Found with PFGW Version 3.7.5

4862^12357+12357^4862 is 2-PRP! (66.3417s+0.0040s)
4862^12357+12357^4862 is 3-PRP! (66.6137s+0.0041s)
4862^12357+12357^4862 is 5-PRP! (67.4117s+0.0045s)
4862^12357+12357^4862 is 7-PRP! (66.3177s+0.0040s)
4862^12357+12357^4862 is 11-PRP! (72.5284s+0.0089s)

Primality testing 4862^12357+12357^4862 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.05% proof)
4862^12357+12357^4862 is Fermat and Lucas PRP! (373.0543s+0.0048s)

To be completed...