Found with PFGW Version 3.6.0

3000^3871-3871^3000 is 2-PRP! (8.8334s+0.0021s)
3000^3871-3871^3000 is 3-PRP! (9.2109s+0.0032s)
3000^3871-3871^3000 is 5-PRP! (9.1136s+0.0020s)
3000^3871-3871^3000 is 7-PRP! (9.1498s+0.0019s)
3000^3871-3871^3000 is 11-PRP! (9.3099s+0.0020s)

Primality testing 3000^3871-3871^3000 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N-1 BLS with factored part 0.19% and helper 0.07% (0.64% proof)
3000^3871-3871^3000 is Fermat and Lucas PRP! (43.1252s+0.0036s)

To be completed...