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Unviginticentillion is equal to 10366 in the short scale, or 10726 in the long scale.[1]

This number is also called primo-vigesmo-centillion, which is part of a naming scheme first proposed by Professor Henkle in 1904 and subsequently popularized in 1968 in an article by Dmitri Borgmann.[1][2] In Henkles scheme the Latin ordinals represent their corresponding values, while the cardinals represent multipliers to be applied primarily to the milli- prefix.

Professor Henkle's system is notable for being the earliest known attempt to extend the zillion series to the millionth member. It may also have served as the impetus and blue print later systems, including the popular Conway & Guy naming scheme.

This number is also called cenunvigintillion.[3][4]

Approximations

For short scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{366}\)
Arrow notation \(10\uparrow366\)
Steinhaus-Moser Notation 165[3] 166[3]
Copy notation 9[366] 1[367]
Taro's multivariable Ackermann function A(3,1212) A(3,1213)
Pound-Star Notation #*((232))*12 #*((233))*12
BEAF {10,366}
Hyper-E notation E366
Bashicu matrix system (0)(0)(0)(0)(0)(0)(0)[723] (0)(0)(0)(0)(0)(0)(0)[724]
Hyperfactorial array notation 196! 197!
Fast-growing hierarchy \(f_2(1\,205)\) \(f_2(1\,206)\)
Hardy hierarchy \(H_{\omega^2}(1\,205)\) \(H_{\omega^2}(1\,206)\)
Slow-growing hierarchy \(g_{\omega^{\omega^23+\omega6+6}}(10)\)

For long scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{726}\)
Arrow notation \(10\uparrow726\)
Steinhaus-Moser Notation 294[3] 295[3]
Copy notation 9[726] 1[727]
Taro's multivariable Ackermann function A(3,2408) A(3,2409)
Pound-Star Notation #*((1086))*16 #*((1087))*16
BEAF {10,726}
Hyper-E notation E726
Bashicu matrix system (0)(1)[8] (0)(1)[9]
Hyperfactorial array notation 344! 345!
Fast-growing hierarchy \(f_2(2\,400)\) \(f_2(2\,401)\)
Hardy hierarchy \(H_{\omega^2}(2\,400)\) \(H_{\omega^2}(2\,401)\)
Slow-growing hierarchy \(g_{\omega^{\omega^27+\omega2+6}}(10)\)

Sources

  1. 1.0 1.1 Robert Munafo, Large Numbers -- Notes (page 2) at MROB
  2. Sbiis Saibian, 2.4.5 Professor Henkle's One Million illions - Large Numbers
  3. English names of the first 10000 powers of 10 (American system)
  4. English names of the first 10000 powers of 10 (European system)

See also

Main article: -illion
1–9: million · billion · trillion · quadr · quint · sext · sept · oct · non
10–19: decillion · undec · duodec · tredec · quattuordec · quindec · sexdec · septendec · octodec · novemdec
20–29: vigintillion · unvigint · duovigint · trevigint · quattuorvigint · quinvigint · sexvigint · septenvigint · octovigint · novemvigint
30–39: trigintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
40–49: quadragintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
50–59: quinquagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
60–69: sexagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
70–79: septuagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
80–89: octogintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
90–99: nonagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
100–900: centillion · unviginticent · ducent · trecent · duotrigintatrecent · quadringent · quingent · sescent · septuagintisescent · septingent · octingent · nongent
1,000–1024: millillion · dumill · trimill · quadrimill · quinmill · sexmill · septimill · octimill · nonimill · myr · centimill · micr · nan · pic · femt · att · zept · yoct
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-)