Proth primes of the form 9•2ⁿ+1

Current data

`k` , `b` :	9 , 2
Type :	3
Count :	66
Nash :	2297
Max `n` :	5,000,000
Date :	2024-04-30

1^[1], 2^[2], 3^[3], 6^[4], 7^[5], 11^[6], 14^[7], 17^[8], 33^[9], 42^[10], 43^[11], 63^[12], 65^[13], 67^[14], 81^[15], 134^[16], 162^[17], 206^[18], 211^[19], 366^[20], 663^[21], 782^[22], 1305^[23], 1411^[24], 1494^[25], 2297^[26], 2826^[27], 3230^[28], 3354^[29], 3417^[30], 3690^[31], 4842^[32], 5802^[33], 6937^[34], 7967^[35], 9431^[36], 13903^[37], 22603^[38], 24422^[39], 39186^[40], 43963^[41], 47003^[42], 49902^[43], 67943^[44], 114854^[45], 127003^[46], 145247^[47], 147073^[48], 149143^[49], 304607^[50], 384990^[51], 412034^[52], 435743^[53], 461081^[54], 834810^[55], 1051026^[56], 1807574^[57], 2543551^[58], 3497442^[59], 5642513^[60], 9778263^[61], 11158963^[62], 11366286^[63], 11500843^[64], 12406887^[65], 13334487^[66]

Remarks :

The sequence A002256 in OEIS

For all even n-values 9•2ⁿ+1 is a Generalized Fermat number.
Even n still needs to be searched for 5,000,000 ≤ n ≤ 9,000,000.

Notes

↑ Twin n=1
↑ Is GF Divisor of xGF(1,11,8)
↑ Is GF Divisor of xGF(2,7,3) [+3], Twin n=3
↑ Is GF Divisor of xGF(5,6,5) [+4]
↑ Is GF Divisor of xGF(5,3,2) [+5], Twin n=7
↑ Is GF Divisor of xGF(10,5,4) [+1]
↑ Is GF Divisor of xGF(10,4,3) [+6]
↑ Is GF Divisor of xGF(11,5,4) [+3]
↑ Is GF Divisor of GF(29,3) [+5]
↑ Is GF Divisor of xGF(41,5,4) [+6]
↑ Is GF Divisor of xGF(38,3,2) [+6], Twin n=43
↑ Is GF Divisor of GF(61,3) [+10], Twin n=63
↑ Is GF Divisor of GF(63,6) [+2]
↑ Is GF Divisor of F(63) [+19]
↑ Is GF Divisor of GF(79,3) [+9]
↑ Is GF Divisor of xGF(132,8,7) [+2]
↑ Is GF Divisor of GF(158,3) [+7]
↑ Is GF Divisor of GF(205,5) [+5]
↑ Is GF Divisor of xGF(210,5,4) [+3], Twin n=211
↑ Is GF Divisor of xGF(365,7,4) [+4]
↑ Is GF Divisor of xGF(662,5,3) [+3]
↑ Is GF Divisor of xGF(781,6,5) [+4]
↑ Is GF Divisor of GF(1303,3) [+2]
↑ Is GF Divisor of xGF(1409,3,2) [+1]
↑ Is GF Divisor of GF(1488,3) [+1]
↑ Is GF Divisor of GF(2294,6) [+3]
↑ Is GF Divisor of GF(2822,3) [+7]
↑ Is GF Divisor of xGF(3229,7,5) [+4]
↑ Is GF Divisor of GF(3353,7) [+4]
↑ Is GF Divisor of xGF(3408,5,3) [+5]
↑ Is GF Divisor of GF(3684,3) [+5]
↑ Is GF Divisor of GF(4838,3) [+7]
↑ Is GF Divisor of xGF(5801,8,7) [+6]
↑ Is GF Divisor of xGF(6935,3,2) [+3]
↑ Is GF Divisor of xGF(7966,5,3) [+4]
↑ Is GF Divisor of F(9428) [+8]
↑ Is GF Divisor of xGF(13900,3,2) [+5]
↑ Is GF Divisor of xGF(22602,5,3) [+2]
↑ Is GF Divisor of xGF(24417,4,3) [+5]
↑ Is GF Divisor of GF(39177,3) [+4]
↑ Is GF Divisor of xGF(43960,3,2) [+1]
↑ Is GF Divisor of xGF(47001,4,3) [+6]
↑ Is GF Divisor of xGF(49901,5,3) [+4]
↑ Is GF Divisor of xGF(67941,4,3) [+5]
↑ Is GF Divisor of xGF(114850,4,3) [+4]
↑ Is GF Divisor of xGF(127002,5,3) [+3]
↑ Is GF Divisor of xGF(145245,4,3) [+7]
↑ Is GF Divisor of xGF(147069,5,2) [+4]
↑ Is GF Divisor of xGF(149142,5,2) [+2]
↑ Is GF Divisor of xGF(304604,4,3) [+3]
↑ Is GF Divisor of xGF(384989,5,3) [+2]
↑ Is GF Divisor of xGF(412030,4,3) [+9]
↑ Is GF Divisor of xGF(435741,7,6) [+4]
↑ Is GF Divisor of F(461076) [+16]
↑ Is GF Divisor of xGF(834809,5,4) [+4]
↑ Is GF Divisor of xGF(1051025,8,7) [+4]
↑ Is GF Divisor of xGF(1807570,4,3) [+2]
↑ Is GF Divisor of F(2543548) [+16]
↑ Is GF Divisor of GF(3497441,7) [+5]
↑ Is GF Divisor of xGF(5642511,5,3) [+3]
↑ Is GF Divisor of xGF(9778262,6,5) [+4]
↑ Is GF Divisor of xGF(11158961,3,2) [+5]
↑ Is GF Divisor of xGF(11366285,7,4) [+6]
↑ Is GF Divisor of xGF(11500842,5,3) [+4]
↑ Is GF Divisor of GF(12406885,3) [+3]
↑ Is GF Divisor of GF(13334485,3) [+6]

