How to show that there is infinitely many prime numbers of the form:
$p=\sum_{i=0}^{a} n^{i}+m\cdot\sum_{i=0}^{b} n^{i}$
where: $m\in \mathbb{Z}^{*}$ , $a,b,n\in \mathbb{N}$ , $\gcd(a+1,b+1)=1$
For example:
$\sum_{i=0}^{6} 10^{335\cdot i}+8648\cdot \sum_{i=0}^{4} 10^{335\cdot i}$ is prime number.