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Googology Wiki

Nirabhilapya nirabhilapya parivarta (Bukeshuo bukeshuo zhuan 不可說不可說轉)[1] which appeared as Bodhisattva's math in Avatamsaka Sutra[2] is a large number in Bodhisattva's sutra which was translated by Śikṣānanda (實叉難陀, 652–710)[3]. It's equal to \(10^{7 \times 2^{122}}\) or \(10^{37,218,383,881,977,644,441,306,597,687,849,648,128}\), where complete list of calculated numbers are available in the Chinese version of this page.

Other versions

As described in Avatamsaka Sutra, Avatamsaka Sutra has other versions of translations to Chinese. The version translated by Prajñā (般若)[4] also has 不可說不可說轉[5] as the largest number but it has different value of \(10^{7\times2^{142}}=10^{39026304097428590497687506977134632635465728}\).

The version which was translated by Buddhabhadra (佛馱跋陀羅, 359-429)[6] which has different value of the largest number, which is \(10^{5 \times 2^{121}} = 10^{13292279957849158729038070602803445760}\) , was translated to English by Thomas Cleary[7], which has a different value of the highest value "untold" which is supposed to have the value of \(10^{5 \times 2^{123}}\), where "square untold" \(10^{5 \times 2^{124}}\) is also mentioned. Chinese name of this number is also different (不可說轉轉). This number is larger than centyllion, but smaller than gogolplex.

Approximation in other notations

Notation Lower bound Upper bound
Arrow notation \((10\uparrow7)\uparrow4\uparrow61\)
Down-arrow notation \(716\downarrow\downarrow14\) \(301\downarrow\downarrow16\)
Steinhaus-Moser Notation 25[3][3] 26[3][3]
Copy notation 3[3[38]] 4[4[38]]
H* function H(12H(11)) H(13H(11))
Taro's multivariable Ackermann function A(3,A(3,123)) A(3,A(3,124))
Pound-Star Notation #*((1))*(3,1)*13 #*((1))*(1,2,1,2)*4
BEAF {{10,7},{4,61}}
Hyper-E notation E(7E[4]61)
Bashicu matrix system (0)(1)[11] (0)(1)[12]
Hyperfactorial array notation (32!)! (33!)!
Fast-growing hierarchy \(f_2(f_2(119))\) \(f_2(f_2(120))\)
Hardy hierarchy \(H_{\omega^22}(119)\) \(H_{\omega^22}(120)\)
Slow-growing hierarchy \(g_{\omega^{\omega^{\omega3+7}3}}(10)\) \(g_{\omega^{\omega^{\omega3+7}4}}(10)\)


See also