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Difference between revisions of "Proth prime 2 9"
(add & correct history and release) |
(add Cullen primes) |
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| Line 4: | Line 4: | ||
|PCount=66 | |PCount=66 | ||
|PNash=2297 | |PNash=2297 | ||
| − | |PMaxn= | + | |PMaxn= |
| − | |PDate= | + | |PDate= |
|PReserved= | |PReserved= | ||
| − | |PMultiRes= | + | |PMultiRes=1 |
|PNlist= | |PNlist= | ||
1;T:T | 1;T:T | ||
2;T:G | 2;T:G | ||
| − | 3;T:GT | + | 3;T:GT;C:{{NWi|PP|8|1}} |
| − | 6;T:G | + | 6;T:G;C:{{NWi|PP|8|2}} |
7;T:GT | 7;T:GT | ||
11;T:G | 11;T:G | ||
14;T:G | 14;T:G | ||
17;T:G | 17;T:G | ||
| − | 33;T:G | + | 33;T:G;C:{{NWi|PP|8|11}} |
| − | 42;T:G | + | 42;T:G;C:{{NWi|PP|8|14}} |
43;T:GT | 43;T:GT | ||
| − | 63;T:GT | + | 63;T:GT;C:{{NCu|128|9}}, {{NWi|PP|8|21}} |
65;T:G | 65;T:G | ||
67;T:G | 67;T:G | ||
| − | 81;T:G | + | 81;T:G;C:{{NCu|512|9}}, {{NWi|PP|8|27}} |
134;T:G | 134;T:G | ||
| − | 162;T:G | + | 162;T:G;C:{{NWi|PP|8|54}} |
206;T:G | 206;T:G | ||
211;T:GT | 211;T:GT | ||
| − | 366;T:G | + | 366;T:G;C:{{NWi|PP|8|122}} |
| − | 663;T:G | + | 663;T:G;C:{{NWi|PP|8|221}} |
782;T:G | 782;T:G | ||
| − | 1305;T:G | + | 1305;T:G;C:{{NWi|PP|8|435}} |
1411;T:G | 1411;T:G | ||
| − | 1494;T:G | + | 1494;T:G;C:{{NWi|PP|8|498}} |
2297;T:G | 2297;T:G | ||
| − | 2826;T:G | + | 2826;T:G;C:{{NWi|PP|8|942}} |
3230;T:G | 3230;T:G | ||
| − | 3354;56509;T:G | + | 3354;56509;T:G;C:{{NWi|PP|8|1118}} |
| − | 3417;56001;T:G | + | 3417;56001;T:G;C:{{NWi|PP|8|1139}} |
| − | 3690;51936;T:G | + | 3690;51936;T:G;C:{{NWi|PP|8|1230}} |
| − | 4842;39625;T:G | + | 4842;39625;T:G;C:{{NWi|PP|8|1614}} |
| − | 5802;38118;T:G | + | 5802;38118;T:G;C:{{NWi|PP|8|1934}} |
6937;34858;T:G | 6937;34858;T:G | ||
7967;32237;T:G | 7967;32237;T:G | ||
| Line 48: | Line 48: | ||
22603;21686;T:G | 22603;21686;T:G | ||
24422;20432;T:G | 24422;20432;T:G | ||
| − | 39186;16396;T:G | + | 39186;16396;T:G;C:{{NWi|PP|8|13062}} |
43963;14381;T:G | 43963;14381;T:G | ||
47003;13256;T:G | 47003;13256;T:G | ||
| − | 49902;12820;T:G | + | 49902;12820;T:G;C:{{NWi|PP|8|16634}} |
67943;8517;T:G | 67943;8517;T:G | ||
114854;2840;T:G | 114854;2840;T:G | ||
| Line 59: | Line 59: | ||
149143;1305;T:G | 149143;1305;T:G | ||
304607;222;T:G | 304607;222;T:G | ||
| − | 384990;91;T:G | + | 384990;91;T:G;C:{{NWi|PP|8|128330}} |
412034;64729;T:G | 412034;64729;T:G | ||
435743;65451;T:G | 435743;65451;T:G | ||
461081;65770;T:G | 461081;65770;T:G | ||
| − | 834810;71697;T:G | + | 834810;71697;T:G;C:{{NWi|PP|8|278270}} |
| − | 1051026;72753;T:G | + | 1051026;72753;T:G;C:{{NWi|PP|8|350342}} |
