Difference between revisions of "Proth prime 2 13"

Latest revision as of 01:14, 27 September 2024

Current data

`k` , `b` :	13 , 2
Type :	Low
Count :	28
Nash :	920
Max `n` :	9,000,000
Date :	2023-10-11

2^[1], 8^[2], 10^[3], 20^[4], 28^[5], 82^[6], 188^[7], 308^[8], 316^[9], 1000^[10], 28280^[11], 38008^[12], 43856^[13], 88018^[14], 109258^[15], 114296^[16], 521306^[17], 562456^[18], 684560^[19], 1038896^[20], 1499876^[21], 1861732^[22], 4998362^[23], 5523860^[24], 6481780^[25], 8989858^[26], 15294536^[27], 16828072^[28]

Remarks :

The sequence A032356 in OEIS

Notes

↑ Is GF Divisor of xGF(1,12,11)
↑ Is GF Divisor of xGF(7,6,5) [+2]
↑ Is GF Divisor of GF(9,7) [+2]
↑ Is GF Divisor of F(18) [+8]
↑ Is GF Divisor of xGF(27,5,3) [+2], Near Cullen 26•2²⁷+1
↑ Is GF Divisor of GF(81,10)
↑ Is GF Divisor of xGF(187,5,3) [+6]
↑ Is GF Divisor of GF(307,12)
↑ Is GF Divisor of xGF(315,6,5) [+1]
↑ Is GF Divisor of GF(999,3) [+3]
↑ Is GF Divisor of xGF(28278,9,2)
↑ Is GF Divisor of xGF(38005,7,6) [+2]
↑ Is GF Divisor of xGF(43853,5,4) [+2]
↑ Is GF Divisor of xGF(88017,11,4) [+1]
↑ Is GF Divisor of xGF(109256,5,3) [+2]
↑ Is GF Divisor of F(114293) [+5]
↑ Is GF Divisor of xGF(521305,4,3) [+1]
↑ Is GF Divisor of GF(562454,5) [+1]
↑ Is GF Divisor of xGF(684559,5,3) [+5]
↑ Is GF Divisor of xGF(1038895,5,3) [+1]
↑ Is GF Divisor of GF(1499875,3) [+5]
↑ Is GF Divisor of GF(1861731,6) [+2]
↑ Is GF Divisor of xGF(4998361,5,2) [+2]
↑ Is GF Divisor of F(5523858) [+6]
↑ Is GF Divisor of xGF(6481774,5,2) [+5]
↑ Is GF Divisor of xGF(8989854,6,5) [+3]
↑ Is GF Divisor of xGF(15294533,9,2) [+1]
↑ Is GF Divisor of xGF(16828071,7,2) [+4]

History

2023-10-11: Found n = 16828072, Ryan Propper
2023-09-30: Found n = 15294536, Ryan Propper
2021-04-01: Checked to n = 9000000, PrimeGrid Fermat Divisor Search
2020-03-10: Found n = 8989858, Ryan Propper
2020-03-09: Found n = 6481780, Ryan Propper
2020-01-22: Found n = 5523860, James Scott Brown, PrimeGrid Fermat Divisor Search (Official announcement)
2019-07: Checked n = 3322000 - 3640000, PrimeGrid Proth Mega Prime Search
2014-07-15: Found n = 4998362, Mark Rodenkirch
2005-11-14: Found n = 1861732, Peter Grobstich
2004-12-30: Found n = 1499876, Peter Grobstich
2004-01-21: Found n = 1038896, Peter Grobstich
2003-07-01: Found n = 684560, Peter Grobstich
2003-06-10: Found n = 562456, Peter Grobstich
2003-05-14: Found n = 521306, Peter Grobstich
1995-08: Found n = 114296, Jeffrey Young
1995-08: Found n = 109258, Jeffrey Young
1995-08: Found n = 88018, Jeffrey Young
1993-05: Found n = 43856, Jeffrey Young
1992: Found n = 38008, Harvey Dubner
1992-10: Found n = 28280, Harvey Dubner
1979: Checked n = 1500 - 4000, Gordon V. Cormack, Hugh C. Williams
1886: Found n = 28, Paul Seelhoff
1886: Found n = 20, Paul Seelhoff

[1] Is GF Divisor of xGF(1,12,11)

[2] Is GF Divisor of xGF(7,6,5) [+2]

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

[4] Is GF Divisor of F(18) [+8]

[5] Is GF Divisor of xGF(27,5,3) [+2], Near Cullen 26•2²⁷+1

[6] Is GF Divisor of GF(81,10)

[7] Is GF Divisor of xGF(187,5,3) [+6]

[8] Is GF Divisor of GF(307,12)

