Found with PFGW Version 3.7.5

6241^10488-10488^6241 is 2-PRP! (33.7443s+0.0017s)
6241^10488-10488^6241 is 3-PRP! (33.7582s+0.0016s)
6241^10488-10488^6241 is 5-PRP! (33.8059s+0.0020s)
6241^10488-10488^6241 is 7-PRP! (33.8146s+0.0016s)
6241^10488-10488^6241 is 11-PRP! (33.7048s+0.0016s)

Primality testing 6241^10488-10488^6241 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 7
Running N+1 test using discriminant 31, base 1+sqrt(31)
Calling N+1 BLS with factored part 0.03% and helper 0.03% (0.12% proof)
6241^10488-10488^6241 is Fermat and Lucas PRP! (203.2893s+0.0027s)

To be completed...