Found with PFGW Version 3.7.5

135^23541+134 is 2-PRP! (17.9076s+0.0016s)
135^23541+134 is 3-PRP! (17.8600s+0.0024s)
135^23541+134 is 5-PRP! (17.8967s+0.0018s)
135^23541+134 is 7-PRP! (17.8738s+0.0015s)
135^23541+134 is 11-PRP! (17.8940s+0.0018s)

Primality testing 135^23541+134 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 17, base 3+sqrt(17)
Calling N+1 BLS with factored part 0.06% and helper 0.01% (0.19% proof)
135^23541+134 is Fermat and Lucas PRP! (124.3021s+0.0029s)

To be completed...