Let $R(n)$ denote the classical Ramsey-number, that is, the smallest natural $N$, for which every blue-red edge-colouring of $K_N$ admits a monochromatic $K_n$.
Consider the conjecture: $R(n)-1$ is prime for all $n\geq 3$.
Obviously, there is little to support the conjecture because we only know $R(3)=6$, $R(4)=18$ and that $R(5)=44$ (or, less likely, $R(5)=48$) is not impossible. However, maybe there is some value in asking whether there is some evidence against the conjecture, that is, is there some conceptual, heuristic etc. reason why the above is an unreasonable guess other than the mere scarcity of data?