pg(k) 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.
The numbers are formed by the concatenation base 10 of two consecutive Mersenne numbers, examples are 157, 40952047.
I conjectured that there is no prime of this form congruent to 6 modulo 7. Has somebody an efficient routine for Sage for testing this conjecture?