LLR:
(58*10^83878+23)/9 is base 3-Strong Fermat PRP! (83879 decimal digits) Time : 125.119 sec.
(58*10^83878+23)/9 is strong-Fermat, Lucas and Frobenius PRP! (P = 5, Q = 3, D = 13) Time : 479.162 sec.

To be completed...