311..11 near rep-unit PRPs.

(28*10^134122-1)/9 is base 3-Strong Fermat PRP! (134123 decimal digits) Time : 95.984 sec.
(28*10^134122-1)/9 is strong-Fermat, Lucas and Frobenius PRP! (P = 5, Q = 3, D = 13) Time : 395.299 sec.
(28*10^165358-1)/9 is base 3-Strong Fermat PRP! (165359 decimal digits) Time : 137.440 sec.
(28*10^165358-1)/9 is strong-Fermat, Lucas and Frobenius PRP! (P = 5, Q = 3, D = 13) Time : 516.918 sec.
(28*10^183760-1)/9 is base 3-Strong Fermat PRP! (183761 decimal digits) Time : 160.124 sec.
(28*10^183760-1)/9 is strong-Fermat, Lucas and Frobenius PRP! (P = 5, Q = 2, D = 17) Time : 593.889 sec.

To be completed...