Found with PFGW Version 3.8.0

10413^11182-11182^10413 is 2-PRP! (39.0871s+0.0066s)
10413^11182-11182^10413 is 3-PRP! (38.3987s+0.0069s)
10413^11182-11182^10413 is 5-PRP! (38.8796s+0.0067s)
10413^11182-11182^10413 is 7-PRP! (40.5972s+0.0068s)
10413^11182-11182^10413 is 11-PRP! (38.5400s+0.0066s)

Primality testing 10413^11182-11182^10413 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 0.01% and helper 0.00% (0.02% proof)
10413^11182-11182^10413 is Fermat and Lucas PRP! (187.6375s+0.0075s)

To be completed...