Found with PFGW Version 3.8.0

12001^13104-13104^12001 is 2-PRP! (54.7564s+0.0174s)
12001^13104-13104^12001 is 3-PRP! (54.6948s+0.0106s)
12001^13104-13104^12001 is 5-PRP! (54.6166s+0.0155s)
12001^13104-13104^12001 is 7-PRP! (54.7173s+0.0099s)
12001^13104-13104^12001 is 11-PRP! (54.6574s+0.0103s)

Primality testing 12001^13104-13104^12001 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 11
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N-1 BLS with factored part 0.04% and helper 0.02% (0.13% proof)
12001^13104-13104^12001 is Fermat and Lucas PRP! (332.2516s+0.0109s)

To be completed...