Found with PFGW Version 3.7.5

6937^9732-9732^6937 is 2-PRP! (26.6441s+0.0014s)
6937^9732-9732^6937 is 3-PRP! (26.4457s+0.0015s)
6937^9732-9732^6937 is 5-PRP! (26.1237s+0.0011s)
6937^9732-9732^6937 is 7-PRP! (25.9700s+0.0013s)
6937^9732-9732^6937 is 11-PRP! (25.7346s+0.0011s)

Primality testing 6937^9732-9732^6937 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 13
Running N-1 test using base 17
Running N-1 test using base 23
Running N+1 test using discriminant 53, base 1+sqrt(53)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.08% proof)
6937^9732-9732^6937 is Fermat and Lucas PRP! (225.8097s+0.0073s)

To be completed...