The logarithmic Cunningham-chain bound beyond 5

Let $\mathbb{P}$ denote the primes, let $i\in\{1,2\}$, and let $C_i[p]$ be the Cunningham chain associated with $p$. The logarithmic Cunningham-chain bound. For every prime $p>5$,

$$|C_i[p]|<\log_2(p+1).$$

The source presents this as a consequence anticipated from the rogue divisor conjecture; since that conjecture is unproved, this bound is also presented without a proof for general primes.