Difference between revisions of "Proth prime 2 9"

Latest revision as of 18:48, 9 April 2023

Reserved! This sequence is currently part of Multi Reservation 1: PrimeGrid Proth Prime Search.

Current data

`k` , `b` :	9 , 2
Type :	3
Count :	66
Nash :	2297
Max `n` :	4,850,000
Date :	2024-03-28
Reserved :	PrimeGridPrimeGrid/Reserved

1^[1], 2^[2], 3^[3], 6^[4], 7^[5], 11^[6], 14^[7], 17^[8], 33^[9], 42^[10], 43^[11], 63^[12], 65^[13], 67^[14], 81^[15], 134^[16], 162^[17], 206^[18], 211^[19], 366^[20], 663^[21], 782^[22], 1305^[23], 1411^[24], 1494^[25], 2297^[26], 2826^[27], 3230^[28], 3354^[29], 3417^[30], 3690^[31], 4842^[32], 5802^[33], 6937^[34], 7967^[35], 9431^[36], 13903^[37], 22603^[38], 24422^[39], 39186^[40], 43963^[41], 47003^[42], 49902^[43], 67943^[44], 114854^[45], 127003^[46], 145247^[47], 147073^[48], 149143^[49], 304607^[50], 384990^[51], 412034^[52], 435743^[53], 461081^[54], 834810^[55], 1051026^[56], 1807574^[57], 2543551^[58], 3497442^[59], 5642513^[60], 9778263^[61], 11158963^[62], 11366286^[63], 11500843^[64], 12406887^[65], 13334487^[66]

Remarks :

The sequence A002256 in OEIS
For all even n-values 9•2ⁿ+1 is a Generalized Fermat number.

