Playing Doublets with the Primes

I can confirm that the corresponding graph is connected. Moreover, it has a hamiltonian cycle:

Hamiltonian cycle


For the first question the answer is yes, for the second question the answer is 6,

To solve the question i used both (Java and Wolfram), the idea is this i made a graph with nodes being the primes with 3-digits and there is a line between two nodes iff the primes representing the nodes are 1-Doublet(meaning with one digit change we can transfer one into another) and then we can state you question as graph theory question which are :

1) is the graph connected ?

2) what is the graph diameter ?

building the graph using Java and answering the questions using Wolfram we are done.

it seems that this is true for any number of digits primes, but i don't think there is a simple proof.

Tags:

Graph Theory

Hamiltonian Path

Prime Numbers

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