Found with PFGW Version 3.7.5

6231^8230-8230^6231 is 2-PRP! (31.0631s+0.0038s)
6231^8230-8230^6231 is 3-PRP! (29.5174s+0.0035s)
6231^8230-8230^6231 is 5-PRP! (29.8341s+0.0036s)
6231^8230-8230^6231 is 7-PRP! (35.6072s+0.0037s)
6231^8230-8230^6231 is 11-PRP! (29.6319s+0.0035s)

Primality testing 6231^8230-8230^6231 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 11
Running N-1 test using base 13
Running N-1 test using base 17
Running N+1 test using discriminant 29, base 4+sqrt(29)
Calling N-1 BLS with factored part 0.05% and helper 0.05% (0.21% proof)
6231^8230-8230^6231 is Fermat and Lucas PRP! (278.5935s+0.0054s)

To be completed...