Question: Primes $ p$ of the form $ 10^{m}(2^{k}−1)+2^{k-1}−1$ , where $ m$ is the number of decimal digits of $ 2^{k-1}$ . For example: $ k=2$ then $ p=31$ . $ k=3$ then $ p=73$ . $ k=4$ then $ p=157.$ Conjecture: (1) None of the $ p$ ‘s is congruent to $ 6\pmodRead more