Found with PFGW Version 3.6.0

3478^4869-4869^3478 is 2-PRP! (13.0765s+0.0023s)
3478^4869-4869^3478 is 3-PRP! (13.1164s+0.0023s)
3478^4869-4869^3478 is 5-PRP! (13.0794s+0.0035s)
3478^4869-4869^3478 is 7-PRP! (13.2742s+0.0021s)
3478^4869-4869^3478 is 11-PRP! (13.0684s+0.0022s)

Primality testing 3478^4869-4869^3478 [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 0.06% and helper 0.02% (0.20% proof)
3478^4869-4869^3478 is Fermat and Lucas PRP! (62.7147s+0.0034s)

To be completed...