| Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3). |
Navigation
| Topics | Help • Register • News • History • How to • Sequences statistics • Template prototypes |
Difference between revisions of "Williams prime MM 5"
(2019-01-17) |
(new n=754611) |
||
| Line 2: | Line 2: | ||
==Definition== | ==Definition== | ||
| − | [[Prime number|Primes]] of the form <math>4 \cdot {5^n{-}1}</math>. | + | [[Prime number|Primes]] of the form <math>4 \cdot {5^n{-}1}</math>, ''n'' ≥ 1. |
==Primes for ''n''== | ==Primes for ''n''== | ||
| − | 1, 3, 9, 13, 15, 25, 39, 69, 165, 171, 209, 339, 2033, 6583, 15393, 282989, 498483, 504221 | + | 1, 3, 9, 13, 15, 25, 39, 69, 165, 171, 209, 339, 2033, 6583, 15393, 282989, 498483, 504221, {{PP|125947|754611}} |
==Search range== | ==Search range== | ||
| − | + | 765000 (2019-01-30) | |
==History== | ==History== | ||
| Line 14: | Line 14: | ||
!Date!!Remark | !Date!!Remark | ||
|- | |- | ||
| − | |2019-01- | + | |2019-01-27||found ''n'' = 754611, [[User:Karbon|Karsten Bonath]] |
|- | |- | ||
| − | |2018-12- | + | |2018-12-24||found ''n'' = 504221, [[User:Karbon|Karsten Bonath]] |
|- | |- | ||
| − | | | + | |2018-12-23||found ''n'' = 498483, [[User:Karbon|Karsten Bonath]] |
|- | |- | ||
| − | | | + | |2018-12-06||Checked to ''n'' = 1 - 321000, found ''n'' = 282989, [[User:Karbon|Karsten Bonath]] |
|- | |- | ||
| − | | | + | |2007-20-12||Checked to ''n'' = 200000, Geoff Reynolds |
|- | |- | ||
| − | |1981||Checked to ''n''=500, found ''n''=1 ... 339, [http://matwbn.icm.edu.pl/ksiazki/aa/aa39/aa3912.pdf H. C. Williams] | + | |2007-07-13||Checked to ''n'' = 110000, Geoff Reynolds |
| + | |- | ||
| + | |2006-08||Found ''n'' = 15393, antiroach | ||
| + | |- | ||
| + | |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 primes]] | ||
==External links== | ==External links== | ||
| − | * [ | + | *[[Wikipedia:Williams_number|Wikipedia]] |
| − | * [https://www.mersenneforum.org/showthread.php?t=6131 | + | *[https://www.mersenneforum.org/showthread.php?t=6131 Thread] at [[MersenneForum]] |
| − | * [https://oeis.org/A046865 The On-Line Encyclopedia of Integer Sequences OEIS: A046865] | + | *[https://oeis.org/A046865 The On-Line Encyclopedia of Integer Sequences OEIS: A046865] |
| − | |||
[[Category:Williams primes|#.....5]] | [[Category:Williams primes|#.....5]] | ||
[[Category:(b-1)*b^n-1|#.....5]] | [[Category:(b-1)*b^n-1|#.....5]] | ||
Revision as of 08:21, 30 January 2019
| Reserved! This sequence is currently reserved by: User:Karbon |
Definition
Primes of the form [math]\displaystyle{ 4 \cdot {5^n{-}1} }[/math], n ≥ 1.
Primes for n
1, 3, 9, 13, 15, 25, 39, 69, 165, 171, 209, 339, 2033, 6583, 15393, 282989, 498483, 504221, 754611
Search range
765000 (2019-01-30)
History
| Date | Remark |
|---|---|
| 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 |
