5237732522753

This number is a prime.

                                                              523 7732522753

The 5th prime-digit prime is 23 and 523 is prime. The 23rd prime-digit prime is 773 and 23773 is prime. The 773rd prime-digit prime is 2522753 and 7732522753 is prime. What about the 2522753rd? Curiously, the concatenation of 5, 23, 773 and 2522753 is another prime. [Petrov]