### A routine for testing a conjecture

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 probable prime. I found that up to k=565.000 there is no probable 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 probable prime of this form congruent to 6 mod 7. Has somebody an efficient program for Sage to test this conjecture further?