Found with PFGW Version 3.6.0

4721^5130-5130^4721 is 2-PRP! (15.5078s+0.0024s)
4721^5130-5130^4721 is 3-PRP! (15.6122s+0.0026s)
4721^5130-5130^4721 is 5-PRP! (16.6365s+0.0021s)
4721^5130-5130^4721 is 7-PRP! (16.5872s+0.0023s)
4721^5130-5130^4721 is 11-PRP! (15.3290s+0.0020s)

Primality testing 4721^5130-5130^4721 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N-1 test using base 23
Running N-1 test using base 29
Running N+1 test using discriminant 41, base 8+sqrt(41)
Calling N-1 BLS with factored part 0.11% and helper 0.03% (0.35% proof)
4721^5130-5130^4721 is Fermat and Lucas PRP! (105.0776s+0.0033s)

To be completed...