Are there infinitely many $m\in\mathbb N$ such that $35\times2^m+1$ is $\textbf{not}$ a prime number?


Thanks in advance.



Non primality of a pseudo-like Mersenne numbers
Yes.


For natural $k$ let $m=4+10k$.
Then $35 \times 2^m+1$ is divisible by $11$, since
$35 \cdot 2^{4+10k} \equiv -1 \pmod {11}$
and $2^m$ is periodic modulo all primes.


