Found with PFGW Version 3.6.0

3665^6686-6686^3665 is 2-PRP! (23.3252s+0.0034s)
3665^6686-6686^3665 is 3-PRP! (23.3007s+0.0029s)
3665^6686-6686^3665 is 5-PRP! (23.2875s+0.0029s)
3665^6686-6686^3665 is 7-PRP! (23.3773s+0.0029s)
3665^6686-6686^3665 is 11-PRP! (23.3192s+0.0025s)

Primality testing 3665^6686-6686^3665 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 8+sqrt(11)
Calling N+1 BLS with factored part 0.05% and helper 0.03% (0.18% proof)
3665^6686-6686^3665 is Fermat and Lucas PRP! (113.4497s+0.0024s)

To be completed...