Proth primes of the form 3•2ⁿ+1

Reserved! This sequence is currently part of Multi Reservation 22: PrimeGrid 321 Prime Search.

Current data

`k` , `b` :	3 , 2
Type :	3
Count :	50
Nash :	2132
Max `n` :	22,021,811
Date :	2024-10-13
Reserved :	PrimeGridPrimeGrid/Reserved

1^[1], 2^[2], 5^[3], 6^[4], 8^[5], 12^[6], 18^[7], 30^[8], 36^[9], 41^[10], 66^[11], 189^[12], 201^[13], 209^[14], 276^[15], 353^[16], 408^[17], 438^[18], 534^[19], 2208^[20], 2816^[21], 3168^[22], 3189^[23], 3912^[24], 20909^[25], 34350^[26], 42294^[27], 42665^[28], 44685^[29], 48150^[30], 54792^[31], 55182^[32], 59973^[33], 80190^[34], 157169^[35], 213321^[36], 303093^[37], 362765^[38], 382449^[39], 709968^[40], 801978^[41], 916773^[42], 1832496^[43], 2145353^[44], 2291610^[45], 2478785^[46], 5082306^[47], 7033641^[48], 10829346^[49], 16408818^[50]

Remarks :

The sequence A002253 in OEIS
See also Williams 3•2ⁿ+1 & Williams 3•4ⁿ+1

Notes

↑ Is GF Divisor of xGF(0,11,10), Twin n=1
↑ Is GF Divisor of xGF(1,7,4) [+4], Twin n=2, Near Cullen 3•2²+1, Williams 3•4¹+1
↑ Is GF Divisor of xGF(4,5,2) [+11]
↑ Is GF Divisor of GF(3,3) [+11], Twin n=6, Cullen 3•4³+1, Near Cullen 6•2⁵+1, Williams 3•4³+1
↑ Is GF Divisor of xGF(6,3,2) [+13], Near Cullen 6•2⁷+1, Williams 3•4⁴+1
↑ Is GF Divisor of GF(8,3) [+12], Cullen 3•16³+1, Williams 3•4⁶+1
↑ Is GF Divisor of GF(15,3) [+12], Twin n=18, Cullen 3•64³+1, Williams 3•4⁹+1
↑ Is GF Divisor of GF(26,3) [+12], Cullen 3•1024³+1, Williams 3•4¹⁵+1
↑ Is GF Divisor of GF(32,3) [+14], Cullen 3•4096³+1, Williams 3•4¹⁸+1
↑ Is GF Divisor of F(38) [+9]
↑ Is GF Divisor of GF(63,3) [+14], Williams 3•4³³+1
↑ Is GF Divisor of GF(187,3) [+12]
↑ Is GF Divisor of GF(198,3) [+11]
↑ Is GF Divisor of F(207) [+19]
↑ Is GF Divisor of GF(271,3) [+14], Williams 3•4¹³⁸+1
↑ Is GF Divisor of xGF(350,3,2) [+11]
↑ Is GF Divisor of GF(403,3) [+14], Williams 3•4²⁰⁴+1
↑ Is GF Divisor of GF(435,3) [+12], Williams 3•4²¹⁹+1
↑ Is GF Divisor of GF(531,3) [+12], Williams 3•4²⁶⁷+1
↑ Is GF Divisor of GF(2197,3) [+14], Williams 3•4¹¹⁰⁴+1
↑ Is GF Divisor of xGF(2812,3,2) [+15], Williams 3•4¹⁴⁰⁸+1
↑ Is GF Divisor of GF(3160,3) [+14], Williams 3•4¹⁵⁸⁴+1
↑ Is GF Divisor of GF(3187,3) [+12]
↑ Is GF Divisor of GF(3906,3) [+15], Williams 3•4¹⁹⁵⁶+1
↑ Is GF Divisor of xGF(20905,3,2) [+13]
↑ Is GF Divisor of GF(34346,3) [+12], Williams 3•4¹⁷¹⁷⁵+1
↑ Is GF Divisor of GF(42290,3) [+12], Williams 3•4²¹¹⁴⁷+1
↑ Is GF Divisor of xGF(42662,3,2) [+11]
↑ Is GF Divisor of GF(44683,3) [+16]
↑ Is GF Divisor of GF(48146,3) [+12], Williams 3•4²⁴⁰⁷⁵+1
↑ Is GF Divisor of GF(54787,3) [+15], Williams 3•4²⁷³⁹⁶+1
↑ Is GF Divisor of GF(55178,3) [+11], Williams 3•4²⁷⁵⁹¹+1
↑ Is GF Divisor of GF(59970,3) [+15]
↑ Is GF Divisor of GF(80187,3) [+12], Williams 3•4⁴⁰⁰⁹⁵+1
↑ Is GF Divisor of F(157167) [+20]
↑ Is GF Divisor of F(213319) [+10]
↑ Is GF Divisor of F(303088) [+20]
↑ Is GF Divisor of xGF(362762,3,2) [+12]
↑ Is GF Divisor of F(382447) [+9]
↑ Is GF Divisor of GF(709962,3) [+14], Williams 3•4³⁵⁴⁹⁸⁴+1
↑ Is GF Divisor of GF(801973,3) [+12], Williams 3•4⁴⁰⁰⁹⁸⁹+1
↑ Is GF Divisor of GF(916771,3) [+16]
↑ Is GF Divisor of GF(1832490,3) [+18], Williams 3•4⁹¹⁶²⁴⁸+1
↑ Is GF Divisor of F(2145351) [+19]
↑ Is GF Divisor of GF(2291607,3) [+14], Williams 3•4^1145805+1
↑ Is GF Divisor of F(2478782) [+9]
↑ Is GF Divisor of GF(5082303,3) [+14], Williams 3•4^2541153+1
↑ Is GF Divisor of GF(7033639,3) [+12]
↑ Is GF Divisor of GF(10829343,3) [+14], Williams 3•4^5414673+1
↑ Is GF Divisor of GF(16408814,3) [+12], Williams 3•4^8204409+1

