The asankhyeya (also called asaṃkhyeya) is a number described in Buddhist texts that is equal to $$10^{140}$$, or 1 followed by 140 zeroes. It is pronounced Asougi in Japanese where it is equal to $$10^{56}$$, and means "innumerable".

The Avatamsaka Sutra  gives an alternate description of Asankhyeya as $$10^{7\times2^{103}}$$, defining a series of numbers that are squares of each other starting with one koti equalling $$10^7$$, one koti kotis making an ayuta ($$10^{14}$$), one ayuta ayutas making a nayuta ($$10^{28}$$), and so on, with Asankhyeya being the 104th number in this chain.

## Approximations

For 10140:

Notation Lower bound Upper bound
Scientific notation $$1\times10^{140}$$
Arrow notation $$10\uparrow140$$
Steinhaus-Moser Notation 74 75
Copy notation 9 1
Taro's multivariable Ackermann function A(3,462) A(3,463)
Pound-Star Notation #*(1,2,8,11,9,8,5)*12 #*(4,4,10,5,7,2,5,2)*10
BEAF {10,140}
Hyper-E notation E140
Bashicu matrix system (0)(0)(0)(0)(0) (0)(0)(0)(0)(0)
Hyperfactorial array notation 90! 91!
Fast-growing hierarchy $$f_2(456)$$ $$f_2(457)$$
Hardy hierarchy $$H_{\omega^2}(456)$$ $$H_{\omega^2}(457)$$
Slow-growing hierarchy $$g_{\omega^{\omega^2+\omega4}}(10)$$

For 107×2103:

Notation Lower bound Upper bound
Arrow notation $$(10\uparrow7)\uparrow2\uparrow103$$
Down-arrow notation $$57\downarrow\downarrow19$$ $$715\downarrow\downarrow12$$
Steinhaus-Moser Notation 22 23
Copy notation 6[6] 7[7]
H* function H(23H(9)) H(24H(9))
Taro's multivariable Ackermann function A(3,A(3,104)) A(3,A(3,105))
Pound-Star Notation #*((1))*(1,10,10)*4 #*((1))*(5,2,1)*6
BEAF {{10,7},{2,103}}
Hyper-E notation E(7E103)
Bashicu matrix system (0)(1) (0)(1)
Hyperfactorial array notation (28!)! (29!)!
Fast-growing hierarchy $$f_2(f_2(100))$$ $$f_2(f_2(101))$$
Hardy hierarchy $$H_{\omega^22}(100)$$ $$H_{\omega^22}(101)$$
Slow-growing hierarchy $$g_{\omega^{\omega^{\omega3+1}7}}(10)$$ $$g_{\omega^{\omega^{\omega3+1}8}}(10)$$

## Sources

1. "How large is one Asamkhyeya?" Bodhi Field. http://www.drbachinese.org/vbs/publish/462/vbs462p042.pdf
2.