Knuth -yllion

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". (eg 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 10²ⁿ⁺². "One trigintyllion" would have nearly forty-three myllion digits.

External

• Large Numbers

I really wish I had enough money to write a cheque to put one of these names on, and watch the bank's spinny…