Candice feels the power!Number Theory Level 3
On her way back with a box full of beverage cans, she spots a random man in an overcrowded street. She decides to boast of her mathematical skills and tells the man : "I can solve any mathematics problem in the world! If you don't believe me, ask me anything! ".
Unfortunately, Candice did not realize that this man was a skilled Number Theorist ! He replies : "All right then, I am thinking of a number. The sum of the digits of this number, raised to the number of digits of this number produces this very number itself. What number am I thinking of?". He adds, "To make things simpler, this number has as many digits as the number of primes between \(310\) and \(320\)."
Candice appears dumbstruck and can't get through this question alone. Can you help Candice find this number?