General Fibonacci Sequence whose Terms are all Composite

Theorem
The general Fibonacci sequence $\left\langle{a_n}\right\rangle$ defined as:
 * $a_n = \begin{cases}

r & : n = 0 \\ s & : n = 1 \\ a_{n - 2} + a_{n - 1} & : n > 1 \end{cases}$

where:
 * $r = 62 \, 638 \, 280 \, 004 \, 239 \, 857$
 * $s = 49 \, 463 \, 435 \, 743 \, 205 \, 655$

is such that:
 * $r$ and $s$ are coprime
 * all its terms are composite.