Avatamsaka Sutra's number: Buddhabhadra's translation

The famous large number which appears in Avatamsaka Sutra (Buddhāvataṃsaka Sūtra, 大方廣佛華嚴經), known as Nirabhilapya nirabhilapya parivarta (不可說不可說轉), has various known values. This is because there are several versions of translations, and also several calculations for each translations. Here I summarize several translations and main interpretation of numbers. Note that Chinese translations were translated from Sanskrit, where the original text is lost, and the English translation was translated from Buddhabhadra's translation.

Translator	Year	Text	Name	Value
佛陀跋陀罗 Buddhabhadra	418‐420	Chinese	不可說轉轉	\(10^{5\times2^{121}}\)
實叉難陀 Śikṣānanda	695‐699	Chinese	不可說不可說轉	\(10^{7\times2^{122}}\)
般若 Prājñā	795‐798	Chinese	不可說不可說轉	\(10^{7\times2^{142}}\)
Thomas Cleary	1993	English	square untold	\(10^{5\times2^{124}}\)

Note: Years in Chinese translations are from 世界大百科事典 第２版.

This blog post examines the translation by Buddhabhadra (418‐420), which is the basis of the English translation. In the translation. Other versions of translations are examined in other blog posts as follows.

• Śikṣānanda's translation
• Prājñā's translation
• Cleary's translation

We start reading from 百千百千名一拘梨.

• "百千百千名一拘梨": 百 means hundred, 千 means thousand, 名 means "to name", 一 means one, 拘梨 is a name of a number. Therefore, it literally means "hundred thousand hundred thousand is named one 拘梨". Therefore 拘梨 = \(10^{10}\).
• "拘梨拘梨名一不變": 拘梨 times 拘梨 is named one 不變. Therefore 不變 = 拘梨² = \(10^{20}\).
• "不變不變名一那由他": 不變 times 不變 is named one 那由他. Therefore 那由他 = 不變² = \(10^{40}\).

Like this, squared numbers are named successively. Finally

• "不可說轉不可說轉名一不可說轉轉" names the largest number 不可說轉轉.

Note that the name of the number here is applicable only in this context. For example 那由他 is used in various part of Buddhism's sutra, meaning "very large number", and it is now used in current Japanese counting system, which means \(10^{60}\). Anyway, each names of the numbers can be calculated as the table below. Following this calculation, the largest number 不可說轉轉 is \(10^{5\times2^{121}}\).

Other interpretations based on this translation:

• Japanese mathematician Joichi Suetsuna wrote a book on Avatamsaka Sutra in 1957, where the value is written as \(10^{5\times2^{120}}\). Probably it is a simple mistake. Shinji Suzuki (鈴木真治) introduced the value in Suetsuna's book in his Japanese book about large numbers in 2016.
• Thomas Cleary translated this text into English, where the value can be calculated as \(10^{5\times10^{124}}\). It is discussed in the later blog post.
• Giga Gerald insisted that it could be interpreted with tetration and gave a value of \(10\uparrow\uparrow10^{5\times2^{120}}\).

