I am searching for a prime of this form:

$$(2^k - 1) 10^d + 2^{k-1} - 1$$

where $d$ is the number of decimal digits of $2^{k-1} - 1$, which is congruent to 6 mod 7.

I reached k=565.000 and there is no prime of this form congruent to 6 mod 7.

The primes of this form are formed by the concatenation of two consecutive Mersenne numbers, 40952047 for example.

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put on hold as unclear what you're asking by Wolfgang Bangerth, Christian Clason, Anton Menshov, Mauro Vanzetto, nicoguaro Dec 7 at 15:45

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    Welcome to SciComp.SE. This seems to be off-topic in this site. Actually, there is not clear if you have a question here. – nicoguaro Dec 6 at 16:00
  • I'm voting to close this question as off-topic because it does not belong to CompSci SE. – Anton Menshov Dec 7 at 9:15

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