Generalized Woodall primes of the form `n`•4ⁿ-1

Current data

Base :	4
Count :	21
Max `n` :	2,000,000
Date :	2024-10-25

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
Sequence is the same as Near Woodall (n+1)*2^n-1 for odd n.

Notes

History

2024-10-25: Checked n = 1 - 100000, Gary Barnes, double-check, released
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
2010-11-01: Checked n = 3 - 4000, Steven Harvey, double-check
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

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Generalized Woodall primes of the form `n`•4ⁿ-1

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Generalized Woodall primes of the form n•4n-1

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Generalized Woodall primes of the form `n`•4ⁿ-1