Proth primes of the form 25•2ⁿ+1

Current data

`k` , `b` :	25 , 2
Count :	46
Nash :	2198
Max `n` :	9,000,000
Date :	2022-09-21

2, 4^[1], 6^[2], 10^[3], 20, 22, 52^[4], 64^[5], 78^[6], 184^[7], 232^[8], 268, 340^[9], 448^[10], 554, 664^[11], 740^[12], 748^[13], 1280^[14], 1328^[15], 1640^[16], 3314^[17], 3904^[18], 3938^[19], 5152^[20], 9522, 57488^[21], 66872^[22], 148060^[23], 154254^[24], 216092^[25], 302194^[26], 367294^[27], 627710^[28], 966414^[29], 1211488^[30], 1258562^[31], 1298186, 2141884^[32], 2583690, 2927222^[33], 3733144^[34], 4481024^[35], 8456828^[36], 8788628^[37], 13719266^[38]

Remarks :

The sequence A032362 in OEIS

For all even n-values 25•2ⁿ+1 is a Generalized Fermat number.

Notes

↑ Is GF Divisor of xGF(3,3,2)
↑ Is GF Divisor of xGF(4,9,2)
↑ Is GF Divisor of xGF(8,9,2)
↑ Is GF Divisor of GF(48,10) [+1]
↑ Is GF Divisor of xGF(63,6,5)
↑ Is GF Divisor of xGF(77,3,2) [+2]
↑ Is GF Divisor of xGF(183,5,3) [+1]
↑ Is GF Divisor of xGF(230,9,2)
↑ Is GF Divisor of xGF(338,9,5)
↑ Is GF Divisor of xGF(439,5,2) [+2]
↑ Is GF Divisor of xGF(662,7,2) [+1]
↑ Is GF Divisor of xGF(738,9,8) [+1]
↑ Is GF Divisor of xGF(742,5,2) [+1]
↑ Is GF Divisor of xGF(1278,9,8) [+1]
↑ Is GF Divisor of xGF(1324,12,11)
↑ Is GF Divisor of xGF(1638,7,3) [+1]
↑ Is GF Divisor of xGF(3312,11,8)
↑ Is GF Divisor of GF(3903,6) [+2]
↑ Is GF Divisor of xGF(3934,12,11)
↑ Is GF Divisor of GF(5147,10)
↑ Is GF Divisor of xGF(57484,5,2) [+2]
↑ Is GF Divisor of xGF(66871,4,3) [+1]
↑ Is GF Divisor of xGF(148059,7,6) [+1]
↑ Is GF Divisor of xGF(154252,7,3) [+1]
↑ Is GF Divisor of xGF(216091,11,10)
↑ Is GF Divisor of xGF(302187,8,5)
↑ Is GF Divisor of xGF(367288,8,5)
↑ Is GF Divisor of xGF(627709,3,2) [+1]
↑ Is GF Divisor of xGF(966412,11,5)
↑ Is GF Divisor of GF(1211487,12)
↑ Is GF Divisor of xGF(1258561,7,2)
↑ Is GF Divisor of F(2141872) [+5]
↑ Is GF Divisor of xGF(2927219,7,6) [+1]
↑ Is GF Divisor of xGF(3733139,8,5) [+1]
↑ Is GF Divisor of xGF(4481020,8,5) [+1]
↑ Is GF Divisor of GF(8456827,12)
↑ Is GF Divisor of xGF(8788627,11,4)
↑ Is GF Divisor of xGF(13719265,7,5) [+2]

