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Revision as of 01:02, 2 March 2018
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 | |
| 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
See also
Gar-: garone · gartwo · garthree · garfour · garfive · garsix · garseven · gareight · garnine · garten · garhundred · garmillion · gargoogol · gareceton · gartrialogue · gargoogolplex · gargiggol
Fz-: fzone · fztwo · fzthree · fzfour · fzfive · fzsix · fzseven · fzeight · fznine · fzten · fztwenty · fzhundred · fzthousand · fzmillion · fzgoogol · fzmilliplexion · fzgoogolplex · fzgargoogolplex · fzgargantugoogolplex · fzgiggol
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 · megafugahundred · megafugagoogol · megafugagoogolplex · megafugagargoogolplex · megafugagargantugoogolplex · megafugagrangol
Extensions:
Booga-:: boogaone · boogatwo · boogathree · boogafour · boogafive · boogasix · boogaten · boogahundred · boogagoogol · boogagoogolplex
Gag-:: gagone · gagtwo · gagthree · gagfour · gagfive · gagsix · gagseven · gageight · gagnine · gagten · gaggoogol · gaggoogolplex