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(+1)
(add Cullen & near Cullen primes)
 
(7 intermediate revisions by 3 users not shown)
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{{Proth prime
 
{{Proth prime
 
|Pk=33
 
|Pk=33
 +
|Pb=2
 
|PCount=41
 
|PCount=41
 
|PNash=1960
 
|PNash=1960
Line 9: Line 10:
 
|PNlist=
 
|PNlist=
 
1
 
1
−
6;T:T
+
6;T:GT
−
13
+
13;T:G
−
18
+
18;T:G
−
21
+
21;T:G
−
22;T:T
+
22;T:GT
−
25
+
25;T:G;C:{{NWi|PP|32|5}}
−
28
+
28;T:G
−
66
+
66;T:G;C:{{NCu|4|33}}, {{NCu|+|2|65}}
−
93
+
93;T:G
−
118
+
118;T:G
−
289
+
289;T:G
−
412
+
412;T:G
−
453
+
453;T:G
−
525
+
525;C:{{NWi|PP|32|105}}
−
726
+
726;T:G
−
828
+
828;T:G
−
1420
+
1420;T:G;C:{{NWi|PP|32|284}}
−
1630
+
1630;T:G;C:{{NWi|PP|32|326}}
−
3076
+
3076;T:G
−
3118
+
3118;T:G
 
4452;41459
 
4452;41459
−
4941;39293
+
4941;39293;T:G
−
5236;38702
+
5236;38702;T:G
−
6346;37553
+
6346;37553;T:G
−
9133;30058
+
9133;30058;T:G
−
13401;27310
+
13401;27310;T:G
−
14214;27002
+
14214;27002;T:G
−
18766;23308
+
18766;23308;T:G
−
37249;16821
+
37249;16821;T:G
−
42685;14805
+
42685;14805;T:G;C:{{NWi|PP|32|8537}}
−
47805;13151
+
47805;13151;T:G;C:{{NWi|PP|32|9561}}
−
61372;10083
+
61372;10083;T:G
−
74178;8033
+
74178;8033;T:G
−
600270;75126
+
600270;75126;T:G;C:{{NWi|PP|32|120054}}
−
922782;77104
+
922782;77104;T:G
−
1130884;78090
+
1130884;78090;T:G
−
2345001;113291
+
2345001;113291;T:G
 
3176269;116701
 
3176269;116701
−
3570132;118003;C:Divides {{DGF|3570131|7}}, {{DGF|3570129|5|4}}, {{DGF|3570129|11|6}}
+
3570132;118003;T:G
−
3649810;129931;C:Divides {{DGF|3649809|5|2}}
+
3649810;129931;T:G;C:{{NWi|PP|32|729962}}
−
|PRemarks=
+
|PRemarks=The {{OEIS|l|A032366}}<br>See also {{NWi|PP|32|n}}
 
}}
 
}}
 
==History==
 
==History==
 
{{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
 
{{HistC|2021-04-01|9000000|PrimeGrid Fermat Divisor Search}}
−
{{HistF|2019-09-16|3649810|Kellen Shenton, PrimeGrid Fermat Divisor Search}}
+
{{HistF|2019-09-16|3649810|Kellen Shenton,PrimeGrid Fermat Divisor Search}}
 +
{{HistC|2019-07|3322000-3640000|PrimeGrid Proth Mega Prime Search}}
 +
{{HistF|2014-06-11|3570132|Fabrice Le Foulher,PrimeGrid Proth Mega Prime Search}} ([https://www.primegrid.com/download/mega-3570132.pdf Official announcement])
 +
{{HistF|2013-12-23|3176269|Serge Batalov}}
 +
{{HistF|2013-04-13|2345001|Mariusz Szafrański}}
 +
{{HistF|2006-07-07|1130884|Reto Keiser}}
 +
{{HistF|2006-02-19|922782|Reto Keiser}}
 +
{{HistF|2005-07-20|600270|Reto Keiser}}
 +
{{HistF|1998-06-26|74178|Aaron Swihart}}
 +
{{HistF|1997-05-01|61372|Patrick Demichel}}
 +
{{HistF|1995-08|47805|Jeffrey Young}}
 +
{{HistF|1995-08|42685|Jeffrey Young}}
 +
{{HistF|1993|37249|Jeffrey Young}}
 +
{{HistF|1993-10-01|18766|Harvey Dubner}}
 +
{{HistF|1993-10-01|14214|Harvey Dubner}}
 +
{{HistF|1993-10-01|13401|Harvey Dubner}}
 +
{{HistF|1986|9133|Wilfrid Keller}}
 +
{{HistF|1983|6346|Wilfrid Keller}}
 +
{{HistF|1983|5236|Wilfrid Keller}}
 +
{{HistF|1983|4941|Wilfrid Keller}}
 +
{{HistF|1983|4452|Wilfrid Keller}}

