Magic Constant of Smallest Prime Magic Square with Consecutive Primes from 3

Theorem
The magic constant of the smallest prime magic square whose elements are consecutive odd primes from $3$ upwards is $4514$.

Proof
The smallest prime magic square whose elements are the first consecutive odd primes is:

The fact that this is the smallest is proven here.

The sum of the first $144$ prime numbers can either be calculated or looked up: it is $54 \, 169$.

We see that $2$ is not included in this prime magic square, but instead $1$ is used.

So the total of all the elements of this prime magic square is $54 \, 169 - 2 + 1 = 54 \, 168$.

There are $12$ rows, and $12$ columns, each with the same magic constant.

This magic constant must therefore be $\dfrac {54 \, 168} {12} = 4514$.

As can be seen by inspection, the sums of the elements in the rows, columns and diagonals is $4514$.