Found with PFGW Version 3.7.5

6897^7724-7724^6897 is 2-PRP! (35.6976s+0.0030s)
6897^7724-7724^6897 is 3-PRP! (35.4581s+0.0035s)
6897^7724-7724^6897 is 5-PRP! (35.7141s+0.0036s)
6897^7724-7724^6897 is 7-PRP! (32.2062s+0.0033s)
6897^7724-7724^6897 is 11-PRP! (34.7518s+0.0033s)

Primality testing 6897^7724-7724^6897 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 6+sqrt(13)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.08% proof)
6897^7724-7724^6897 is Fermat and Lucas PRP! (216.8094s+0.0051s)

To be completed...