2 problems

Let … where $\{x\}=x-\left\lfloor x\right\rfloor$. For a rational number $x\geq 2$, define its order under $\mathcal{T}$ to be the least non-negative integer $n$ such that…

Prime-representing function conjecture. There is a constant $A$, possibly near $1.1966746500705764022$, such that $f(n)$ is prime for every integer $n\geq 1$.