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Japanese characters for muryoutaisuu

Muryoutaisuu (無量大数 written in Japanese,无量大数 in Chinese, means "immeasurable large number") is \(10^{68}\) in Japanese counting system[1][2]. It was derived from Chinese counting system, which was derived from Buddism's sutra in India. There are several different versions of counting systems in Chinese, meaning different numbers for the same Chinese character but different pronunciation[3].

It first appeared in Jinkouki (Japanese: 塵劫記) by Mitsuyoshi Yoshida in 1631. In the first edition of Jinkouki published in 1627, numbers up to Fukashigi was defined, and muryoutaisuu did not appear. In the 1631 edition of Jinkouki, definition of Muryoutaisuu was \(10^{88}\), and later in the 1634 edition of Jinkouki, definition changed to \(10^{68}\). Therefore, the definition of Muryoutaisuu is now \(10^{68}\).

In English, it is one hundred unvigintillion in short scale and one hundred undecillion in long scale.

The total mass-energy of the observable universe is estimated to be about 130 muryoutaisuu joules.


Notation Lower bound Upper bound
Scientific notation \(1\times10^{68}\)
Arrow notation \(10\uparrow68\)
Steinhaus-Moser Notation 41[3] 42[3]
Copy notation 9[68] 1[69]
Taro's multivariable Ackermann function A(3,222) A(3,223)
Pound-Star Notation #*(12,0,8,4,3)*10 #*(7,0,8,6,3,1)*8
BEAF & Bird's array notation {10,68}
Hyper-E notation E68
Bashicu matrix system (0)(0)(0)(0)[17782] (0)(0)(0)(0)[17783]
Strong array notation s(10,68)
Hyperfactorial array notation 52! 53!
Fast-growing hierarchy \(f_2(218)\) \(f_2(219)\)
Hardy hierarchy \(H_{\omega^2}(218)\) \(H_{\omega^2}(219)\)
Slow-growing hierarchy \(g_{\omega^{\omega6+8}}(10)\)


See also