No. A prime number is a number that can only be divided by itself and 1. The first prime number is 2 - which is also the only even prime number. The prime numbers from 1 - 20 are: 2 and 3 and 5 and 7...
The smallest prime number in which all of the digits are also prime is 2. The smallest multi-digit prime number in which all of the digits are also prime is 23.