History

2024-04-30: Checked to n = 5000000, PrimeGrid Proth Prime Search
2021-04-01: Checked n = 4000000 - 9000000, PrimeGrid Fermat Divisor Search, odd n-values only
2020-08-06: Found n = 9778263, Ryan Propper
2020-03-31: Found n = 13334487, Ryan Propper
2020-03-29: Found n = 12406887, Ryan Propper
2020-03-26: Found n = 11366286, Ryan Propper
2020-03-13: Found n = 11500843, Ryan Propper
2020-03-13: Found n = 11158963, Ryan Propper
2013-11-29: Found n = 5642513, Serge Batalov
?: Checked to n = 4000000, PrimeGrid Proth Prime Search
2012-10-24: Found n = 3497442, Heinz Ming, PrimeGrid Proth Mega Prime Search (Official announcement)
2011-06-22: Found n = 2543551, James Scott Brown, PrimeGrid Proth Prime Search (Official announcement)
2011-06-22: Found n = 1807574, Reuben Gathright, PrimeGrid Proth Prime Search
2004-12-14: Found n = 1051026, Souichi Murata, Satoshi Noda, Takahiro Nohara
2004-09-22: Found n = 834810, Senji Yamashita, Satoshi Noda, Takahiro Nohara
2003-08-05: Found n = 461081, Takahiro Nohara
2003-07-09: Found n = 435743, Takahiro Nohara
2003-05-19: Found n = 412034, Takahiro Nohara
2002-02-26: Found n = 384990, Takahiro Nohara
1998-07-04: Found n = 304607, Ray Ballinger
1995-08: Found n = 149143, Jeffrey Young
1995-08: Found n = 147073, Jeffrey Young
1995-08: Found n = 145247, Jeffrey Young
1995-08: Found n = 127003, Jeffrey Young
1995-08: Found n = 114854, Jeffrey Young
1995-08: Found n = 67943, Jeffrey Young
1994-07-01: Found n = 43963, Jeffrey Young
1993-10-01: Found n = 49902, Jeffrey Young
1993-10-01: Found n = 47003, Jeffrey Young
1992-12: Found n = 39186, Harvey Dubner
1992-10: Found n = 24422, Harvey Dubner
1992: Found n = 22603, Harvey Dubner
1991: Found n = 13903, Wilfrid Keller
1983: Found n = 9431, Wilfrid Keller
1983: Found n = 6937, Wilfrid Keller
1983: Found n = 4842, Wilfrid Keller
1979: Found n = 7967, A. Oliver L. Atkin, Neil W. Rickert
1979: Found n = 5802, A. Oliver L. Atkin, Neil W. Rickert
1979: Checked n = 1500 - 4000, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 3690, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 3417, Gordon V. Cormack, Hugh C. Williams
1978: Found n = 3354, Gordon V. Cormack, Hugh C. Williams
1978: Found n = 3230, Gordon V. Cormack, Hugh C. Williams
1978: Found n = 2826, Gordon V. Cormack, Hugh C. Williams
1978: Found n = 2297, Gordon V. Cormack, Hugh C. Williams

