Found with PFGW Version 3.7.5

249^10274-10274^249 is 2-PRP! (9.8663s+0.0018s)
249^10274-10274^249 is 3-PRP! (10.1304s+0.0022s)
249^10274-10274^249 is 5-PRP! (10.1323s+0.0018s)
249^10274-10274^249 is 7-PRP! (10.2753s+0.0021s)
249^10274-10274^249 is 11-PRP! (10.1511s+0.0019s)

Primality testing 249^10274-10274^249 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 10+sqrt(13)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.06% proof)
249^10274-10274^249 is Fermat and Lucas PRP! (64.9732s+0.0018s)

To be completed...