## FANDOM

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A googolteen is equal to a $$10^{100} + 10$$, or a googol plus ten.[1] This number is based on the fact that three + ten = thirteen, four + ten = fourteen, five + ten = fifteen, etc., extrapolating to n + ten = n-teen.

Full form written in decimal:

10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,010


Its prime factorization is 2 × 5 × 7 × 112 × 13 × 19 × 23 × 4,093 × 8,779 × 52,579 × 599,144,041 × 7,093,127,053 × 183,411,838,171 × 141,122,524,877,886,182,282,233,539,317,796,144,938,305,111,168,717.

## Approximations

Notation Lower bound Upper bound
Scientific notation $$1\times10^{100}$$ $$1.001\times10^{100}$$
Arrow notation $$10\uparrow100$$ $$53\uparrow58$$
Steinhaus-Moser Notation 56[3] 57[3]
Copy notation 9[100] 1[101]
Taro's multivariable Ackermann function A(3,329) A(3,330)
Pound-Star Notation #*(8,8,2,3,1,7,1)*9 #*(15,0,2,10,2,1)*12
BEAF {10,100} {53,58}
Hyper-E notation E2#2 2E2#2
Bashicu matrix system (0)(0)(0)(0)(0)[1333] (0)(0)(0)(0)(0)[1334]
Hyperfactorial array notation 69! 70!
Fast-growing hierarchy $$f_2(323)$$ $$f_2(324)$$
Hardy hierarchy $$H_{\omega^2}(323)$$ $$H_{\omega^2}(324)$$
Slow-growing hierarchy $$g_{\omega^{\omega^2}+\omega}(10)$$

## Sources

1. Googology by Andre Joyce