Proth primes of the form 26•3ⁿ+1

Current data

`k` , `b` :	26 , 3
Count :	59
Nash :	3752
Max `n` :	1,000,000
Date :	2024-08-19

1, 12^[1], 15^[2], 17, 20, 29, 31, 32, 35, 37, 77, 95, 193, 203, 224, 296, 481^[3], 501, 1069, 1151, 1224^[4], 1248^[5], 1657, 2103^[6], 2121^[7], 2971, 3487, 5433^[8], 8179, 8593, 9804^[9], 10524^[10], 13841, 15943, 21060^[11], 22869^[12], 36691, 38984, 49347^[13], 56257, 67481, 68959, 77393, 107760^[14], 133052, 153841, 165483^[15], 182141, 232935^[16], 250399, 261516^[17], 387984^[18], 404559^[19], 652929^[20], 727825, 1435875^[21], 1565545, 1700041, 1910099

Remarks :

For additional n ≡ 0 mod 3 history, see Williams 26•27ⁿ+1.

Notes

History

2024-08-19: Reservation dropped, Paul Vanderveen
2021-03-07: Checked n = 900000 - 1000000, Paul Vanderveen
2020-12-29: Checked n = 810000 - 900000, Paul Vanderveen
2020-10-16: Found n = 1910099, Paul Vanderveen
2020-10-16: Checked n = 750000 - 810000, Paul Vanderveen
2020-09-14: Checked n = 650000 - 750000, Paul Vanderveen
2020-08-03: Found n = 1565545, Paul Vanderveen
2020-08-02: Checked n = 525000 - 650000, Paul Vanderveen
2020-07-13: Found n = 1700041, Paul Vanderveen
2020-07-05: Found n = 1435875, Paul Vanderveen
2020-07-01: Checked n = 400000 - 525000, Paul Vanderveen
2020-06-08: Checked to n = 400000, Paul Vanderveen
2020-05-24: Reserved by Paul Vanderveen
2020-05-22: Checked n = 1 - 100000, Karsten Bonath
2006-09-24: Found n = 182141, Peter Benson
2006-05-02: Found n = 165483, Peter Benson
2005-05-02: Found n = 153841, Peter Benson
2004-10-22: Found n = 133052, Peter Benson
2004-03-09: Found n = 107760, Peter Benson
1998-11-21: Found n = 15943, David Hanson
1994: Found n = 2121, Wilfrid Keller

[1] Williams 26•27⁴+1

[2] Williams 26•27⁵+1

[3] Williams 26•27¹⁶⁷+1

[4] Williams 26•27⁴⁰⁸+1

[5] Williams 26•27⁴¹⁶+1

[6] Williams 26•27⁷⁰¹+1

[7] Divides Phi(3^2121,2), Williams 26•27⁷⁰⁷+1

[8] Williams 26•27¹⁸¹¹+1

[9] Williams 26•27³²⁶⁸+1

[10] Williams 26•27³⁵⁰⁸+1

[11] Williams 26•27⁷⁰²⁰+1

[12] Williams 26•27⁷⁶²³+1

[13] Williams 26•27¹⁶⁴⁴⁹+1

[14] Williams 26•27³⁵⁹²⁰+1

[15] Williams 26•27⁵⁵¹⁶¹+1

[16] Williams 26•27⁷⁷⁴⁶⁵+1

[17] Williams 26•27⁸⁷¹⁷²+1

[18] Williams 26•27¹²⁹³²⁸+1

[19] Williams 26•27¹³⁴⁸⁵³+1

[20] Williams 26•27²¹⁷⁶⁴³+1

[21] Williams 26•27⁴⁷⁸⁶²⁵+1

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Proth primes of the form 26•3ⁿ+1

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Proth primes of the form 26•3n+1

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Proth primes of the form 26•3ⁿ+1