Found with PFGW Version 3.7.5

2312^6485-6485^2312 is 2-PRP! (16.8382s+0.0022s)
2312^6485-6485^2312 is 3-PRP! (17.4410s+0.0022s)
2312^6485-6485^2312 is 5-PRP! (18.9955s+0.0021s)
2312^6485-6485^2312 is 7-PRP! (20.0181s+0.0032s)
2312^6485-6485^2312 is 11-PRP! (17.9230s+0.0029s)

Primality testing 2312^6485-6485^2312 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 12+sqrt(7)
Calling N+1 BLS with factored part 0.02% and helper 0.02% (0.09% proof)
2312^6485-6485^2312 is Fermat and Lucas PRP! (86.4838s+0.0037s)

To be completed...