Found with PFGW Version 3.5.2

6604^6609-6609^6604 is 2-PRP! (65.7752s+0.0083s)
6604^6609-6609^6604 is 3-PRP! (84.6792s+0.0082s)
6604^6609-6609^6604 is 5-PRP! (135.8881s+0.0131s)
6604^6609-6609^6604 is 7-PRP! (143.7927s+0.0133s)
6604^6609-6609^6604 is 11-PRP! (94.8663s+0.0081s)

Primality testing 6604^6609-6609^6604 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
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 0.03% and helper 0.00% (0.11% proof)
6604^6609-6609^6604 is Fermat and Lucas PRP! (999.9517s+0.0169s)

To be completed...