Smallest Cunningham Chain of the First Kind of Length 7

Theorem
The smallest Cunningham chain of length $7$ is:
 * $\left({1 \, 122 \, 659, 2 \, 245 \, 319, 4 \, 490 \, 639, 8 \, 981 \, 279, 17 \, 962 \, 559, 35 \, 925 \, 119, 71 \, 850 \, 239}\right)$

Proof
Let $C$ denote the sequence in question.

We have that:
 * $\dfrac {1 \, 122 \, 659 - 1} 2 = 561 \, 329 = 83 \times 6763$

and so is not prime.

Thus $1 \, 122 \, 659$ is not a safe prime, as is required for $C$ to be a Cunningham chain.

Then:

Establishing that this is indeed the smallest such Cunningham chain of length $7$ can be done by a computer search.