Primes in a Prime Base

We will convert each of the first seven prime numbers from base 10 to base 7.

$\begin{array}{rcl} 2 & = 0 \times 7^{1} + 2 \times 7^{0} & = 02_{7}\\ 3 & = 0 \times 7^{1} + 3 \times 7^{0} & = 03_{7}\\ 5 & = 0 \times 7^{1} + 5 \times 7^{0} & = 05_{7} \\ 7 & = 1 \times 7^{1} + 0 \times 7 ^ {0} & = 10_{7} \\ 11 & = 1 \times 7^{1} + 4 \times 7 ^ {0} & = 14_{7} \\ 13 & = 1 \times 7^{1} + 6 \times 7 ^ {0} & = 16_{7} \\ 17 & = 2 \times 7^{1} + 3 \times 7 ^ {0} & = 23_{7} \\ \end{array}$

The first seven prime numbers when written in base 7 are 2, 3, 5, 10, 14, 16, 23. Therefore the answer to this problem is $\boxed{ 23510141623 }$ $_\square$

nice solution Gaba.