15 · 21418605 + 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:15 · 21418605 + 1
Verification status (*):Proven
Official Comment:Divides GF(1418600,5), GF(1418601,6)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):g279 : Cooper, NewPGen, PRP, Proth.exe
Decimal Digits:427044   (log10 is 427043.833090161)
Rank (*):3283 (digit rank is 1)
Entrance Rank (*):49
Currently on list? (*):short
Submitted:4/20/2006 04:48:14 CDT
Last modified:7/7/2006 00:52:33 CDT
Database id:77623
Status Flags:none
Score (*):44.0205 (normalized score 1.3013)

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 15, weight 46.7286458870426
Subcategory: "Divides GF(*,6)"
(archival tag id 187057, tag last modified 2016-03-15 13:57:15)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 12, weight 46.7286458870426
Subcategory: "Divides GF(*,5)"
(archival tag id 187056, 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.

Curtis Cooper writes (11 Sep 2014): 
15*2^1418605+1 is a Factor of xGF(1418603,4,3)
15*2^1418605+1 is a Factor of GF(1418600,5)
15*2^1418605+1 is a Factor of GF(1418601,6)
15*2^1418605+1 is a Factor of xGF(1418601,6,5)
15*2^1418605+1 is a Factor of GF(1418603,8)
15*2^1418605+1 is a Factor of xGF(1418603,8,5)
15*2^1418605+1 is a Factor of xGF(1418603,9,2)
15*2^1418605+1 is a Factor of xGF(1418603,10,9)
15*2^1418605+1 is a Factor of GF(1418604,11)
15*2^1418605+1 is a Factor of xGF(1418604,11,5)
15*2^1418605+1 is a Factor of xGF(1418604,11,6)
15*2^1418605+1 is a Factor of xGF(1418604,11,8)

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_id77623
person_id9
machineWinXP Pent_M 1.7GHz Laptop
whatprime
notesCommand: pfgw.exe -n -t -q"15*2^1418605+1" 2>&1
PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Running N-1 test using base 7
N-1: 15*2^1418605+1Primality testing 15*2^1418605+1 [N-1, Brillhart-Lehmer-Selfridge]
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
15*2^1418605+1 is prime! (32179.4791s+0.0786s)
[Elapsed time: 32180 seconds]
modified2006-07-14 06:27:06
created2006-04-20 21:48:35
id84146

fieldvalue
prime_id77623
person_id9
machineGenToo P3 400MHz
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 15 2 1418605 1 2>&1
[Elapsed time: 10.292 seconds]
modified2006-07-14 06:27:04
created2006-07-07 00:52:23
id84636

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