# 15 · 21418605 + 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: 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:

Description: 15 · 21418605 + 1 Proven Divides GF(1418600,5), GF(1418601,6) This prime has 1 user comment below. g279 : Cooper, NewPGen, PRP, Proth.exe 427044   (log10 is 427043.83309016) 9880 (digit rank is 1) 49 short 4/20/2006 04:48:14 CDT 7/7/2006 00:52:33 CDT 77623 none 44.0205 (normalized score 0.5044)

#### 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 20, weight 46.728645887043
Subcategory: "Divides GF(*,6)"
(archival tag id 187057, tag last modified 2022-08-21 08:37:10)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 19, weight 46.728645887043
Subcategory: "Divides GF(*,5)"
(archival tag id 187056, tag last modified 2023-01-19 18:37:29)

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Curtis Cooper writes (11 Sep 2014):  (report abuse)
 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]
modified2020-07-07 17:30:42
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]
modified2020-07-07 17:30:42
created2006-07-07 00:52:23
id84636

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