Found with PFGW Version 3.8.0

10761^10970-10970^10761 is 2-PRP! (36.2298s+0.0062s)
10761^10970-10970^10761 is 3-PRP! (36.2770s+0.0068s)
10761^10970-10970^10761 is 5-PRP! (36.2483s+0.0075s)
10761^10970-10970^10761 is 7-PRP! (37.7357s+0.0070s)
10761^10970-10970^10761 is 11-PRP! (36.2560s+0.0068s)

Primality testing 10761^10970-10970^10761 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 17
Running N+1 test using discriminant 23, base 2+sqrt(23)
Calling N+1 BLS with factored part 0.02% and helper 0.02% (0.09% proof)
10761^10970-10970^10761 is Fermat and Lucas PRP! (223.3432s+0.0077s)

To be completed...