A 511...11 near rep-unit.

Found using sr*sieve + LLR:
(46*10^96798-1)/9 is base 3-Strong Fermat PRP! Time : 36.728 sec.
(46*10^96798-1)/9 is strong-Fermat, Lucas and Frobenius PRP! (P = 5, Q = 2, D = 17) Time : 231.952 sec.

To be completed...