# Primes in a Prime Base

**Number Theory**Level 3

What are the first seven prime numbers when written in base 7?

Concatenate the numbers without any leading zeroes, i.e. each number starts with a non-zero digit.

As an explicit example, the first seven prime numbers when written in base 10 are 2, 3, 5, 7, 11, 13, 17. After concatenation we get 2357111317.