Is the constant 33 important (ie. would it be any less significant if it were 42, or 74 instead) and if so, why?

I was replying that the constants in question include 33, 42 and 74... and realized that I'm late :-) In a more recent survey, though, it is now known that:

> 74 = −284650292555885^3 + 66229832190556^3 + 283450105697727^3 [1] [2].

[1] https://arxiv.org/pdf/1604.07746v1.pdf

[2] https://mathoverflow.net/a/223121

what if I can prove there is no integer solution for it? Is it still publication-worthy?

Even more so!