Found with PFGW Version 3.7.5

3403^5948-5948^3403 is 2-PRP! (14.9910s+0.0020s)
3403^5948-5948^3403 is 3-PRP! (17.0575s+0.0018s)
3403^5948-5948^3403 is 5-PRP! (16.9285s+0.0019s)
3403^5948-5948^3403 is 7-PRP! (14.8892s+0.0020s)
3403^5948-5948^3403 is 11-PRP! (15.4733s+0.0026s)

Primality testing 3403^5948-5948^3403 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.06% and helper 0.03% (0.20% proof)
3403^5948-5948^3403 is Fermat and Lucas PRP! (94.8179s+0.0036s)

To be completed...