Appendix:Knuth numeric system

The suffix -yllion is a proposal from for the terminology and symbols of an alternate decimal superbase system. In it, he adapts the familiar English terms for large numbers to provide a systematic set of names for much larger numbers. In addition to providing an extended range, -yllion also dodges the long and short scale ambiguity of -illion.

Knuth's digit grouping is exponential instead of linear; each division doubles the number of digits, whereas the familiar system only adds three or six more. His system is basically the same as one of the ancient and now-unused Chinese numeral systems, in which units stand for 10$4$, 10$8$, 10$16$, 10$32$, and so on.

Details and examples
For a more extensive table, see Myriad system.

In Knuth's -yllion proposal: Each new number name is the square of the previous one — therefore, each new name covers twice as many digits. Knuth continues borrowing the traditional names changing "illion" to "yllion" on each one. Abstractly, then, "one n -yllion" is $$10^{2^{n+2}}$$. "One trigintyllion" ($$10^{2^{32}}$$) would have nearly forty-three myllion (4300 million) digits. (By contrast, a conventional "trigintillion" has merely 94 digits &mdash; not even a hundred, let alone a hundred million!)
 * 1 to 99 have their usual names.
 * 100 to 9999 are divided before the 2nd-last digit and named "blah hundred blah". (e.g. 1234 is "twelve hundred thirty-four"; 7623 is "seventy-six hundred twenty-three")
 * 104 to 108-1 are divided before the 4th-last digit and named "blah myriad blah". Knuth also introduces at this level a grouping symbol (comma) for the numeral. So, 382,1902 is "3 hundred 82 myriad 19 hundred 2".
 * 108 to 1016-1 are divided before the 8th-last digit and named "blah myllion blah", and a semicolon separates the digits. So 1,0002;0003,0004 is "1 myriad 2 myllion, 3 myriad 4".
 * 1016 to 1032-1 are divided before the 16th-last digit and named "blah byllion blah", and a colon separates the digits. So 12:0003,0004;0506,7089 is "12 byllion, 3 myriad 4 myllion, 5 hundred 6 myriad 70 hundred 89".
 * etc.