It's extremely likely that your guess is correct, although it's probably a big hassle to prove.

Note that your starting prime, if it's different from 3, is always ; since an integer is congruent (mod 3) to the sum of its decimal digits, that leaves you the possibility of using the digits {1,7} at most once at some later step in your algorithm : never if your starting prime is congruent to -1 (mod 3), and at most once if it's congruent to 1 (mod 3). For example so you can only use the digits {3,9}.

Note also that conjectures dependent on the decimal base are considered relatively uninteresting because the decimal base is arbitrary.

And in all cases, to quote Hardy in his book *Ramanujan* (do not take offence!):

*It is comparatively easy to make clever guesses; indeed there are theorems, like "Goldbach's Theorem", which have never been proved and which any fool could have guessed.*