Proth primes of the form 15•2ⁿ+1

Current data

`k` , `b` :	15 , 2
Type :	315
Count :	65
Nash :	2873
Max `n` :	9,000,000
Date :	2024-09-02

1^[1], 2^[2], 4^[3], 9^[4], 10^[5], 12^[6], 27^[7], 37^[8], 38^[9], 44^[10], 48^[11], 78^[12], 112^[13], 168^[14], 229^[15], 297^[16], 339^[17], 517^[18], 522^[19], 654^[20], 900^[21], 1518^[22], 2808^[23], 2875^[24], 3128^[25], 3888^[26], 4410^[27], 6804^[28], 7050^[29], 7392^[30], 19219^[31], 21445^[32], 21550^[33], 24105^[34], 24995^[35], 34224^[36], 34260^[37], 43388^[38], 48444^[39], 61758^[40], 184290^[41], 294894^[42], 300488^[43], 403929^[44], 483098^[45], 635989^[46], 701902^[47], 734400^[48], 1229600^[49], 1244377^[50], 1276177^[51], 1368428^[52], 1418605^[53], 1597510^[54], 1667744^[55], 2393365^[56], 2785940^[57], 2988834^[58], 3162659^[59], 4246384^[60], 4800315^[61], 7300254^[62], 7619838^[63], 9312889^[64], 9830108^[65]

Remarks :

The sequence A002258 in OEIS
See also Williams 15•16ⁿ+1

Notes

↑ Twin n=1
↑ Twin n=2
↑ Is GF Divisor of xGF(3,11,2), Twin n=4, Williams 15•16¹+1
↑ Is GF Divisor of xGF(7,5,3) [+3]
↑ Is GF Divisor of xGF(9,7,6) [+3], Twin n=10
↑ Is GF Divisor of xGF(11,11,4), Williams 15•16³+1
↑ Is GF Divisor of xGF(25,9,2) [+2]
↑ Is GF Divisor of xGF(36,7,5) [+3]
↑ Is GF Divisor of xGF(37,10,7)
↑ Is GF Divisor of xGF(43,7,3) [+3], Williams 15•16¹¹+1
↑ Is GF Divisor of GF(45,8), Williams 15•16¹²+1
↑ Is GF Divisor of xGF(76,7,5)
↑ Is GF Divisor of xGF(110,5,2) [+2], Williams 15•16²⁸+1
↑ Is GF Divisor of xGF(165,7,2) [+3], Williams 15•16⁴²+1
↑ Is GF Divisor of F(226) [+5]
↑ Is GF Divisor of xGF(294,7,4) [+1]
↑ Is GF Divisor of xGF(337,7,3) [+2]
↑ Is GF Divisor of xGF(514,10,9) [+3]
↑ Is GF Divisor of xGF(519,9,5) [+1]
↑ Is GF Divisor of xGF(650,9,5)
↑ Is GF Divisor of GF(896,3) [+3], Williams 15•16²²⁵+1
↑ Is GF Divisor of GF(1513,5) [+3]
↑ Is GF Divisor of xGF(2804,5,2), Williams 15•16⁷⁰²+1
↑ Is GF Divisor of GF(2872,12)
↑ Is GF Divisor of xGF(3125,3,2) [+4], Williams 15•16⁷⁸²+1
↑ Is GF Divisor of xGF(3886,7,5) [+1], Williams 15•16⁹⁷²+1
↑ Is GF Divisor of xGF(4406,9,8) [+1]
↑ Is GF Divisor of GF(6801,6), Williams 15•16¹⁷⁰¹+1
↑ Is GF Divisor of xGF(7048,4,3) [+2]
↑ Is GF Divisor of xGF(7391,11,10), Williams 15•16¹⁸⁴⁸+1
↑ Is GF Divisor of xGF(19218,9,7) [+3]
↑ Is GF Divisor of xGF(21443,10,9) [+1]
↑ Is GF Divisor of xGF(21546,11,8)
↑ Is GF Divisor of xGF(24103,10,9) [+1]
↑ Is GF Divisor of GF(24990,3)
↑ Is GF Divisor of xGF(34221,5,3) [+6], Williams 15•16⁸⁵⁵⁶+1
↑ Is GF Divisor of xGF(34255,9,5) [+1], Williams 15•16⁸⁵⁶⁵+1
↑ Is GF Divisor of GF(43379,6) [+9], Williams 15•16¹⁰⁸⁴⁷+1
↑ Is GF Divisor of xGF(48443,11,8), Williams 15•16¹²¹¹¹+1
↑ Is GF Divisor of xGF(61755,9,2) [+1]
↑ Is GF Divisor of xGF(184288,5,4) [+5]
↑ Is GF Divisor of xGF(294893,11,9)
↑ Is GF Divisor of xGF(300485,4,3) [+6], Williams 15•16⁷⁵¹²²+1
↑ Is GF Divisor of xGF(403927,4,3) [+5]
↑ Is GF Divisor of xGF(483094,6,5) [+3]
↑ Is GF Divisor of xGF(635988,7,2) [+2]
↑ Is GF Divisor of xGF(701895,6,5) [+2]
↑ Is GF Divisor of xGF(734398,9,5) [+1], Williams 15•16¹⁸³⁶⁰⁰+1
↑ Is GF Divisor of xGF(1229599,7,5) [+2], Williams 15•16³⁰⁷⁴⁰⁰+1
↑ Is GF Divisor of xGF(1244376,7,4) [+2]
↑ Is GF Divisor of GF(1276174,3) [+8]
↑ Is GF Divisor of xGF(1368426,8,5) [+3], Williams 15•16³⁴²¹⁰⁷+1
↑ Is GF Divisor of xGF(1418603,4,3) [+11]
↑ Is GF Divisor of xGF(1597505,5,3) [+1]
↑ Is GF Divisor of xGF(1667743,8,7) [+1], Williams 15•16⁴¹⁶⁹³⁶+1
↑ Is GF Divisor of xGF(2393362,5,4) [+3]
↑ Is GF Divisor of xGF(2785939,7,4) [+2], Williams 15•16⁶⁹⁶⁴⁸⁵+1
↑ Is GF Divisor of GF(2988832,8) [+1]
↑ Is GF Divisor of xGF(3162658,10,7) [+2]
↑ Is GF Divisor of GF(4246381,6) [+4], Williams 15•16^1061596+1
↑ Is GF Divisor of GF(4800313,3) [+5]
↑ Is GF Divisor of xGF(7300253,11,8)
↑ Is GF Divisor of xGF(7619837,11,6) [+1]
↑ Is GF Divisor of xGF(9312887,3,2) [+1]
↑ Is GF Divisor of xGF(9830107,7,6) [+1], Williams 15•16^2457527+1

