Fermat prp to base 2, 3, 5, 7, 11, 13, 17, 19. Lucas prp.

Found for http://hjem.get2net.dk/jka/math/consecutive_factorizations.htm.
Together with a trivial factorization and a known prime, this set a record for largest known case of 3 consecutive complete factorizations (with prp factors allowed).

To be completed...