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A cenuntillion, uncentillion, 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 \(2^{1024}\).

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 \(f_2(1006)\) \(f_2(1007)\)
Hardy hierarchy \(H_{\omega^2}(1006)\) \(H_{\omega^2}(1007)\)
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)(1)[8] (0)(1)[9]
Hyperfactorial array notation 296! 297!
Fast-growing hierarchy \(f_2(2002)\) \(f_2(2003)\)
Hardy hierarchy \(H_{\omega^2}(2002)\) \(H_{\omega^2}(2003)\)
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