Found with PFGW Version 3.8.0

1733^13044-13044^1733 is 2-PRP! (35.7845s+0.0139s)
1733^13044-13044^1733 is 3-PRP! (36.6797s+0.0093s)
1733^13044-13044^1733 is 5-PRP! (36.1949s+0.0082s)
1733^13044-13044^1733 is 7-PRP! (36.0707s+0.0090s)
1733^13044-13044^1733 is 11-PRP! (35.9296s+0.0089s)

Primality testing 1733^13044-13044^1733 [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 11
Running N+1 test using discriminant 31, base 1+sqrt(31)
Calling N+1 BLS with factored part 0.04% and helper 0.00% (0.14% proof)
1733^13044-13044^1733 is Fermat and Lucas PRP! (248.3285s+0.0096s)

To be completed...