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Difference between revisions of "Proth prime 2 3"

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{{Proth prime
 
{{Proth prime
 
|Pk=3
 
|Pk=3
 +
|Pb=2
 
|PCount=50
 
|PCount=50
 
|PNash=2132
 
|PNash=2132
Line 8: Line 9:
 
|PMultiRes=22
 
|PMultiRes=22
 
|PNlist=
 
|PNlist=
−
1;T:T
+
1;T:GT
−
2;T:GT
+
2;T:GT;C:{{NCu|+|2|2}}, {{NWi|MP|4|1}}
 
5;T:G
 
5;T:G
−
6;T:GT
+
6;T:GT;C:{{NCu|4|3}}, {{NCu|+|2|5}}, {{NWi|MP|4|3}}
−
8;T:G
+
8;T:G;C:{{NCu|-|2|7}}, {{NWi|MP|4|4}}
−
12;T:G
+
12;T:G;C:{{NCu|16|3}}, {{NWi|MP|4|6}}
−
18;T:GT
+
18;T:GT;C:{{NCu|64|3}}, {{NWi|MP|4|9}}
−
30;T:G
+
30;T:G;C:{{NCu|1024|3}}, {{NWi|MP|4|15}}
−
36;T:G
+
36;T:G;C:{{NCu|4096|3}}, {{NWi|MP|4|18}}
 
41;T:G
 
41;T:G
−
66;T:G
+
66;T:G;C:{{NWi|MP|4|33}}
 
189;T:G
 
189;T:G
 
201;T:G
 
201;T:G
 
209;T:G
 
209;T:G
−
276;C:Divides: GF(271,3)
+
276;T:G;C:{{NWi|MP|4|138}}
−
353;C:Divides: GF(351,12)
+
353;T:G
−
408;C:Divides: GF(403,3), GF(406,5)
+
408;T:G;C:{{NWi|MP|4|204}}
−
438;C:Divides: GF(435,3)
+
438;T:G;C:{{NWi|MP|4|219}}
−
534;C:Divides: GF(531,3)
+
534;T:G;C:{{NWi|MP|4|267}}
−
2208;C:Divides: GF(2197,3), GF(2206,5)
+
2208;T:G;C:{{NWi|MP|4|1104}}
−
2816;C:Divides: GF(2804,5), GF(2811,12)
+
2816;T:G;C:{{NWi|MP|4|1408}}
−
3168;C:Divides: GF(3160,3), GF(3162,5)
+
3168;T:G;C:{{NWi|MP|4|1584}}
−
3189;C:Divides: GF(3187,3)
+
3189;T:G
−
3912;48357;C:Divides: GF(3906,3), GF(3910,5)
+
3912;48357;T:G;C:{{NWi|MP|4|1956}}
−
20909;22329;C:Divides: GF(20908,5), GF(20906,12)
+
20909;22329;T:G
−
34350;17264;C:Divides: GF(34346,3)
+
34350;17264;T:G;C:{{NWi|MP|4|17175}}
−
42294;14919;C:Divides: GF(42290,3)
+
42294;14919;T:G;C:{{NWi|MP|4|21147}}
−
42665;14813;C:Divides: GF(42663,12)
+
42665;14813;T:G
−
44685;14049;C:Divides: GF(44683,3), GF(44684,10)
+
44685;14049;T:G
−
48150;13029;C:Divides: GF(48146,3)
+
48150;13029;T:G;C:{{NWi|MP|4|24075}}
−
54792;C:Divides: GF(54787,3), GF(54786,5)
+
54792;T:G;C:{{NWi|MP|4|27396}}
−
55182;11285;C:Divides: GF(55178,3)
+
55182;11285;T:G;C:{{NWi|MP|4|27591}}
−
59973;10729;C:Divides: GF(59970,3), GF(59972,5)
+
59973;10729;T:G
−
80190;7057;C:Divides: GF(80187,3)
+
80190;7057;T:G;C:{{NWi|MP|4|40095}}
−
157169;1180;C:Divides: F(157167), GF(157167,3), GF(157168,5), GF(157163,6), GF(157168,10), GF(157167,12)
+
157169;1180;T:G
−
213321;401;C:Divides: F(213319), GF(213319,5), GF(213316,6), GF(213319,12)
+
213321;401;T:G
−
303093;223;C:Divides: F(303088), GF(303088,3), GF(303092,5), GF(303086,6), GF(303092,10), GF(303088,12)
+
303093;223;T:G
−
362765;101;C:Divides: GF(362764,10), GF(362763,12)
+
362765;101;T:G
−
382449;94;C:Divides: F(382447), GF(382447,3), GF(382443,6), GF(382447,12)
+
382449;94;T:G
−
709968;74546;C:Divides: GF(709962,3), GF(709963,5)
+
709968;74546;T:G;C:{{NWi|MP|4|354984}}
−
801978;75498;C:Divides: GF(801973,3), GF(801977,5)
+
801978;75498;T:G;C:{{NWi|MP|4|400989}}
−
916773;22;C:Divides: GF(916771,3) GF(916772,10)
+
916773;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}}
−
16408818;131362;T:G
+
16408818;131362;T:G;C:{{NWi|MP|4|8204409}}
−
|PRemarks=The {{OEIS|l|A002253}}
+
|PRemarks=The {{OEIS|l|A002253}}<br>See also {{NWi|PP|2|n}} & {{NWi|MP|4|n}}
 
}}
 
}}
−
 
 
==History==
 
==History==
−
{{HistF|2020-10-28|16408818|James Scott Brown, PrimeGrid|561613}}
+
{{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}}

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

  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•41145805+1
  46. ↑ Is GF Divisor of F(2478782) [+9]
  47. ↑ Is GF Divisor of GF(5082303,3) [+14], Williams 3•42541153+1
  48. ↑ Is GF Divisor of GF(7033639,3) [+12]
  49. ↑ Is GF Divisor of GF(10829343,3) [+14], Williams 3•45414673+1
  50. ↑ Is GF Divisor of GF(16408814,3) [+12], Williams 3•48204409+1

History

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