Found with PFGW Version 3.6.0

3608^4787-4787^3608 is 2-PRP! (12.6158s+0.0022s)
3608^4787-4787^3608 is 3-PRP! (12.8943s+0.0031s)
3608^4787-4787^3608 is 5-PRP! (12.9680s+0.0009s)
3608^4787-4787^3608 is 7-PRP! (12.8903s+0.0008s)
3608^4787-4787^3608 is 11-PRP! (12.9108s+0.0008s)

Primality testing 3608^4787-4787^3608 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N-1 test using base 13
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N+1 BLS with factored part 0.05% and helper 0.03% (0.19% proof)
3608^4787-4787^3608 is Fermat and Lucas PRP! (87.7410s+0.0033s)

To be completed...