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7,625,597,484,987 is a positive integer equal to \(3^{27} = 3^{3^3} = 3 \uparrow\uparrow 3 = 3 \uparrow\uparrow\uparrow 2\). It is the largest power tower of 3's expressible in compact digital form (\(^43 = 3^{3^{3^3}}\) has 3 trillion digits). It appears frequently when inputting threes into functions based on the hyper operators. Tritri, for example, is a 7,625,597,484,987-sized power tower of threes.

In the short scale number-naming system, it is seven trillion, six hundred twenty-five billion, five hundred ninety-seven million, four hundred eighty-four thousand, nine hundred eighty-seven.

In the long scale, it is seven billion, six hundred twenty-five milliard, five hundred ninety-seven million, four hundred eighty-four thousand, nine hundred eighty-seven.

Using Alistair Cockburn's megafuga- prefix, 7,625,597,484,987 can be named "megafugathree".[1]

Wiki user Hyp cos calls this number a tribo, and it's equal to s(3,3,2), s(3,2,3), s(3,2,1,2), and s(3,2{2}2) in his strong array notation.[2]

In other notations

There are many notations where 7,625,597,484,987 can be expressed:

Notation Lower bound Upper bound
Scientific notation \(7.625597484987\times10^{12}\)
Arrow notation \(3\uparrow\uparrow3\)
Steinhaus-Moser Notation 11[3] 12[3]
Copy notation 6[13] 7[13]
Taro's multivariable Ackermann function A(3,39) A(3,40)
Pound-Star Notation #*(4,4,4)*4 #*(5,4,4)*4
BEAF {3,3,2}
Hyper-E notation E[3]1#3
Bashicu matrix system (0)(0)[1661] (0)(0)[1662]
Hyperfactorial array notation 3![1]
Fast-growing hierarchy \(f_2(37)\) \(f_2(38)\)
Hardy hierarchy \(H_{\omega^2}(37)\) \(H_{\omega^2}(38)\)
Slow-growing hierarchy \(g_{\omega^{\varepsilon_0+\omega^22+\omega2}}(3)\)

Sources

  1. 3.2.2 - The Fz, The Fuga & The Megafuga
  2. Numbers from linear array notation | Steps Toward Infinity!

See also

Numbers named with the fuga- family of prefixes

Gar-: garone · gartwo · garthree · garfour · garfive · garsix · garseven · gareight · garnine · garten · garhundred · gargoogol · gargoogolplex
Fz-: fzone · fztwo · fzthree · fzfour · fzfive · fzsix · fzseven · fzeight · fznine · fzten · fzeleven · fztwenty · fzhundred · fzgoogol · fzmillion · fzmilliplexion · fzgoogolplex · fzgargoogolplex · fzgargantugoogolplex
Fuga-: fugaone · fugatwo · fugathree · fugafour · fugafive · fugasix · fugaseven · fugaeight · fuganine · fugaten · fugahundred · fugagoogol · fugagoogolplex · fugagargoogolplex · fugagargantugoogolplex · fugagiggol
Megafuga-: megafugaone · megafugatwo · megafugathree · megafugafour · megafugafive · megafugasix · megafugaseven · megafugaeight · megafuganine · megafugaten · megafugaeleven · megafugatwelve · megafugathirteen · megafugafourteen · megafugafifteen · megafugasixteen · megafugaseventeen · megafugaeighteen · megafuganineteen · megafugatwenty · megafugathirty · megafugaforty · megafugafifty · megafugasixty · megafugaseventy · megafugaeighty · megafuganinety · megafugahundred · megafugagoogol · megafugagoogolplex · megafugagargoogolplex · megafugagargantugoogolplex
Booga-: boogaone · boogatwo · boogathree · boogafour · boogafive · boogasix · boogaseven · boogaeight · booganine · boogaten · boogahundred · boogagoogol · boogagoogolplex