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quinviginticentillion is equal to \(10^{378}\) in the short scale and \(10^{750}\) in the long scale by the Conway and Guy's naming system[1][2][3][4] as it is the 125th -illion number.

In the long scale, \(10^{378}\) is called tresexagintillion.

Approximations[]

For the short scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{378}\) (exact)
Arrow notation \(10\uparrow 378\) (exact)
Steinhaus-Moser Notation 169[3] 170[3]
Chained arrow notation \(10\rightarrow 378\) (exact)
Taro's multivariable Ackermann function A(3,1252) A(3,1253)
BEAF & Bird's array notation {10,378} (exact)
Hyper-E notation E378 (exact)
s(n) map \(s(1)^3(\lambda x.x+1)(7)\) \(s(1)^3(\lambda x.x+1)(8)\)
m(n) map m(1)(169) m(1)(170)
Bashicu matrix system (0)(0)(0)(0)(0)(0)(0)(0)[29] (0)(0)(0)(0)(0)(0)(0)(0)[30]
Fast-growing hierarchy \(f_2(1245)\) \(f_2(1246)\)
Hardy hierarchy \(H_{\omega^2}(1245)\) \(H_{\omega^2}(1246)\)
Slow-growing hierarchy \(g_{\omega^{\omega^2 3+\omega 7+8}}(10)\) (exact)

For the long scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{750}\) (exact)
Arrow notation \(10\uparrow 750\) (exact)
Steinhaus-Moser Notation 302[3] 303[3]
Chained arrow notation \(10\rightarrow 750\) (exact)
Taro's multivariable Ackermann function A(3,2488) A(3,2489)
BEAF & Bird's array notation {10,750} (exact)
Hyper-E notation E750 (exact)
s(n) map \(s(1)^3(\lambda x.x+1)(8)\) \(s(1)^3(\lambda x.x+1)(9)\)
m(n) map m(1)(302) m(1)(303)
Bashicu matrix system (0)(0)(0)(0)(0)(0)(0)(0)(0)[29] (0)(0)(0)(0)(0)(0)(0)(0)(0)[30]
Fast-growing hierarchy \(f_2(2480)\) \(f_2(2481)\)
Hardy hierarchy \(H_{\omega^2}(2480)\) \(H_{\omega^2}(2481)\)
Slow-growing hierarchy \(g_{\omega^{\omega^2 7+\omega 5}}(10)\) (exact)

Sources[]

  1. Conway and Guy. (1995) "The book of Numbers" Copernicus
  2. Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-11.
  3. Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-11.
  4. Fish. Conway's zillion numbers. Retrieved 2023-02-11.

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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