Found with PFGW Version 3.7.5

249^38030+38030^249 is 2-PRP! (162.4004s+0.0028s)
249^38030+38030^249 is 3-PRP! (163.1067s+0.0028s)
249^38030+38030^249 is 5-PRP! (160.0072s+0.0030s)
249^38030+38030^249 is 7-PRP! (159.6060s+0.0029s)
249^38030+38030^249 is 11-PRP! (159.3536s+0.0030s)

Primality testing 249^38030+38030^249 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 17
Running N+1 test using discriminant 29, base 16+sqrt(29)
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.05% proof)
249^38030+38030^249 is Fermat and Lucas PRP! (987.0747s+0.0029s)

To be completed...