Found with PFGW Version 3.7.5

3338^10739-10739^3338 is 2-PRP! (26.0315s+0.0015s)
3338^10739-10739^3338 is 3-PRP! (26.0809s+0.0014s)
3338^10739-10739^3338 is 5-PRP! (26.5166s+0.0014s)
3338^10739-10739^3338 is 7-PRP! (26.4663s+0.0014s)
3338^10739-10739^3338 is 11-PRP! (26.4784s+0.0016s)

Primality testing 3338^10739-10739^3338 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N-1 BLS with factored part 0.05% and helper 0.01% (0.15% proof)
3338^10739-10739^3338 is Fermat and Lucas PRP! (176.1431s+0.0026s)

To be completed...