Found with PFGW Version 3.6.0

3371^3872-3872^3371 is 2-PRP! (8.9837s+0.0021s)
3371^3872-3872^3371 is 3-PRP! (9.3253s+0.0020s)
3371^3872-3872^3371 is 5-PRP! (9.2480s+0.0019s)
3371^3872-3872^3371 is 7-PRP! (9.2848s+0.0033s)
3371^3872-3872^3371 is 11-PRP! (9.3189s+0.0035s)

Primality testing 3371^3872-3872^3371 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 17, base 8+sqrt(17)
Calling N-1 BLS with factored part 0.04% and helper 0.03% (0.15% proof)
3371^3872-3872^3371 is Fermat and Lucas PRP! (43.7791s+0.0034s)

To be completed...