Found with PFGW Version 3.6.0

4623^6272-6272^4623 is 2-PRP! (21.3168s+0.0022s)
4623^6272-6272^4623 is 3-PRP! (26.2194s+0.0027s)
4623^6272-6272^4623 is 5-PRP! (25.9737s+0.0031s)
4623^6272-6272^4623 is 7-PRP! (25.9778s+0.0020s)
4623^6272-6272^4623 is 11-PRP! (25.4028s+0.0019s)

Primality testing 4623^6272-6272^4623 [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 0.04% and helper 0.01% (0.13% proof)
4623^6272-6272^4623 is Fermat and Lucas PRP! (123.0736s+0.0033s)

To be completed...