Found with PFGW Version 3.7.5

1733^5478-5478^1733 is 2-PRP! (9.9922s+0.0020s)
1733^5478-5478^1733 is 3-PRP! (12.4925s+0.0024s)
1733^5478-5478^1733 is 5-PRP! (15.3295s+0.0036s)
1733^5478-5478^1733 is 7-PRP! (11.3196s+0.0031s)
1733^5478-5478^1733 is 11-PRP! (11.4094s+0.0023s)

Primality testing 1733^5478-5478^1733 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 8+sqrt(17)
Calling N-1 BLS with factored part 0.06% and helper 0.01% (0.18% proof)
1733^5478-5478^1733 is Fermat and Lucas PRP! (53.6123s+0.0047s)

To be completed...