Difference between revisions of "Williams prime MM 5"

Revision as of 14:35, 7 March 2019

Reserved! This sequence is currently reserved by: User:Karbon

Williams prime (b-1)× bⁿ-1 with b = 5 (primes of the form 4 × 5ⁿ-1, n ≥ 1).

1, 3, 9, 13, 15, 25, 39, 69, 165, 171, 209, 339, 2033, 6583, 15393, 282989, 498483, 504221, 754611, 864751

n = 905000 (2019-03-07)

Date	Remark
2019-02-23	found n = 864751, Karsten Bonath
2019-01-27	found n = 754611, Karsten Bonath
2018-12-24	found n = 504221, Karsten Bonath
2018-12-23	found n = 498483, Karsten Bonath
2018-12-06	Checked to n = 1 - 321000, found n = 282989, Karsten Bonath
2007-20-12	Checked to n = 200000, Geoff Reynolds
2007-07-13	Checked to n = 110000, Geoff Reynolds
2006-08	Found n = 15393, antiroach
1981	Checked to n = 500, found n = 1 ... 339, H. C. Williams

@@ Line 2: / Line 2: @@
 ==Definition==
-[[Prime]]s of the form <math>4 \cdot {5^n{-}1}</math>, ''n'' ≥ 1.
+[[Williams prime]] ''(b-1)&times; b<sup>n</sup>-1'' with ''b'' = 5 ([[prime]]s of the form 4 &times; 5<sup>n</sup>-1, ''n'' ≥ 1).
-==Primes for ''n''==
+==Prime for ''n''==
-, 3, 9, 13, 15, 25, 39, 69, 165, 171, 209, 339, 2033, 6583, 15393, 282989, 498483, 504221, {{PP|125947|754611}}
+, 3, 9, 13, 15, 25, 39, 69, 165, 171, 209, 339, 2033, 6583, 15393, 282989, 498483, 504221, {{PP|125947|754611}}, {{PP|126245|864751}}
 ==Search range==
-(2019-01-30)
+''n'' = 905000 (2019-03-07)
 ==History==
 {|class="wikitable"
 !Date!!Remark
+|-
+|2019-02-23||found ''n'' = 864751, [[User:Karbon|Karsten Bonath]]
 |-
 |2019-01-27||found ''n'' = 754611, [[User:Karbon|Karsten Bonath]]
@@ Line 30: / Line 32: @@
 |1981||Checked to ''n'' = 500, found ''n'' = 1 ... 339, [http://matwbn.icm.edu.pl/ksiazki/aa/aa39/aa3912.pdf H. C. Williams]
 |}
-==See also==
-*[[Williams prime]]
 ==External links==
-*[[Wikipedia:Williams_number|Wikipedia]]
+*[[Wikipedia:Williams_number|Williams number]]
 *[https://www.mersenneforum.org/showthread.php?t=6131 Thread] at [[MersenneForum]]
-*[https://oeis.org/A046865 The On-Line Encyclopedia of Integer Sequences OEIS: A046865]
+*The {{OEIS|l|A046865}}
 [[Category:Williams prime|#.....5]]