Found with PFGW Version 3.8.3

15445^15782-15782^15445 is 2-PRP! (52.6640s+0.0030s)
15445^15782-15782^15445 is 3-PRP! (50.1191s+0.0032s)
15445^15782-15782^15445 is 5-PRP! (50.3323s+0.0031s)
15445^15782-15782^15445 is 7-PRP! (50.4017s+0.0031s)
15445^15782-15782^15445 is 11-PRP! (50.4660s+0.0030s)

Primality testing 15445^15782-15782^15445 [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 discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.02% and helper 0.00% (0.05% proof)
15445^15782-15782^15445 is Fermat and Lucas PRP! (364.2371s+0.0036s)

To be completed...