Proth primes of the form 33•2ⁿ+1

Current data

`k` , `b` :	33 , 2
Type :	3
Count :	41
Nash :	1960
Max `n` :	9,000,000
Date :	2021-04-01

1, 6^[1], 13^[2], 18^[3], 21^[4], 22^[5], 25^[6], 28^[7], 66^[8], 93^[9], 118^[10], 289^[11], 412^[12], 453^[13], 525^[14], 726^[15], 828^[16], 1420^[17], 1630^[18], 3076^[19], 3118^[20], 4452, 4941^[21], 5236^[22], 6346^[23], 9133^[24], 13401^[25], 14214^[26], 18766^[27], 37249^[28], 42685^[29], 47805^[30], 61372^[31], 74178^[32], 600270^[33], 922782^[34], 1130884^[35], 2345001^[36], 3176269, 3570132^[37], 3649810^[38]

Remarks :

The sequence A032366 in OEIS
See also Williams 33•32ⁿ+1

Notes

↑ Is GF Divisor of xGF(5,11,5), Twin n=6
↑ Is GF Divisor of xGF(12,6,5)
↑ Is GF Divisor of xGF(17,10,9)
↑ Is GF Divisor of xGF(20,6,5) [+1]
↑ Is GF Divisor of xGF(21,10,9) [+2], Twin n=22
↑ Is GF Divisor of GF(23,8) [+1], Williams 33•32⁵+1
↑ Is GF Divisor of xGF(26,5,3)
↑ Is GF Divisor of GF(65,5) [+2]
↑ Is GF Divisor of xGF(92,6,5)
↑ Is GF Divisor of xGF(114,11,9)
↑ Is GF Divisor of GF(288,5)
↑ Is GF Divisor of xGF(410,7,4)
↑ Is GF Divisor of xGF(452,5,4) [+1]
↑ Williams 33•32¹⁰⁵+1
↑ Is GF Divisor of xGF(721,10,7)
↑ Is GF Divisor of GF(826,5) [+1]
↑ Is GF Divisor of GF(1418,7) [+1], Williams 33•32²⁸⁴+1
↑ Is GF Divisor of xGF(1629,8,5) [+1], Williams 33•32³²⁶+1
↑ Is GF Divisor of xGF(3072,5,2) [+3]
↑ Is GF Divisor of GF(3116,7) [+3]
↑ Is GF Divisor of xGF(4940,11,5)
↑ Is GF Divisor of xGF(5229,9,7)
↑ Is GF Divisor of GF(6341,6)
↑ Is GF Divisor of xGF(9130,3,2)
↑ Is GF Divisor of GF(13399,8)
↑ Is GF Divisor of xGF(14212,3,2)
↑ Is GF Divisor of F(18757) [+5]
↑ Is GF Divisor of GF(37248,5) [+2]
↑ Is GF Divisor of xGF(42683,4,3), Williams 33•32⁸⁵³⁷+1
↑ Is GF Divisor of xGF(47804,11,7), Williams 33•32⁹⁵⁶¹+1
↑ Is GF Divisor of GF(61369,8) [+1]
↑ Is GF Divisor of xGF(74175,11,4)
↑ Is GF Divisor of GF(600269,5) [+1], Williams 33•32¹²⁰⁰⁵⁴+1
↑ Is GF Divisor of xGF(922779,7,5) [+3]
↑ Is GF Divisor of GF(1130881,12)
↑ Is GF Divisor of xGF(2345000,7,2)
↑ Is GF Divisor of xGF(3570129,5,4) [+2]
↑ Is GF Divisor of xGF(3649809,5,2), Williams 33•32⁷²⁹⁹⁶²+1