Program used for creating tables

Name	Value
拘梨	\(10^{5 \times 2^{1}} = 10^{10}\)
不變	\(10^{5 \times 2^{2}} = 10^{20}\)
那由他	\(10^{5 \times 2^{3}} = 10^{40}\)
鞞婆邏	\(10^{5 \times 2^{4}} = 10^{80}\)
作	\(10^{5 \times 2^{5}} = 10^{160}\)
來	\(10^{5 \times 2^{6}} = 10^{320}\)
勝	\(10^{5 \times 2^{7}} = 10^{640}\)
復次	\(10^{5 \times 2^{8}} = 10^{1280}\)
阿婆邏	\(10^{5 \times 2^{9}} = 10^{2560}\)
得勝	\(10^{5 \times 2^{10}} = 10^{5120}\)
分界	\(10^{5 \times 2^{11}} = 10^{10240}\)
充滿	\(10^{5 \times 2^{12}} = 10^{20480}\)
量	\(10^{5 \times 2^{13}} = 10^{40960}\)
解	\(10^{5 \times 2^{14}} = 10^{81920}\)
此解	\(10^{5 \times 2^{15}} = 10^{163840}\)
離欲	\(10^{5 \times 2^{16}} = 10^{327680}\)
捨	\(10^{5 \times 2^{17}} = 10^{655360}\)
聚	\(10^{5 \times 2^{18}} = 10^{1310720}\)
通	\(10^{5 \times 2^{19}} = 10^{2621440}\)
頻申	\(10^{5 \times 2^{20}} = 10^{5242880}\)
網	\(10^{5 \times 2^{21}} = 10^{10485760}\)
眾流	\(10^{5 \times 2^{22}} = 10^{20971520}\)
出	\(10^{5 \times 2^{23}} = 10^{41943040}\)
分	\(10^{5 \times 2^{24}} = 10^{83886080}\)
分別	\(10^{5 \times 2^{25}} = 10^{167772160}\)
稱	\(10^{5 \times 2^{26}} = 10^{335544320}\)
持	\(10^{5 \times 2^{27}} = 10^{671088640}\)
不顛倒	\(10^{5 \times 2^{28}} = 10^{1342177280}\)
不幡	\(10^{5 \times 2^{29}} = 10^{2684354560}\)
正	\(10^{5 \times 2^{30}} = 10^{5368709120}\)
慧	\(10^{5 \times 2^{31}} = 10^{10737418240}\)
第一	\(10^{5 \times 2^{32}} = 10^{21474836480}\)
覺	\(10^{5 \times 2^{33}} = 10^{42949672960}\)
毘遮妬	\(10^{5 \times 2^{34}} = 10^{85899345920}\)
極高	\(10^{5 \times 2^{35}} = 10^{171798691840}\)
妙	\(10^{5 \times 2^{36}} = 10^{343597383680}\)
邏婆	\(10^{5 \times 2^{37}} = 10^{687194767360}\)
訶梨婆	\(10^{5 \times 2^{38}} = 10^{1374389534720}\)
解脫	\(10^{5 \times 2^{39}} = 10^{2748779069440}\)
黃	\(10^{5 \times 2^{40}} = 10^{5497558138880}\)
訶梨那	\(10^{5 \times 2^{41}} = 10^{10995116277760}\)
因	\(10^{5 \times 2^{42}} = 10^{21990232555520}\)
賢覺	\(10^{5 \times 2^{43}} = 10^{43980465111040}\)
明相	\(10^{5 \times 2^{44}} = 10^{87960930222080}\)
摩樓陀	\(10^{5 \times 2^{45}} = 10^{175921860444160}\)
忍	\(10^{5 \times 2^{46}} = 10^{351843720888320}\)
枝	\(10^{5 \times 2^{47}} = 10^{703687441776640}\)
摩樓摩	\(10^{5 \times 2^{48}} = 10^{1407374883553280}\)
等	\(10^{5 \times 2^{49}} = 10^{2814749767106560}\)
離疑	\(10^{5 \times 2^{50}} = 10^{5629499534213120}\)
種	\(10^{5 \times 2^{51}} = 10^{11258999068426240}\)
不放逸	\(10^{5 \times 2^{52}} = 10^{22517998136852480}\)
摩多羅	\(10^{5 \times 2^{53}} = 10^{45035996273704960}\)
動	\(10^{5 \times 2^{54}} = 10^{90071992547409920}\)
到	\(10^{5 \times 2^{55}} = 10^{180143985094819840}\)
說	\(10^{5 \times 2^{56}} = 10^{360287970189639680}\)
白	\(10^{5 \times 2^{57}} = 10^{720575940379279360}\)
了別	\(10^{5 \times 2^{58}} = 10^{1441151880758558720}\)
究竟	\(10^{5 \times 2^{59}} = 10^{2882303761517117440}\)
清涼	\(10^{5 \times 2^{60}} = 10^{5764607523034234880}\)
阿羅	\(10^{5 \times 2^{61}} = 10^{11529215046068469760}\)
潮	\(10^{5 \times 2^{62}} = 10^{23058430092136939520}\)
油	\(10^{5 \times 2^{63}} = 10^{46116860184273879040}\)
祇邏	\(10^{5 \times 2^{64}} = 10^{92233720368547758080}\)
味	\(10^{5 \times 2^{65}} = 10^{184467440737095516160}\)
泥邏	\(10^{5 \times 2^{66}} = 10^{368934881474191032320}\)
戲	\(10^{5 \times 2^{67}} = 10^{737869762948382064640}\)
斯羅	\(10^{5 \times 2^{68}} = 10^{1475739525896764129280}\)
聚沫	\(10^{5 \times 2^{69}} = 10^{2951479051793528258560}\)
彌羅	\(10^{5 \times 2^{70}} = 10^{5902958103587056517120}\)
