Found with PFGW Version 3.8.0

12601^13128-13128^12601 is 2-PRP! (56.6627s+0.0113s)
12601^13128-13128^12601 is 3-PRP! (56.7530s+0.0109s)
12601^13128-13128^12601 is 5-PRP! (56.4986s+0.0106s)
12601^13128-13128^12601 is 7-PRP! (56.5756s+0.0117s)
12601^13128-13128^12601 is 11-PRP! (56.9425s+0.0122s)

Primality testing 12601^13128-13128^12601 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 7
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 6+sqrt(17)
Calling N-1 BLS with factored part 0.03% and helper 0.02% (0.10% proof)
12601^13128-13128^12601 is Fermat and Lucas PRP! (392.2492s+0.0111s)

To be completed...