Knuth -yllion
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Donald Knuth adapted the familiar naming schemes to handle much larger numbers, dodging ambiguity by changing the -illion to -yllion.
Knuth's digit grouping is exponential instead of linear; each division doubles the number of digits handled, whereas the familiar system only adds 3 or 6 more.
- 1 to 99 have their usual names. (In fact 1–999 have their usual names, and will be used below to save space; but to emphasize the pattern, this group is separate.)
- 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 "382 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 506 myriad 70 hundred 89"
- etc (although what separator follows is not obvious)
Abstractly, then, "one n-yllion" is 
. "One trigintyllion" would have nearly forty-three myllion digits.
This system is basically the same as one of the ancient Chinese numeral systems, in which units stand for 104, 108, 1016, 1032, and so on, though the system is not used today.
[edit] See also
[edit] References
- Donald E. Knuth. Supernatural Numbers in The Mathematical Gardener (edited by D. A. Klarner). Wadsworth, Belmont, CA, 1981. 310 — 325.
