The bored author

A poet has grown tired of writing poems. Instead, he decides to take a large amount of paper and, on each piece of paper, write down a different poem of $100$ characters using an alphabet of $22$ letters, a comma, a space and a period. (Surely one of them will be a masterpiece!)

Let $P$ be the number of pieces of paper he must use if he is to write down every possible poem of $100$ characters.

How many digits are in $P$ ? (You may use the fact that $\log_{10}(2) \approx 0.301$ )