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An uncentillion is equal to \(10^{306}\) in the short scale and \(10^{606}\) in the long scale by Conway and Guy's naming system[1][2][3][4] as it is the 101st -illion number. Jonathan Bowers called this number cenuntillion.[5] Aarex Tiaokhiao called this number cebillion.[6][dead link] It is the largest -illion expressible in the double-precision floating-point format, as it maxes out at \(2^{1,024}\).

In the long scale, \(10^{306}\) is called unquinquagintillion.

Approximations[]

For short scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{306}\)
Arrow notation \(10\uparrow306\)
Steinhaus-Moser Notation 142[3] 143[3]
Copy notation 9[306] 1[307]
Taro's multivariable Ackermann function A(3,1013) A(3,1014)
Pound-Star Notation #*((437))*11 #*((438))*11
BEAF {10,306}
Hyper-E notation E306
Bashicu matrix system (0)(0)(0)(0)(0)(0)[60429] (0)(0)(0)(0)(0)(0)[60430]
Hyperfactorial array notation 169! 170!
Fast-growing hierarchy \(f_2(1\,006)\) \(f_2(1\,007)\)
Hardy hierarchy \(H_{\omega^2}(1\,006)\) \(H_{\omega^2}(1\,007)\)
Slow-growing hierarchy \(g_{\omega^{\omega^23+6}}(10)\)

For long scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{606}\)
Arrow notation \(10\uparrow606\)
Steinhaus-Moser Notation 252[3] 253[3]
Copy notation 9[606] 1[607]
Taro's multivariable Ackermann function A(3,2010) A(3,2011)
Pound-Star Notation #*((187))*15 #*((188))*15
BEAF {10,606}
Hyper-E notation E606
Bashicu matrix system (0)(0)(0)(0)(0)(0)(0)[54246] (0)(0)(0)(0)(0)(0)(0)[54247]
Hyperfactorial array notation 296! 297!
Fast-growing hierarchy \(f_2(2\,002)\) \(f_2(2\,003)\)
Hardy hierarchy \(H_{\omega^2}(2\,002)\) \(H_{\omega^2}(2\,003)\)
Slow-growing hierarchy \(g_{\omega^{\omega^26+6}}(10)\)

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. Illion Numbers
  6. Aarex Tiaokhiao's illion numbers

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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