Lewis Carroll's famous game of Doublets is well known. In it you are asked to transform a given word into another by changing only one letter at a time, forming a genuine new word (not a proper name) with each letter change.
Doublets with primes is identical except that instead of playing with words you play with prime numbers, say two 3-digit primes.
Question 1. Can any 3-digit prime be transformed into any other 3-digit number following the Doublet rule?
Question 2. What is the longest distance (i.e. the largest number of links required) between two 3-digit primes?
One could ask the same questions about 4-digit primes.