Found with PFGW Version 3.6.0

1723^3846-3846^1723 is 2-PRP! (5.6298s+0.0018s)
1723^3846-3846^1723 is 3-PRP! (5.6071s+0.0031s)
1723^3846-3846^1723 is 5-PRP! (5.6825s+0.0017s)
1723^3846-3846^1723 is 7-PRP! (5.5996s+0.0018s)
1723^3846-3846^1723 is 11-PRP! (5.5954s+0.0018s)

Primality testing 1723^3846-3846^1723 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.09% and helper 0.06% (0.34% proof)
1723^3846-3846^1723 is Fermat and Lucas PRP! (28.6973s+0.0031s)

To be completed...