Is an−(a−1)$a^n-(a-1)$ always composite for a=71$a=71$?

I have been investigating the primality of the sequence f(n)=71n−70$f(n)={71}^n-70$ for n>1$n>1$ . Preliminary computational tests using the Miller-Rabin primality test show no primes for n≤5000$n\le 5000$.

The sequence seems to be "protected" by a dense system of congruences. For instance:

If n≡0(mod2)$n\equiv 0(\mathrm{mod}2)$ then 3|f(n)$3|f(n)$.

If n≡3(mod5)$n\equiv 3(\mathrm{mod}5)$ then 11|f(n)$11|f(n)$.

If n≡0(mod11)$n\equiv 0(\mathrm{mod}11)$ then 23|f(n)$23|f(n)$.

If n≡6(mod15)$n\equiv 6(\mathrm{mod}15)$ then 31|f(n)$31|f(n)$.

If n≡7(mod9)$n\equiv 7(\mathrm{mod}9)$ then 37|f(n)$37|f(n)$.

If n≡9(mod40)$n\equiv 9(\mathrm{mod}40)$ then 41|f(n)$41|f(n)$.

Given that a=71$a=71$ is a prime of the form 30k+11$30k+11$ , it appears to be an exceptionally "resistant" base, similar to Sierpinski numbers or Riesel numbers, but for the an−(a−1)$a^n-(a-1)$ construction. My questions are:

Is there a known covering system for a=71$a=71$ that proves 71n−70${71}^n-70$ is always composite?

Is a=71$a=71$ the smallest prime base for which no primes have been found in this type of sequence for n<5000$n<5000$ ?

Are there any known primality results for this specific sequence in larger ranges?