The 15 is here numbers

Introduction

Since Googology Wiki turned 15 years old recently, I decided to coin numbers based on number 15 and some multiples of 15 numbers (30, 45, 60, 75, 90, etc.) here.

Note: f_x(n) is fast-growing hierarchy. Wainer hierarchy, Veblen function, Buchholz's psi function is used in FGH.

All BMS numbers are defined with respect to version 4, simulating Hardy hierarchy.

This list only consists of 105 numbers.

Update 2024-12-05: Googology Wiki is now 16 years old. So, I will do a sequel based on 16 and other powers of 16 (namely: Crystal Papers series).

Update 2025-03-02: Fixed googolism number 72, "The other side of zeraphine array".

Update 2025-03-20: Fixed googolism number 100, The even deeper side of zeraphine array, as the array is not fully well defined.

Numbers in this series

1. First emirpimes / emirpimes dozen = 15

2. Quindecimal-zeralum = f_0(15) = 16

3. added emirpimes dozen / quindecimal-unalum = 15+15 = f_1(15) = 30

4. multiplied emirpimes dozen / garfifteen = 15*15 = 15^2 = 225

5. The optimism fifteen / trarfifteen = 15^3 = 3375

6. Quindecimal-balum = f_2(15) = 15*2^15 = 491,520

7. Fifteenbang = 15! = 1,307,674,368,000

8. Quadrillion (short scale) = 10^15

9. Emirpimes dozen powered itself / quindecimal-small-fry / fzfifteen = 15^15 = 437,893,890,380,859,375

10. Googoxvy = 30^15 = 1.4348907*10^22

11. quindecimal-googol = 15^100

12. Fifteendubang = (15!)! = 1,307,674,368,000!

13. Googoxvyplexvy = 15^30^15 ~ 10^1.4348907*10^22

14. quindecimal-googolplex = 15^15^100

15. fifteen-expobang = 15!1, in Hyperfactorial array notation

16. Quindecimal-tralum / quindecargum-tralum = f_3(15)

17. quindecimal-giggol = 15^^100

18. quindecimal-grangol = E[15]100#100 in Hyper-E

19. fifteen-tetrobang = 15!2, in Hyperfactorial array notation

20. Quindecimal-quadralum = f_4(15)

21. quindecimal-gaggol = 15^^^100

22. Quindecimal-quintalum = f_5(15)

23. Quindecimal-sextalum = f_6(15)

24. Quindecimal-zeraddom = f_ω(15)

25. triquindecal / triple M = {15,15,15}

26. fifteen-hyperbang = 15![1] in Hyperfactorial array notation

27. quindecimal-boogol = {15,15,100}

28. quindecimal-gugold = E[15]100##100 in Extended Hyper-E

29. Quindecimal-unaddom = f_(ω+1)(15)

30. Quindecimal-baddom = f_(ω+2)(15)

31. Quindecimal-bultom = f_(ω2)(15)

32. Quindecinet = 15(15)(15)15 using Hayden's Array Notation

33. Quindecimal-bexom = f_(ω^2)(15)

34. tetraquindecal = {15,15,15,15} in BEAF

35. quindecimal-throogol = E[15]100###100 in Extended Hyper-E

36. Getting the quinze dip = E[15]150###15###15###15 (in Extended Hyper-E)

37. Kjoy qrvvlfjkg = E[15]225###225###100##100##46 (in Extended Hyper-E)

38. zophora quindecinet = 15(10)(10)(15)15 using Hayden's Array Notation

39. Quindecimal-trexom = f_(ω^3)(15)

40. pentaquindecal = {15,15,15,15,15} in BEAF

41. luzophora quindecinet = 15(15)(15)(15)15 using Hayden's Array Notation

42. Quindecimal-quadrexom = f_(ω^4)(15)

43. sazophora quindecinet = 15(15)(15)(15)(15)15 using Hayden's Array Notation

44. A delightful thought = {75,90,75,60,45,30,15} in BEAF

45. septophora quindecinet = 15(15)(15)(15)(15)(15)15 using Hayden's Array Notation

46. superquindecal = {15,15,15,15,15,15,15,15,15,15,15,15,15,15,15}, 15 & 15 in BEAF

