Found with PFGW Version 3.6.0

3651^6280-6280^3651 is 2-PRP! (21.9312s+0.0023s)
3651^6280-6280^3651 is 3-PRP! (21.8871s+0.0025s)
3651^6280-6280^3651 is 5-PRP! (21.8143s+0.0026s)
3651^6280-6280^3651 is 7-PRP! (21.8468s+0.0032s)
3651^6280-6280^3651 is 11-PRP! (21.8699s+0.0028s)

Primality testing 3651^6280-6280^3651 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.04% and helper 0.01% (0.13% proof)
3651^6280-6280^3651 is Fermat and Lucas PRP! (105.3333s+0.0045s)

To be completed...