Notes

↑ Twin n=1
↑ Is GF Divisor of xGF(1,11,8)
↑ Is GF Divisor of xGF(2,7,3) [+3], Twin n=3
↑ Is GF Divisor of xGF(5,6,5) [+4]
↑ Is GF Divisor of xGF(5,3,2) [+5], Twin n=7
↑ Is GF Divisor of xGF(10,5,4) [+1]
↑ Is GF Divisor of xGF(10,4,3) [+6]
↑ Is GF Divisor of xGF(11,5,4) [+3]
↑ Is GF Divisor of GF(29,3) [+5]
↑ Is GF Divisor of xGF(41,5,4) [+6]
↑ Is GF Divisor of xGF(38,3,2) [+6], Twin n=43
↑ Is GF Divisor of GF(61,3) [+10], Twin n=63
↑ Is GF Divisor of GF(63,6) [+2]
↑ Is GF Divisor of F(63) [+19]
↑ Is GF Divisor of GF(79,3) [+9]
↑ Is GF Divisor of xGF(132,8,7) [+2]
↑ Is GF Divisor of GF(158,3) [+7]
↑ Is GF Divisor of GF(205,5) [+5]
↑ Is GF Divisor of xGF(210,5,4) [+3], Twin n=211
↑ Is GF Divisor of xGF(365,7,4) [+4]
↑ Is GF Divisor of xGF(662,5,3) [+3]
↑ Is GF Divisor of xGF(781,6,5) [+4]
↑ Is GF Divisor of GF(1303,3) [+2]
↑ Is GF Divisor of xGF(1409,3,2) [+1]
↑ Is GF Divisor of GF(1488,3) [+1]
↑ Is GF Divisor of GF(2294,6) [+3]
↑ Is GF Divisor of GF(2822,3) [+7]
↑ Is GF Divisor of xGF(3229,7,5) [+4]
↑ Is GF Divisor of GF(3353,7) [+4]
↑ Is GF Divisor of xGF(3408,5,3) [+5]
↑ Is GF Divisor of GF(3684,3) [+5]
↑ Is GF Divisor of GF(4838,3) [+7]
↑ Is GF Divisor of xGF(5801,8,7) [+6]
↑ Is GF Divisor of xGF(6935,3,2) [+3]
↑ Is GF Divisor of xGF(7966,5,3) [+4]
↑ Is GF Divisor of F(9428) [+8]
↑ Is GF Divisor of xGF(13900,3,2) [+5]
↑ Is GF Divisor of xGF(22602,5,3) [+2]
↑ Is GF Divisor of xGF(24417,4,3) [+5]
↑ Is GF Divisor of GF(39177,3) [+4]
↑ Is GF Divisor of xGF(43960,3,2) [+1]
↑ Is GF Divisor of xGF(47001,4,3) [+6]
↑ Is GF Divisor of xGF(49901,5,3) [+4]
↑ Is GF Divisor of xGF(67941,4,3) [+5]
↑ Is GF Divisor of xGF(114850,4,3) [+4]
↑ Is GF Divisor of xGF(127002,5,3) [+3]
↑ Is GF Divisor of xGF(145245,4,3) [+7]
↑ Is GF Divisor of xGF(147069,5,2) [+4]
↑ Is GF Divisor of xGF(149142,5,2) [+2]
↑ Is GF Divisor of xGF(304604,4,3) [+3]
↑ Is GF Divisor of xGF(384989,5,3) [+2]
↑ Is GF Divisor of xGF(412030,4,3) [+9]
↑ Is GF Divisor of xGF(435741,7,6) [+4]
↑ Is GF Divisor of F(461076) [+16]
↑ Is GF Divisor of xGF(834809,5,4) [+4]
↑ Is GF Divisor of xGF(1051025,8,7) [+4]
↑ Is GF Divisor of xGF(1807570,4,3) [+2]
↑ Is GF Divisor of F(2543548) [+16]
↑ Is GF Divisor of GF(3497441,7) [+5]
↑ Is GF Divisor of xGF(5642511,5,3) [+3]
↑ Is GF Divisor of xGF(9778262,6,5) [+4]
↑ Is GF Divisor of xGF(11158961,3,2) [+5]
↑ Is GF Divisor of xGF(11366285,7,4) [+6]
↑ Is GF Divisor of xGF(11500842,5,3) [+4]
↑ Is GF Divisor of GF(12406885,3) [+3]
↑ Is GF Divisor of GF(13334485,3) [+6]

History

2021-04-01: Checked n = 4000000-9000000, PrimeGrid Fermat Divisor Search, odd n-values only
2020-08-06: Found n = 9778263, Ryan Propper
2020-03-31: Found n = 13334487, Ryan Propper
2020-03-29: Found n = 12406887, Ryan Propper
2020-03-26: Found n = 11366286, Ryan Propper
2020-03-13: Found n = 11500843, Ryan Propper
2020-03-13: Found n = 11158963, Ryan Propper
2013-11-29: Found n = 5642513, Serge Batalov
?: Checked to n = 4000000, PrimeGrid Proth Prime Search
2012-10-24: Found n = 3497442, Heinz Ming, PrimeGrid Proth Prime Search (Official announcement)
2011-06-22: Found n = 2543551, James Scott Brown, PrimeGrid Proth Prime Search (Official announcement)
2011-06-22: Found n = 1807574, Reuben Gathright, PrimeGrid Proth Prime Search
2004-12-14: Found n = 1051026, Souichi Murata, Satoshi Noda, Takahiro Nohara
2004-09-22: Found n = 834810, Senji Yamashita, Satoshi Noda, Takahiro Nohara
2003-08-05: Found n = 461081, Takahiro Nohara
2003-07-09: Found n = 435743, Takahiro Nohara
2003-05-19: Found n = 412034, Takahiro Nohara
2002-02-26: Found n = 384990, Takahiro Nohara
1998-07-04: Found n = 304607, Ray Ballinger
1995-08: Found n = 149143, Jeffrey Young
1995-08: Found n = 147073, Jeffrey Young
1995-08: Found n = 145247, Jeffrey Young
1995-08: Found n = 127003, Jeffrey Young
1995-08: Found n = 114854, Jeffrey Young
1995-08: Found n = 67943, Jeffrey Young
1994-07-01: Found n = 43963, Jeffrey Young
1993-10-01: Found n = 49902, Jeffrey Young
1993-10-01: Found n = 47003, Jeffrey Young
1992-12: Found n = 39186, Harvey Dubner
1992-10: Found n = 24422, Harvey Dubner
1992: Found n = 22603, Harvey Dubner
1991: Found n = 13903, Wilfrid Keller
1983: Found n = 9431, Wilfrid Keller
1983: Found n = 6937, Wilfrid Keller
1983: Found n = 4842, Wilfrid Keller
1979: Found n = 7967, A. Oliver L. Atkin, Neil W. Rickert
1979: Found n = 5802, A. Oliver L. Atkin, Neil W. Rickert
1979: Checked n = 1500-4000, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 3690, Gordon V. Cormack, Hugh C. Williams
1979: Found n = 3417, Gordon V. Cormack, Hugh C. Williams
1978: Found n = 3354, Gordon V. Cormack, Hugh C. Williams
1978: Found n = 3230, Gordon V. Cormack, Hugh C. Williams
1978: Found n = 2826, Gordon V. Cormack, Hugh C. Williams
1978: Found n = 2297, Gordon V. Cormack, Hugh C. Williams

