Found with PFGW Version 3.6.0

2294^3639-3639^2294 is 2-PRP! (5.5203s+0.0008s)
2294^3639-3639^2294 is 3-PRP! (5.7202s+0.0005s)
2294^3639-3639^2294 is 5-PRP! (5.7610s+0.0005s)
2294^3639-3639^2294 is 7-PRP! (5.7883s+0.0023s)
2294^3639-3639^2294 is 11-PRP! (5.7980s+0.0005s)

Primality testing 2294^3639-3639^2294 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.06% and helper 0.05% (0.23% proof)
2294^3639-3639^2294 is Fermat and Lucas PRP! (28.5833s+0.0021s)

To be completed...