Found with PFGW Version 3.7.5

2511^12352+12352^2511 is 2-PRP! (60.9211s+0.0036s)
2511^12352+12352^2511 is 3-PRP! (60.9979s+0.0039s)
2511^12352+12352^2511 is 5-PRP! (62.8809s+0.0050s)
2511^12352+12352^2511 is 7-PRP! (65.8782s+0.0080s)
2511^12352+12352^2511 is 11-PRP! (64.7182s+0.0050s)

Primality testing 2511^12352+12352^2511 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 6+sqrt(13)
Calling N-1 BLS with factored part 0.05% and helper 0.01% (0.16% proof)
2511^12352+12352^2511 is Fermat and Lucas PRP! (330.3126s+0.0049s)

To be completed...