Found with PFGW Version 3.6.0

1253^13542+13542^1253 is 2-PRP! (82.2483s+0.0030s)
1253^13542+13542^1253 is 3-PRP! (82.7179s+0.0029s)
1253^13542+13542^1253 is 5-PRP! (82.9634s+0.0031s)
1253^13542+13542^1253 is 7-PRP! (82.1787s+0.0027s)
1253^13542+13542^1253 is 11-PRP! (82.9976s+0.0030s)

Primality testing 1253^13542+13542^1253 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N-1 test using base 13
Running N-1 test using base 19
Running N-1 test using base 23
Running N-1 test using base 29
Running N+1 test using discriminant 43, base 2+sqrt(43)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
1253^13542+13542^1253 is Fermat and Lucas PRP! (712.6368s+0.0029s)

To be completed...