Found with PFGW Version 3.7.5

6257^9098-9098^6257 is 2-PRP! (22.3092s+0.0024s)
6257^9098-9098^6257 is 3-PRP! (22.2246s+0.0017s)
6257^9098-9098^6257 is 5-PRP! (21.8636s+0.0017s)
6257^9098-9098^6257 is 7-PRP! (21.9096s+0.0016s)
6257^9098-9098^6257 is 11-PRP! (21.7968s+0.0017s)

Primality testing 6257^9098-9098^6257 [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)
6257^9098-9098^6257 is Fermat and Lucas PRP! (112.3715s+0.0030s)

To be completed...