Found with PFGW Version 3.7.5

165^20972-20972^165 is 2-PRP! (40.8477s+0.0024s)
165^20972-20972^165 is 3-PRP! (40.8407s+0.0026s)
165^20972-20972^165 is 5-PRP! (40.7078s+0.0026s)
165^20972-20972^165 is 7-PRP! (40.7201s+0.0026s)
165^20972-20972^165 is 11-PRP! (40.7992s+0.0025s)

Primality testing 165^20972-20972^165 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 8+sqrt(13)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.08% proof)
165^20972-20972^165 is Fermat and Lucas PRP! (205.1897s+0.0034s)

To be completed...