Found with PFGW Version 3.6.0

1235^4512-4512^1235 is 2-PRP! (9.5397s+0.0032s)
1235^4512-4512^1235 is 3-PRP! (9.5588s+0.0032s)
1235^4512-4512^1235 is 5-PRP! (9.5791s+0.0046s)
1235^4512-4512^1235 is 7-PRP! (9.4991s+0.0032s)
1235^4512-4512^1235 is 11-PRP! (9.5094s+0.0046s)

Primality testing 1235^4512-4512^1235 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 7
Running N+1 test using discriminant 19, base 2+sqrt(19)
Calling N+1 BLS with factored part 0.04% and helper 0.02% (0.15% proof)
1235^4512-4512^1235 is Fermat and Lucas PRP! (53.2330s+0.0019s)

To be completed...