History

2020-10-25: Found n = 16408818, James Scott Brown, PrimeGrid 321 Prime Search (Official announcement)
2012-01-14: Found n = 10829346, Sai Yik Tang, PrimeGrid 321 Prime Search (Official announcement)
2011-02-21: Found n = 7033641, Michael Herder, PrimeGrid 321 Prime Search (Official announcement)
2009-04-03: Found n = 5082306, Andy Brady, PrimeGrid 321 Prime Search (Official announcement)
2008-08-11: Found n = 2291610, Thomas Wolfram, PrimeGrid 321 Prime Search (Official announcement)
2007-07-27: Found n = 1832496, Joseph Bohanon
2005-09-02: Found n = 801978, Keith P. Adney
2005-05-21: Found n = 709968, Keith P. Adney
2003-10-14: Found n = 2478785, John Cosgrave
2003-02-25: Found n = 2145353, John Cosgrave
2002-07-30: Found n = 362765, John Cosgrave
2001-06-02: Found n = 916773, John Cosgrave
1999-07-23: Found n = 382449, John Cosgrave
1998-01: Found n = 303093, Jeffrey Young
1997-05: Found n = 213321, Jeffrey Young
1995-08: Found n = 157169, Jeffrey Young
1995-08: Found n = 80190, Jeffrey Young
1995-08: Found n = 59973, Jeffrey Young
1993-10: Found n = 55182, Jeffrey Young
1993-10-01: Found n = 48150, Jeffrey Young
1993: Found n = 44685, Jeffrey Young
1993: Found n = 42665, Jeffrey Young
1993-07-01: Found n = 42294, Jeffrey Young
1992-10: Found n = 34350, Harvey Dubner
1985: Found n = 20909, Wilfrid Keller
1979: Checked n = 1500 - 4000, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 3912, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 3189, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 3168, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 2816, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 2208, Gordon V. Cormack, Hugh C. Williams

[1] Is GF Divisor of xGF(0,11,10), Twin n=1

[2] Is GF Divisor of xGF(1,7,4) [+4], Twin n=2, Near Cullen 3•2²+1, Williams 3•4¹+1

[3] Is GF Divisor of xGF(4,5,2) [+11]

[4] Is GF Divisor of GF(3,3) [+11], Twin n=6, Cullen 3•4³+1, Near Cullen 6•2⁵+1, Williams 3•4³+1

