Googlek

Googlek is equal to \(16^{256} = 2^{1024}\), or \(2^{2^{10}}\) , intended as a hexadecimal analog of googol. It was described on a page on the site "intuitor.com" which proposes a method for pronouncing numbers in hexadecimal. To the best of our knowledge, the page was written in 2007 by Tom Rogers, a high school teacher in South Carolina, USA. We have a successor for this number, the 10th fermat number, since 2^1,024 is equal to 2^2^10.
It is approximately \(1.797 \times 10^{308}\), or 179.769 uncentillion in the short scale and about 179.769 unquinquagintillion in the long scale.
It is the smallest power of two not expressible as a double-precision floating point number according to IEEE 754 (a double has an exponent width of 11 bits, one of which is the sign, so the exponent has a maximum of 210 - 1). As a result, it is the floating-point limit for numbers in many programming languages. For example, numbers equal to this or larger in JavaScript will simply be expressed as "Infinity".
JavaScript HyperCalc maxes out at a power tower of tens this many terms high, or \(10\uparrow\uparrow(2^{1024})\).
2^1024 is the maximum amount of money, coins etc. for games like AdVenture Capitalist or Cookie Clicker.
Username5243 calls this number Binary-Goodcolplex.Part 1 - My Large Numbers
== Digit expansions ==
Its full decimal expansion is:
Its full hexadecimal expansion is:
Its full ternary expansion is:
Its full binary expansion is:
==Approximations==
Notation 	Lower bound 	Upper bound
Scientific notation 	\(1.797\times10^{308}\) 	\(1.798\times10^{308}\)
Arrow notation 	\(16\uparrow256\) 	\(16\uparrow256\)
Steinhaus-Moser Notation 	143[3] 	144[3]
Copy notation 	1[309] 	2[309]
Taro's multivariable Ackermann function	A(3,1021) 	A(3,1022)
Pound-Star Notation 	#*((560))*11 	#*((561))*11
BEAF & Bird's array notation 	{16,256} 	{16,256}
Hyper-E notation 	E[16]2#2 	E[16]2#2
Bashicu matrix system 	(0)(0)(0)(0)(0)(0)[65536] 	(0)(0)(0)(0)(0)(0)[65536]
Hyperfactorial array notation 	170! 	171!
Fast-growing hierarchy 	\(f_2(1014)\) 	\(f_2(1015)\)
Hardy hierarchy 	\(H_{\omega^2}(1014)\) 	\(H_{\omega^2}(1015)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^2}}(16)\)	\(g_{\omega^{\omega^2}}(16)\)
== Sources ==
Category:Numbers
Category:Class 2
Category:Powers of 2
Category:Googol series
Category:Numbers with 101 to 999 digits
Category:Computers