Found with PFGW Version 3.7.5

43^38700+42 is 2-PRP! (52.8563s+0.0067s)
43^38700+42 is 3-PRP! (60.2149s+0.0063s)
43^38700+42 is 5-PRP! (53.3815s+0.0058s)
43^38700+42 is 7-PRP! (52.9537s+0.0065s)
43^38700+42 is 11-PRP! (52.6306s+0.0062s)

Primality testing 43^38700+42 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 3
Running N-1 test using base 5
Running N-1 test using base 7
Running N-1 test using base 17
Running N+1 test using discriminant 37, base 1+sqrt(37)
Calling N-1 BLS with factored part 0.02% and helper 0.00% (0.07% proof)
43^38700+42 is Fermat and Lucas PRP! (600.1270s+0.0072s)

To be completed...