Found with PFGW Version 3.8.0

611^23586+23586^611 is 2-PRP! (89.4367s+0.0065s)
611^23586+23586^611 is 3-PRP! (87.0301s+0.0071s)
611^23586+23586^611 is 5-PRP! (88.6030s+0.0075s)
611^23586+23586^611 is 7-PRP! (88.2535s+0.0070s)
611^23586+23586^611 is 11-PRP! (89.3798s+0.0093s)

Primality testing 611^23586+23586^611 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 7
Running N+1 test using discriminant 19, base 2+sqrt(19)
Calling N+1 BLS with factored part 0.01% and helper 0.00% (0.04% proof)
611^23586+23586^611 is Fermat and Lucas PRP! (567.6876s+0.0080s)

To be completed...