Proth primes of the form 35•2ⁿ+1

Current data

`k` , `b` :	35 , 2
Count :	43
Nash :	2115
Max `n` :	9,000,000
Date :	2021-04-01

1, 3, 7, 9^[1], 13^[2], 15^[3], 31^[4], 45, 47^[5], 49^[6], 55^[7], 147, 245^[8], 327^[9], 355, 663^[10], 1423^[11], 1443^[12], 2493, 3627^[13], 4737, 6541^[14], 9667^[15], 22645, 27321, 61963, 68281^[16], 144397^[17], 151741, 187859, 191509^[18], 273251^[19], 494607, 696935^[20], 768063^[21], 831411^[22], 1040005^[23], 1357881^[24], 1765449^[25], 2099769, 2241049^[26], 3570777^[27], 3587843^[28]

Remarks :

The sequence A032367 in OEIS

Notes

↑ Is GF Divisor of xGF(6,9,8) [+1]
↑ Is GF Divisor of xGF(12,3,2)
↑ Is GF Divisor of xGF(14,5,3)
↑ Is GF Divisor of xGF(28,10,9)
↑ Is GF Divisor of xGF(33,7,5)
↑ Is GF Divisor of xGF(46,5,2)
↑ Is GF Divisor of xGF(52,12,11)
↑ Is GF Divisor of xGF(244,10,3) [+1], Cullen 35•128³⁵+1
↑ Is GF Divisor of GF(325,7) [+1]
↑ Is GF Divisor of xGF(662,7,3) [+1]
↑ Is GF Divisor of xGF(1422,4,3) [+2]
↑ Is GF Divisor of xGF(1441,9,5)
↑ Is GF Divisor of xGF(3625,5,2)
↑ Is GF Divisor of xGF(6540,6,5)
↑ Is GF Divisor of xGF(9665,11,2)
↑ Is GF Divisor of xGF(68279,5,2) [+1]
↑ Is GF Divisor of xGF(144395,10,9) [+1]
↑ Is GF Divisor of xGF(191508,11,7)
↑ Is GF Divisor of xGF(273249,9,5)
↑ Is GF Divisor of xGF(696934,7,3)
↑ Is GF Divisor of GF(768062,3)
↑ Is GF Divisor of GF(831410,3)
↑ Is GF Divisor of xGF(1040004,11,4)
↑ Is GF Divisor of xGF(1357878,7,5)
↑ Is GF Divisor of xGF(1765448,7,3) [+1]
↑ Is GF Divisor of xGF(2241047,7,5)
↑ Is GF Divisor of xGF(3570776,6,5) [+1]
↑ Is GF Divisor of GF(3587841,5)

History

2021-04-01: Checked to n = 9000000, PrimeGrid Fermat Divisor Search
2019-07: Checked n = 3322000 - 3640000, PrimeGrid Proth Mega Prime Search
2014-07-05: Found n = 3587843, Peter Tibbott, PrimeGrid Proth Mega Prime Search (Official announcement)
2014-06-11: Found n = 3570777, Robert Lacroix, PrimeGrid Proth Mega Prime Search (Official announcement)
2013-03-28: Found n = 2241049, Ernst Fluttert, PrimeGrid Proth Prime Search
2013-03-17: Found n = 2099769, Serge Batalov
2011-09-01: Found n = 1765449, James Scott Brown, PrimeGrid Proth Prime Search
2006-08-21: Found n = 1357881, Curtis Cooper
2006-07-24: Found n = 1040005, Curtis Cooper
2006-06-05: Found n = 831411, Curtis Cooper
2005-12-30: Found n = 768063, Reto Keiser
2005-10-15: Found n = 696935, Reto Keiser
2005-05-03: Found n = 494607, Reto Keiser
2004-01-08: Found n = 273251, Hans Overmann
2001-06-25: Found n = 191509, Peter Dodson
2001-06-18: Found n = 187859, Peter Dodson
2000-07-14: Found n = 151741, Michael Ian Hartley
2000-07-11: Found n = 144397, Peter Dodson
1998-05-16: Found n = 68281, Robert L. Clark
1997-05-01: Found n = 61963, Patrick Demichel
1995-08: Found n = 27321, Jeffrey Young
1995-08: Found n = 22645, Jeffrey Young
1986: Found n = 9667, Wilfrid Keller
1983: Found n = 6541, Wilfrid Keller
1983: Found n = 4737, Wilfrid Keller
1983: Found n = 3627, Wilfrid Keller

[1] Is GF Divisor of xGF(6,9,8) [+1]

[2] Is GF Divisor of xGF(12,3,2)

[3] Is GF Divisor of xGF(14,5,3)

[4] Is GF Divisor of xGF(28,10,9)

[5] Is GF Divisor of xGF(33,7,5)

[6] Is GF Divisor of xGF(46,5,2)

[7] Is GF Divisor of xGF(52,12,11)

[8] Is GF Divisor of xGF(244,10,3) [+1], Cullen 35•128³⁵+1

[9] Is GF Divisor of GF(325,7) [+1]

[10] Is GF Divisor of xGF(662,7,3) [+1]

[11] Is GF Divisor of xGF(1422,4,3) [+2]

[12] Is GF Divisor of xGF(1441,9,5)

[13] Is GF Divisor of xGF(3625,5,2)

[14] Is GF Divisor of xGF(6540,6,5)

[15] Is GF Divisor of xGF(9665,11,2)

[16] Is GF Divisor of xGF(68279,5,2) [+1]

[17] Is GF Divisor of xGF(144395,10,9) [+1]

[18] Is GF Divisor of xGF(191508,11,7)

[19] Is GF Divisor of xGF(273249,9,5)

[20] Is GF Divisor of xGF(696934,7,3)

[21] Is GF Divisor of GF(768062,3)

[22] Is GF Divisor of GF(831410,3)

[23] Is GF Divisor of xGF(1040004,11,4)

[24] Is GF Divisor of xGF(1357878,7,5)

[25] Is GF Divisor of xGF(1765448,7,3) [+1]

[26] Is GF Divisor of xGF(2241047,7,5)

[27] Is GF Divisor of xGF(3570776,6,5) [+1]

[28] Is GF Divisor of GF(3587841,5)

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Proth primes of the form 35•2ⁿ+1

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Proth primes of the form 35•2ⁿ+1