# 63 · 21686050 + 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.

Description: 63 · 21686050 + 1 Proven Divides GF(1686047,12) This prime has 1 user comment below. L2085 : Dodson1, PSieve, Srsieve, PrimeGrid, LLR 507554   (log10 is 507553.4235298) 4082 (digit rank is 1) 148 short 8/3/2011 19:21:37 CDT 8/8/2011 15:20:04 CDT 101002 none 44.5511 (normalized score 1.178)

#### 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 14, weight 48.69431546493
Subcategory: "Divides GF(*,12)"
(archival tag id 213361, tag last modified 2021-01-28 16:20:27)

#### User comments about this prime (disclaimer):

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Lennart Vogel writes (11 Sep 2014):  (report abuse)
 63*2^1686050+1 is a Factor of xGF(1686046,7,4)!!!! 63*2^1686050+1 is a Factor of xGF(1686048,9,8)!!!! 63*2^1686050+1 is a Factor of xGF(1686048,11,8)!!!! 63*2^1686050+1 is a Factor of xGF(1686042,11,9)!!!! 63*2^1686050+1 is a Factor of GF(1686047,12)!!!!

#### 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_id101002
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"63*2^1686050+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 63*2^1686050+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 63*2^1686050+1 is prime! (6994.1477s+0.0013s) [Elapsed time: 1.94 hours]
modified2020-07-07 17:30:31
created2011-08-03 19:23:01
id131570

fieldvalue
prime_id101002
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 63 2 1686050 1 2>&1 [Elapsed time: 10.121 seconds]
modified2020-07-07 17:30:31
created2011-08-03 19:35:01
id131571

Query times: 0.0006 seconds to select prime, 0.0013 seconds to seek comments.