History

2024-09-02: Checked n = 8 - 400000 only n ≡ 0 mod 4, Mark Rodenkirch, double-check, released
2024-08-22: Reserved by Mark Rodenkirch for n = 8 - 400000 only n ≡ 0 mod 4, double-check
2023-08-19: Found n = 9830108, Ryan Propper
2023-08-07: Found n = 9312889, Ryan Propper
2021-04-01: Checked to n = 9000000, PrimeGrid Fermat Divisor Search
2020-12-24: Found n = 7619838, (Anonymous), PrimeGrid Fermat Divisor Search (Official announcement)
2020-10-25: Found n = 7300254, Robert Gelhar, PrimeGrid Fermat Divisor Search (Official announcement)
2019-10-16: Found n = 4800315, Ricky L. Hubbard, PrimeGrid Fermat Divisor Search
2019-07: Checked n = 3322000 - 3640000, PrimeGrid Proth Mega Prime Search
2013-05-18: Found n = 4246384, Serge Batalov
2012-12-30: Found n = 3162659, Serge Batalov
2012-12-15: Found n = 2988834, Serge Batalov
2012-11-25: Found n = 2785940, Serge Batalov
2010-04-14: Found n = 2393365, Darren Wallace, PrimeGrid Proth Prime Search
2007-04-16: Found n = 1667744, Curtis Cooper
2006-08-19: Found n = 1597510, Curtis Cooper
2006-04-20: Found n = 1418605, Curtis Cooper
2006-03-15: Found n = 1229600, Curtis Cooper
2006-02-15: Found n = 1276177, Curtis Cooper
2006-02-09: Found n = 1368428, Curtis Cooper
2006-01-31: Found n = 1244377, Curtis Cooper
2004-10-25: Found n = 734400, Payam Samidoost
2004-10-18: Found n = 635989, Payam Samidoost
2004-10-05: Found n = 701902, Payam Samidoost
2004-02-09: Found n = 483098, Payam Samidoost
2003-10-06: Found n = 294894, Payam Samidoost
2002-10: Found n = 403929, Payam Samidoost
2002-02-12: Found n = 300488, Payam Samidoost
1998-10-01: Found n = 184290, Jeffrey Young
1995-08: Found n = 61758, Jeffrey Young
1995-08: Found n = 48444, Jeffrey Young
1995-08: Found n = 43388, Jeffrey Young
1993-10-01: Found n = 34260, Harvey Dubner
1993: Found n = 34224, Harvey Dubner
1993-10-01: Found n = 24995, Harvey Dubner
1993-10-01: Found n = 24105, Harvey Dubner
1993-03: Found n = 21550, Harvey Dubner
1992-12-01: Found n = 21445, Harvey Dubner
1992-12-01: Found n = 19219, Harvey Dubner
1983: Found n = 7392, Wilfrid Keller
1983: Found n = 7050, Wilfrid Keller
1983: Found n = 6804, Wilfrid Keller
1983: Found n = 4410, Wilfrid Keller
1979: Checked n = 1500 - 4000, Gordon V. Cormack, Hugh C. Williams, missed n=1518
1979: Found n = 3888, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 3128, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 2875, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 2808, Gordon V. Cormack, Hugh C. Williams

[1] Twin n=1

[2] Twin n=2

[3] Is GF Divisor of xGF(3,11,2), Twin n=4, Williams 15•16¹+1

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

[5] Is GF Divisor of xGF(9,7,6) [+3], Twin n=10

[6] Is GF Divisor of xGF(11,11,4), Williams 15•16³+1

[7] Is GF Divisor of xGF(25,9,2) [+2]

