Found with PFGW Version 3.7.5

6611^7398-7398^6611 is 2-PRP! (28.2067s+0.0064s)
6611^7398-7398^6611 is 3-PRP! (30.3036s+0.0016s)
6611^7398-7398^6611 is 5-PRP! (30.3494s+0.0014s)
6611^7398-7398^6611 is 7-PRP! (29.5309s+0.0015s)
6611^7398-7398^6611 is 11-PRP! (29.7261s+0.0015s)

Primality testing 6611^7398-7398^6611 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Running N+1 test using discriminant 23, base 6+sqrt(23)
Calling N-1 BLS with factored part 0.03% and helper 0.02% (0.11% proof)
6611^7398-7398^6611 is Fermat and Lucas PRP! (158.5712s+0.0032s)

To be completed...