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Not to be confused with tethrafact.

Tetrafact is the mixed factorial of 4, written as 4*, and equal to $$((1+2) \times 3)^{4} = 6,561$$.[1] The term was coined by SpongeTechX.

It is also an output of the Exploding Tree Function: $$E(3) = 6,561$$. It is also the number of ways to add 11 ordinals.

## Etymology

The name of this number is based on the Greek prefix "tetra-" and the word "factorial".

## Approximation

Notation Lower bound Upper bound
Scientific notation $$6.561\times10^3$$
Arrow notation $$3\uparrow8$$
Steinhaus-Moser Notation 5[3] 6[3]
Copy notation 5[4] 6[4]
Taro's multivariable Ackermann function A(3,9) A(3,10)
Pound-Star Notation #*(57)*2 #*(3,5)*2
BEAF {3,8}
Bird's Array Notation {3,8}
Graham Array Notation [3,8]
Strong array Notation s(3,8)
Hyper-E notation E[3]8
Bashicu matrix system (0)[81]
Hyperfactorial array notation 7! 8!
Fast-growing hierarchy $$f_2(9)$$ $$f_2(10)$$
Hardy hierarchy $$H_{\omega^2}(9)$$ $$H_{\omega^2}(10)$$
Slow-growing hierarchy $$g_{\omega^4}(9)$$