Found with PFGW Version 3.4.8

43^13815+42 is 2-PRP! (15.0312s+0.0097s)
43^13815+42 is 3-PRP! (15.0233s+0.0057s)
43^13815+42 is 5-PRP! (19.4989s+0.0056s)
43^13815+42 is 7-PRP! (25.3656s+0.0069s)
43^13815+42 is 11-PRP! (30.2213s+0.0076s)

Primality testing 43^13815+42 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.08% and helper 0.02% (0.26% proof)
43^13815+42 is Fermat and Lucas PRP! (253.0331s+0.0148s)

To be completed...