Infinitely many prime values of the j-function coefficients

Let $c_n$ denote the coefficients of the $j$-function considered in the paper. Prime-value conjecture. There are infinitely many $n$ such that $c_n$ is prime. The computation finds several prime values of $c_n$ up to $n=2\cdot 10^7$, but only the smallest listed value has been certified by ECPP; the conjecture remains open.