Is there a prime number ending with the natural number $n$

Question

if $n$ not is divisible by 2 or 5?

Example: given

  813075843967837637675737563754361301, there is a prime
20813075843967837637675737563754361301

or given

   31415926535897932384626433832795028841971693993751, there is a prime
10331415926535897932384626433832795028841971693993751

Etc.

Answer 1

Note that $n$ should not end with $0,2,4,5,6$ or $8$ for anything to work. The rest will follow from Dirichlet's theorem on arithmetic progressions