mathematics - 答えはまた二桁の数字、その３ (The answer is another two-digit number, #3)

A colleague at work gives you a slip of paper at work one day, with symbols written on it:

・のいろ・はおに・・
みほくへ・やしと・ち
・ま・り・・・・・ぬ
・るゑ・ひ・・を・け

もわ・かせふ・よ・・
・・こた・え・・・れ
・そ・・・・・つて・
あね・な・・・・さら
・・・む・・き・・う
・ゆ・・・・・ゐめ・

す = ?

Every symbol in Japanese hiragana appears on the grid except for す and ん. The question is simple: Where does す go, and what number corresponds to it?

Answer

Solved it :-) The puzzle is based on two things:

いろは (iroha), an ancient Japanese poem that uses every hiragana character once only (except for ん),

and

素数, oops, sorry. I mean prime numbers.

Specifically,

The 10×10 grid can be regarded as a list of 100 cells numbered from 0 to 99. Each character of the poem is placed at a cell corresponding to a prime number. So the first character い goes in cell #2, the second character ろ goes in cell #3, the characters はにほへと go in cells 5, 7, 11, 13 and 17, and so on.

For prime numbers greater than 99, we have to start again at the beginning of the list, but this time we skip over cells that are already filled. So for example the 26th character の is associated with the prime number 101 and thus goes in cell #1. But the 27th character (for the prime number 103) ends up in cell #6 because we have to step over three characters (い, ろ and は).

Carry on in this fashion to the end of the poem, and you'll end up with the following grid, where characters that are filled in on the first, second and third pass are coloured red, orange and blue.

The final character す can be found in the 4th cell of the 7th row, which corresponds to the number 63.