Found with PFGW Version 3.8.0

3398^13349-13349^3398 is 2-PRP! (42.1092s+0.0049s)
3398^13349-13349^3398 is 3-PRP! (42.1529s+0.0048s)
3398^13349-13349^3398 is 5-PRP! (42.9267s+0.0050s)
3398^13349-13349^3398 is 7-PRP! (43.1177s+0.0052s)
3398^13349-13349^3398 is 11-PRP! (42.1757s+0.0052s)

Primality testing 3398^13349-13349^3398 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N-1 BLS with factored part 0.06% and helper 0.00% (0.17% proof)
3398^13349-13349^3398 is Fermat and Lucas PRP! (243.1253s+0.0052s)

To be completed...