Found with PFGW Version 3.7.5

1032^7637-7637^1032 is 2-PRP! (20.8082s+0.0035s)
1032^7637-7637^1032 is 3-PRP! (21.0864s+0.0037s)
1032^7637-7637^1032 is 5-PRP! (19.5429s+0.0017s)
1032^7637-7637^1032 is 7-PRP! (20.9198s+0.0038s)
1032^7637-7637^1032 is 11-PRP! (21.3304s+0.0034s)

Primality testing 1032^7637-7637^1032 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 19
Running N-1 test using base 23
Running N+1 test using discriminant 37, base 1+sqrt(37)
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.04% proof)
1032^7637-7637^1032 is Fermat and Lucas PRP! (130.7989s+0.0037s)

To be completed...