Found with PFGW Version 3.7.5

3187^5772-5772^3187 is 2-PRP! (14.4506s+0.0099s)
3187^5772-5772^3187 is 3-PRP! (14.7732s+0.0014s)
3187^5772-5772^3187 is 5-PRP! (14.6439s+0.0012s)
3187^5772-5772^3187 is 7-PRP! (14.6603s+0.0011s)
3187^5772-5772^3187 is 11-PRP! (14.6465s+0.0012s)

Primality testing 3187^5772-5772^3187 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 11
Running N+1 test using discriminant 19, base 2+sqrt(19)
Calling N-1 BLS with factored part 0.07% and helper 0.07% (0.29% proof)
3187^5772-5772^3187 is Fermat and Lucas PRP! (86.7299s+0.0019s)

To be completed...