Conjecture on prime values of polynomial floor sequences

Let $t$ and $d$ be positive integers, with $t$ odd and $d\geq 2$. Consider the integer sequence with general term

$$\left\lfloor\frac{n^t}{d}\right\rfloor.$$

Prime-value conjecture for odd powers. (a) If $t\equiv 0\pmod 3$ and $d\neq 2,9$, then there are infinitely many primes of the form

$$\left\lfloor\frac{n^t}{d}\right\rfloor.$$

(b) If $t\not\equiv 0\pmod 3$ and $d\neq 2$, then there are infinitely many primes of the form

$$\left\lfloor\frac{n^t}{d}\right\rfloor.$$

The paper has already established that the excluded cases $d=2$ and, when $3\mid t$, $d=9$ yield eventually prime-free sequences. The conjecture proposes that these are the only such exceptions among odd exponents, while the asserted infinitude of prime values remains open.