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Googlek is equal to $$16^{256} = 2^{1024}$$, or $$2^{2^{10}}$$ , intended as a hexadecimal analog of googol.[1] 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.[2]

## Digit expansions

Its full decimal expansion is:

179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216

Its full hexadecimal expansion is:

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Its full ternary expansion is:

10020200012020012100112000100111100022202212112100000000220012221210111211022000021021222102211022101010001120211122022202222100021002121110212011201100221120022112221101022221202200022002021122102001212012222021020211101221121211111112212000220112111200012222101011002120111121210010000221202111212212120201111102201110102120112002222220121102202020120101202100201020112210002020210120101201112011012000212121121220122021002120202012000102101002101111200111000221021110210202101200212210001210121001000112201210102202000120100002000112100221012002110222022002211011212110111011010112010211220220201010001001202011200010102010101110020211220012021

Its full binary expansion is:

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

## Approximations

Notation Lower bound Upper bound
Scientific notation $$1.797\times10^{308}$$ $$1.798\times10^{308}$$
Arrow notation $$16\uparrow256$$
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}
Hyper-E notation E[16]2#2
Bashicu matrix system (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 $$g_{\omega^{\omega^2}}(16)$$