[5] Is GF Divisor of xGF(6,3,2) [+13], Near Cullen 6•2⁷+1, Williams 3•4⁴+1

[6] Is GF Divisor of GF(8,3) [+12], Cullen 3•16³+1, Williams 3•4⁶+1

[7] Is GF Divisor of GF(15,3) [+12], Twin n=18, Cullen 3•64³+1, Williams 3•4⁹+1

[8] Is GF Divisor of GF(26,3) [+12], Cullen 3•1024³+1, Williams 3•4¹⁵+1

[9] Is GF Divisor of GF(32,3) [+14], Cullen 3•4096³+1, Williams 3•4¹⁸+1

[10] Is GF Divisor of F(38) [+9]

[11] Is GF Divisor of GF(63,3) [+14], Williams 3•4³³+1

[12] Is GF Divisor of GF(187,3) [+12]

[13] Is GF Divisor of GF(198,3) [+11]

[14] Is GF Divisor of F(207) [+19]

[15] Is GF Divisor of GF(271,3) [+14], Williams 3•4¹³⁸+1

[16] Is GF Divisor of xGF(350,3,2) [+11]

[17] Is GF Divisor of GF(403,3) [+14], Williams 3•4²⁰⁴+1

[18] Is GF Divisor of GF(435,3) [+12], Williams 3•4²¹⁹+1

[19] Is GF Divisor of GF(531,3) [+12], Williams 3•4²⁶⁷+1

[20] Is GF Divisor of GF(2197,3) [+14], Williams 3•4¹¹⁰⁴+1

[21] Is GF Divisor of xGF(2812,3,2) [+15], Williams 3•4¹⁴⁰⁸+1

[22] Is GF Divisor of GF(3160,3) [+14], Williams 3•4¹⁵⁸⁴+1

[23] Is GF Divisor of GF(3187,3) [+12]

[24] Is GF Divisor of GF(3906,3) [+15], Williams 3•4¹⁹⁵⁶+1

[25] Is GF Divisor of xGF(20905,3,2) [+13]

[26] Is GF Divisor of GF(34346,3) [+12], Williams 3•4¹⁷¹⁷⁵+1

[27] Is GF Divisor of GF(42290,3) [+12], Williams 3•4²¹¹⁴⁷+1

[28] Is GF Divisor of xGF(42662,3,2) [+11]

[29] Is GF Divisor of GF(44683,3) [+16]

[30] Is GF Divisor of GF(48146,3) [+12], Williams 3•4²⁴⁰⁷⁵+1

[31] Is GF Divisor of GF(54787,3) [+15], Williams 3•4²⁷³⁹⁶+1

[32] Is GF Divisor of GF(55178,3) [+11], Williams 3•4²⁷⁵⁹¹+1

[33] Is GF Divisor of GF(59970,3) [+15]

[34] Is GF Divisor of GF(80187,3) [+12], Williams 3•4⁴⁰⁰⁹⁵+1

[35] Is GF Divisor of F(157167) [+20]

[36] Is GF Divisor of F(213319) [+10]

[37] Is GF Divisor of F(303088) [+20]

[38] Is GF Divisor of xGF(362762,3,2) [+12]

[39] Is GF Divisor of F(382447) [+9]

[40] Is GF Divisor of GF(709962,3) [+14], Williams 3•4³⁵⁴⁹⁸⁴+1

[41] Is GF Divisor of GF(801973,3) [+12], Williams 3•4⁴⁰⁰⁹⁸⁹+1

[42] Is GF Divisor of GF(916771,3) [+16]

[43] Is GF Divisor of GF(1832490,3) [+18], Williams 3•4⁹¹⁶²⁴⁸+1

[44] Is GF Divisor of F(2145351) [+19]

[45] Is GF Divisor of GF(2291607,3) [+14], Williams 3•4^1145805+1

[46] Is GF Divisor of F(2478782) [+9]

[47] Is GF Divisor of GF(5082303,3) [+14], Williams 3•4^2541153+1

[48] Is GF Divisor of GF(7033639,3) [+12]

[49] Is GF Divisor of GF(10829343,3) [+14], Williams 3•4^5414673+1

[50] Is GF Divisor of GF(16408814,3) [+12], Williams 3•4^8204409+1

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Proth primes of the form 3•2ⁿ+1

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Proth primes of the form 3•2ⁿ+1