Found with PFGW Version 3.6.0

1953^3938-3938^1953 is 2-PRP! (6.6253s+0.0018s)
1953^3938-3938^1953 is 3-PRP! (6.6276s+0.0018s)
1953^3938-3938^1953 is 5-PRP! (6.5903s+0.0032s)
1953^3938-3938^1953 is 7-PRP! (6.5678s+0.0019s)
1953^3938-3938^1953 is 11-PRP! (6.5900s+0.0021s)

Primality testing 1953^3938-3938^1953 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 12+sqrt(17)
Calling N+1 BLS with factored part 0.04% and helper 0.03% (0.16% proof)
1953^3938-3938^1953 is Fermat and Lucas PRP! (39.6316s+0.0017s)

To be completed...