Found with PFGW Version 3.7.5

7829^8462-8462^7829 is 2-PRP! (21.2283s+0.0016s)
7829^8462-8462^7829 is 3-PRP! (21.1748s+0.0018s)
7829^8462-8462^7829 is 5-PRP! (21.4560s+0.0020s)
7829^8462-8462^7829 is 7-PRP! (21.4038s+0.0016s)
7829^8462-8462^7829 is 11-PRP! (21.3608s+0.0016s)

Primality testing 7829^8462-8462^7829 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.02% and helper 0.00% (0.06% proof)
7829^8462-8462^7829 is Fermat and Lucas PRP! (104.7083s+0.0029s)

To be completed...