Latest revision as of 01:56, 27 September 2024

Current data

k , b : 33 , 2
Type : 3
Count : 41
Nash : 1960
Max n : 9,000,000
Date : 2021-04-01
1, 6[1], 13[2], 18[3], 21[4], 22[5], 25[6], 28[7], 66[8], 93[9], 118[10], 289[11], 412[12], 453[13], 525[14], 726[15], 828[16], 1420[17], 1630[18], 3076[19], 3118[20], 4452, 4941[21], 5236[22], 6346[23], 9133[24], 13401[25], 14214[26], 18766[27], 37249[28], 42685[29], 47805[30], 61372[31], 74178[32], 600270[33], 922782[34], 1130884[35], 2345001[36], 3176269, 3570132[37], 3649810[38]
Remarks :
The sequence A032366 in OEIS
See also Williams 33•32n+1

Notes

  1. ↑ Is GF Divisor of xGF(5,11,5), Twin n=6
  2. ↑ Is GF Divisor of xGF(12,6,5)
  3. ↑ Is GF Divisor of xGF(17,10,9)
  4. ↑ Is GF Divisor of xGF(20,6,5) [+1]
  5. ↑ Is GF Divisor of xGF(21,10,9) [+2], Twin n=22
  6. ↑ Is GF Divisor of GF(23,8) [+1], Williams 33•325+1
  7. ↑ Is GF Divisor of xGF(26,5,3)
  8. ↑ Is GF Divisor of GF(65,5) [+2], Cullen 33•433+1, Near Cullen 66•265+1
  9. ↑ Is GF Divisor of xGF(92,6,5)
  10. ↑ Is GF Divisor of xGF(114,11,9)
  11. ↑ Is GF Divisor of GF(288,5)
  12. ↑ Is GF Divisor of xGF(410,7,4)
  13. ↑ Is GF Divisor of xGF(452,5,4) [+1]
  14. ↑ Williams 33•32105+1
  15. ↑ Is GF Divisor of xGF(721,10,7)
  16. ↑ Is GF Divisor of GF(826,5) [+1]
  17. ↑ Is GF Divisor of GF(1418,7) [+1], Williams 33•32284+1
  18. ↑ Is GF Divisor of xGF(1629,8,5) [+1], Williams 33•32326+1
  19. ↑ Is GF Divisor of xGF(3072,5,2) [+3]
  20. ↑ Is GF Divisor of GF(3116,7) [+3]
  21. ↑ Is GF Divisor of xGF(4940,11,5)
  22. ↑ Is GF Divisor of xGF(5229,9,7)
  23. ↑ Is GF Divisor of GF(6341,6)
  24. ↑ Is GF Divisor of xGF(9130,3,2)
  25. ↑ Is GF Divisor of GF(13399,8)
  26. ↑ Is GF Divisor of xGF(14212,3,2)
  27. ↑ Is GF Divisor of F(18757) [+5]
  28. ↑ Is GF Divisor of GF(37248,5) [+2]
  29. ↑ Is GF Divisor of xGF(42683,4,3), Williams 33•328537+1
  30. ↑ Is GF Divisor of xGF(47804,11,7), Williams 33•329561+1
  31. ↑ Is GF Divisor of GF(61369,8) [+1]
  32. ↑ Is GF Divisor of xGF(74175,11,4)
  33. ↑ Is GF Divisor of GF(600269,5) [+1], Williams 33•32120054+1
  34. ↑ Is GF Divisor of xGF(922779,7,5) [+3]
  35. ↑ Is GF Divisor of GF(1130881,12)
  36. ↑ Is GF Divisor of xGF(2345000,7,2)
  37. ↑ Is GF Divisor of xGF(3570129,5,4) [+2]
  38. ↑ Is GF Divisor of xGF(3649809,5,2), Williams 33•32729962+1

History

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