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The tetracontillion is equal to $$10^{3\left(10^{120}\right)+3}$$, or $$10^{3\text{ novemtrigintillion }3}$$.[1] The term was coined by Jonathan Bowers.

## Etymology

The name of this number is based on the suffix "-illion" and the prefix "tetraconta-" (from Greek 40).

## Approximations

Notation Lower bound Upper bound
Arrow notation $$1000\uparrow(1+10\uparrow120)$$
Down-arrow notation $$1000\downarrow\downarrow41$$ $$535\downarrow\downarrow45$$
Steinhaus-Moser Notation 65[3][3] 66[3][3]
Copy notation 2[2[121]] 3[3[121]]
H* function H(H(39))
Taro's multivariable Ackermann function A(3,A(3,398)) A(3,A(3,399))
Pound-Star Notation #*((1))*(4,0,4,6,1,1)*7 #*((1))*(9,7,0,3,2,6)*6
BEAF {1000,1+{10,120}}
Hyper-E notation E(3+3E120)
Bashicu matrix system (0)(1)[397] (0)(1)[398]
Hyperfactorial array notation (79!)! (80!)!
Fast-growing hierarchy $$f_2(f_2(393))$$ $$f_2(f_2(394))$$
Hardy hierarchy $$H_{\omega^22}(393)$$ $$H_{\omega^22}(394)$$
Slow-growing hierarchy $$g_{\omega^{\omega^{\omega^2+\omega2}3+3}}(10)$$

## Sources

1. Illion Numbers by Jonathan Bowers