Found with PFGW Version 3.6.0

706^4125-4125^706 is 2-PRP! (5.3173s+0.0029s)
706^4125-4125^706 is 3-PRP! (5.5170s+0.0030s)
706^4125-4125^706 is 5-PRP! (5.5165s+0.0036s)
706^4125-4125^706 is 7-PRP! (5.5292s+0.0039s)
706^4125-4125^706 is 11-PRP! (5.5424s+0.0039s)

Primality testing 706^4125-4125^706 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N-1 BLS with factored part 0.14% and helper 0.11% (0.52% proof)
706^4125-4125^706 is Fermat and Lucas PRP! (32.6371s+0.0016s)

To be completed...