Found with PFGW Version 3.5.2

2541^3478-3478^2541 is 2-PRP! (14.3261s+0.0089s)
2541^3478-3478^2541 is 3-PRP! (29.8918s+0.0125s)
2541^3478-3478^2541 is 5-PRP! (31.1732s+0.0113s)
2541^3478-3478^2541 is 7-PRP! (29.7489s+0.0126s)
2541^3478-3478^2541 is 11-PRP! (33.8918s+0.0127s)

Primality testing 2541^3478-3478^2541 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 17, base 17+sqrt(17)
Calling N-1 BLS with factored part 0.15% and helper 0.09% (0.56% proof)
2541^3478-3478^2541 is Fermat and Lucas PRP! (149.2874s+0.0173s)

To be completed...