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quattuorcentillion is equal to \(10^{315}\) in the short scale and \(10^{624}\) in the long scale by Conway and Guy's naming system[1][2][3][4] as it is the 104th -illion number.

The least example \(n\) of \(\pi(n) > \mathrm{li}(n)\) must be smaller than 14 quattuorcentillion.[5]

In the long scale, \(10^{315}\) is called duoquinquagintilliard.

Approximations[]

Notation Lower bound Upper bound
Scientific notation \(1\times10^{315}\)
Arrow notation \(10\uparrow315\)
Steinhaus-Moser Notation 145[3] 146[3]
Copy notation 9[315] 10[158]
Chained arrow notation 10→315
H* function H(104)
Taro's multivariable Ackermann function A(3,1043) A(3,1044)
Pound-Star Notation #*((1173))*11 #*((1174))*11
BEAF & Bird's array notation {10,315}
Hyper-E notation E315
Bashicu matrix system (0)(0)(0)(0)(0)(0)[83536] (0)(0)(0)(0)(0)(0)[83537]
Hyperfactorial array notation 173! 174!
Fast-growing hierarchy \(f_2(1\,036)\) \(f_2(1\,037)\)
Hardy hierarchy \(H_{\omega^2}(1\,036)\) \(H_{\omega^2}(1\,037)\)
Slow-growing hierarchy \(g_{\omega^{\omega^23+\omega+5}}(10)\)

Sources[]

  1. Conway and Guy. (1995) "The book of Numbers" Copernicus
  2. Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-08.
  3. Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-08.
  4. Fish. Conway's zillion numbers. Retrieved 2023-02-08.
  5. Y. Saouter and P. Demichel (2010) A sharp region where π(x) - li(n) is positive. Math. Comp. 79, 2395-2405. doi:10.1090/S0025-5718-10-02351-3 Theorem 6.3

See also[]

Main article: -illion
100–109: centillion (un- · duo- · tres- · quattuor- · quin- · sex- · septen- · octo- · noven-)
110–119: decicentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
120–129: viginticentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septem- · octo- · novem-)
130–139: trigintacentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
140–149: quadragintacentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
150–159: quinquagintacentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
160–169: sexagintacentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
170–179: septuagintacentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
180–189: octogintacentillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
190–199: nonagintacentillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)
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