Found with PFGW Version 3.7.5

3783^8572-8572^3783 is 2-PRP! (16.2349s+0.0013s)
3783^8572-8572^3783 is 3-PRP! (16.1309s+0.0013s)
3783^8572-8572^3783 is 5-PRP! (16.4799s+0.0016s)
3783^8572-8572^3783 is 7-PRP! (16.0943s+0.0013s)
3783^8572-8572^3783 is 11-PRP! (16.1741s+0.0013s)

Primality testing 3783^8572-8572^3783 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.03% and helper 0.02% (0.12% proof)
3783^8572-8572^3783 is Fermat and Lucas PRP! (81.1385s+0.0024s)

To be completed...