Difference between revisions of "Woodall prime 4"

Latest revision as of 09:07, 17 October 2024

Current data

Base :	4
Count :	21
Max `n` :	2,000,000
Date :	2015

1^[1], 2^[2], 3^[3], 5^[4], 8^[5], 14^[6], 23^[7], 63^[8], 107^[9], 132^[10], 428^[11], 530^[12], 1137^[13], 1973^[14], 2000^[15], 7064^[16], 20747^[17], 79574^[18], 113570^[19], 293912^[20], 1993191^[21]

Remarks :

The sequence A086661 in OEIS
See early history at Generalized Woodall news, Generalized Woodall primes, & Generalized Woodall completed ranges.
Sequence is the same as Near Woodall (n+1)*2^n-1 for odd n.

Notes

History

2015-05-01: Checked n = 1000000 - 2000000, Serge Batalov
2015-05-01: Found n = 1993191, Serge Batalov
2014-05-29: Checked n = 608749 - 1000000, Steven Harvey
2014-03-13: Checked to n = 25000, Steven Harvey, double-check
2012-10-10: Checked to n = 25000, Thomas Ritschel
2011-09-09: Checked n = 532007 - 608749, Steven Harvey
2009-10-09: Checked n = 282500 - 317900, Steven Harvey
2009-09-11: Found n = 293912, Steven Harvey
2009-01-03: Checked n = 520000 - 532007, Thomas Wolter
2007-11-29: Checked n = 425000 - 520000, Thomas Wolter
2005-11-27: Checked n = 250000 - 282500, 335200 - 425000, Thomas Wolter, released
2005-01-21: Reserved by Thomas Wolter to n = 400000
2005-01-03: Checked n = 5000 - 10000, Mark Rodenkirch
2004-12-28: Checked n = 317900 - 335200, Thomas Wolter
2004-12-21: Reserved by Mark Rodenkirch to n = 10000
2004-12-21: Checked n = 3 - 5000, Mark Rodenkirch
2004-12-15: Reserved by Mark Rodenkirch to n = 6000
2004-12-03: Reserved by Mark Rodenkirch to n = 5000
2004-09-20: Checked to n = 250000, Steven Harvey
2004-09-15: Reserved by Thomas Wolter to n = 300000
2004-03-30: Reserved by Steven Harvey to n = 250000
2000-07-28: Found n = 113570, Ray Ballinger
2000-05-19: Found n = 79574, Ray Ballinger
1998-07-03: Found n = 20747, Henri Lifchitz
1998-07-03: Found n = 7064, Henri Lifchitz
1998-07-03: Found n = 2000, Henri Lifchitz
1998-07-03: Found n = 1973, Henri Lifchitz

