The ec numbers are so defined: ec(k)=(2^k-1)10^d+2^(k-1)-1, where d is the number of decimal digits of 2^(k-1)-1. In other words these numbers are formed by the base 10 concatenation of two consecutive Mersenne numbers, for example: 157, 12763, 40952047... For some values of k, ec(k) is prime. I found that up to k=565.000 there is no prime of the form (2^k-1)10^d+2^(k-1)-1 which is congruent to 6 mod 7. So I conjectured that there is no prime of this form congruent to 6 mod 7. Has somebody an efficient program for Sage to test this conjecture further?