Found with PFGW Version 3.7.5

7964^9089-9089^7964 is 2-PRP! (22.7577s+0.0016s)
7964^9089-9089^7964 is 3-PRP! (22.5209s+0.0019s)
7964^9089-9089^7964 is 5-PRP! (22.4402s+0.0018s)
7964^9089-9089^7964 is 7-PRP! (22.4925s+0.0018s)
7964^9089-9089^7964 is 11-PRP! (22.8219s+0.0018s)

Primality testing 7964^9089-9089^7964 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 8+sqrt(7)
Calling N+1 BLS with factored part 0.06% and helper 0.04% (0.21% proof)
7964^9089-9089^7964 is Fermat and Lucas PRP! (117.2175s+0.0027s)

To be completed...