Found with PFGW Version 3.7.5

3436^7455-7455^3436 is 2-PRP! (21.2283s+0.0025s)
3436^7455-7455^3436 is 3-PRP! (21.1868s+0.0021s)
3436^7455-7455^3436 is 5-PRP! (21.5024s+0.0021s)
3436^7455-7455^3436 is 7-PRP! (21.4294s+0.0022s)
3436^7455-7455^3436 is 11-PRP! (21.1925s+0.0021s)

Primality testing 3436^7455-7455^3436 [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 discriminant 17, base 1+sqrt(17)
Calling N+1 BLS with factored part 0.04% and helper 0.02% (0.13% proof)
3436^7455-7455^3436 is Fermat and Lucas PRP! (130.4918s+0.0034s)

To be completed...