Found with PFGW Version 3.7.5

6110^7811-7811^6110 is 2-PRP! (39.9470s+0.0034s)
6110^7811-7811^6110 is 3-PRP! (33.7687s+0.0026s)
6110^7811-7811^6110 is 5-PRP! (38.4053s+0.0027s)
6110^7811-7811^6110 is 7-PRP! (27.7662s+0.0023s)
6110^7811-7811^6110 is 11-PRP! (27.4415s+0.0023s)

Primality testing 6110^7811-7811^6110 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 11
Running N-1 test using base 19
Running N+1 test using discriminant 37, base 1+sqrt(37)
Calling N+1 BLS with factored part 0.03% and helper 0.00% (0.08% proof)
6110^7811-7811^6110 is Fermat and Lucas PRP! (240.5850s+0.0051s)

To be completed...