2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127-PRPs!

The covering set for a sequence of composite numbers like the Fibonacci sequence also covers the range of all negative integers.
The original Graham sequence (containing an unfortunate mistake) for which:

S(1) = 1786772701928802632268715130455793,
S(2) = 1059683225053915111058165141686995.

"A Fibonacci-like sequence of composite numbers", R.L. Graham, Math. Mag. 37, 1964.

The first PRP number (a counterexample for this sequence) was found in the negative range.

To be completed...