[1] Twin n=1

[2] Is GF Divisor of xGF(1,11,8)

[3] Is GF Divisor of xGF(2,7,3) [+3], Twin n=3

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

[5] Is GF Divisor of xGF(5,3,2) [+5], Twin n=7

[6] Is GF Divisor of xGF(10,5,4) [+1]

[7] Is GF Divisor of xGF(10,4,3) [+6]

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

[9] Is GF Divisor of GF(29,3) [+5]

[10] Is GF Divisor of xGF(41,5,4) [+6]

[11] Is GF Divisor of xGF(38,3,2) [+6], Twin n=43

[12] Is GF Divisor of GF(61,3) [+10], Twin n=63

[13] Is GF Divisor of GF(63,6) [+2]

[14] Is GF Divisor of F(63) [+19]

[15] Is GF Divisor of GF(79,3) [+9]

[16] Is GF Divisor of xGF(132,8,7) [+2]

[17] Is GF Divisor of GF(158,3) [+7]

[18] Is GF Divisor of GF(205,5) [+5]

[19] Is GF Divisor of xGF(210,5,4) [+3], Twin n=211

[20] Is GF Divisor of xGF(365,7,4) [+4]

[21] Is GF Divisor of xGF(662,5,3) [+3]

[22] Is GF Divisor of xGF(781,6,5) [+4]

[23] Is GF Divisor of GF(1303,3) [+2]

[24] Is GF Divisor of xGF(1409,3,2) [+1]

[25] Is GF Divisor of GF(1488,3) [+1]

[26] Is GF Divisor of GF(2294,6) [+3]

[27] Is GF Divisor of GF(2822,3) [+7]

[28] Is GF Divisor of xGF(3229,7,5) [+4]

[29] Is GF Divisor of GF(3353,7) [+4]

[30] Is GF Divisor of xGF(3408,5,3) [+5]

[31] Is GF Divisor of GF(3684,3) [+5]

[32] Is GF Divisor of GF(4838,3) [+7]

[33] Is GF Divisor of xGF(5801,8,7) [+6]

[34] Is GF Divisor of xGF(6935,3,2) [+3]

[35] Is GF Divisor of xGF(7966,5,3) [+4]

[36] Is GF Divisor of F(9428) [+8]

[37] Is GF Divisor of xGF(13900,3,2) [+5]

[38] Is GF Divisor of xGF(22602,5,3) [+2]

[39] Is GF Divisor of xGF(24417,4,3) [+5]

[40] Is GF Divisor of GF(39177,3) [+4]

