[math-fun] Primes with strokes

Hello Math-Fun, I was wondering if this seq S was sound: "Put a stroke behind every prime digit. Any integer formed by the concatenated digits between two strokes is prime." S = 1,3,2,4,7,5,6,8,9,10,11,14,16,18,83,13,17,,... The same with the strokes: S = 1,3,\2,\4,7\,5,\6,8,9,10,11,14,16,18,83\,13\,17\,... If I'm not wrong, S is the lexicographically first seq of distinct terms with this property. The successive primes are: 13, 2, 47, 5, 689101114161883, 13, 17,... What do you think? Best, É.