Found with PFGW Version 3.7.5

7063^7638-7638^7063 is 2-PRP! (34.3123s+0.0037s)
7063^7638-7638^7063 is 3-PRP! (35.5794s+0.0037s)
7063^7638-7638^7063 is 5-PRP! (32.4561s+0.0031s)
7063^7638-7638^7063 is 7-PRP! (34.6103s+0.0033s)
7063^7638-7638^7063 is 11-PRP! (35.0465s+0.0034s)

Primality testing 7063^7638-7638^7063 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 6+sqrt(13)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.12% proof)
7063^7638-7638^7063 is Fermat and Lucas PRP! (175.1813s+0.0053s)

To be completed...