Proth primes of the form 29•2ⁿ+1

Current data

`k` , `b` :	29 , 2
Count :	45
Nash :	2120
Max `n` :	9,000,000
Date :	2021-04-01

1, 3^[1], 5^[2], 11^[3], 27, 43, 57^[4], 75, 77^[5], 93^[6], 103, 143^[7], 185, 231^[8], 245^[9], 391^[10], 1053^[11], 1175^[12], 2027^[13], 3627^[14], 4727^[15], 5443^[16], 7927^[17], 8533^[18], 9067^[19], 14185^[20], 25723^[21], 88117^[22], 96947^[23], 144937^[24], 219317^[25], 252227^[26], 261031^[27], 339123, 343601, 627167, 742191^[28], 800191, 1152765^[29], 1416873, 1574753, 3964697^[30], 4532463^[31], 7374577^[32], 7899985^[33]

Remarks :

The sequence A032364 in OEIS

Notes

↑ Is GF Divisor of GF(2,12)
↑ Is GF Divisor of xGF(4,12,11)
↑ Is GF Divisor of GF(10,3)
↑ Is GF Divisor of F(55) [+4]
↑ Is GF Divisor of xGF(74,11,6)
↑ Is GF Divisor of xGF(92,12,5)
↑ Is GF Divisor of GF(142,10) [+3]
↑ Is GF Divisor of F(228)
↑ Is GF Divisor of xGF(242,5,4) [+5]
↑ Is GF Divisor of xGF(390,8,5)
↑ Is GF Divisor of xGF(1051,9,7) [+1]
↑ Is GF Divisor of xGF(1174,8,7)
↑ Is GF Divisor of F(2023) [+3]
↑ Is GF Divisor of xGF(3626,3,2)
↑ Is GF Divisor of F(4724) [+8]
↑ Is GF Divisor of xGF(5441,7,6)
↑ Is GF Divisor of xGF(7925,6,5) [+3]
↑ Is GF Divisor of xGF(8532,5,3)
↑ Is GF Divisor of xGF(9063,11,7)
↑ Is GF Divisor of xGF(14184,9,7) [+1]
↑ Is GF Divisor of GF(25722,11)
↑ Is GF Divisor of xGF(88115,7,6) [+1]
↑ Is GF Divisor of GF(96946,11)
↑ Is GF Divisor of xGF(144936,3,2)
↑ Is GF Divisor of xGF(219315,7,3)
↑ Is GF Divisor of xGF(252226,8,5)
↑ Is GF Divisor of xGF(261030,3,2)
↑ Is GF Divisor of xGF(742190,4,3) [+2]
↑ Is GF Divisor of xGF(1152762,7,5) [+3]
↑ Is GF Divisor of GF(3964696,11)
↑ Is GF Divisor of xGF(4532462,3,2) [+1]
↑ Is GF Divisor of GF(7374576,3) [+4]
↑ Is GF Divisor of xGF(7899983,5,4) [+5]

History

2021-04-01: Checked to n = 9000000, PrimeGrid Fermat Divisor Search
2021-01-15: Found n = 7899985, Tom Greer, PrimeGrid Fermat Divisor Search (Official announcement)
2020-10-28: Found n = 7374577, Pavel Atnashev, PrimeGrid Fermat Divisor Search (Official announcement)
2019-10-13: Found n = 4532463, Jack Harris, PrimeGrid Fermat Divisor Search
2019-09-29: Found n = 3964697, James Scott Brown, PrimeGrid Fermat Divisor Search
2019-07: Checked n = 3322000 - 3640000, PrimeGrid Proth Mega Prime Search
2008-02-16: Found n = 1574753, Mark Rodenkirch
2007-04-09: Found n = 1416873, Jay Berg
2005-09-20: Found n = 1152765, Matt Zilmer
2005-08-03: Found n = 800191, Jiong Sun
2005-07-03: Found n = 742191, Jiong Sun
2005-06-08: Found n = 627167, Jiong Sun
2002-08-12: Found n = 343601, Tadashi Taura
2002-07-24: Found n = 339123, Tadashi Taura
1999-09-03: Found n = 261031, Tadashi Taura
1999-07-28: Found n = 252227, Tadashi Taura
1999-05-28: Found n = 219317, Tadashi Taura
1999-05-02: Found n = 144937, Sturle Sunde
1995-08: Found n = 96947, Jeffrey Young
1995-08: Found n = 88117, Jeffrey Young
1993-10-01: Found n = 25723, Harvey Dubner
1991: Found n = 14185, Wilfrid Keller
1986: Found n = 9067, Wilfrid Keller
1986: Found n = 8533, Wilfrid Keller
1979: Checked n = 1500 - 8000, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 7927, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 5443, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 4727, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 3627, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 2027, Gordon V. Cormack, Hugh C. Williams

[1] Is GF Divisor of GF(2,12)

[2] Is GF Divisor of xGF(4,12,11)

[3] Is GF Divisor of GF(10,3)

[4] Is GF Divisor of F(55) [+4]

[5] Is GF Divisor of xGF(74,11,6)

[6] Is GF Divisor of xGF(92,12,5)

[7] Is GF Divisor of GF(142,10) [+3]

[8] Is GF Divisor of F(228)

[9] Is GF Divisor of xGF(242,5,4) [+5]

[10] Is GF Divisor of xGF(390,8,5)

[11] Is GF Divisor of xGF(1051,9,7) [+1]

[12] Is GF Divisor of xGF(1174,8,7)

[13] Is GF Divisor of F(2023) [+3]

[14] Is GF Divisor of xGF(3626,3,2)

[15] Is GF Divisor of F(4724) [+8]

[16] Is GF Divisor of xGF(5441,7,6)

[17] Is GF Divisor of xGF(7925,6,5) [+3]

[18] Is GF Divisor of xGF(8532,5,3)

[19] Is GF Divisor of xGF(9063,11,7)

[20] Is GF Divisor of xGF(14184,9,7) [+1]

[21] Is GF Divisor of GF(25722,11)

[22] Is GF Divisor of xGF(88115,7,6) [+1]

[23] Is GF Divisor of GF(96946,11)

[24] Is GF Divisor of xGF(144936,3,2)

[25] Is GF Divisor of xGF(219315,7,3)

[26] Is GF Divisor of xGF(252226,8,5)

[27] Is GF Divisor of xGF(261030,3,2)

[28] Is GF Divisor of xGF(742190,4,3) [+2]

[29] Is GF Divisor of xGF(1152762,7,5) [+3]

[30] Is GF Divisor of GF(3964696,11)

[31] Is GF Divisor of xGF(4532462,3,2) [+1]

[32] Is GF Divisor of GF(7374576,3) [+4]

[33] Is GF Divisor of xGF(7899983,5,4) [+5]

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Proth primes of the form 29•2ⁿ+1

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Proth primes of the form 29•2n+1

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Proth primes of the form 29•2ⁿ+1