Found with PFGW Version 3.7.5

3920^5371-5371^3920 is 2-PRP! (11.3828s+0.0033s)
3920^5371-5371^3920 is 3-PRP! (11.4861s+0.0030s)
3920^5371-5371^3920 is 5-PRP! (11.0082s+0.0029s)
3920^5371-5371^3920 is 7-PRP! (11.8027s+0.0024s)
3920^5371-5371^3920 is 11-PRP! (11.2196s+0.0020s)

Primality testing 3920^5371-5371^3920 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.02% and helper 0.02% (0.07% proof)
3920^5371-5371^3920 is Fermat and Lucas PRP! (61.8190s+0.0037s)

To be completed...