Found with PFGW Version 3.8.0

5925^13406-13406^5925 is 2-PRP! (47.8968s+0.0057s)
5925^13406-13406^5925 is 3-PRP! (47.2664s+0.0056s)
5925^13406-13406^5925 is 5-PRP! (47.2652s+0.0064s)
5925^13406-13406^5925 is 7-PRP! (49.7473s+0.0060s)
5925^13406-13406^5925 is 11-PRP! (48.3948s+0.0067s)

Primality testing 5925^13406-13406^5925 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Running N-1 test using base 19
Running N+1 test using discriminant 29, base 4+sqrt(29)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.08% proof)
5925^13406-13406^5925 is Fermat and Lucas PRP! (368.7811s+0.0062s)

To be completed...