堅固	\(10^{5 \times 2^{71}} = 10^{11805916207174113034240}\)
風	\(10^{5 \times 2^{72}} = 10^{23611832414348226068480}\)
滿	\(10^{5 \times 2^{73}} = 10^{47223664828696452136960}\)
不可稱量	\(10^{5 \times 2^{74}} = 10^{94447329657392904273920}\)
根	\(10^{5 \times 2^{75}} = 10^{188894659314785808547840}\)
微細	\(10^{5 \times 2^{76}} = 10^{377789318629571617095680}\)
蓮華	\(10^{5 \times 2^{77}} = 10^{755578637259143234191360}\)
摩伽婆	\(10^{5 \times 2^{78}} = 10^{1511157274518286468382720}\)
不可度	\(10^{5 \times 2^{79}} = 10^{3022314549036572936765440}\)
醯樓	\(10^{5 \times 2^{80}} = 10^{6044629098073145873530880}\)
語	\(10^{5 \times 2^{81}} = 10^{12089258196146291747061760}\)
劫	\(10^{5 \times 2^{82}} = 10^{24178516392292583494123520}\)
婆婆	\(10^{5 \times 2^{83}} = 10^{48357032784585166988247040}\)
間	\(10^{5 \times 2^{84}} = 10^{96714065569170333976494080}\)
無間	\(10^{5 \times 2^{85}} = 10^{193428131138340667952988160}\)
離垢	\(10^{5 \times 2^{86}} = 10^{386856262276681335905976320}\)
實勝	\(10^{5 \times 2^{87}} = 10^{773712524553362671811952640}\)
彌羅覆	\(10^{5 \times 2^{88}} = 10^{1547425049106725343623905280}\)
遮摩羅	\(10^{5 \times 2^{89}} = 10^{3094850098213450687247810560}\)
法	\(10^{5 \times 2^{90}} = 10^{6189700196426901374495621120}\)
波羅摩馱	\(10^{5 \times 2^{91}} = 10^{12379400392853802748991242240}\)
決定	\(10^{5 \times 2^{92}} = 10^{24758800785707605497982484480}\)
流轉	\(10^{5 \times 2^{93}} = 10^{49517601571415210995964968960}\)
廣說	\(10^{5 \times 2^{94}} = 10^{99035203142830421991929937920}\)
無盡	\(10^{5 \times 2^{95}} = 10^{198070406285660843983859875840}\)
等真實	\(10^{5 \times 2^{96}} = 10^{396140812571321687967719751680}\)
無我	\(10^{5 \times 2^{97}} = 10^{792281625142643375935439503360}\)
阿槃陀	\(10^{5 \times 2^{98}} = 10^{1584563250285286751870879006720}\)
青蓮華	\(10^{5 \times 2^{99}} = 10^{3169126500570573503741758013440}\)
數	\(10^{5 \times 2^{100}} = 10^{6338253001141147007483516026880}\)
趣	\(10^{5 \times 2^{101}} = 10^{12676506002282294014967032053760}\)
受	\(10^{5 \times 2^{102}} = 10^{25353012004564588029934064107520}\)
阿僧祇	\(10^{5 \times 2^{103}} = 10^{50706024009129176059868128215040}\)
阿僧祇轉	\(10^{5 \times 2^{104}} = 10^{101412048018258352119736256430080}\)
無量	\(10^{5 \times 2^{105}} = 10^{202824096036516704239472512860160}\)
無量轉	\(10^{5 \times 2^{106}} = 10^{405648192073033408478945025720320}\)
無分齊	\(10^{5 \times 2^{107}} = 10^{811296384146066816957890051440640}\)
無分齊轉	\(10^{5 \times 2^{108}} = 10^{1622592768292133633915780102881280}\)
無周遍	\(10^{5 \times 2^{109}} = 10^{3245185536584267267831560205762560}\)
無周遍轉	\(10^{5 \times 2^{110}} = 10^{6490371073168534535663120411525120}\)
無數	\(10^{5 \times 2^{111}} = 10^{12980742146337069071326240823050240}\)
無數轉	\(10^{5 \times 2^{112}} = 10^{25961484292674138142652481646100480}\)
不可稱	\(10^{5 \times 2^{113}} = 10^{51922968585348276285304963292200960}\)
不可稱轉	\(10^{5 \times 2^{114}} = 10^{103845937170696552570609926584401920}\)
不可思議	\(10^{5 \times 2^{115}} = 10^{207691874341393105141219853168803840}\)
不可思議轉	\(10^{5 \times 2^{116}} = 10^{415383748682786210282439706337607680}\)
不可量	\(10^{5 \times 2^{117}} = 10^{830767497365572420564879412675215360}\)
不可量轉	\(10^{5 \times 2^{118}} = 10^{1661534994731144841129758825350430720}\)
不可說	\(10^{5 \times 2^{119}} = 10^{3323069989462289682259517650700861440}\)
不可說轉	\(10^{5 \times 2^{120}} = 10^{6646139978924579364519035301401722880}\)
不可說轉轉	\(10^{5 \times 2^{121}} = 10^{13292279957849158729038070602803445760}\)