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in: Numbers named with the fuga- family of prefixes, Fuga-, Fuga- family,
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Wiki user [[User:Hyp cos|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]].<ref>[https://stepstowardinfinity.wordpress.com/2015/07/24/lan-numbers/ Numbers from linear array notation | Steps Toward Infinity!]</ref>
  
Wiki user [[User:Hyp cos|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]].<ref>[https://stepstowardinfinity.wordpress.com/2015/07/24/lan-numbers/ Numbers from linear array notation | Steps Toward Infinity!]</ref>
   
  +
It is also called '''Heads-Bi-3-primol''' by [[User:Licorneuhh|Licorneuhh]]. It is equal to R***(2) using [[Primarial Functions]].<ref>[https://sites.google.com/view/licorneuhhs-numbers-site/numbers Numbers | Licorneuhh's numbers site] (retrieved at UTC 09:53 13/02/2021) </ref>
⚫
== In other notations ==
  
   
  ⚫
== In other notations ==
−
There are many notations where 7,625,597,484,987 can be expressed:
 +
There are many notations where 7,625,597,484,987 can be expressed :
−
{| class="article-table" border="0" cellpadding="1" cellspacing="1" style="width: 500px;"
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{| border="0" cellpadding="1" cellspacing="1" class="article-table"
 
|-
  
|-
 
! scope="col"|Notation
  
! scope="col"|Notation
−
! scope="col"|Expression
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! scope="col"|Lower bound
  +
! scope="col"|Upper bound
 
|-
  
|-
 
|[[Scientific notation]]
  
|[[Scientific notation]]
−
|\(7.625597484987 \times 10^{12}\) (exact)
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|colspan="2" align="center"|\(7.625597484987\times10^{12}\)
 
|-
  
|-
−
|[[Arrow notation|Up-arrow notation]]
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|[[Arrow notation]]
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|colspan="2" align="center"|\(3\uparrow\uparrow3\)
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|\(3 \uparrow\uparrow 3\), \(3 \uparrow^{2} 3\), \(3 \uparrow^{3} 2\) (all exact)
  
 
|-
  
|-
  +
|[[Steinhaus-Moser Notation]]
−
|[[BEAF]]
  
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|11[3]
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|\(\{3,3,2\}\), \(\{3,2,3\}\) (both exact)
  
  +
|12[3]
 
|-
  
|-
−
|[[Chained arrow notation]]
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|[[Copy notation]]
  +
|6[13]
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|\(3 \rightarrow 3 \rightarrow 2\), \(3 \rightarrow 2 \rightarrow 3\) (both exact)
  
  +
|7[13]
 
|-
  
|-
  +
|[[Taro's multivariable Ackermann function]]
−
|[[Hyper-E notation]]
  
  +
|A(3,39)
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|\(E(3)1\#3\), \(E(3)3\#2\) (both exact)
  
  +
|A(3,40)
 
|-
  
|-
  +
|[[Pound-Star Notation]]
−
|[http://googology.wikia.com/wiki/Hyperfactorial_array_notation Hyperfactorial array notation]
  
  +
|#*(4,4,4)*4
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|\(3!3\) or \(3![1]\) (both exact)
  
  +
|#*(5,4,4)*4
 
|-
  
|-
−
|[[Factorial]]
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|[[BEAF]]
  +
|colspan="2" align="center"|{3,3,2}
⚫
|\(16!\)
  
 
|-
  
|-
−
|[[Down-arrow notation]]
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|[[Hyper-E notation]]
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|colspan="2" align="center"|E[3]1#3
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|\(3 \downarrow\downarrow 4\) (exact)
  
 
|-
  
|-
−
|[[Notation Array Notation]]
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|[[Bashicu matrix system]]
  +
|(0)(0)[1661]
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|\((3\{3,2\}3)\) (exact)
  
  +
|(0)(0)[1662]
 
|-
  
|-
−
|[[Strong array notation]]
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|[[Hyperfactorial array notation]]
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|colspan="2" align="center"|3![1]
−
|\(s(3,3,2)\), \(s(3,2,3)\), \(s(3,2,1,2)\), \(s(3,2\{2\}2)\) (all exact)
  
 
|-
  
|-
 
|[[Fast-growing hierarchy]]
  
|[[Fast-growing hierarchy]]
−
|\(f_{2} (37)\)
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|\(f_2(37)\)
  ⚫
|\(f_2(38)\)
⚫
|-
  
⚫
|[[Slow-growing hierarchy]]
  
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|\(g_{\omega^{\omega^{\omega<nowiki>}}}</nowiki> (3)\), \(g_{\varepsilon_0} (3)\) (both are exact)
  
 
|-
  
|-
 
|[[Hardy hierarchy]]
  
|[[Hardy hierarchy]]
−
|\(H_{\omega^2} (37)\)
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|\(H_{\omega^2}(37)\)
  +
|\(H_{\omega^2}(38)\)
  ⚫
|-
  ⚫
|[[Slow-growing hierarchy]]
  +
| colspan="2" align="center" |\(g_{\varepsilon_0}(3)\)
 
|}
  
|}
   
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[[Category:3 entry linear]]
  
[[Category:3 entry linear]]
 
[[Category:Class 2]]
  
[[Category:Class 2]]
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[[Category:Composite numbers]]
  
 
[[Category:Non-pandigital numbers]]
  
[[Category:Non-pandigital numbers]]
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[[Category:Numbers with 10 to 21 digits]]
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[[Category:Numbers with 7 to 29 digits]]
 
[[Category:Powers of 3]]
  
[[Category:Powers of 3]]
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[[Category:Tetration]]
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[[Category:Megafuga-]]
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[[Category:Toogol Regiment]]
  ⚫
[[Category:Unnamed numbers]]
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[[Category:Unnamed numbers with 7 to 29 digits]]
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[[Category:Unnamed numbers with googological uses]]

Revision as of 10:15, 13 February 2021

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]

It is also called Heads-Bi-3-primol by Licorneuhh. It is equal to R***(2) using Primarial Functions.[3]

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 \(g_{\varepsilon_0}(3)\)

Sources

  1. ↑ 3.2.2 - The Fz, The Fuga & The Megafuga
  2. ↑ Numbers from linear array notation | Steps Toward Infinity!
  3. ↑ Numbers | Licorneuhh's numbers site (retrieved at UTC 09:53 13/02/2021)

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

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