Found with PFGW Version 3.6.0

1624^4491-4491^1624 is 2-PRP! (9.8504s+0.0018s)
1624^4491-4491^1624 is 3-PRP! (9.8533s+0.0036s)
1624^4491-4491^1624 is 5-PRP! (9.8388s+0.0018s)
1624^4491-4491^1624 is 7-PRP! (9.8579s+0.0017s)
1624^4491-4491^1624 is 11-PRP! (9.8311s+0.0019s)

Primality testing 1624^4491-4491^1624 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N-1 test using base 11
Running N-1 test using base 23
Running N-1 test using base 41
Running N-1 test using base 47
Running N-1 test using base 59
Running N-1 test using base 61
Running N+1 test using discriminant 71, base 2+sqrt(71)
Calling N+1 BLS with factored part 0.06% and helper 0.05% (0.25% proof)
1624^4491-4491^1624 is Fermat and Lucas PRP! (115.2486s+0.0036s)

To be completed...