LLR:
(44*10^55558-17)/9 is base 3-Strong Fermat PRP! (55559 decimal digits) Time : 61.065 sec.
(44*10^55558-17)/9 is strong-Fermat, Lucas and Frobenius PRP! (P = 5, Q = 2, D = 17) Time : 248.078 sec.

To be completed...