Prove $18080108080 \sum_{k=0}^{1560-1} 10^{10k}+1$ is prime

Question

I saw this fact on twitter:

I would like to know how one would show this number is prime. Is there an elementary way to show that this number is prime? Is there a simplified primality testing algorithm in this case that possibly I could code and run on my computer? Is there a reference to a paper that can be given?

Answer 1

Maple's probabilistic primality test "isprime" returns true for this number. Here's the Maple code:

p:=18080108080*add(10^(10*k),k=0..1560-1) +1: isprime(p);