Found with PFGW Version 3.7.5

975^8044-8044^975 is 2-PRP! (18.4596s+0.0028s)
975^8044-8044^975 is 3-PRP! (21.3348s+0.0036s)
975^8044-8044^975 is 5-PRP! (16.4878s+0.0017s)
975^8044-8044^975 is 7-PRP! (23.3541s+0.0036s)
975^8044-8044^975 is 11-PRP! (15.9385s+0.0017s)

Primality testing 975^8044-8044^975 [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 discriminant 17, base 6+sqrt(17)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.10% proof)
975^8044-8044^975 is Fermat and Lucas PRP! (143.7038s+0.0047s)

To be completed...