[9] Is GF Divisor of xGF(315,6,5) [+1]

[10] Is GF Divisor of GF(999,3) [+3]

[11] Is GF Divisor of xGF(28278,9,2)

[12] Is GF Divisor of xGF(38005,7,6) [+2]

[13] Is GF Divisor of xGF(43853,5,4) [+2]

[14] Is GF Divisor of xGF(88017,11,4) [+1]

[15] Is GF Divisor of xGF(109256,5,3) [+2]

[16] Is GF Divisor of F(114293) [+5]

[17] Is GF Divisor of xGF(521305,4,3) [+1]

[18] Is GF Divisor of GF(562454,5) [+1]

[19] Is GF Divisor of xGF(684559,5,3) [+5]

[20] Is GF Divisor of xGF(1038895,5,3) [+1]

[21] Is GF Divisor of GF(1499875,3) [+5]

[22] Is GF Divisor of GF(1861731,6) [+2]

[23] Is GF Divisor of xGF(4998361,5,2) [+2]

[24] Is GF Divisor of F(5523858) [+6]

[25] Is GF Divisor of xGF(6481774,5,2) [+5]

[26] Is GF Divisor of xGF(8989854,6,5) [+3]

[27] Is GF Divisor of xGF(15294533,9,2) [+1]

[28] Is GF Divisor of xGF(16828071,7,2) [+4]

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

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[18]

[19]

[20]

[21]

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@@ Line 1: / Line 1: @@
 {{Proth prime
 |Pk=13
-|PCount=26
+|Pb=2
+|PCount=28
 |PNash=920
-|PMaxn=3100000
+|PMaxn=9000000
-|PDate=2009-02-11
+|PDate=2023-10-11
 |PReserved=
+|PMultiRes=
 |PNlist=
+;T:G
+;T:G
+;T:G
+;T:G
+;T:G;C:{{NCu|-|2|27}}
+;T:G
+;T:G
+;T:G
+;T:G
+;T:G
-;19086
+;19086;T:G
-;16653;C:Divides: {{DGF|10|38005}}
+;16653;T:G
-;14422
+;14422;T:G
-;6349
+;6349;T:G
-;3034
+;3034;T:G
-;2855;C:Divides: {{DGF|114293}}, {{DGF|5|114292}}, {{DGF|10|114293}}
+;2855;T:G
-;64694
+;64694;T:G
-;65036;C:Divides: {{DGF|5|562454}}
+;65036;T:G
-;65345;C:Divides: {{DGF|10|684557}}, {{DGF|6|684559}}
+;65345;T:G
-1038896;68465
+1038896;68465;T:G
-1499876;72917;C:Divides: {{DGF|3|1499875}}
+1499876;72917;T:G
-1861732;76172;C:Divides: {{DGF|6|1861731}}
+1861732;76172;T:G
-4998362;118181
+4998362;118181;T:G
-5523860;130274;C:Divides: {{DGF|5523858}}, {{DGF|11|5523856}}
+5523860;130274;T:G
-6481780;130749
+6481780;130749;T:G
-8989858;130753
+8989858;130753;T:G
-|PRemarks=
+15294536;136486;T:G
+16828072;136522;T:G
+|PRemarks=The {{OEIS|l|A032356}}
 }}
 ==History==
+{{HistF|2023-10-11|16828072|Ryan Propper}}
+{{HistF|2023-09-30|15294536|Ryan Propper}}
+{{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
 {{HistF|2020-03-10|8989858|Ryan Propper}}
 {{HistF|2020-03-09|6481780|Ryan Propper}}
-{{HistF|2020-01-22|5523860|James Scott Brown}}, [http://www.primegrid.com/download/DIV-F5523858.pdf Official announcement]
+{{HistF|2020-01-22|5523860|James Scott Brown,PrimeGrid Fermat Divisor Search}} ([http://www.primegrid.com/download/DIV-F5523858.pdf Official announcement])
+{{HistC|2019-07|3322000-3640000|PrimeGrid Proth Mega Prime Search}}
 {{HistF|2014-07-15|4998362|Mark Rodenkirch}}
 {{HistF|2005-11-14|1861732|Peter Grobstich}}
@@ Line 52: / Line 60: @@
 {{HistF|1992|38008|Harvey Dubner}}
 {{HistF|1992-10|28280|Harvey Dubner}}
+{{HistC|1979|1500-4000|Gordon V. Cormack,Hugh C. Williams}}
+{{HistF|1886|28|Paul Seelhoff}}
+{{HistF|1886|20|Paul Seelhoff}}

Difference between revisions of "Proth prime 2 13"

Latest revision as of 01:14, 27 September 2024

Current data

Notes

History

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