Found with PFGW Version 3.7.5

352^8067-8067^352 is 2-PRP! (18.1644s+0.0027s)
352^8067-8067^352 is 3-PRP! (19.4060s+0.0038s)
352^8067-8067^352 is 5-PRP! (16.8290s+0.0028s)
352^8067-8067^352 is 7-PRP! (19.5794s+0.0032s)
352^8067-8067^352 is 11-PRP! (15.7610s+0.0013s)

Primality testing 352^8067-8067^352 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 6+sqrt(7)
Calling N+1 BLS with factored part 0.04% and helper 0.03% (0.16% proof)
352^8067-8067^352 is Fermat and Lucas PRP! (100.1226s+0.0035s)

To be completed...