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Thirty-threes is equal to $$3 \lfloor 10^{30} / 9\rfloor$$, or 30 copies of 3:[1]

333,333,333,333,333,333,333,333,333,333 or hypermathematically with interior superscription as $$3^{28}3$$

Its prime factorization is 32 × 7 × 11 × 13 × 31 × 37 × 41 × 211 × 241 × 271 × 2,161 × 9,091 × 2,906,161.

## Approximations Edit

Notation Lower bound Upper bound
Scientific notation $$3.333\times10^{29}$$ $$3.334\times10^{29}$$
Arrow notation $$70\uparrow16$$ $$93\uparrow15$$
Steinhaus-Moser Notation 21[3] 22[3]
Copy notation 3[30]
Taro's multivariable Ackermann function A(3,95) A(3,96)
Pound-Star Notation #*(5,4,2,4)*6 #*(6,4,2,4)*6
BEAF {70,16} {93,15}
Hyper-E notation 3E29 4E29
Bashicu matrix system (0)(0)(0)[4901] (0)(0)(0)[4902]
Hyperfactorial array notation 28! 29!
Fast-growing hierarchy $$f_2(91)$$ $$f_2(92)$$
Hardy hierarchy $$H_{\omega^2}(91)$$ $$H_{\omega^2}(92)$$
Slow-growing hierarchy $$g_{\omega^{\omega4+6}6+\omega^{\omega4+5}}(7)$$ $$g_{\omega^{\omega+6}16+\omega^{\omega+5}12}(17)$$

## Sources Edit

1. Halm, Michael Joseph. neologisms. Archived from the original on 2014-02-19. Retrieved 2018-02-26.