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Proth primes of the form 27•2n+1

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Current data

k , b : 27 , 2
Type : 3
Count : 49
Nash : 2142
Max n : 10,000,000
Date : 2024-05-23
2[1], 4[2], 7, 16, 19[3], 20[4], 22[5], 26[6], 40[7], 44[8], 46[9], 47[10], 50[11], 56[12], 59[13], 64[14], 92, 175, 215[15], 275[16], 407[17], 455[18], 1076[19], 1090[20], 3080[21], 3322, 6419[22], 7639[23], 19360, 30500[24], 38770[25], 44164[26], 50696[27], 114760[28], 117784[29], 153847[30], 160874[31], 178739[32], 379880[33], 405514[34], 672007[35], 974752[36], 1164664[37], 1476347[38], 2218064[39], 5213635[40], 7046834[41], 7963247[42], 12184319[43]
Remarks :
The sequence A032363 in OEIS

PrimeGrid Proth Prime Search is double-checking n>5000000 even n.

Notes

  1. Twin n=2
  2. Is GF Divisor of xGF(2,11,3), Twin n=4
  3. Is GF Divisor of GF(18,5)
  4. Is GF Divisor of xGF(17,11,5)
  5. Is GF Divisor of xGF(20,9,5)
  6. Is GF Divisor of xGF(24,5,3) [+1], Near Cullen 27•226+1
  7. Is GF Divisor of xGF(39,10,9) [+1]
  8. Is GF Divisor of xGF(43,12,5)
  9. Is GF Divisor of xGF(43,9,5)
  10. Is GF Divisor of GF(45,8) [+1]
  11. Is GF Divisor of xGF(49,11,10)
  12. Is GF Divisor of xGF(55,7,5) [+3], Near Cullen 54•255+1
  13. Is GF Divisor of xGF(56,7,4) [+1]
  14. Is GF Divisor of xGF(62,7,5) [+2]
  15. Is GF Divisor of xGF(214,10,3) [+2]
  16. Is GF Divisor of xGF(274,6,5)
  17. Is GF Divisor of GF(405,7) [+1]
  18. Is GF Divisor of F(452)
  19. Is GF Divisor of xGF(1073,9,7) [+1]
  20. Is GF Divisor of xGF(1089,7,6) [+2]
  21. Is GF Divisor of xGF(3079,11,3)
  22. Is GF Divisor of xGF(6416,11,6) [+1]
  23. Is GF Divisor of xGF(7638,8,5)
  24. Is GF Divisor of xGF(30499,10,3) [+1]
  25. Is GF Divisor of xGF(38769,11,10)
  26. Is GF Divisor of xGF(44161,11,6)
  27. Is GF Divisor of GF(50695,11)
  28. Is GF Divisor of xGF(114759,9,7)
  29. Is GF Divisor of xGF(117783,9,7)
  30. Is GF Divisor of xGF(153844,10,7)
  31. Is GF Divisor of xGF(160869,11,3) [+1]
  32. Is GF Divisor of xGF(178738,5,2) [+3]
  33. Is GF Divisor of xGF(379879,10,7)
  34. Is GF Divisor of xGF(405513,7,5) [+3]
  35. Is GF Divisor of F(672005) [+7]
  36. Is GF Divisor of xGF(974749,7,5) [+1]
  37. Is GF Divisor of xGF(1164663,9,7)
  38. Is GF Divisor of xGF(1476345,11,3)
  39. Is GF Divisor of xGF(2218063,9,5) [+1]
  40. Is GF Divisor of xGF(5213634,7,6) [+1]
  41. Is GF Divisor of xGF(7046830,10,3) [+1]
  42. Is GF Divisor of F(7963245)
  43. Is GF Divisor of GF(12184313,8) [+1]

History