History

2022-09-21: Found n = 13719266, Ryan Propper
2021-04-01: Checked to n = 9000000, PrimeGrid Fermat Divisor Search
2021-03-01: Found n = 8788628, Tom Greer, PrimeGrid Fermat Divisor Search (Official announcement)
2021-01-28: Found n = 8456828, Wolfgang Schwieger, PrimeGrid Fermat Divisor Search (Official announcement)
2019-10-12: Found n = 4481024, Will Steinbach, PrimeGrid Fermat Divisor Search
2019-09-18: Found n = 3733144, Tom Greer, PrimeGrid Fermat Divisor Search
2019-07: Checked n = 3322000 - 3640000, PrimeGrid Proth Mega Prime Search
2013-04-22: Found n = 2927222, Rick Channing, PrimeGrid Proth Prime Search
2013-04-20: Found n = 2583690, Håkan Lind, PrimeGrid Proth Prime Search
2011-09-12: Found n = 2141884, Grzegorz Granowski, PrimeGrid Proth Prime Search
2005-05-19: Found n = 1298186, Curtis Cooper
2005-01-20: Found n = 1211488, Curtis Cooper
2004-12-02: Found n = 1258562, Curtis Cooper
2004-05-06: Found n = 966414, Curtis Cooper
2004-04-10: Found n = 627710, Curtis Cooper
2004-03-24: Found n = 367294, Curtis Cooper
2003-11-15: Found n = 302194, Payam Samidoost
2001-01-17: Found n = 216092, Nestor Sergio de Araujo Melo
1999-11-28: Found n = 148060, Sturle Sunde
1999-09-10: Found n = 154254, Peter Dodson
1995-08: Found n = 66872, Jeffrey Young
1995-08: Found n = 57488, Jeffrey Young
1983: Found n = 9522, Wilfrid Keller
1983: Found n = 5152, Wilfrid Keller
1979: Checked n = 1500 - 4000, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 3938, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 3904, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 3314, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 1640, Gordon V. Cormack, Hugh C. Williams

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

[2] Is GF Divisor of xGF(4,9,2)

[3] Is GF Divisor of xGF(8,9,2)

[4] Is GF Divisor of GF(48,10) [+1]

[5] Is GF Divisor of xGF(63,6,5)

[6] Is GF Divisor of xGF(77,3,2) [+2]

[7] Is GF Divisor of xGF(183,5,3) [+1]

[8] Is GF Divisor of xGF(230,9,2)

[9] Is GF Divisor of xGF(338,9,5)

[10] Is GF Divisor of xGF(439,5,2) [+2]

[11] Is GF Divisor of xGF(662,7,2) [+1]

[12] Is GF Divisor of xGF(738,9,8) [+1]

[13] Is GF Divisor of xGF(742,5,2) [+1]

[14] Is GF Divisor of xGF(1278,9,8) [+1]

[15] Is GF Divisor of xGF(1324,12,11)

[16] Is GF Divisor of xGF(1638,7,3) [+1]

[17] Is GF Divisor of xGF(3312,11,8)

[18] Is GF Divisor of GF(3903,6) [+2]

[19] Is GF Divisor of xGF(3934,12,11)

[20] Is GF Divisor of GF(5147,10)

[21] Is GF Divisor of xGF(57484,5,2) [+2]

[22] Is GF Divisor of xGF(66871,4,3) [+1]

[23] Is GF Divisor of xGF(148059,7,6) [+1]

[24] Is GF Divisor of xGF(154252,7,3) [+1]

[25] Is GF Divisor of xGF(216091,11,10)

[26] Is GF Divisor of xGF(302187,8,5)

[27] Is GF Divisor of xGF(367288,8,5)

[28] Is GF Divisor of xGF(627709,3,2) [+1]

[29] Is GF Divisor of xGF(966412,11,5)

[30] Is GF Divisor of GF(1211487,12)

[31] Is GF Divisor of xGF(1258561,7,2)

[32] Is GF Divisor of F(2141872) [+5]

[33] Is GF Divisor of xGF(2927219,7,6) [+1]

[34] Is GF Divisor of xGF(3733139,8,5) [+1]

[35] Is GF Divisor of xGF(4481020,8,5) [+1]

[36] Is GF Divisor of GF(8456827,12)

[37] Is GF Divisor of xGF(8788627,11,4)

[38] Is GF Divisor of xGF(13719265,7,5) [+2]

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Proth primes of the form 25•2ⁿ+1

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Proth primes of the form 25•2n+1

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Proth primes of the form 25•2ⁿ+1