Ec primes are primes of the form:
$(2^n-1)\cdot 10^d+2^{n-1}-1=ec(n)$, where d Is the Number of decimal digits of $2^{n-1}$.
I conjecture that there are infinitely many primes of this form with n either $\equiv 0\pmod {67}$ or $\equiv 1\pmod {67}$
Verification: for $n=67, 6231,51456, 79798, 285019$ $ec(n)$ is probable prime. Is that another coincidence or law of small numbers?
The multiples of $67$, that Is 6231 and 51456 are also multiple of 3. And $79797$, $285018$ are divisible by 3 too. Is there a particular reason?
$79797=201\cdot 397$ Is a palindromic Number Just a curio.