267479812356209999007⟹22=2×11⟹6776=2×3388⟹479974=2×239987⟹81233218=2×40616609⟹5620990265=5×1124198053⟹999007700999=7×142715385857
You have a machine that does some very interesting prime arithmetic. The machine takes in a prime number, reverses its digits, and attaches the resulting number to the prime input to form a new number.
It seems that for every prime number shown above (in the far left column), the machine produces a composite number (as implied by the right side of the equation).
Does there exist a prime for which the machine will produce another prime?