Found with PFGW Version 3.6.0

3527^4338-4338^3527 is 2-PRP! (10.4106s+0.0028s)
3527^4338-4338^3527 is 3-PRP! (10.6376s+0.0043s)
3527^4338-4338^3527 is 5-PRP! (10.8480s+0.0035s)
3527^4338-4338^3527 is 7-PRP! (10.4035s+0.0042s)
3527^4338-4338^3527 is 11-PRP! (10.2866s+0.0043s)

Primality testing 3527^4338-4338^3527 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 13+sqrt(13)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
3527^4338-4338^3527 is Fermat and Lucas PRP! (49.7236s+0.0070s)

To be completed...