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    $\begingroup$ You could follow the examples of papers published here: tandfonline.com/journals/uexm20/… depending on the relevance of your conjecture and your computations, you could publish your results there too $\endgroup$ Commented Feb 26 at 0:34
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    $\begingroup$ There are journals that publish experimental results (like the Journal of Experimental Mathematics), but it is unusual to publish work that is purely experimental. In general, it is not easy to publish papers that don't prove something. There are papers that are meant to state conjectures and assemble evidence for them. For instance, I wrote one here: arxiv.org/abs/1208.3216. However, I would discourage someone from writing a paper like that if they don't already have a track record of proving theorems since it will probably be hard to get it published. $\endgroup$ Commented Feb 26 at 1:12
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    $\begingroup$ But "prove something" doesn't always mean "prove what you want to prove". I think a paper which states an appealing conjecture and verifies many special cases numerically can be a very nice paper. And if you can get a preprint version in front of the right experts, they may prove your conjecture! That's what happened for us with arxiv.org/abs/1607.00047v1 . In our case, Luke Pebody proved our conjecture after seeing arXiv v1, but I think it would have made a good paper even if he hadn't. $\endgroup$ Commented Feb 26 at 2:26
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    $\begingroup$ @jpvigneaux The board of Experimental Mathematics resigned en masse a couple of years ago and many of them are now with the Journal of Experimental Mathematics. $\endgroup$ Commented 2 days ago
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    $\begingroup$ Since you ask about "papers/books on certified computation in analytic number theory (or adjacent areas)", keep in mind that analytic number theory is notorious for having had conjectures supported by a lot of numerical data turn out to be wrong. $\endgroup$ Commented 11 hours ago