The 15 is here

is a series of numbers coined by wiki user AR Googol - The 15 is here accessed 2024-01-05 and 2024-08-31 mostly based on the number 15 and multiples of 15 to celebrate the 15th anniversary of Googology Wiki.
There are 90 numbers in the series.
== List of numbers ==
# 	Name 	Definition 	FGH approximation 	SGH approximationUsing the fundamental sequences for limit ordinals of finitary Veblen function.
1 	First emirpimes / emirpimes dozen 	15 	\(f_0(14)\) (exact) 	\(g_{\omega3}(5)\) (exact)
2 	Quindecimal-zeralum 	16 = \(f_0(15)\) in Fast-growing hierarchy 	\(f_1(8)\) (exact) 	\(g_{\omega^2}(4)\) (exact)
3 	Quindecimal-unalum / added emirpimes dozen 	30 = \(f_1(15)\) in Fast-growing hierarchy 	\(f_1(15)\) (definition) 	\(g_{\omega^3+\omega}(3)\) (exact)
4 	Garfifteen 	225 	\(f_2(5)\) (lower bound), \(f_2(6)\) (upper bound) 	\(g_{\omega^2}(15)\) (exact)
5 	Trarfifteen 	3375 	\(f_2(8)\) (lower bound), \(f_2(9)\) (upper bound) 	\(g_{\omega^3}(15)\) (exact)
6 	Quindecimal-balum 	15*215 = 491,520 = \(f_2(15)\) in Fast-growing hierarchy 	\(f_2(15)\) (definition) 	\(g_{\omega^{15}\times 15}(2)\) (exact)
7 	Fifteenbang 	15! = 1,307,674,368,000 	\(f_2(35)\) (lower bound), \(f_2(36)\) (upper bound) 	\(g_{\omega^{12}+\omega^{11}\times 3+\omega^9\times 7+\omega^8\times 6+\omega^7\times 7+\omega^6\times 4+\omega^5\times 3+\omega^4\times 6+\omega^3\times 8}(10)\) (exact)
8 	Quadrillion (short scale) 	1015 	\(f_2(44)\) (lower bound), \(f_2(45)\) (upper bound) 	\(g_{\omega^{\omega+5}}(10)\) (exact)
9 	Emirpimes dozen powered itself / quindecimal-small-fry / fzfifteen	1515 = 437,893,890,380,859,375 	\(f_2(52)\) (lower bound), \(f_2(53)\) (upper bound) 	\(g_{\omega^\omega}(15)\) (exact)
10	Googoxvy 	3015 = 1.4348907*1022 	\(f_2(67)\) (lower bound), \(f_2(68)\) (upper bound) 	\(g_{\omega^{15}}(30)\) (exact)
11	Quindecimal-googol 	15100 	\(f_2(382)\) (lower bound), \(f_2(383)\) (upper bound) 	\(g_{\omega^{\omega6+10}}(15)\) (exact)
12	Fifteendubang 	(15!)! = 1,307,674,368,000! ~ 5.908597073055873*1015,276,520,209,205	\(f_2(50747501675029)\) (lower bound), \(f_2(50747501675030)\) (upper bound)	\(g_{\omega^{\omega^{13}}}(10)\) (lower bound), \(g_{\omega^{\omega^{13}}}(11)\) (upper bound)
13	Googoxvyplexvy 	153015 ~ 101.687562409970287*1022 	\(f_2(f_2(69))\) (lower bound), \(f_2(f_2(70))\) (upper bound) 	\(g_{\omega^{\omega^{16}}}(24)\) (lower bound), \(g_{\omega^{\omega^{17}}}(20)\) (upper bound)
14	Quindecimal-googolplex 	1515100 	\(f_2(f_2(384))\) (lower bound), \(f_2(f_2(385))\) (upper bound) 	\(g_{\omega^{\omega^{\omega6+10}}}(15)\) (exact)
15	Fifteen-expobang 	15!1 in Hyperfactorial array notation 	\(f_2^{12}(15)\) (lower bound), \(f_2^{12}(16)\) (upper bound) 	\(g_{\omega\uparrow\uparrow 12}(39830)\) (lower bound), \(g_{\omega\uparrow\uparrow 12}(39831)\) (upper bound)
16	Quindecimal-tralum 	\(f_3(15)\) in fast-growing hierarchy 	\(f_3(15)\) (by definition) 	\(g_{\varepsilon_0}(15)\)
17	Quindecimal-giggol 	\(15\uparrow\uparrow 100\) in Arrow notation 	\(f_2^{99}(54)\) (lower bound), \(f_2^{99}(55)\) (upper bound) 	\(g_{\omega\uparrow\uparrow 100}(15)\) (exact)
18	Quindecimal-grangol 	E[15]100#100 in Hyper-E notation 	\(f_2^{100}(388)\) (lower bound), \(f_2^{100}(389)\) (upper bound) 	\(g_{\varepsilon_0}(100)\)
19	Fifteen-tetrobang 	15!2 in Hyperfactorial array notation 	\(f_3^{12}(15)\) (lower bound), \(f_3^{12}(16)\) (upper bound) 	\(g_{\zeta_0[12]}(15)\)
20	Quindecimal-quadralum 	\(f_4(15)\) in fast-growing hierarchy 	\(f_4(15)\) (by definition) 	\(g_{\zeta_0}(15)\)
21	Quindecimal-gaggol 	\(15\uparrow\uparrow\uparrow 100\) in Arrow notation 	\(f_4(99)\) 	\(g_{\zeta_0}(99)\)
22	Quindecimal-quintalum 	\(f_5(15)\) in fast-growing hierarchy 	\(f_5(15)\) (by definition) 	\(g_{\eta_0}(15)\)
23	Quindecimal-sextalum 	\(f_6(15)\) in fast-growing hierarchy 	\(f_6(15)\) (by definition) 	\(g_{\varphi(4,0)}(15)\)
24	Quindecimal-zeraddom 	\(f_{\omega}(15)\) in fast-growing hierarchy 	\(f_{\omega}(15)\) (by definition) 	\(g_{\varphi(13,0)}(15)\)
25	Triquindecal / Triple M 	{15,15,15} in BEAF 	\(f_{\omega}(16)\) 	\(g_{\varphi(14,0)}(15)\)
26	Fifteen-hyperbang 	15![1] in Hyperfactorial array notation 	\(f_{\omega}(17)\) 	\(g_{\varphi(\omega,0)}(15)\)
27	Quindecimal-boogol 	{15,15,100} in BEAF 	\(f_{\omega}(100)\) 	\(g_{\varphi(\omega,0)}(100)\)
28	Quindecimal-gugold 	E[15]100##100 in Extended Hyper-E notation 	\(f_{\omega}(100)\) 	\(g_{\varphi(\omega,0)}(100)\)
29	Quindecimal-unaddom 	\(f_{\omega+1}(15)\) in fast-growing hierarchy 	\(f_{\omega+1}(15)\) (by definition) 	\(g_{\Gamma_0}(15)\)
30	Quindecimal-baddom 	\(f_{\omega+2}(15)\) in fast-growing hierarchy 	\(f_{\omega+2}(15)\) (by definition) 	\(g_{\varphi(1,1,0)}(15)\)
==Footnotes==
== Sources ==
== See also ==
Googology Wiki 15th anniversary special series
Category:Numbers
Category:Numbers by ARsygo
Category:Class 1
Category:Class 2
Category:Class 3
Category:Tetration level
Category:Up-arrow notation level
Category:Linear omega level
Category:Powers of 15
Category:Series