Found with PFGW Version 3.6.0

6130^6549-6549^6130 is 2-PRP! (24.3715s+0.0028s)
6130^6549-6549^6130 is 3-PRP! (24.1617s+0.0030s)
6130^6549-6549^6130 is 5-PRP! (24.4961s+0.0049s)
6130^6549-6549^6130 is 7-PRP! (24.2354s+0.0052s)
6130^6549-6549^6130 is 11-PRP! (24.3958s+0.0048s)

Primality testing 6130^6549-6549^6130 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N-1 test using base 11
Running N-1 test using base 13
Running N+1 test using discriminant 23, base 2+sqrt(23)
Calling N-1 BLS with factored part 0.05% and helper 0.04% (0.19% proof)
6130^6549-6549^6130 is Fermat and Lucas PRP! (196.7199s+0.0031s)

To be completed...