Found with PFGW Version 3.7.5

2699^7070-7070^2699 is 2-PRP! (20.5503s+0.0025s)
2699^7070-7070^2699 is 3-PRP! (21.6111s+0.0039s)
2699^7070-7070^2699 is 5-PRP! (21.0500s+0.0037s)
2699^7070-7070^2699 is 7-PRP! (21.1849s+0.0026s)
2699^7070-7070^2699 is 11-PRP! (21.7342s+0.0022s)

Primality testing 2699^7070-7070^2699 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 13
Running N+1 test using discriminant 19, base 2+sqrt(19)
Calling N+1 BLS with factored part 0.06% and helper 0.03% (0.20% proof)
2699^7070-7070^2699 is Fermat and Lucas PRP! (137.2210s+0.0045s)

To be completed...