(* This is the number 37765 37764 37763 ... 5 4 3 2 1 *)

ReverseConsecutiveIntegers[n_] :=
FromDigits[Flatten[IntegerDigits /@ Range[n, 1, -1]]]

Timing[PrimeQ[ReverseConsecutiveIntegers[37765]]]
{154064.357366, True}

(* Mathematica s PRP test returns True after ~1.75 CPU days *)

To be completed...