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An uncentillion, cenuntillion, centummillion[1] or cebillion as named by Aarex Tiaokhiao,[2] is equal to \(10^{306}\)[3] in short scale, and \(10^{606}\) in long scale. It is the largest -illion expressible in the double-precision floating-point format, as it maxes out at \(2^{1,024}\).

ApproximationsEdit

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 Edit

  1. http://users.skynet.be/nizgorur/very_big_numbers.htm
  2. Aarex Tiaokhiao's illion numbers
  3. Illion Numbers

See also Edit

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