Difference between revisions of "Proth prime 2 3"

Latest revision as of 20:27, 26 September 2024

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

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[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]

@@ Line 1: / Line 1: @@
 {{Proth prime
 |Pk=3
-|PCount=49
+|Pb=2
+|PCount=50
 |PNash=2132
-|PMaxn=16168000
+|PMaxn=
-|PDate=2020-10-04
+|PDate=
-|PReserved=PrimeGrid
+|PReserved=
+|PMultiRes=22
 |PNlist=
-;T:T
+;T:GT
-;T:T
+;T:GT;C:{{NCu|+|2|2}}, {{NWi|MP|4|1}}
-;C:Divides: GF(3,12)
+;T:G
-;T:T;C:Divides: GF(3,3)
+;T:GT;C:{{NCu|4|3}}, {{NCu|+|2|5}}, {{NWi|MP|4|3}}
-;C:Divides: GF(6,5), GF(5,12)
+;T:G;C:{{NCu|-|2|7}}, {{NWi|MP|4|4}}
-;C:Divides: GF(8,3)
+;T:G;C:{{NCu|16|3}}, {{NWi|MP|4|6}}
-;T:T;C:Divides: GF(15,3), GF(17,5)
+;T:GT;C:{{NCu|64|3}}, {{NWi|MP|4|9}}
-;C:Divides: GF(26,3)
+;T:G;C:{{NCu|1024|3}}, {{NWi|MP|4|15}}
-;C:Divides: GF(32,3)
+;T:G;C:{{NCu|4096|3}}, {{NWi|MP|4|18}}
-;C:Divides: F(38), GF(38,3), GF(35,6), GF(38,12)
+;T:G
-;C:Divides: GF(63,3), GF(65,5)
+;T:G;C:{{NWi|MP|4|33}}
-;C:Divides: GF(187,3), GF(188,5)
+;T:G
-;C:Divides: GF(198,3)
+;T:G
-;C:Divides: {{DGF|207}}, {{DGF|207|3}}, {{DGF|208|5}}, {{DGF|203|6}}, {{DGF|208|10}}, {{DGF|207|12}}, {{DGF|206|3|2}}, {{DGF|207|4|3}}, {{DGF|208|5|2}}, {{DGF|208|5|3}}, {{DGF|208|5|4}}, {{DGF|208|6|5}}, {{DGF|205|8|3}}, {{DGF|208|8|5}}, {{DGF|207|9|2}}, {{DGF|208|9|5}}, {{DGF|207|9|8}}, {{DGF|208|10|3}}, {{DGF|208|10|9}}, xGF(208,12,5)
+;T:G
-;C:Divides: GF(271,3)
+;T:G;C:{{NWi|MP|4|138}}
-;C:Divides: GF(351,12)
+;T:G
-;C:Divides: GF(403,3), GF(406,5)
+;T:G;C:{{NWi|MP|4|204}}
-;C:Divides: GF(435,3)
+;T:G;C:{{NWi|MP|4|219}}
-;C:Divides: GF(531,3)
+;T:G;C:{{NWi|MP|4|267}}
-;C:Divides: GF(2197,3), GF(2206,5)
+;T:G;C:{{NWi|MP|4|1104}}
-;C:Divides: GF(2804,5), GF(2811,12)
+;T:G;C:{{NWi|MP|4|1408}}
-;C:Divides: GF(3160,3), GF(3162,5)
+;T:G;C:{{NWi|MP|4|1584}}
-;C:Divides: GF(3187,3)
+;T:G
-;48357;C:Divides: GF(3906,3), GF(3910,5)
+;48357;T:G;C:{{NWi|MP|4|1956}}
-;22329;C:Divides: GF(20908,5), GF(20906,12)
+;22329;T:G
-;17264;C:Divides: GF(34346,3)
+;17264;T:G;C:{{NWi|MP|4|17175}}
-;14919;C:Divides: GF(42290,3)
+;14919;T:G;C:{{NWi|MP|4|21147}}
-;14813;C:Divides: GF(42663,12)
+;14813;T:G
-;14049;C:Divides: GF(44683,3), GF(44684,10)
+;14049;T:G
-;13029;C:Divides: GF(48146,3)
+;13029;T:G;C:{{NWi|MP|4|24075}}
-;C:Divides: GF(54787,3), GF(54786,5)
+;T:G;C:{{NWi|MP|4|27396}}
-;11285;C:Divides: GF(55178,3)
+;11285;T:G;C:{{NWi|MP|4|27591}}
-;10729;C:Divides: GF(59970,3), GF(59972,5)
+;10729;T:G
-;7057;C:Divides: GF(80187,3)
+;7057;T:G;C:{{NWi|MP|4|40095}}
-;1180;C:Divides: F(157167), GF(157167,3), GF(157168,5), GF(157163,6), GF(157168,10), GF(157167,12)
+;1180;T:G
-;401;C:Divides: F(213319), GF(213319,5), GF(213316,6), GF(213319,12)
+;401;T:G
-;223;C:Divides: F(303088), GF(303088,3), GF(303092,5), GF(303086,6), GF(303092,10), GF(303088,12)
+;223;T:G
-;101;C:Divides: GF(362764,10), GF(362763,12)
+;101;T:G
-;94;C:Divides: F(382447), GF(382447,3), GF(382443,6), GF(382447,12)
+;94;T:G
-;74546;C:Divides: GF(709962,3), GF(709963,5)
+;74546;T:G;C:{{NWi|MP|4|354984}}
-;75498;C:Divides: GF(801973,3), GF(801977,5)