1807574;100561;T:G | 1807574;100561;T:G | ||
2543551;100563;T:G | 2543551;100563;T:G | ||
| − | 3497442;109930;T:G | + | 3497442;109930;T:G;C:{{NWi|PP|8|1165814}} |
5642513;116472;T:G | 5642513;116472;T:G | ||
| − | 9778263;131055;T:G | + | 9778263;131055;T:G;C:{{NWi|PP|8|3259421}} |
11158963;130768;T:G | 11158963;130768;T:G | ||
| − | 11366286;130799;T:G | + | 11366286;130799;T:G;C:{{NWi|PP|8|3788762}} |
11500843;130770;T:G | 11500843;130770;T:G | ||
| − | 12406887;130801;T:G | + | 12406887;130801;T:G;C:{{NWi|PP|8|4135629}} |
| − | 13334487;130806;T:G | + | 13334487;130806;T:G;C:{{NWi|PP|8|4444829}} |
| − | |PRemarks=The {{OEIS|l|A002256}}<br> | + | |PRemarks=The {{OEIS|l|A002256}}<br>For all even {{Vn}}-values {{Kbn|+|9|2|n}} is a [[Generalized Fermat number]].<br>See also {{NWi|PP|8|n}} |
| − | For all even {{Vn}}-values {{Kbn|+|9|2|n}} is a [[Generalized Fermat number]].<br> | ||
| − | |||
}} | }} | ||
==History== | ==History== | ||
| + | {{HistR|2024-05-23|PrimeGrid Proth Prime Search|P#10194#172168}}, even {{Vn}}-values only | ||
{{HistC|2024-04-30|5000000|PrimeGrid Proth Prime Search}} | {{HistC|2024-04-30|5000000|PrimeGrid Proth Prime Search}} | ||
| − | {{HistC|2021-04-01|4000000-9000000|PrimeGrid Fermat Divisor Search|P#8778# | + | {{HistC|2021-04-01|4000000-9000000|PrimeGrid Fermat Divisor Search|P#8778#149792}}, odd {{Vn}}-values only |
{{HistF|2020-08-06|9778263|Ryan Propper}} | {{HistF|2020-08-06|9778263|Ryan Propper}} | ||
{{HistF|2020-03-31|13334487|Ryan Propper}} | {{HistF|2020-03-31|13334487|Ryan Propper}} | ||
| Line 88: | Line 87: | ||
{{HistF|2020-03-13|11500843|Ryan Propper}} | {{HistF|2020-03-13|11500843|Ryan Propper}} | ||
{{HistF|2020-03-13|11158963|Ryan Propper}} | {{HistF|2020-03-13|11158963|Ryan Propper}} | ||
| − | |||
{{HistF|2013-11-29|5642513|Serge Batalov}} | {{HistF|2013-11-29|5642513|Serge Batalov}} | ||
{{HistC|?|4000000|PrimeGrid Proth Prime Search}} | {{HistC|?|4000000|PrimeGrid Proth Prime Search}} | ||
| − | {{HistF|2012-10-24|3497442|Heinz Ming,PrimeGrid Proth | + | {{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|2543551|James Scott Brown,PrimeGrid Proth Prime Search}} ([http://www.primegrid.com/download/pps-F2543548.pdf Official announcement]) | {{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|2011-06-22|1807574|Reuben Gathright,PrimeGrid Proth Prime Search}} | ||
Latest revision as of 01:04, 27 September 2024
| Reserved! This sequence is currently part of Multi Reservation 1: PrimeGrid Proth Prime Search. |
Current data
|
|
Remarks : |
