Found with PFGW Version 3.7.5

1023^5624-5624^1023 is 2-PRP! (11.2850s+0.0018s)
1023^5624-5624^1023 is 3-PRP! (12.3318s+0.0015s)
1023^5624-5624^1023 is 5-PRP! (12.1519s+0.0016s)
1023^5624-5624^1023 is 7-PRP! (12.1947s+0.0019s)
1023^5624-5624^1023 is 11-PRP! (12.7694s+0.0019s)

Primality testing 1023^5624-5624^1023 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.07% and helper 0.04% (0.26% proof)
1023^5624-5624^1023 is Fermat and Lucas PRP! (59.4278s+0.0031s)

To be completed...