This question is bourn out of my recent answer to a question asked here
Now this is true for certain prime numbers , e.g., $3, 7, 109$ and $673$ that if you concatenate any two of these numbers in any order , the resulting number will be a prime . As in this case, Concatenating $7$ at the end of $673$ results in $6737$ which is a prime. This lead me to make a conjecture, that concatenation of the pair of twin prime, taken in order (with larger prime being concatenated after the smaller of the twin prime numbers ),would never yield a Prime. Is this conjecture true?