[1] Twin n=1, Mersenne 2²-1, Near Woodall 2•2¹-1, Near Woodall 1•2²-1

[2] Mersenne 2⁵-1, Near Woodall 4•2³-1

[3] Twin n=3, Riesel 3•2⁶-1, Near Woodall 6•2⁵-1

[4] Riesel 5•2¹⁰-1, Near Woodall 10•2⁹-1

[5] Mersenne 2¹⁹-1, Near Woodall 16•2¹⁵-1

[6] Riesel 7•2²⁹-1, Near Woodall 28•2²⁷-1

[7] Riesel 23•2⁴⁶-1, Near Woodall 46•2⁴⁵-1

[8] Riesel 63•2¹²⁶-1, Near Woodall 126•2¹²⁵-1

[9] Riesel 107•2²¹⁴-1, Near Woodall 214•2²¹³-1

[10] Riesel 33•2²⁶⁶-1, Near Woodall 264•2²⁶³-1

[11] Riesel 107•2⁸⁵⁸-1, Near Woodall 856•2⁸⁵⁵-1

[12] Riesel 265•2¹⁰⁶¹-1, Near Woodall 1060•2¹⁰⁵⁹-1

[13] Riesel 1137•2²²⁷⁴-1, Near Woodall 2274•2²²⁷³-1

[14] Riesel 1973•2³⁹⁴⁶-1, Near Woodall 3946•2³⁹⁴⁵-1

[15] Riesel 125•2⁴⁰⁰⁴-1, Near Woodall 4000•2³⁹⁹⁹-1

[16] Riesel 883•2¹⁴¹³¹-1, Near Woodall 14128•2¹⁴¹²⁷-1

[17] Riesel 20747•2⁴¹⁴⁹⁴-1, Near Woodall 41494•2⁴¹⁴⁹³-1

[18] Riesel 39787•2¹⁵⁹¹⁴⁹-1, Near Woodall 159148•2¹⁵⁹¹⁴⁷-1

[19] Riesel 56785•2²²⁷¹⁴¹-1, Near Woodall 227140•2²²⁷¹³⁹-1

[20] Riesel 36739•2⁵⁸⁷⁸²⁷-1, Near Woodall 587824•2⁵⁸⁷⁸²³-1

[21] Riesel 1993191•2^3986382-1, Near Woodall 3986382•2^3986381-1

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

@@ Line 5: / Line 5: @@
 |WoReserved=
 |WoNlist=
-;T:T;C:[[Riesel prime 1|{{Kbn|2}}]], Near Woodall: {{Kbn|2|1}} & {{Kbn|1|2}}
+;T:T;C:{{NRi|2}}, {{NWo|+|1}}, {{NWo|-|2}}
-;C:[[Riesel prime 1|{{Kbn|5}}]], Near Woodall: {{Kbn|4|3}}
+;C:{{NRi|5}}, {{NWo|+|3}}
-;T:T;C:[[Riesel prime 3|{{Kbn|3|6}}]], Near Woodall: {{Kbn|6|5}}
+;T:T;C:{{NRi|3|6}}, {{NWo|+|5}}
-;C:[[Riesel prime 5|{{Kbn|5|10}}]], Near Woodall: {{Kbn|10|9}}
+;C:{{NRi|5|10}}, {{NWo|+|9}}
-;C:[[Riesel prime 1|{{Kbn|19}}]], Near Woodall: {{Kbn|16|15}}
+;C:{{NRi|19}}, {{NWo|+|15}}
-;C:[[Riesel prime 7|{{Kbn|7|29}}]], Near Woodall: {{Kbn|28|27}}
+;C:{{NRi|7|29}}, {{NWo|+|27}}
-;C:[[Riesel prime 23|{{Kbn|23|46}}]], Near Woodall: {{Kbn|46|45}}
+;C:{{NRi|23|46}}, {{NWo|+|45}}
-;C:{{Kbn|63|126}}, Near Woodall: {{Kbn|126|125}}
+;C:{{NRi|63|126}}, {{NWo|+|125}}
-;C:{{Kbn|107|214}}, Near Woodall: {{Kbn|214|213}}
+;C:{{NRi|107|214}}, {{NWo|+|213}}
-;C:{{Kbn|33|266}}, Near Woodall: {{Kbn|264|263}}
+;C:{{NRi|33|266}}, {{NWo|+|263}}
-;C:{{Kbn|107|858}}, Near Woodall: {{Kbn|856|855}}
+;C:{{NRi|107|858}}, {{NWo|+|855}}
-;C:{{Kbn|265|1061}}, Near Woodall: {{Kbn|1060|1059}}
+;C:{{NRi|265|1061}}, {{NWo|+|1059}}
-;C:{{Kbn|1137|2274}}, Near Woodall: {{Kbn|2274|2273}}
+;C:{{NRi|1137|2274}}, {{NWo|+|2273}}
-;47591;C:{{Kbn|1973|3946}}, Near Woodall: {{Kbn|3946|3945}}
+;47591;C:{{NRi|1973|3946}}, {{NWo|+|3945}}
-;46892;C:{{Kbn|125|4004}}, Near Woodall: {{Kbn|4000|3999}}