[1] Twin n=1

[2] Is GF Divisor of xGF(1,11,8)

[3] Is GF Divisor of xGF(2,7,3) [+3], Twin n=3

[4] Is GF Divisor of xGF(5,6,5) [+4]

[5] Is GF Divisor of xGF(5,3,2) [+5], Twin n=7

[6] Is GF Divisor of xGF(10,5,4) [+1]

[7] Is GF Divisor of xGF(10,4,3) [+6]

[8] Is GF Divisor of xGF(11,5,4) [+3]

[9] Is GF Divisor of GF(29,3) [+5]

[10] Is GF Divisor of xGF(41,5,4) [+6]

[11] Is GF Divisor of xGF(38,3,2) [+6], Twin n=43

[12] Is GF Divisor of GF(61,3) [+10], Twin n=63

[13] Is GF Divisor of GF(63,6) [+2]

[14] Is GF Divisor of F(63) [+19]

[15] Is GF Divisor of GF(79,3) [+9]

[16] Is GF Divisor of xGF(132,8,7) [+2]

[17] Is GF Divisor of GF(158,3) [+7]

[18] Is GF Divisor of GF(205,5) [+5]

[19] Is GF Divisor of xGF(210,5,4) [+3], Twin n=211

[20] Is GF Divisor of xGF(365,7,4) [+4]

[21] Is GF Divisor of xGF(662,5,3) [+3]

[22] Is GF Divisor of xGF(781,6,5) [+4]

[23] Is GF Divisor of GF(1303,3) [+2]

[24] Is GF Divisor of xGF(1409,3,2) [+1]

[25] Is GF Divisor of GF(1488,3) [+1]

[26] Is GF Divisor of GF(2294,6) [+3]

[27] Is GF Divisor of GF(2822,3) [+7]

[28] Is GF Divisor of xGF(3229,7,5) [+4]

[29] Is GF Divisor of GF(3353,7) [+4]

[30] Is GF Divisor of xGF(3408,5,3) [+5]

[31] Is GF Divisor of GF(3684,3) [+5]

[32] Is GF Divisor of GF(4838,3) [+7]

[33] Is GF Divisor of xGF(5801,8,7) [+6]

[34] Is GF Divisor of xGF(6935,3,2) [+3]

[35] Is GF Divisor of xGF(7966,5,3) [+4]

[36] Is GF Divisor of F(9428) [+8]

[37] Is GF Divisor of xGF(13900,3,2) [+5]

[38] Is GF Divisor of xGF(22602,5,3) [+2]

[39] Is GF Divisor of xGF(24417,4,3) [+5]

[40] Is GF Divisor of GF(39177,3) [+4]

[41] Is GF Divisor of xGF(43960,3,2) [+1]

[42] Is GF Divisor of xGF(47001,4,3) [+6]

[43] Is GF Divisor of xGF(49901,5,3) [+4]

[44] Is GF Divisor of xGF(67941,4,3) [+5]

[45] Is GF Divisor of xGF(114850,4,3) [+4]

[46] Is GF Divisor of xGF(127002,5,3) [+3]

[47] Is GF Divisor of xGF(145245,4,3) [+7]

[48] Is GF Divisor of xGF(147069,5,2) [+4]

[49] Is GF Divisor of xGF(149142,5,2) [+2]

[50] Is GF Divisor of xGF(304604,4,3) [+3]

[51] Is GF Divisor of xGF(384989,5,3) [+2]

[52] Is GF Divisor of xGF(412030,4,3) [+9]

[53] Is GF Divisor of xGF(435741,7,6) [+4]

[54] Is GF Divisor of F(461076) [+16]

[55] Is GF Divisor of xGF(834809,5,4) [+4]

[56] Is GF Divisor of xGF(1051025,8,7) [+4]

[57] Is GF Divisor of xGF(1807570,4,3) [+2]

[58] Is GF Divisor of F(2543548) [+16]

[59] Is GF Divisor of GF(3497441,7) [+5]

[60] Is GF Divisor of xGF(5642511,5,3) [+3]

[61] Is GF Divisor of xGF(9778262,6,5) [+4]

[62] Is GF Divisor of xGF(11158961,3,2) [+5]

[63] Is GF Divisor of xGF(11366285,7,4) [+6]

[64] Is GF Divisor of xGF(11500842,5,3) [+4]

[65] Is GF Divisor of GF(12406885,3) [+3]

[66] Is GF Divisor of GF(13334485,3) [+6]

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Proth primes of the form 9•2ⁿ+1

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Proth primes of the form 9•2n+1

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Proth primes of the form 9•2ⁿ+1