Novel Prime Factors of Repunits
Proof that every repunit has a novel prime factor
Using Zsigmondy's Theorem, the proof is simple. From Wikipedia:

In number theory, Zsigmondy's theorem, named after Karl Zsigmondy,
states that if a &gt; b &gt; 0 are coprime integers, then for any integer n
≥ 1, there is a prime number p (called a primitive prime divisor) that
divides an − bn and does not divide ak − bk for any positive integer k
&lt; n, with the following exceptions: [things that don't apply here].

Consider the repunits times 9: that is, 10n-1. By Zsigmondy's Theorem with a=10, b=1, there is some prime p | 10n-1 that does not divide any 10k-1, k &lt; n.

Since p is prime and 10n-1 = 9 · Rn, it must divide either 9 or Rn.

p cannot divide 9, since 9 = 101-1.

Therefore p divides Rn.

p cannot divide any Rk, since it doesn't divide 10k-1 = 9 · Rk.


Therefore the p from Zsigmondy's Theorem is a novel prime factor of any Rn, n ≥ 2. ∎

An example of a repeated novel prime factor
The prime 487 is a repeated prime factor of R486:
By the Fermat-Euler theorem, 10487-1 ≡ 1 (mod 487). The order of 10 mod 487, that is, the smallest power of 10 that is 1 mod 487, therefore must be a divisor of 486. In fact, the order is equal to 486. It also happens that not only is 10486 ≡ 1 (mod 487), it's also 1 (mod 4872).
See here that the order of 10 mod 487 is 486; that is, that no smaller 10k-1 is divisible by 487. Obviously, 487 doesn't divide 9, so it must divide R486.