The sequence A002256 in OEIS For all even n-values 9•2n+1 is a Generalized Fermat number. See also Williams 9•8n+1 |
Notes
- ↑ Twin n=1
- ↑ Is GF Divisor of xGF(1,11,8)
- ↑ Is GF Divisor of xGF(2,7,3) [+3], Twin n=3, Williams 9•81+1
- ↑ Is GF Divisor of xGF(5,6,5) [+4], Williams 9•82+1
- ↑ 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], Williams 9•811+1
- ↑ Is GF Divisor of xGF(41,5,4) [+6], Williams 9•814+1
- ↑ Is GF Divisor of xGF(38,3,2) [+6], Twin n=43
- ↑ Is GF Divisor of GF(61,3) [+10], Twin n=63, Cullen 9•1289+1, Williams 9•821+1
- ↑ Is GF Divisor of GF(63,6) [+2]
- ↑ Is GF Divisor of F(63) [+19]
- ↑ Is GF Divisor of GF(79,3) [+9], Cullen 9•5129+1, Williams 9•827+1
- ↑ Is GF Divisor of xGF(132,8,7) [+2]
- ↑ Is GF Divisor of GF(158,3) [+7], Williams 9•854+1
- ↑ 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], Williams 9•8122+1
- ↑ Is GF Divisor of xGF(662,5,3) [+3], Williams 9•8221+1
- ↑ Is GF Divisor of xGF(781,6,5) [+4]
- ↑ Is GF Divisor of GF(1303,3) [+2], Williams 9•8435+1
- ↑ Is GF Divisor of xGF(1409,3,2) [+1]
- ↑ Is GF Divisor of GF(1488,3) [+1], Williams 9•8498+1
- ↑ Is GF Divisor of GF(2294,6) [+3]
- ↑ Is GF Divisor of GF(2822,3) [+7], Williams 9•8942+1
- ↑ Is GF Divisor of xGF(3229,7,5) [+4]
- ↑ Is GF Divisor of GF(3353,7) [+4], Williams 9•81118+1
- ↑ Is GF Divisor of xGF(3408,5,3) [+5], Williams 9•81139+1
- ↑ Is GF Divisor of GF(3684,3) [+5], Williams 9•81230+1
- ↑ Is GF Divisor of GF(4838,3) [+7], Williams 9•81614+1
- ↑ Is GF Divisor of xGF(5801,8,7) [+6], Williams 9•81934+1
- ↑ 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], Williams 9•813062+1
- ↑ 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], Williams 9•816634+1
- ↑ 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], Williams 9•8128330+1
- ↑ 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], Williams 9•8278270+1
- ↑ Is GF Divisor of xGF(1051025,8,7) [+4], Williams 9•8350342+1
- ↑ Is GF Divisor of xGF(1807570,4,3) [+2]
- ↑ Is GF Divisor of F(2543548) [+16]
- ↑ Is GF Divisor of GF(3497441,7) [+5], Williams 9•81165814+1
- ↑ Is GF Divisor of xGF(5642511,5,3) [+3]
- ↑ Is GF Divisor of xGF(9778262,6,5) [+4], Williams 9•83259421+1
- ↑ Is GF Divisor of xGF(11158961,3,2) [+5]
- ↑ Is GF Divisor of xGF(11366285,7,4) [+6], Williams 9•83788762+1
- ↑ Is GF Divisor of xGF(11500842,5,3) [+4]
- ↑ Is GF Divisor of GF(12406885,3) [+3], Williams 9•84135629+1
- ↑ Is GF Divisor of GF(13334485,3) [+6], Williams 9•84444829+1
History
- 2024-05-23: Reserved by PrimeGrid Proth Prime Search, even n-values only
- 2024-04-30: Checked to n = 5000000, PrimeGrid Proth Prime Search
- 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
