Found with PFGW Version 3.7.5

1401^8344-8344^1401 is 2-PRP! (12.3893s+0.0012s)
1401^8344-8344^1401 is 3-PRP! (12.0171s+0.0013s)
1401^8344-8344^1401 is 5-PRP! (12.3078s+0.0019s)
1401^8344-8344^1401 is 7-PRP! (12.0107s+0.0014s)
1401^8344-8344^1401 is 11-PRP! (12.1113s+0.0011s)

Primality testing 1401^8344-8344^1401 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N-1 test using base 11
Running N-1 test using base 13
Running N+1 test using discriminant 19, base 3+sqrt(19)
Calling N-1 BLS with factored part 0.06% and helper 0.04% (0.21% proof)
1401^8344-8344^1401 is Fermat and Lucas PRP! (111.7889s+0.0022s)

To be completed...