Found with PFGW Version 3.7.5

6741^8842-8842^6741 is 2-PRP! (21.9847s+0.0024s)
6741^8842-8842^6741 is 3-PRP! (22.1804s+0.0025s)
6741^8842-8842^6741 is 5-PRP! (22.5747s+0.0024s)
6741^8842-8842^6741 is 7-PRP! (21.8833s+0.0026s)
6741^8842-8842^6741 is 11-PRP! (22.4579s+0.0031s)

Primality testing 6741^8842-8842^6741 [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 0.00% (0.18% proof)
6741^8842-8842^6741 is Fermat and Lucas PRP! (109.8731s+0.0025s)

To be completed...