Recently, I was studying prime sequences of the form k * 2^n + 1$k \cdot 2^n + 1$, and I noticed that primes of the form n * 2^n + 1$n \cdot 2^n + 1$ almost do not exist, except for the n = 1$n = 1$ case. Are there other prime numbers, or infiniteinfinitely many prime numbers, when n > 1$n > 1$?