33337 and 11119- type near repunit PRPs. Found with sr*sieve + LLR.

(10^162138+11)/3 is base 3-Strong Fermat PRP! (162138 decimal digits) Time : 143.148 sec.
(10^162138+11)/3 is strong-Fermat, Lucas and Frobenius PRP! (P = 5, Q = 2, D = 17) Time : 589.155 sec.
(10^180689+71)/9 is base 3-Strong Fermat PRP! (180689 decimal digits) Time : 191.550 sec.
(10^180689+71)/9 is strong-Fermat, Lucas and Frobenius PRP! (P = 6, Q = 3, D = 24) Time : 823.941 sec.
(10^279978+11)/3 is base 3-Strong Fermat PRP! (279978 decimal digits) Time : 410.160 sec.
(10^279978+11)/3 is strong-Fermat, Lucas and Frobenius PRP! (P = 5, Q = 2, D = 17) Time : 1861.130 sec.
(10^330906+71)/9 is base 3-Strong Fermat PRP! (330906 decimal digits) Time : 833.631 sec.
(10^330906+71)/9 is strong-Fermat, Lucas and Frobenius PRP! (P = 5, Q = 2, D = 17) Time : 3361.887 sec.

To be completed...