Ec primes dividing ec numbers

A conjecture about numbers of the form $10^{m}(2^{k}−1)+2^{k-1}−1$, where $m$ is the number of decimal digits of $ 2^{k-1}$.

In this question ec numbers are introduced, formed by the concatenation of two consecutive Mersenne numbers ($157$ for example is denoted by $ec(4)$).
The ec prime $ec(7)=12763$ divides ec numbers $ec(7717)$, $ec(14259)$, $ec(15906)$,...

Does $ec(7)$ divide an infinite number of ec-numbers?

Is $255127$ the largest ec prime dividing at least one ec number besides itself?