Found with PFGW Version 3.6.0

7127^10040-10040^7127 is 2-PRP! (68.4380s+0.0033s)
7127^10040-10040^7127 is 3-PRP! (68.2649s+0.0050s)
7127^10040-10040^7127 is 5-PRP! (68.2463s+0.0050s)
7127^10040-10040^7127 is 7-PRP! (68.1947s+0.0040s)
7127^10040-10040^7127 is 11-PRP! (68.2457s+0.0048s)

Primality testing 7127^10040-10040^7127 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 7+sqrt(11)
Calling N+1 BLS with factored part 0.04% and helper 0.03% (0.15% proof)
7127^10040-10040^7127 is Fermat and Lucas PRP! (409.8365s+0.0049s)

To be completed...