# My Take On Champernowne's Constant

**Computer Science**Level 5

\[ \large 0.12345678910111213\ldots \]

The number above is an irrational decimal number created by concatenating all the positive integers in ascending order, and it is called *Champernowne's constant*.

Let the \(i^\text{th}\) digit of fractional part of Champernowne's constant (base 10) be denoted by \(a_{i}\). Calculate the *digital sum* of product of all non-zero \(a_{i}\) where \(i\) is a prime number less than 1000.

**Clarification**:

The *digital sum* is sum of all digits of a number. For example, product of \(a_i\) where \(i\) is prime less than \(8\) is \(2\times 3\times 5\times 7=210\). Its digital sum is \(2+1+0=3\).