[yharris]

That's a very good point - and it really motivates these kinds of computer searches.

The Nature paper has quite a lot of detail in its supplementary

https://static-content.springer.com/esm/art%3A10.1038%2Fs415...

Table 3 inside also shows new conjectures for constants such as Catalan's and zeta(3). These results do not seem to trivially arise from known knowledge.