History

2021-04-01: Checked to n = 9000000, PrimeGrid Fermat Divisor Search
2019-09-16: Found n = 3649810, Kellen Shenton, PrimeGrid Fermat Divisor Search
2019-07: Checked n = 3322000 - 3640000, PrimeGrid Proth Mega Prime Search
2014-06-11: Found n = 3570132, Fabrice Le Foulher, PrimeGrid Proth Mega Prime Search (Official announcement)
2013-12-23: Found n = 3176269, Serge Batalov
2013-04-13: Found n = 2345001, Mariusz Szafrański
2006-07-07: Found n = 1130884, Reto Keiser
2006-02-19: Found n = 922782, Reto Keiser
2005-07-20: Found n = 600270, Reto Keiser
1998-06-26: Found n = 74178, Aaron Swihart
1997-05-01: Found n = 61372, Patrick Demichel
1995-08: Found n = 47805, Jeffrey Young
1995-08: Found n = 42685, Jeffrey Young
1993: Found n = 37249, Jeffrey Young
1993-10-01: Found n = 18766, Harvey Dubner
1993-10-01: Found n = 14214, Harvey Dubner
1993-10-01: Found n = 13401, Harvey Dubner
1986: Found n = 9133, Wilfrid Keller
1983: Found n = 6346, Wilfrid Keller
1983: Found n = 5236, Wilfrid Keller
1983: Found n = 4941, Wilfrid Keller
1983: Found n = 4452, Wilfrid Keller

[1] Is GF Divisor of xGF(5,11,5), Twin n=6

[2] Is GF Divisor of xGF(12,6,5)

[3] Is GF Divisor of xGF(17,10,9)

[4] Is GF Divisor of xGF(20,6,5) [+1]

[5] Is GF Divisor of xGF(21,10,9) [+2], Twin n=22

[6] Is GF Divisor of GF(23,8) [+1], Williams 33•32⁵+1

[7] Is GF Divisor of xGF(26,5,3)

[8] Is GF Divisor of GF(65,5) [+2]

[9] Is GF Divisor of xGF(92,6,5)

[10] Is GF Divisor of xGF(114,11,9)

[11] Is GF Divisor of GF(288,5)

[12] Is GF Divisor of xGF(410,7,4)

[13] Is GF Divisor of xGF(452,5,4) [+1]

[14] Williams 33•32¹⁰⁵+1

[15] Is GF Divisor of xGF(721,10,7)

[16] Is GF Divisor of GF(826,5) [+1]

[17] Is GF Divisor of GF(1418,7) [+1], Williams 33•32²⁸⁴+1

[18] Is GF Divisor of xGF(1629,8,5) [+1], Williams 33•32³²⁶+1

[19] Is GF Divisor of xGF(3072,5,2) [+3]

[20] Is GF Divisor of GF(3116,7) [+3]

[21] Is GF Divisor of xGF(4940,11,5)

[22] Is GF Divisor of xGF(5229,9,7)

[23] Is GF Divisor of GF(6341,6)

[24] Is GF Divisor of xGF(9130,3,2)

[25] Is GF Divisor of GF(13399,8)

[26] Is GF Divisor of xGF(14212,3,2)

[27] Is GF Divisor of F(18757) [+5]

[28] Is GF Divisor of GF(37248,5) [+2]

[29] Is GF Divisor of xGF(42683,4,3), Williams 33•32⁸⁵³⁷+1

[30] Is GF Divisor of xGF(47804,11,7), Williams 33•32⁹⁵⁶¹+1

[31] Is GF Divisor of GF(61369,8) [+1]

[32] Is GF Divisor of xGF(74175,11,4)

[33] Is GF Divisor of GF(600269,5) [+1], Williams 33•32¹²⁰⁰⁵⁴+1

[34] Is GF Divisor of xGF(922779,7,5) [+3]

[35] Is GF Divisor of GF(1130881,12)

[36] Is GF Divisor of xGF(2345000,7,2)

[37] Is GF Divisor of xGF(3570129,5,4) [+2]

[38] Is GF Divisor of xGF(3649809,5,2), Williams 33•32⁷²⁹⁹⁶²+1

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Proth primes of the form 33•2ⁿ+1

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Proth primes of the form 33•2n+1

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Proth primes of the form 33•2ⁿ+1