[seqfan] Primes with strokes

[Éric Angelini]

(This message was published by mistake
on Math-Fun -- again, with no answer)

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 seq 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 positive terms with this property. 
 The successive primes are:
 13, 2, 47, 5, 689101114161883, 13, 17,... 
 What do you think?
Best,
É.