Found with PFGW Version 3.7.5

6182^9865-9865^6182 is 2-PRP! (25.8861s+0.0015s)
6182^9865-9865^6182 is 3-PRP! (25.7332s+0.0017s)
6182^9865-9865^6182 is 5-PRP! (25.7970s+0.0015s)
6182^9865-9865^6182 is 7-PRP! (25.6916s+0.0016s)
6182^9865-9865^6182 is 11-PRP! (25.7083s+0.0015s)

Primality testing 6182^9865-9865^6182 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 8+sqrt(7)
Calling N-1 BLS with factored part 0.04% and helper 0.00% (0.11% proof)
6182^9865-9865^6182 is Fermat and Lucas PRP! (157.4158s+0.0027s)

To be completed...