Found with PFGW Version 3.7.5

6849^7760-7760^6849 is 2-PRP! (25.5246s+0.0025s)
6849^7760-7760^6849 is 3-PRP! (25.5791s+0.0052s)
6849^7760-7760^6849 is 5-PRP! (27.7198s+0.0026s)
6849^7760-7760^6849 is 7-PRP! (29.1922s+0.0025s)
6849^7760-7760^6849 is 11-PRP! (25.7856s+0.0024s)

Primality testing 6849^7760-7760^6849 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 17
Running N+1 test using discriminant 23, base 8+sqrt(23)
Calling N-1 BLS with factored part 0.04% and helper 0.01% (0.13% proof)
6849^7760-7760^6849 is Fermat and Lucas PRP! (145.2984s+0.0040s)

To be completed...