47. Quindecimal-bitetrom = f_(ω^ω)(15)

48. Quindecimal-unaddom-exom = f_(ω^(ω+1))(15)

49. Sevastopols in lot = (0)(1)(2)(3)(4)(1)(2)(3)[15] in BMS v4

50. Lash collect = f_(ω^(ω+15 * 14))(15)

51. Quindecimal-bultom-exom = f_(ω^(ω2))(15)

52. Quindecimal-bexom-exom / quindecimal-bex-bitetrom = f_(ω^(ω^2))(15)

53. Quindecimal-trexom-exom = f_(ω^(ω^3))(15)

54. Quindecimal-tritetrom = f_(ω^ω^ω)(15)

55. zeraphine = E15#^#^#####150 in Cascading-E notation

56. Toplining fifteens = {15,15 (90,90,90,90) 2} in BEAF

57. Quindecimal-quadritetrom = f_(ω^ω^ω^ω)(15)

58. Quindecimal-quintitetrom = f_(ω^^5)(15)

59. Quindecimal-sextitetrom = f_(ω^^6)(15)

60. Quindecimal-zeraddep = f_(ε_0)(15)

61. Leive it up = E15#^^#*#^##*##15 in Extended Cascading-E notation

62. Locked out in 15: {15,15[1\15,30]3} in Bird's array notation

63. Quindecimal-quattuordecinep = f_(zeta_0)(15)

64. seraph zeraphine = E15#^^##*#^####150 in Extended Cascading-E notation

65. Locked out more in 15: {15,15[1\15\30]3} in Bird's array notation

66. Quindecimal-quattuordecinzet = f_(eta_0)(15)

67. Sevastopols in more = (0,0)(1,1)(2,1)(2,0)(2,1)[15] in BMS v4

68. The other side of array = {15,15[1\2\3\4]5} in Bird's array notation

69. Quindecimal-quattuordecinet = f_(varphi(4,0))(15) in FGH using Veblen hierarchy

70. Quindecimal-zeraddomphi = f_(varphi(omega,0))(15) in FGH using Veblen hierarchy

71. Saraph zeraphine = E15#^^#^#*#^#^#^##150 in Extended Cascading-E notation

72. The other side of zeraphine array = {15,15[1[3¬2]2]5} in Bird's array notation (modified Hierarchial Hyper Nested Array Notation)

73. Try it here = 15[1{1/15}2]15 in DeepLineMadom's array notation

74. Quindecimal-zeraddgam = f_(Gamma_0)(15) in FGH (or f_(varphi(1,0,0))(15) using extended Veblen hierarchy)

75. More zeraphine = E15#^^^##*#^^##*##150 in Extended Cascading-E notation

76. Quindecimal-zeraddomtriphi = f_(varphi(omega,0,0))(15) in FGH using extended Veblen hierarchy

77. Colossal zeraphine = E15#{#}##*#^^##*##150 in Hyper Extended Cascading-E notation

78. Quindecimal-bexommthet = f_(theta(Omega^2)(15) in FGH using Feferman's theta function (or f_(varphi(1,0,0,0))(15) using extended Veblen hierarchy, f_(psi_0(Omega^Omega^2)(15) using Buchholz's psi function)

79. Ludicrously colossal ludicriss = E15&(#+1)15 in Hyper-Hyper Extended Cascading-E notation

80. Quindecimal-zeraddomterphi = f_(varphi(omega,0,0,0))(15) in FGH using extended Veblen hierarchy

81. Quindecimal-trexommthet = f_(theta(Omega^3)(15) in FGH using Feferman's theta function (or f_(varphi(1,0,0,0,0))(15) using extended Veblen hierarchy, f_(psi_0(Omega^Omega^3)(15) using Buchholz's psi function)

82. Sovlara = E[15]15#{&&}#225 in Collapsing-E notation (&E)

83. Quindecimal-zeraddomquinphi = f_(varphi(omega,0,0,0,0))(15) in FGH using extended Veblen hierarchy

84. Quindecimal-quadrexommthet = f_(theta(Omega^4)(15) in FGH using Feferman's theta function (or f_(varphi(1,0,0,0,0,0))(15) using extended Veblen hierarchy, f_(psi_0(Omega^Omega^4)(15) using Buchholz's psi function)

85. Quindecimal-quintexommthet = f_(theta(Omega^5)(15) in FGH using Feferman's theta function

86. Quindecimal-sextexommthet = f_(theta(Omega^6)(15) in FGH using Feferman's theta function

87. Quindecimal-small Veblen = f_(psi_0(Omega^Omega^omega))(15) using Buchholz's psi function

88. Quindecimal-large Veblen = f_(psi_0(Omega^Omega^Omega))(15) using Buchholz's psi function

89. Try for more fifteens = 15[1 <1 / 2> 2 // 2]15 in DeepLineMadom's array notation

90. Let's look fifteens = 15[1 <1 / 15> 16 // 2]15 in DeepLineMadom's array notation

91. Larger than mite = 15[1{1 // 1 // 1 // 1 // 5}2]15 in DeepLineMadom's array notation

92. Quindecimal-Bachmann = f_(psi_0(Omega_2))(15) using Buchholz's psi function

93. The deeper side of zeraphine array = {15,15[1[1[1¬31¬2]2]2]5} in Bird's array notation (modified Hierarchial Hyper Nested Array Notation)

94. Grow-up to more = (0,0)(1,1)(2,0)(2,1)[15] in BMS w.r.t v4

95. Sivlara = E[15]15#{&_2}#225 in Extended Collapsing-E notation (&E)

96. Vispera = 15[1 /// 3]15 in DeepLineMadom's array notation

97. Savlara = E[15]15#{&_3}#225 in Extended Collapsing-E notation (&E)

98. Skip a few more fifteens = (0,0)(1,1)(2,0)(2,1)(2,2)[15] in BMS w.r.t v4

99. Velspera = 15[1 //// 3 // 2]15 in DeepLineMadom's array notation

100. The even deeper side of zeraphine array = {15,15[1[1¬3¬1¬2]2]5} in Bird's array notation (modified Hierarchial Hyper Nested Array Notation)

101. Seevlara = E[15]15#{&_4}#225 in Extended Collapsing-E notation (&E)

102. Vuspera = 15[1 ///// 3 //// 2]15 in DeepLineMadom's array notation

103. Vaspera = 15[1 <<<<<1,2>>>>> 2]15 in DeepLineMadom's array notation

104. See more seevlara = E[15]15#{&_5}#3375 in Extended Collapsing-E notation (&E)

105. Ultimate sovlara = E[15]15#{&_#}#225 in Extended Collapsing-E notation (&E)