Found with PFGW Version 3.6.0

4651^6068-6068^4651 is 2-PRP! (20.6878s+0.0097s)
4651^6068-6068^4651 is 3-PRP! (25.1940s+0.0015s)
4651^6068-6068^4651 is 5-PRP! (26.3429s+0.0011s)
4651^6068-6068^4651 is 7-PRP! (24.4913s+0.0015s)
4651^6068-6068^4651 is 11-PRP! (24.9353s+0.0034s)

Primality testing 4651^6068-6068^4651 [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 0.06% and helper 0.01% (0.18% proof)
4651^6068-6068^4651 is Fermat and Lucas PRP! (117.6204s+0.0023s)

To be completed...