All pure mathematicians know that the goal is to produce insight, rather than to simply obtain results. However, it might sometimes be of value to disseminate largely empirical work. In the same spirit as this question, which journals publish experimental and computational work in pure maths? Experimental Mathematics is one obvious answer, but what others exist?

$\begingroup$ I think this is very broad. Depending what "experimental" is supposed to mean exactly, most any journal might publish something "experimental". $\endgroup$– user9072Dec 11 '15 at 11:24

$\begingroup$ I specifically mean "something with gives results, but doesn't otherwise have much explanatory power or yield further insight". Essentially, the sort of thing that Appel & Haken's proof of the 4 color theorem was criticized for. $\endgroup$– NietzscheanAIDec 11 '15 at 11:31

2$\begingroup$ I am assuming you have a theorem that is not a priori a statement about a single finite set, and your proof is to reduce the statement to some statement about a large finite set, which you then check by massive computation. In that case, you should submit the paper to whatever journal you would have assuming you proved the theorem in a more classical manner, unless you already know that this journal does not value papers with your approach. Your paper may eventually be accepted only at a journal one or two tiers down, but the people interested in your result are the people in your subfield. $\endgroup$– Alexander WooDec 11 '15 at 12:34

3$\begingroup$ Also, almost all journals will publish counterexamples to important conjectures, which in principle could have been found via computation. $\endgroup$– Sam HopkinsDec 11 '15 at 17:44
I think one suitable journal is "Mathematics of Computation", an AMS journal. http://www.ams.org/publications/journals/journalsframework/mcom
Also, specific to algebra, the Journal of Algebra has a computational section: http://www.journals.elsevier.com/journalofalgebra/

3$\begingroup$ In both cases, these are not really journals that specialize in publishing theorems proved by massive computation, but rather journals that publish theorems abstractly about computation (involving certain types of objects). Theorems about computation are not particularly more likely to be proved by massive computation than theorems about anything else, though occasionally researchers will happen to prove Theorem X about Algorithm A because they need a massive computation using Algorithm A to prove Theorem Y. These journals are primarily for Theorem X, not Theorem Y in this kind of case. $\endgroup$ Dec 11 '15 at 12:46
There is LMS Journal of Mathematics and Computation, which is currently in an unclear position, as the LMS Council (the governing body of LMS) wants to shut it down as unprofitable (sic!), but due to objections by a considerable number of members (IMHO Council is just dead wrong on this, and lives in the past, as far as publishing matters go) a special meeting of LMS will take place in February 2016 to discuss and (hopefully) reverse this.
For some reason this meeting cannot be found in LMS agenda.

$\begingroup$ For info LMS Journal of Mathematics and Computation has ceased publication. $\endgroup$– KlangenJul 23 '19 at 9:35

$\begingroup$ yes, sure. It was quite a riot at LMS... $\endgroup$ Jul 23 '19 at 9:39
Electronic Journal of Combinatorics does publish experimental things, provided they are sufficiently related to discrete mathematics.
Arnold Mathematical Journal has this option. See the Journal Description, AMJ, Vol 1, pp 1  3:
Following Arnold, we will try to unhide this process and made it public by encouraging the authors to include informal discussion of their motivation, possibly unsuccessful lines of attack, experimental data and close by research directions.
Computational Methods in Science and Technology is a Polish physicsoriented journal, but also lists experimental mathematics as a field of interest in its ''Aims and Scope'' section.