Found with PFGW Version 3.6.0

2782^3933-3933^2782 is 2-PRP! (9.1469s+0.0020s)
2782^3933-3933^2782 is 3-PRP! (9.1325s+0.0020s)
2782^3933-3933^2782 is 5-PRP! (9.0898s+0.0035s)
2782^3933-3933^2782 is 7-PRP! (9.0461s+0.0022s)
2782^3933-3933^2782 is 11-PRP! (9.0982s+0.0020s)

Primality testing 2782^3933-3933^2782 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N+1 test using discriminant 41, base 2+sqrt(41)
Calling N+1 BLS with factored part 0.11% and helper 0.08% (0.41% proof)
2782^3933-3933^2782 is Fermat and Lucas PRP! (51.5056s+0.0019s)

To be completed...