Found with PFGW Version 3.7.5

11542^12787+12787^11542 is 2-PRP! (48.5556s+0.0028s)
11542^12787+12787^11542 is 3-PRP! (49.0823s+0.0028s)
11542^12787+12787^11542 is 5-PRP! (49.7262s+0.0027s)
11542^12787+12787^11542 is 7-PRP! (48.6721s+0.0026s)
11542^12787+12787^11542 is 11-PRP! (48.4396s+0.0026s)

Primality testing 11542^12787+12787^11542 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 17, base 10+sqrt(17)
Calling N-1 BLS with factored part 0.01% and helper 0.00% (0.04% proof)
11542^12787+12787^11542 is Fermat and Lucas PRP! (299.8428s+0.0028s)

To be completed...