Found with PFGW Version 3.7.5

2781^5180-5180^2781 is 2-PRP! (9.5327s+0.0024s)
2781^5180-5180^2781 is 3-PRP! (9.8740s+0.0025s)
2781^5180-5180^2781 is 5-PRP! (9.5810s+0.0024s)
2781^5180-5180^2781 is 7-PRP! (9.4448s+0.0021s)
2781^5180-5180^2781 is 11-PRP! (10.6326s+0.0021s)

Primality testing 2781^5180-5180^2781 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N-1 test using base 19
Running N-1 test using base 29
Running N+1 test using discriminant 41, base 10+sqrt(41)
Calling N-1 BLS with factored part 0.05% and helper 0.04% (0.20% proof)
2781^5180-5180^2781 is Fermat and Lucas PRP! (66.6862s+0.0017s)

To be completed...