Found with PFGW Version 3.6.0

3906^4547-4547^3906 is 2-PRP! (11.9466s+0.0023s)
3906^4547-4547^3906 is 3-PRP! (11.6828s+0.0024s)
3906^4547-4547^3906 is 5-PRP! (11.6993s+0.0038s)
3906^4547-4547^3906 is 7-PRP! (11.7125s+0.0023s)
3906^4547-4547^3906 is 11-PRP! (11.6853s+0.0024s)

Primality testing 3906^4547-4547^3906 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N+1 BLS with factored part 0.06% and helper 0.00% (0.20% proof)
3906^4547-4547^3906 is Fermat and Lucas PRP! (64.4708s+0.0021s)

To be completed...