Found with PFGW Version 3.7.5

11641^12310+12310^11641 is 2-PRP! (109.2187s+0.0060s)
11641^12310+12310^11641 is 3-PRP! (106.4140s+0.0061s)
11641^12310+12310^11641 is 5-PRP! (104.6430s+0.0059s)
11641^12310+12310^11641 is 7-PRP! (107.8302s+0.0070s)
11641^12310+12310^11641 is 11-PRP! (107.0809s+0.0059s)

Primality testing 11641^12310+12310^11641 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 8+sqrt(11)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
11641^12310+12310^11641 is Fermat and Lucas PRP! (670.8102s+0.0060s)

To be completed...