[8] Is GF Divisor of xGF(36,7,5) [+3]

[9] Is GF Divisor of xGF(37,10,7)

[10] Is GF Divisor of xGF(43,7,3) [+3], Williams 15•16¹¹+1

[11] Is GF Divisor of GF(45,8), Williams 15•16¹²+1

[12] Is GF Divisor of xGF(76,7,5)

[13] Is GF Divisor of xGF(110,5,2) [+2], Williams 15•16²⁸+1

[14] Is GF Divisor of xGF(165,7,2) [+3], Williams 15•16⁴²+1

[15] Is GF Divisor of F(226) [+5]

[16] Is GF Divisor of xGF(294,7,4) [+1]

[17] Is GF Divisor of xGF(337,7,3) [+2]

[18] Is GF Divisor of xGF(514,10,9) [+3]

[19] Is GF Divisor of xGF(519,9,5) [+1]

[20] Is GF Divisor of xGF(650,9,5)

[21] Is GF Divisor of GF(896,3) [+3], Williams 15•16²²⁵+1

[22] Is GF Divisor of GF(1513,5) [+3]

[23] Is GF Divisor of xGF(2804,5,2), Williams 15•16⁷⁰²+1

[24] Is GF Divisor of GF(2872,12)

[25] Is GF Divisor of xGF(3125,3,2) [+4], Williams 15•16⁷⁸²+1

[26] Is GF Divisor of xGF(3886,7,5) [+1], Williams 15•16⁹⁷²+1

[27] Is GF Divisor of xGF(4406,9,8) [+1]

[28] Is GF Divisor of GF(6801,6), Williams 15•16¹⁷⁰¹+1

[29] Is GF Divisor of xGF(7048,4,3) [+2]

[30] Is GF Divisor of xGF(7391,11,10), Williams 15•16¹⁸⁴⁸+1

[31] Is GF Divisor of xGF(19218,9,7) [+3]

[32] Is GF Divisor of xGF(21443,10,9) [+1]

[33] Is GF Divisor of xGF(21546,11,8)

[34] Is GF Divisor of xGF(24103,10,9) [+1]

[35] Is GF Divisor of GF(24990,3)

[36] Is GF Divisor of xGF(34221,5,3) [+6], Williams 15•16⁸⁵⁵⁶+1

[37] Is GF Divisor of xGF(34255,9,5) [+1], Williams 15•16⁸⁵⁶⁵+1

[38] Is GF Divisor of GF(43379,6) [+9], Williams 15•16¹⁰⁸⁴⁷+1

[39] Is GF Divisor of xGF(48443,11,8), Williams 15•16¹²¹¹¹+1

[40] Is GF Divisor of xGF(61755,9,2) [+1]

[41] Is GF Divisor of xGF(184288,5,4) [+5]

[42] Is GF Divisor of xGF(294893,11,9)

[43] Is GF Divisor of xGF(300485,4,3) [+6], Williams 15•16⁷⁵¹²²+1

[44] Is GF Divisor of xGF(403927,4,3) [+5]

[45] Is GF Divisor of xGF(483094,6,5) [+3]

[46] Is GF Divisor of xGF(635988,7,2) [+2]

[47] Is GF Divisor of xGF(701895,6,5) [+2]

[48] Is GF Divisor of xGF(734398,9,5) [+1], Williams 15•16¹⁸³⁶⁰⁰+1

[49] Is GF Divisor of xGF(1229599,7,5) [+2], Williams 15•16³⁰⁷⁴⁰⁰+1

[50] Is GF Divisor of xGF(1244376,7,4) [+2]

[51] Is GF Divisor of GF(1276174,3) [+8]

[52] Is GF Divisor of xGF(1368426,8,5) [+3], Williams 15•16³⁴²¹⁰⁷+1

[53] Is GF Divisor of xGF(1418603,4,3) [+11]

[54] Is GF Divisor of xGF(1597505,5,3) [+1]

[55] Is GF Divisor of xGF(1667743,8,7) [+1], Williams 15•16⁴¹⁶⁹³⁶+1

[56] Is GF Divisor of xGF(2393362,5,4) [+3]

[57] Is GF Divisor of xGF(2785939,7,4) [+2], Williams 15•16⁶⁹⁶⁴⁸⁵+1

[58] Is GF Divisor of GF(2988832,8) [+1]

[59] Is GF Divisor of xGF(3162658,10,7) [+2]

[60] Is GF Divisor of GF(4246381,6) [+4], Williams 15•16^1061596+1

[61] Is GF Divisor of GF(4800313,3) [+5]

[62] Is GF Divisor of xGF(7300253,11,8)

[63] Is GF Divisor of xGF(7619837,11,6) [+1]

[64] Is GF Divisor of xGF(9312887,3,2) [+1]

[65] Is GF Divisor of xGF(9830107,7,6) [+1], Williams 15•16^2457527+1

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Proth primes of the form 15•2ⁿ+1

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Proth primes of the form 15•2n+1

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Proth primes of the form 15•2ⁿ+1