Found with PFGW Version 3.7.5

973^7772-7772^973 is 2-PRP! (15.6015s+0.0021s)
973^7772-7772^973 is 3-PRP! (15.5982s+0.0017s)
973^7772-7772^973 is 5-PRP! (15.7766s+0.0020s)
973^7772-7772^973 is 7-PRP! (15.8678s+0.0018s)
973^7772-7772^973 is 11-PRP! (15.7446s+0.0035s)

Primality testing 973^7772-7772^973 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.06% and helper 0.05% (0.23% proof)
973^7772-7772^973 is Fermat and Lucas PRP! (81.8063s+0.0041s)

To be completed...