Found with PFGW Version 3.7.5

3696^5255-5255^3696 is 2-PRP! (11.1757s+0.0021s)
3696^5255-5255^3696 is 3-PRP! (11.3993s+0.0027s)
3696^5255-5255^3696 is 5-PRP! (12.5377s+0.0020s)
3696^5255-5255^3696 is 7-PRP! (13.6906s+0.0026s)
3696^5255-5255^3696 is 11-PRP! (11.5592s+0.0026s)

Primality testing 3696^5255-5255^3696 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 17
Running N+1 test using discriminant 31, base 1+sqrt(31)
Calling N-1 BLS with factored part 0.07% and helper 0.03% (0.24% proof)
3696^5255-5255^3696 is Fermat and Lucas PRP! (58.5083s+0.0038s)

To be completed...