+;75498;T:G;C:{{NWi|MP|4|400989}}
-;22;C:Divides: GF(916771,3) GF(916772,10)
+;22;T:G
-1832496;81819;C:Divides: GF(1832490,3), GF(1832494,5)
+1832496;81819;T:G;C:{{NWi|MP|4|916248}}
-2145353;64011;C:Divides: F(2145351), GF(2145351,3), GF(2145352,5), GF(2145348,6), GF(2145352,10), GF(2145351,12)
+2145353;64011;T:G
-2291610;85438;C:Divides: GF(2291607,3), GF(2291609,5)
+2291610;85438;T:G;C:{{NWi|MP|4|1145805}}
-2478785;66628;C:Divides: F(2478782), GF(2478782,3), GF(2478776,6), GF(2478782,12)
+2478785;66628;T:G
-5082306;87449;C:Divides: GF(5082303,3), GF(5082305,5), GF(5082304,8), GF(5082305,11)
+5082306;87449;T:G;C:{{NWi|MP|4|2541153}}
-7033641;98959;C:Divides: GF(7033639,3)
+7033641;98959;T:G
-10829346;116922;C:Divides GF(10829343,3), GF(10829345,5),GF(10829344,8), GF(10829345,11)
+10829346;116922;T:G;C:{{NWi|MP|4|5414673}}
-|PRemarks=The {{OEIS|l|A002253}}
+16408818;131362;T:G;C:{{NWi|MP|4|8204409}}
+|PRemarks=The {{OEIS|l|A002253}}<br>See also {{NWi|PP|2|n}} & {{NWi|MP|4|n}}
 }}
+==History==
+{{HistF|2020-10-25|16408818|James Scott Brown,PrimeGrid 321 Prime Search|561613}} ([https://www.primegrid.com/download/321-16408818.pdf Official announcement])
+{{HistF|2012-01-14|10829346|Sai Yik Tang,PrimeGrid 321 Prime Search}} ([https://www.primegrid.com/download/321-10829346.pdf Official announcement])
+{{HistF|2011-02-21|7033641|Michael Herder,PrimeGrid 321 Prime Search}} ([https://www.primegrid.com/download/321-7033641.pdf Official announcement])
+{{HistF|2009-04-03|5082306|Andy Brady,PrimeGrid 321 Prime Search}} ([https://www.primegrid.com/download/321-5082306.pdf Official announcement])
+{{HistF|2008-08-11|2291610|Thomas Wolfram,PrimeGrid 321 Prime Search}} ([https://www.primegrid.com/download/321-2291610.pdf Official announcement])
+{{HistF|2007-07-27|1832496|Joseph Bohanon}}
+{{HistF|2005-09-02|801978|Keith P. Adney}}
+{{HistF|2005-05-21|709968|Keith P. Adney}}
+{{HistF|2003-10-14|2478785|John Cosgrave}}
+{{HistF|2003-02-25|2145353|John Cosgrave}}
+{{HistF|2002-07-30|362765|John Cosgrave}}
+{{HistF|2001-06-02|916773|John Cosgrave}}
+{{HistF|1999-07-23|382449|John Cosgrave}}
+{{HistF|1998-01|303093|Jeffrey Young}}
+{{HistF|1997-05|213321|Jeffrey Young}}
+{{HistF|1995-08|157169|Jeffrey Young}}
+{{HistF|1995-08|80190|Jeffrey Young}}
+{{HistF|1995-08|59973|Jeffrey Young}}
+{{HistF|1993-10|55182|Jeffrey Young}}
+{{HistF|1993-10-01|48150|Jeffrey Young}}
+{{HistF|1993|44685|Jeffrey Young}}
+{{HistF|1993|42665|Jeffrey Young}}
+{{HistF|1993-07-01|42294|Jeffrey Young}}
+{{HistF|1992-10|34350|Harvey Dubner}}
+{{HistF|1985|20909|Wilfrid Keller}}
+{{HistC|1979|1500-4000|Gordon V. Cormack,Hugh C. Williams}}
+{{HistF|1979|3912|Gordon V. Cormack,Hugh C. Williams}}
+{{HistF|1979|3189|Gordon V. Cormack,Hugh C. Williams}}
+{{HistF|1979|3168|Gordon V. Cormack,Hugh C. Williams}}
+{{HistF|1979|2816|Gordon V. Cormack,Hugh C. Williams}}
+{{HistF|1979|2208|Gordon V. Cormack,Hugh C. Williams}}

Difference between revisions of "Proth prime 2 3"

Latest revision as of 20:27, 26 September 2024

Current data

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History

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