Found with PFGW Version 3.6.0

369^4868-4868^369 is 2-PRP! (5.8953s+0.0031s)
369^4868-4868^369 is 3-PRP! (5.9980s+0.0032s)
369^4868-4868^369 is 5-PRP! (5.8721s+0.0017s)
369^4868-4868^369 is 7-PRP! (5.8556s+0.0016s)
369^4868-4868^369 is 11-PRP! (5.8706s+0.0017s)

Primality testing 369^4868-4868^369 [N-1/N+1, Brillhart-Lehmer-Selfridge]
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 0.13% and helper 0.08% (0.46% proof)
369^4868-4868^369 is Fermat and Lucas PRP! (29.1298s+0.0018s)

To be completed...