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Difference between revisions of "Williams prime MM 5"

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(new n=754611)
(add history & 5 primes)
 
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{{Reserved|User:Karbon}}
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{{Williams prime
 
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|WiBase=5
==Definition==
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|WiMaxn=1000000
[[Prime number|Primes]] of the form <math>4 \cdot {5^n{-}1}</math>, ''n'' ≥ 1.
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|WiDate=2024-08-30
 
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|WiReserved=
==Primes for ''n''==
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|WiNlist=
1, 3, 9, 13, 15, 25, 39, 69, 165, 171, 209, 339, 2033, 6583, 15393, 282989, 498483, 504221, {{PP|125947|754611}}
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1
 
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3
==Search range==
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9
765000 (2019-01-30)
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13
 
+
15
 +
25
 +
39
 +
69
 +
165
 +
171
 +
209
 +
339
 +
2033
 +
6583
 +
15393
 +
282989
 +
498483
 +
504221
 +
754611;125947
 +
864751;126245
 +
1132659;134153
 +
1292915;134143
 +
1330541;134144
 +
3189669;134156
 +
6181673;134170
 +
|WiRemarks=The {{OEIS|l|A046865}}<br>See [https://www.mersenneforum.org/showthread.php?t=6131 Thread] at [[MersenneForum]]
 +
}}
 
==History==
 
==History==
{|class="wikitable"
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{{HistC|2024-08-30|'''Reservation''' dropped|Dylan Delgado}}
!Date!!Remark
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{{HistF|2022-07-15|6181673|Ryan Propper}}
|-
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{{HistF|2022-07-12|3189669|Ryan Propper}}
|2019-01-27||found ''n'' = 754611, [[User:Karbon|Karsten Bonath]]
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{{HistF|2022-07-11|1330541|Ryan Propper}}
|-
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{{HistF|2022-07-11|1292915|Ryan Propper}}
|2018-12-24||found ''n'' = 504221, [[User:Karbon|Karsten Bonath]]
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{{HistF|2022-07-11|1132659|Ryan Propper}}
|-
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{{HistR|2019-05-11|Dylan Delgado|516518}}
|2018-12-23||found ''n'' = 498483, [[User:Karbon|Karsten Bonath]]
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{{HistC|2019-04-04|695000-1000000|Karsten Bonath|512625}}
|-
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{{HistF|2019-02-25|864751|Karsten Bonath|509418}}
|2018-12-06||Checked to ''n'' = 1 - 321000, found ''n'' = 282989, [[User:Karbon|Karsten Bonath]]
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{{HistF|2019-01-28|754611|Karsten Bonath|507005}}
|-
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{{HistC|2019-01-17|320000-695000|Karsten Bonath|506202}}
|2007-20-12||Checked to ''n'' = 200000, Geoff Reynolds
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{{HistF|2019-01-17|498483 & 504221|Karsten Bonath|506202}}
|-
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{{HistC|2018-12-07|1-320000|Karsten Bonath}}
|2007-07-13||Checked to ''n'' = 110000, Geoff Reynolds
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{{HistF|2018-12-07|282989|Karsten Bonath|501959}}
|-
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{{HistC|2007-12-20|110000-200000|Geoffrey Reynolds}}
|2006-08||Found ''n'' = 15393, antiroach
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{{HistC|2007-07-13|100000-110000|Geoffrey Reynolds}}
|-
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{{HistC|2006-09-22|50000-100000|Geoffrey Reynolds|87710}}
|1981||Checked to ''n'' = 500, found ''n'' = 1 ... 339, [http://matwbn.icm.edu.pl/ksiazki/aa/aa39/aa3912.pdf H. C. Williams]
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{{HistC|2006-07-19|50000|(antiroach)|83800}}
|}
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{{HistF|2006-07-17|15393|(antiroach)|83718}}
 
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{{HistC|2003-01-26|1-8100|Robert G. Wilson}}
==See also==
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{{HistC|1981|1-500|Hugh C. Williams}}
*[[Williams primes]]
 
 
 
==External links==
 
*[[Wikipedia:Williams_number|Wikipedia]]
 
*[https://www.mersenneforum.org/showthread.php?t=6131 Thread] at [[MersenneForum]]
 
*[https://oeis.org/A046865 The On-Line Encyclopedia of Integer Sequences OEIS: A046865]
 
[[Category:Williams primes|#.....5]]
 
[[Category:(b-1)*b^n-1|#.....5]]
 

Latest revision as of 09:03, 1 October 2024

Current data

Base : 5
Count : 25
Max n : 1,000,000
Date : 2024-08-30
1, 3, 9, 13, 15, 25, 39, 69, 165, 171, 209, 339, 2033, 6583, 15393, 282989, 498483, 504221, 754611, 864751, 1132659, 1292915, 1330541, 3189669, 6181673
Remarks :
The sequence A046865 in OEIS
See Thread at MersenneForum

History