Single Sink Conjecture: False!
Posted on 2025-03-04 23:45
In a recent post, I conjectured that the only sink node in the prime sum graph would be the largest prime in the list. This turns out to be false, as the graph of primes less than or equal to 149 shows. The graph itself is an unreadable monstrosity, as you can see here:

However, here are some zoom ins on portions of the graph that show that 139 and 149 are both leaf/sink node primes.

and

So, my hasty conjecture about sink nodes is proven false. Also, the python code on github has been updated to allow you to identify sink nodes analytically from the adjacency matrix without generating the whole graph.
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