Found with PFGW Version 3.8.0

7009^13352-13352^7009 is 2-PRP! (48.3347s+0.0181s)
7009^13352-13352^7009 is 3-PRP! (48.5593s+0.0014s)
7009^13352-13352^7009 is 5-PRP! (48.4025s+0.0019s)
7009^13352-13352^7009 is 7-PRP! (49.0477s+0.0019s)
7009^13352-13352^7009 is 11-PRP! (47.4695s+0.0020s)

Primality testing 7009^13352-13352^7009 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 7+sqrt(11)
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.04% proof)
7009^13352-13352^7009 is Fermat and Lucas PRP! (294.2300s+0.0305s)

To be completed...