Riesel primes of the form 31•2ⁿ-1

Reserved! This sequence is currently reserved by: Michael Curtis, Ryan Propper

Current data

`k` , `b` :	31 , 2
Count :	55
Nash :	2188
Max `n` :	3,350,000
Date :	2025-02-09
Reserved :	Michael Curtis, Ryan PropperMichael Curtis/ReservedRyan Propper/Reserved

1, 5^[1], 7, 11, 13, 23, 33, 35^[2], 37, 47, 115^[3], 205^[4], 235^[5], 271, 409, 739, 837, 887, 2189, 3465^[6], 4653, 5073, 8011, 8061, 21957, 24589, 25657, 44653, 50321, 57647, 62083, 78179, 80021, 81655^[7], 111667, 150265^[8], 177089, 196433, 274115^[9], 306751, 311389, 315523, 406105^[10], 421129, 666285^[11], 773227, 1142093, 1611311, 1755317, 2585311, 3259185^[12], 3326149, 9088085^[13], 13514933, 15145093

Remarks :

The sequence A050541 in OEIS
See also Williams 31•32ⁿ-1

Notes

History

2025-02-09: Found n = 15145093, Ryan Propper
2025-02-09: Found n = 13514933, Ryan Propper
2025-02-09: Reserved by Ryan Propper, for n = 12000000 - 18000000
2025-02-04: Checked n = 6000000 - 12000000, Ryan Propper, released
2024-09-24: Checked n = 3259185 - 3350000, Michael Curtis
2024-09-24: Found n = 3326149, Michael Curtis
2024-08-27: Found n = 9088085, Ryan Propper
2024-08-16: Reserved by Ryan Propper, for n = 6000000 - 12000000
2024-05-22: Checked n = 3000000 - 3259185, Michael Curtis
2024-05-20: Found n = 3259185, Michael Curtis
2023-07-17: Checked n = 2282000 - 3000000, Michael Curtis
2022-12-03: Found n = 2585311, Michael Curtis
2021-03-21: Checked n = 1 - 1000000, Gary Barnes, double check, results included
2021-02-13: Reserved by Michael Curtis
2016-01-27: Checked n = 2100000 - 2282000, Steven Tjung
2014-01-13: Checked n = 2066000 - 2100000, Steven Tjung
2014-09-13: Checked n = 2020000 - 2066000, Steven Tjung
2013-08-22: none, Steven Tjung
2012-08-19: Checked n = 1600000 - 2020000, Steven Tjung
2011-01-28: Found n = 1755317, Steven Tjung
2010-02-24: Found n = 1611311, Steven Tjung
2009-12-05: Checked n = 1570000 - 1600000, Steven Tjung
2009-10-06: Checked n = 1510000 - 1570000, Steven Tjung
2009-07-26: Checked n = 1650000 - 1652063?, (unknown), See range done at RPS other completed ranges.
2009-05-15: Checked n = 1370000 - 1510000, Steven Tjung
2009-04-06: Checked n = 1350000 - 1370000, Steven Tjung
2009-02-12: Checked n = 1300000 - 1350000, Steven Tjung
2009-01-09: Checked n = 950000 - 1015948, 1140029 - 1162645, 1430011 - 1445009, 1652063 - 1722449, 1967593 - 2002883, Peter Benson
2008-12-09: Found n = 421129, Raffaele De Troia, missing prime found
2008-12-02: Found n = 406105, Raffaele De Troia, missing prime found
2008-11-21: Checked n = 735000 - 1300000, Steven Tjung
2008-04-02: Found n = 1142093, Peter Benson
2008-01-31: Checked n = 707000 - 735000, Steven Tjung
2008-01-02: Checked n = 646000 - 707000, Steven Tjung
2007-12-30: Found n = 666285, Steven Tjung
2007-12-08: Checked n = 645000 - 646000, Steven Tjung
2007-12-07: Found n = 773227, Steven Tjung
2007-11-01: Checked n = 570000 - 645000, Steven Tjung
2007-09-06: Checked n = 567000 - 570000, Steven Tjung
2007-07-13: Checked n = 558000 - 567000, Steven Tjung
2007-06-25: Checked n = 527000 - 558000, Steven Tjung
2007-04-22: Checked n = 525000 - 527000, Steven Tjung
2007-03-10: Checked n = 507000 - 525000, Steven Tjung
2007-01-12: Checked n = 500000 - 507000, Steven Tjung
2006-11-03: Reserved by Steven Tjung to n = 2000000
2004-08-18: Checked n = 494600 - 500000, Steven Harvey, released
2004-08-06: Checked n = 493000 - 494600, Steven Harvey
2004-08-03: Checked n = 492500 - 493000, Steven Harvey
2004-08-01: Checked n = 492000 - 492500, Steven Harvey
2004-07-26: Checked n = 426000 - 492000, Steven Harvey
2004-06-24: Checked n = 395119 - 400000, 400729 - 426000, Steven Harvey
2004-05-19: Checked n = 313000 - 395119, 400000 - 400729, Steven Harvey
2004-04-28: Found n = 315523, Steven Harvey
2004-04-27: Checked n = 143000 - 150000, 307553 - 313000, Steven Harvey
2004-04-27: Found n = 311389, Steven Harvey
2004-04-26: Checked n = 1 - 110000, 120000 - 143000, 294739 - 307553, Steven Harvey
2004-04-26: Found n = 306751, Steven Harvey
2004-04-21: Checked n = 110000 - 120000, 150000 - 294739, Steven Harvey
2004-04-19: Found n = 274115, Steven Harvey
2004-04-05: Found n = 196433, Steven Harvey
2004-04-04: Found n = 177089, Steven Harvey
2003-03-20: Found n = 111667, Steven Harvey
2000-06-03: Found n = 62083, Phil Carmody
2000-05-31: Found n = 57647, Phil Carmody
2000-05-22: Found n = 44653, Phil Carmody
1998-08-13: Found n = 25657, Wilfrid Keller
1998-08-13: Found n = 24589, Wilfrid Keller
1998-08-09: Found n = 21957, Wilfrid Keller

[1] Jump up ↑ Williams 31•32¹-1

[2] Jump up ↑ Williams 31•32⁷-1

[3] Jump up ↑ Williams 31•32²³-1

[4] Jump up ↑ Williams 31•32⁴¹-1

[5] Jump up ↑ Williams 31•32⁴⁷-1

[6] Jump up ↑ Williams 31•32⁶⁹³-1

[7] Jump up ↑ Williams 31•32¹⁶³³¹-1

[8] Jump up ↑ Williams 31•32³⁰⁰⁵³-1

[9] Jump up ↑ Williams 31•32⁵⁴⁸²³-1

[10] Jump up ↑ Williams 31•32⁸¹²²¹-1

[11] Jump up ↑ Williams 31•32¹³³²⁵⁷-1

[12] Jump up ↑ Williams 31•32⁶⁵¹⁸³⁷-1

[13] Jump up ↑ Williams 31•32^1817617-1

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Riesel primes of the form 31•2ⁿ-1

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Riesel primes of the form 31•2n-1

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Riesel primes of the form 31•2ⁿ-1