Here's a quick shot:

4972*3^16384+1 is prime! (7821 digits)

13506*3^16384+1 is prime! (7822 digits)

43728*3^16384+1 is prime! (7822 digits)

50490*3^16384+1 is prime! (7822 digits)

So you want to collect those small primes? You could do a list of the Sierpinski (Proth) side of primes like I do for the

Riesel side.

I got thousands of them listed!