Found with PFGW Version 3.7.5

1345^5898-5898^1345 is 2-PRP! (9.8659s+0.0017s)
1345^5898-5898^1345 is 3-PRP! (10.1667s+0.0020s)
1345^5898-5898^1345 is 5-PRP! (11.0287s+0.0024s)
1345^5898-5898^1345 is 7-PRP! (9.7540s+0.0015s)
1345^5898-5898^1345 is 11-PRP! (11.7591s+0.0027s)

Primality testing 1345^5898-5898^1345 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.04% and helper 0.03% (0.14% proof)
1345^5898-5898^1345 is Fermat and Lucas PRP! (69.6923s+0.0143s)

To be completed...