Found with PFGW Version 3.7.5

3753^7222-7222^3753 is 2-PRP! (36.0336s+0.0051s)
3753^7222-7222^3753 is 3-PRP! (35.9772s+0.0047s)
3753^7222-7222^3753 is 5-PRP! (35.8443s+0.0051s)
3753^7222-7222^3753 is 7-PRP! (34.4480s+0.0032s)
3753^7222-7222^3753 is 11-PRP! (35.1763s+0.0046s)

Primality testing 3753^7222-7222^3753 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.05% and helper 0.01% (0.16% proof)
3753^7222-7222^3753 is Fermat and Lucas PRP! (175.7359s+0.0054s)

To be completed...