Found with PFGW Version 3.7.5

6498^9749-9749^6498 is 2-PRP! (26.2219s+0.0017s)
6498^9749-9749^6498 is 3-PRP! (25.9548s+0.0020s)
6498^9749-9749^6498 is 5-PRP! (26.2393s+0.0017s)
6498^9749-9749^6498 is 7-PRP! (25.5057s+0.0017s)
6498^9749-9749^6498 is 11-PRP! (25.5808s+0.0017s)

Primality testing 6498^9749-9749^6498 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.06% and helper 0.01% (0.18% proof)
6498^9749-9749^6498 is Fermat and Lucas PRP! (147.5060s+0.0024s)

To be completed...