The **-yllion** system is a fabricated system invented by Donald Knuth for naming large numbers.^{[1]}

## Usage

Numbers up to 999 are named as they are normally.

Numbers from 1000 to 9999 are written without a comma and pronounced "*a*-ty *b* hundred *c*-ty *d*" for the number *abcd*. For example, 7283 is pronounced "seventy-two hundred eighty-three." The word thousand is not used in this system.

\(10^4\) is called the myriad. All numbers from the myriad up to 9999,9999 are written with a comma between the ten thousands and thousands place. For example, 54325 would be written 5,4325.

Such numbers are pronounced like so:

- 45,7839 is pronounced "forty-five myriad seventy-eight hundred thirty-nine."
- 2423,3000 is pronounced "twenty-four hundred twenty-three myriad thirty hundred."
- 9999,9999 is pronounced "ninety-nine hundred ninety-nine myriad ninety-nine hundred ninety-nine."

\(10^8\) is called the myllion. It is written 1;0000,0000. Note that a new punctuation mark, a semicolon, was used to represent the myllions place. Numbers up to 9999,9999;9999,9999 are named in the same way as the above numbers are pronounced: each group of four digits is pronounced as written above, and the commas are pronounced "myriad." The only difference is that the semicolon (;) is pronounced "myllion."

\(10^{16}\) is called the byllion. It is written 1:0000,0000;0000,0000. Note that a new punctuation mark, a colon, was used to represent the byllions place. Numbers up to 9999,9999;9999,9999:9999,9999;9999,9999 are pronounced as above, but the colon (:) is pronounced "byllion."

Continuing in this method, we have *n*-yllion \(= 10^{2^{n+2}}\), allowing the tryllion, quadryllion, quintyllion, etc.

## In googological notations

Notation | Upper bound | Condition |
---|---|---|

Fast-growing hierarchy | \(f_2^2(n)\) | \(n>13\) |

Hardy hierarchy | \(H_{\omega^2 2}(n)\) | \(n>13\) |

Slow-growing hierarchy | \(g_{\omega^{\omega^\omega}}(n)\) | \(n>3\) |

## Sources

## See also

The Chinese numeral system also had one scale in which each symbol was the square of the next.

**Suffixes**: -teen · -ty · -plex · -illion · **-yllion** · -exian · -chime · -toll · -gong · -bong · -throng**Prefixes**: gar- · fz- · fuga- · megafuga- · booga-**SI prefixes**: deca- · hecto- · kilo- · mega- · giga- · tera- · peta- · exa- · zetta- · yotta-**Obsolete SI prefixes**: myria-**Extended SI prefixes**: 666 · 10^{5} · 10^{7} · 10^{27} · 10^{30} · 10^{33} · 10^{36} · 10^{39} · 10^{42} · 10^{45} · 10^{48} · 10^{51} · 10^{54} · 10^{57} · 10^{60} · 10^{63} · 10^{90} · 10^{100} · 10^{120} · 10^{150} · 10^{180} · 10^{210} · 10^{240} · 10^{270} · 10^{300} · 10^{600} · 10^{900} · 10^{1200} · 10^{1500} · 10^{1800} · 10^{2100} · 10^{2400} · 10^{2700} · 10^{3000} and higher