RR discriminant degree conjectures for products of projective spaces

For the products $\mathbb P^1\times\mathbb P^{n-1}$ and $\mathbb P^2\times\mathbb P^{n-1}$, consider the corresponding RR discriminants and their nonisotropic parts. Product RR discriminant degree conjecture. The nonisotropic part for $\mathbb P^1\times\mathbb P^{n-1}$ is a hypersurface of degree

$$24\binom{n+1}{3},$$

while the nonisotropic part for $\mathbb P^2\times\mathbb P^{n-1}$ is a hypersurface of degree

$$24n^2\binom{n}{2}.$$

These formulas are proposed after tabulated computations and are not stated as proved in the supplied text.