Found with PFGW Version 3.7.5

1309^10194-10194^1309 is 2-PRP! (35.5658s+0.0047s)
1309^10194-10194^1309 is 3-PRP! (34.3780s+0.0050s)
1309^10194-10194^1309 is 5-PRP! (36.2315s+0.0052s)
1309^10194-10194^1309 is 7-PRP! (34.4939s+0.0047s)
1309^10194-10194^1309 is 11-PRP! (34.7676s+0.0050s)

Primality testing 1309^10194-10194^1309 [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 17
Running N-1 test using base 19
Running N+1 test using discriminant 31, base 1+sqrt(31)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
1309^10194-10194^1309 is Fermat and Lucas PRP! (305.0483s+0.0056s)

To be completed...