Found with PFGW Version 3.7.5

6372^10537-10537^6372 is 2-PRP! (34.6238s+0.0017s)
6372^10537-10537^6372 is 3-PRP! (34.5113s+0.0016s)
6372^10537-10537^6372 is 5-PRP! (35.1304s+0.0017s)
6372^10537-10537^6372 is 7-PRP! (34.5269s+0.0018s)
6372^10537-10537^6372 is 11-PRP! (34.5525s+0.0017s)

Primality testing 6372^10537-10537^6372 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N-1 BLS with factored part 0.04% and helper 0.02% (0.16% proof)
6372^10537-10537^6372 is Fermat and Lucas PRP! (167.5139s+0.0024s)

To be completed...