Found with PFGW Version 3.5.2

1729^3564-3564^1729 is 2-PRP! (13.4176s+0.0048s)
1729^3564-3564^1729 is 3-PRP! (19.2068s+0.0051s)
1729^3564-3564^1729 is 5-PRP! (26.1247s+0.0116s)
1729^3564-3564^1729 is 7-PRP! (30.2577s+0.0111s)
1729^3564-3564^1729 is 11-PRP! (16.1214s+0.0052s)

Primality testing 1729^3564-3564^1729 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 8+sqrt(13)
Calling N-1 BLS with factored part 0.08% and helper 0.02% (0.25% proof)
1729^3564-3564^1729 is Fermat and Lucas PRP! (177.1562s+0.0149s)

To be completed...