Let $R$ be the polynomial ring over the finite field $\mathbb{F}_p$ with $n$ variables.
Let $I$ be an ideal of $R$ generated by homogeneous polynomials whose coefficients are 1 or -1.
Are there any criterions showing the primality of I ?
I have several examples which I tested using the function is_prime in SAGE but it seems that the software do not produce any answer when the number of variables and the number of generators of I is "big" (more or less 25...).