[41] Is GF Divisor of xGF(43960,3,2) [+1]

[42] Is GF Divisor of xGF(47001,4,3) [+6]

[43] Is GF Divisor of xGF(49901,5,3) [+4]

[44] Is GF Divisor of xGF(67941,4,3) [+5]

[45] Is GF Divisor of xGF(114850,4,3) [+4]

[46] Is GF Divisor of xGF(127002,5,3) [+3]

[47] Is GF Divisor of xGF(145245,4,3) [+7]

[48] Is GF Divisor of xGF(147069,5,2) [+4]

[49] Is GF Divisor of xGF(149142,5,2) [+2]

[50] Is GF Divisor of xGF(304604,4,3) [+3]

[51] Is GF Divisor of xGF(384989,5,3) [+2]

[52] Is GF Divisor of xGF(412030,4,3) [+9]

[53] Is GF Divisor of xGF(435741,7,6) [+4]

[54] Is GF Divisor of F(461076) [+16]

[55] Is GF Divisor of xGF(834809,5,4) [+4]

[56] Is GF Divisor of xGF(1051025,8,7) [+4]

[57] Is GF Divisor of xGF(1807570,4,3) [+2]

[58] Is GF Divisor of F(2543548) [+16]

[59] Is GF Divisor of GF(3497441,7) [+5]

[60] Is GF Divisor of xGF(5642511,5,3) [+3]

[61] Is GF Divisor of xGF(9778262,6,5) [+4]

[62] Is GF Divisor of xGF(11158961,3,2) [+5]

[63] Is GF Divisor of xGF(11366285,7,4) [+6]

[64] Is GF Divisor of xGF(11500842,5,3) [+4]

[65] Is GF Divisor of GF(12406885,3) [+3]

[66] Is GF Divisor of GF(13334485,3) [+6]

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[3]

[4]

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[8]

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[11]

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[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

[25]

[26]

[27]

[28]

[29]

[30]

[31]

[32]

[33]

[34]

[35]

[36]

[37]

[38]

[39]

[40]

[41]

[42]

[43]

[44]

[45]

[46]

[47]

[48]

[49]

[50]

[51]

[52]

[53]

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[66]

