Pg primes congruent to 1111 mod 42^2

[enzocreti]

pg numbers are so defined:


pg(k)=(2^k-1)*10^d+2^(k-1)-1 where d is the number of decimal digits of 2^(k-1)-1.


pg(8), pg(176006) and pg(541456) are probable primes. They are cogruent to 19 mod (42) and to 1111 mod(42^2).



Do you believe these primes are infinitely many?


primes pg congruent to 19 mod 42 and to 1111 (mod 42^2)?