111...11X type near repunit PRPs. Found using sr*sieve + LLR.
(10^111902+71)/9 is strong-Fermat, Lucas and Frobenius PRP! (P = 5, Q = 2, D = 17) Time : 321.464 sec.
(10^112067+53)/9 is strong-Fermat, Lucas and Frobenius PRP! (P = 4, Q = 2, D = 8) Time : 312.617 sec.
(10^146063+71)/9 is strong-Fermat, Lucas and Frobenius PRP! (P = 6, Q = 3, D = 24) Time : 551.600 sec.

To be completed...