Taking the viewpoint that "attempts" are "experiments" which may or may not yield information, a "failure" may yield considerable information even while not achieving a decisive conclusion... and, therefore, be interesting.
Oppositely, some experiments seem fairly pointless "in advance", and/or prove unsurprisingly boring and uninformative, ... so are not interesting.
A possibly useful distinction is that a relatively expert mathematician may be able to relatively easily anticipate that a given experiment will yield no (interesting) information, while a relatively inexperienced person might not see the pointlessness of going down a particular road. At the same time, an inexperienced person may themselves acquire to-them-valuable information by performing to-expert-pointless experiments, to see first-hand (and viscerally?) how things work. Yet, as privately informative as this might be, it would fail by the stronger criterion of "informative to experienced experts".
Altogether hard-to-say, subjective.
Also, "it depends" on what one means by "publication": trying to get something "peer-reviewed" to score professional points is quite different from literal publication, e.g., on the internet, to inform any interested parties.