The sign painter is a little eccentric, and instead of charging by the hour, he charges by the brush stroke, which can be any shape and can touch, but must not cover, an already painted area (except where changing direction). He paints capital letters in a simple style (no serifs) and does not use two strokes where a single stroke will do. For example, E, F, G, H, I, N, O, R, S, T, U, V, W, X, Z would require 2, 2, 2, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, and 1 strokes, respectively.
My shop number, which I had spelled out for the painter when he arrived, is a prime number, consisting of three different digits. He charges $1 per stroke, regardless of the length of the stroke. By coincidence, the cost of my number in dollars was equal to the sum of the three digits in the shop number and was a prime.
What is my shop number?
