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The pentacontillion is equal to $$10^{3\left(10^{150}\right)+3}$$, or $$10^{3\text{ novemquadragintillion }3}$$.[1] The term was coined by Jonathan Bowers.

## Etymology

The name of this number is based on the suffix "-illion" and the prefix "pentaconta-" (from Greek 50).

## Approximations

Notation Lower bound Upper bound
Arrow notation $$1000\uparrow(1+10\uparrow150)$$
Down-arrow notation $$1000\downarrow\downarrow51$$ $$22\downarrow\downarrow113$$
Steinhaus-Moser Notation 78[3][3] 79[3][3]
Copy notation 2[2[151]] 3[3[151]]
H* function H(H(49))
Taro's multivariable Ackermann function A(3,A(3,498)) A(3,A(3,499))
Pound-Star Notation #*((1))*(4,1,6,8,2,4)*8 #*((1))*(5,0,6,5,0,1)*9
BEAF {1000,1+{10,150}}
Hyper-E notation E(3+3E150)
Bashicu matrix system (0)(1)[497] (0)(1)[498]
Hyperfactorial array notation (95!)! (96!)!
Fast-growing hierarchy $$f_2(f_2(492))$$ $$f_2(f_2(493))$$
Hardy hierarchy $$H_{\omega^22}(492)$$ $$H_{\omega^22}(493)$$
Slow-growing hierarchy $$g_{\omega^{\omega^{\omega^2+\omega5}3+3}}(10)$$

## Sources

1. Illion Numbers by Jonathan Bowers