Found with PFGW Version 3.7.5

3697^7626-7626^3697 is 2-PRP! (30.1469s+0.0042s)
3697^7626-7626^3697 is 3-PRP! (31.1844s+0.0043s)
3697^7626-7626^3697 is 5-PRP! (27.8506s+0.0024s)
3697^7626-7626^3697 is 7-PRP! (31.2919s+0.0040s)
3697^7626-7626^3697 is 11-PRP! (31.2331s+0.0044s)

Primality testing 3697^7626-7626^3697 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 17, base 6+sqrt(17)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.06% proof)
3697^7626-7626^3697 is Fermat and Lucas PRP! (156.5296s+0.0044s)

To be completed...