## Prime Chains

### July 4, 2017

We studied word chains in a previous exercise; for instance, you can convert HEAD to TAIL by the word chain HEAD, HEAL, TEAL, TELL, TALL, TAIL in which each word differs from its predecessor by a single letter. Today’s exercise is similar, but asks you to find the chain from one prime number to another, with all intermediate numbers also prime, by changing one digit at a time; for instance, the chain 71549, 71569, 71069, 11069, 10069, 10067 converts 71549 to 10067.

Your task is to write a program to find prime chains. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

In Python. This is taken from the book Python Algorithms by Hetland. In the book code is given for finding chains of words from a dictionary. I only had to change the method “variants”. The A* method is used to find the shortest path with a distance heuristic that counts the number of mismatches in the numbers.

Hi,

Created a Depth-First search algorithm. This, off-course, goes bananas without a proper heuristic on getting closer to the target prime. This was done using the Hamming distance. Also set a limit of max depth (best) = 100 due to recursion depth limits.

Also found out that the is_prime function has many calls with the same argument, so cached the results using memoization.

I recon BFS would be a better approach judging from your solutions, anyway here’s my result: