Found with PFGW Version 3.8.0

444^12791-12791^444 is 2-PRP! (22.8980s+0.0039s)
444^12791-12791^444 is 3-PRP! (22.8350s+0.0045s)
444^12791-12791^444 is 5-PRP! (23.5355s+0.0038s)
444^12791-12791^444 is 7-PRP! (23.1305s+0.0043s)
444^12791-12791^444 is 11-PRP! (23.0232s+0.0042s)

Primality testing 444^12791-12791^444 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.04% and helper 0.02% (0.14% proof)
444^12791-12791^444 is Fermat and Lucas PRP! (114.7102s+0.0069s)

To be completed...