@@ Line 1: / Line 1: @@
 {{Proth prime
 |Pk=9
+|Pb=2
 |PCount=66
 |PNash=2297
@@ Line 6: / Line 7: @@
 |PDate=
 |PReserved=
-|PMultiRes=20
+|PMultiRes=1
 |PNlist=
 ;T:T
+;T:G
-;T:T;C:Divides: GF(2,10)
+;T:GT
+;T:G
-;T:T
+;T:GT
-;C:Divides: GF(8,6)
+;T:G
+;T:G
+;T:G
-;C:Divides: GF(29,3)
+;T:G
+;T:G
-;T:T
+;T:GT
-;T:T;C:Divides: GF(61,3), GF(62,10)
+;T:GT
-;C:Divides: GF(63,6)
+;T:G
-;C:Divides: F(63), GF(64,3), GF(66,5), GF(64,6), GF(66,10), GF(64,12)
+;T:G
-;C:Divides: GF(79,3)
+;T:G
+;T:G
-;C:Divides: GF(158,3)
+;T:G
-;C:Divides: GF(205,5)
+;T:G
-;T:T;C:Divides: GF(204,12)
+;T:GT
+;T:G
+;T:G
+;T:G
-;C:Divides: GF(1303,3)
+;T:G
+;T:G
-;C:Divides: GF(1488,3)
+;T:G
-;C:Divides: GF(2294,6)
+;T:G
-;C:Divides: GF(2822,3)
+;T:G
+;T:G
-;56509;C:Divides: GF(3353,10)
+;56509;T:G
-;56001
+;56001;T:G
-;51936;C:Divides: GF(3684,3)
+;51936;T:G
-;39625;C:Divides: GF(4838,3)
+;39625;T:G
-;38118
+;38118;T:G
-;34858
+;34858;T:G
-;32237;C:Divides: GF(7964,6), GF(7966,10)
+;32237;T:G
-;29962;C:Divides: F(9428), GF(9429,3), GF(9429,6), GF(9429,12)
+;29962;T:G
-;27077;C:Divides: GF(13902,5)
+;27077;T:G
-;21686;C:Divides: GF(22601,12)
+;21686;T:G
-;20432
+;20432;T:G
-;16396;C:Divides: GF(39177,3)
+;16396;T:G
-;14381
+;14381;T:G
-;13256
+;13256;T:G
-;12820
+;12820;T:G
-;8517;C:Divides: GF(67941,6)
+;8517;T:G
-;2840
+;2840;T:G
-;2560;C:Divides: GF(126999,12)
+;2560;T:G
-;1371
+;1371;T:G
-;1341;C:Divides: GF(147070,12)
+;1341;T:G
-;1305;C:Divides: GF(149141,12)
+;1305;T:G
-;222;C:Divides: GF(304604,6)
+;222;T:G
-;91
+;91;T:G
-;64729
+;64729;T:G
-;65451;C:Divides: GF(435742,10)
+;65451;T:G
-;65770;C:Divides: F(461076), GF(461077,3), GF(461077,6), GF(461077,12)
+;65770;T:G
-;71697
+;71697;T:G
-1051026;72753
+1051026;72753;T:G
-1807574;100561
+1807574;100561;T:G
-2543551;100563
+2543551;100563;T:G
-3497442;109930;C:Divides: GF(3497441,7), xGF(3497438,9,8), GF(3497441,10), xGF(3497439,11,3), xGF(3497441,12,5)
+3497442;109930;T:G
-5642513;116472;C:Divides: GF(5642510,7), xGF(5642511,5,3), xGF(5642509,9,2), xGF(5642512,12,11)
+5642513;116472;T:G
-9778263;131055;C:Divides: GF(9778262,7), xGF(9778262,6,5), xGF(9778256,9,8), xGF(9778260,11,10), xGF(9778262,12,11)
+9778263;131055;T:G
-11158963;130768;C:Divides: GF(11158962,5), xGF(11158961,3,2), xGF(11158962,10,3), xGF(11158962,11,4), xGF(11158962,11,6), xGF(11158962,11,9)
+11158963;130768;T:G
-11366286;130799;C:Divides: xGF(11366285,7,4), xGF(11366285,8,5), xGF(11366285,9,5), xGF(11366281,9,8), xGF(11366285,11,5), xGF(11366284,11,8), xGF(11366284,11,9)
+11366286;130799;T:G
-11500843;130770;C:Divides: GF(11500840,12), xGF(11500842,5,3), xGF(11500842,9,7), xGF(11500841,11,7), xGF(11500842,11,9)
+11500843;130770;T:G
-12406887;130801;C:Divides: GF(12406885,3), GF(12406883,11), xGF(12406886,7,2), xGF(12406886,7,6), xGF(12406886,8,5), xGF(12406885,11,3), xGF(12406884,11,9)
+12406887;130801;T:G
-13334487;130806;C:Divides: GF(13334485,3), GF(13334486,7), GF(13334484,8), xGF(13334486,7,3), xGF(13334485,8,3), xGF(13334486,8,7), xGF(13334486,9,7), xGF(13334483,9,8)
