Found with PFGW Version 3.8.0

572^23601+23601^572 is 2-PRP! (85.1054s+0.0064s)
572^23601+23601^572 is 3-PRP! (85.4525s+0.0067s)
572^23601+23601^572 is 5-PRP! (86.6570s+0.0064s)
572^23601+23601^572 is 7-PRP! (87.0187s+0.0062s)
572^23601+23601^572 is 11-PRP! (88.3158s+0.0083s)

Primality testing 572^23601+23601^572 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 19, base 3+sqrt(19)
Calling N+1 BLS with factored part 0.02% and helper 0.00% (0.08% proof)
572^23601+23601^572 is Fermat and Lucas PRP! (507.9813s+0.0067s)

To be completed...