A 511...11 near rep-unit, written in decimal as "5" followed by 51111 "1"s...

(46*10^51111-1)/9 is base 3-Strong Fermat PRP! (51112 decimal digits) Time : 22.806 sec.
(46*10^51111-1)/9 is strong-Fermat, Lucas and Frobenius PRP! (P = 5, Q = 3, D = 13) Time : 88.194 sec.

To be completed...