Label the vertices (or nodes) of this graph with positive integers so that any two nodes are joined by a edge (or line) if and only if the corresponding integers have a common divisor greater than 1 (i.e. they are not relatively prime). Do so in such a way that the total sum of the 13 numbers is minimum.
Answer
My best (manually)
With a sum of
79623
Update:
An exhaustive search of all 28.74 billion distinct arrangements with the lowest primes in the center has confirmed that this is the optimal solution. The C code for this search can be viewed here.
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