Concatenate the Fermat numbers $F_0=2^{2^0}+1$ to $F_{26}=2^{2^{26}}+1$ in base $10$.
This gives $$3517257655374294967297\cdots9215379822913519617$$ a huge number with $$40\ 403\ 579$$ digits. Because of its size it is extremely likely that it is composite. Were it prime , it would be a new record prime number.
But what is its smallest prime factor ? According to my search , there is no prime factor below $2\cdot 10^9$. Can we do anything better than trial division despite the enormous size of the given number ? Maybe , ECM ?