(5082305,5)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L780 : Brady, Srsieve, PrimeGrid, LLR
Decimal Digits:1529928   (log10 is 1529927.03026428)
Rank (*):50 (digit rank is 1)
Entrance Rank (*):15
Currently on list? (*):short
Submitted:4/4/2009 09:54:03 CDT
Last modified:4/16/2009 13:50:03 CDT
Database id:87449
Status Flags:none
Score (*):47.9373 (normalized score 67.2645)

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: yes, rank 3, weight 49.0359234472639
Subcategory: "Divides GF(*,3)"
(archival tag id 208974, tag last modified 2016-03-15 13:57:15)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 2, weight 49.0359234472639
Subcategory: "Divides GF(*,5)"
(archival tag id 208975, tag last modified 2016-03-15 13:57:15)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

PrimeGrid writes (11 Sep 2014): 
3*2^5082306+1 is a Factor of GF(5082303,3)
3*2^5082306+1 is a Factor of GF(5082305,5)
3*2^5082306+1 is a Factor of xGF(5082305,5,3)
3*2^5082306+1 is a Factor of xGF(5082302,7,4)
3*2^5082306+1 is a Factor of GF(5082304,8)
3*2^5082306+1 is a Factor of xGF(5082304,8,3)
3*2^5082306+1 is a Factor of xGF(5082305,8,5)
3*2^5082306+1 is a Factor of xGF(5082305,9,5)
3*2^5082306+1 is a Factor of xGF(5082304,9,8)
3*2^5082306+1 is a Factor of GF(5082305,11)
3*2^5082306+1 is a Factor of xGF(5082305,11,3)
3*2^5082306+1 is a Factor of xGF(5082302,11,5)
3*2^5082306+1 is a Factor of xGF(5082305,11,8)
3*2^5082306+1 is a Factor of xGF(5082305,11,9)
3*2^5082306+1 is a Factor of xGF(5082303,12,7)

For more information, please see the Official Announcement.

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_id87449
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 3 2 5082306 1 2>&1
[Elapsed time: 10.697 seconds]
modified2011-12-27 16:48:44
created2009-04-04 09:59:11
id104262

fieldvalue
prime_id87449
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"3*2^5082306+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 3*2^5082306+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(786432,19) to FFT(786432,18)
Reduced from FFT(786432,18) to FFT(786432,17)
Reduced from FFT(786432,17) to FFT(786432,16)
10164624 bit request FFT size=(786432,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
3*2^5082306+1 is prime! (-1634.5699s+0.0100s)
[Elapsed time: 3.72 days]
modified2009-05-25 07:25:57
created2009-04-04 10:23:02
id104263

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