@MartinHopf Amusing challenge ! Find a prime number containing 2024 in the decimal expansion and dividing some generalized Fermat number with base 2024 , in other words a number of the form $$2024^{2^n}+1$$ I know no such prime factor !

Also, I know no such prime factor of a number of the form $$\frac{2024^n-1}{2023}$$ , a generlized Mersenne number , if $n$ is prime. For $n=260$ , there is one even beginning with 2024.