+13334487;130806;T:G
-|PRemarks=
+|PRemarks=The {{OEIS|l|A002256}}<br>For all even {{Vn}}-values {{Kbn|+|9|2|n}} is a [[Generalized Fermat number]].
 }}
 ==History==
+{{HistC|2021-04-01|4000000-9000000|PrimeGrid Fermat Divisor Search|P#8778#132715}}, odd {{Vn}}-values only
 {{HistF|2020-08-06|9778263|Ryan Propper}}
 {{HistF|2020-03-31|13334487|Ryan Propper}}
 {{HistF|2020-03-29|12406887|Ryan Propper}}
+{{HistF|2020-03-26|11366286|Ryan Propper}}
 {{HistF|2020-03-13|11500843|Ryan Propper}}
-{{HistF|2020-03-26|11366286|Ryan Propper}}
 {{HistF|2020-03-13|11158963|Ryan Propper}}
 {{HistF|2013-11-29|5642513|Serge Batalov}}
-{{HistF|2012-10-24|3497442|Heinz Ming}}, [http://www.primegrid.com/download/PPS-3497442.pdf Official announcement]
+{{HistC|?|4000000|PrimeGrid Proth Prime Search}}
-{{HistF|2011-06-22|2543551|Dr. James Scott Brown}}, [http://www.primegrid.com/download/pps-F2543548.pdf Official announcement]
+{{HistF|2012-10-24|3497442|Heinz Ming,PrimeGrid Proth Prime Search}} ([http://www.primegrid.com/download/PPS-3497442.pdf Official announcement])
-{{HistF|2011-06-22|1807574|Reuben Gathright}}
+{{HistF|2011-06-22|2543551|James Scott Brown,PrimeGrid Proth Prime Search}} ([http://www.primegrid.com/download/pps-F2543548.pdf Official announcement])
+{{HistF|2011-06-22|1807574|Reuben Gathright,PrimeGrid Proth Prime Search}}
 {{HistF|2004-12-14|1051026|Souichi Murata,Satoshi Noda,Takahiro Nohara}}
 {{HistF|2004-09-22|834810|Senji Yamashita,Satoshi Noda,Takahiro Nohara}}
@@ Line 100: / Line 103: @@
 {{HistF|1995-08|114854|Jeffrey Young}}
 {{HistF|1995-08|67943|Jeffrey Young}}
+{{HistF|1994-07-01|43963|Jeffrey Young}}
 {{HistF|1993-10-01|49902|Jeffrey Young}}
 {{HistF|1993-10-01|47003|Jeffrey Young}}
-{{HistF|1994-07-01|43963|Jeffrey Young}}
+{{HistF|1992-12|39186|Harvey Dubner}}
-{{HistF|1992|39186|Harvey Dubner}}
 {{HistF|1992-10|24422|Harvey Dubner}}
 {{HistF|1992|22603|Harvey Dubner}}
 {{HistF|1991|13903|Wilfrid Keller}}
 {{HistF|1983|9431|Wilfrid Keller}}
+{{HistF|1983|6937|Wilfrid Keller}}
+{{HistF|1983|4842|Wilfrid Keller}}
 {{HistF|1979|7967|A. Oliver L. Atkin,Neil W. Rickert}}
-{{HistF|1983|6937|Wilfrid Keller}}
 {{HistF|1979|5802|A. Oliver L. Atkin,Neil W. Rickert}}
-{{HistF|1983|4842|Wilfrid Keller}}
+{{HistC|1979|1500-4000|Gordon V. Cormack,Hugh C. Williams}}
-{{HistF|1979|3690|G. V. Cormack}}
+{{HistF|1979|3690|Gordon V. Cormack,Hugh C. Williams}}
-{{HistF|1979|3417|G. V. Cormack}}
+{{HistF|1979|3417|Gordon V. Cormack,Hugh C. Williams}}
-{{HistF|1978|3354|G. V. Cormack}}
+{{HistF|1978|3354|Gordon V. Cormack,Hugh C. Williams}}
+{{HistF|1978|3230|Gordon V. Cormack,Hugh C. Williams}}
+{{HistF|1978|2826|Gordon V. Cormack,Hugh C. Williams}}
+{{HistF|1978|2297|Gordon V. Cormack,Hugh C. Williams}}

Difference between revisions of "Proth prime 2 9"

Latest revision as of 18:48, 9 April 2023

Current data

Notes

History

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