Update: I let the program run even further. I now got 351166 solutions.
The highest one is:
139372413: {15485807, 15485801, 15485857, 15485837, 15485773, 15485843, 15485849, 15485783, 15485863};
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Update: I let the program run even further. I now got 351166 solutions.
The highest one is:
139372413: {15485807, 15485801, 15485857, 15485837, 15485773, 15485843, 15485849, 15485783, 15485863};
This starts to look like prime k-tuplets; in our case 9-tuplets.
I started reading on the concept of admissible 9-tuplets, and why some patterns are not admissible.
This is the fun of pushing what at first appears to be a silly puzzle ;-)
I made the problem up myself as I was teaching a small group how to solve the simpler problem of placing the numbers 1 to 9 in the same triangle. That puzzle has a neat insight that cuts the solutions down enormously.