Found with PFGW Version 3.6.0

3212^4267-4267^3212 is 2-PRP! (10.1445s+0.0021s)
3212^4267-4267^3212 is 3-PRP! (10.1127s+0.0026s)
3212^4267-4267^3212 is 5-PRP! (10.0518s+0.0039s)
3212^4267-4267^3212 is 7-PRP! (10.0720s+0.0021s)
3212^4267-4267^3212 is 11-PRP! (10.1518s+0.0026s)

Primality testing 3212^4267-4267^3212 [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 13, base 2+sqrt(13)
Calling N+1 BLS with factored part 0.10% and helper 0.03% (0.34% proof)
3212^4267-4267^3212 is Fermat and Lucas PRP! (57.9487s+0.0020s)

To be completed...