What is the significance of a prime number - 1? Such as 43-1 or 29 - 1?
What is the context? Lots of things are true, for example $\displaystyle p-1$ is always even for $\displaystyle p \neq 2$, so for $\displaystyle p\neq 3$, $\displaystyle p-1$ is not prime. This is somewhat uninteresting though.
However, what is interesting is that $\displaystyle a^{p-1} \equiv 1 \text{ mod } p$. This is called Fermat's Little Theorem.