+;46892;C:{{NRi|125|4004}}, {{NWo|+|3999}}
-;27021;C:{{Kbn|883|14131}}, Near Woodall: {{Kbn|14128|14127}}
+;27021;C:{{NRi|883|14131}}, {{NWo|+|14127}}
-;15177;C:{{Kbn|20747|41494}}, Near Woodall: {{Kbn|41494|41493}}
+;15177;C:{{NRi|20747|41494}}, {{NWo|+|41493}}
-;1152;C:{{Kbn|39787|159149}}, Near Woodall: {{Kbn|159148|159147}}
+;1152;C:{{NRi|39787|159149}}, {{NWo|+|159147}}
-;356;C:{{Kbn|56785|227141}}, Near Woodall: {{Kbn|227140|227139}}
+;356;C:{{NRi|56785|227141}}, {{NWo|+|227139}}
-;89940;C:{{Kbn|36739|587827}}, Near Woodall: {{Kbn|587824|587823}}
+;89940;C:{{NRi|36739|587827}}, {{NWo|+|587823}}
-1993191;119835;C:{{Kbn|1993191|3986382}}, Near Woodall: {{Kbn|3986382|3986381}}
+1993191;119835;C:{{NRi|1993191|3986382}}, {{NWo|+|3986381}}
-|WoRemarks=The {{OEIS|l|A086661}}
+|WoRemarks=The {{OEIS|l|A086661}}<br>See early history at [https://harvey563.tripod.com/GWNews.txt Generalized Woodall news], [https://harvey563.tripod.com/GeneralizedWoodallPrimes.txt Generalized Woodall primes], & [https://harvey563.tripod.com/gwranges.txt Generalized Woodall completed ranges].<br>Sequence is the same as [[Woodall prime P 2|Near Woodall ({{Vn}}+1)*2^{{Vn}}-1]] for odd {{Vn}}.
 }}
 ==History==
+{{HistC|2015-05-01|1000000-2000000|Serge Batalov}}
 {{HistF|2015-05-01|1993191|Serge Batalov}}
+{{HistC|2014-05-29|608749-1000000|Steven Harvey}}
+{{HistC|2014-03-13|25000|Steven Harvey}}, double-check
+{{HistC|2012-10-10|25000|Thomas Ritschel}}
+{{HistC|2011-09-09|532007-608749|Steven Harvey}}
+{{HistC|2009-10-09|282500-317900|Steven Harvey}}
 {{HistF|2009-09-11|293912|Steven Harvey}}
+{{HistC|2009-01-03|520000-532007|Thomas Wolter}}
+{{HistC|2007-11-29|425000-520000|Thomas Wolter}}
+{{HistC|2005-11-27|250000-282500, 335200-425000|Thomas Wolter}}, released
+{{HistR|2005-01-21|Thomas Wolter}} to {{Rn|400000|400000}}
+{{HistC|2005-01-03|5000-10000|Mark Rodenkirch}}
+{{HistC|2004-12-28|317900-335200|Thomas Wolter}}
+{{HistR|2004-12-21|Mark Rodenkirch}} to {{Rn|10000|10000}}
+{{HistC|2004-12-21|3-5000|Mark Rodenkirch}}
+{{HistR|2004-12-15|Mark Rodenkirch}} to {{Rn|6000|6000}}
+{{HistR|2004-12-03|Mark Rodenkirch}} to {{Rn|5000|5000}}
+{{HistC|2004-09-20|250000|Steven Harvey}}
+{{HistR|2004-09-15|Thomas Wolter}} to {{Rn|300000|300000}}
+{{HistR|2004-03-30|Steven Harvey}} to {{Rn|250000|250000}}
 {{HistF|2000-07-28|113570|Ray Ballinger}}
 {{HistF|2000-05-19|79574|Ray Ballinger}}

Difference between revisions of "Woodall prime 4"

Latest revision as of 09:07, 17 October 2024

Current data

Notes

History

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