# Prepostorous Primes

Number Theory Level 4

Let $$n=\overline{abc}$$ be a 3-digit number such that all of the following 7 numbers are prime:

$\overline{abc}$ $\overline{ab}$ $\overline{ac}$ $\overline{bc}$ $\overline{ba}$ $\overline{ca}$ $\overline{cb}$

Find the sum of all possible values of $$n$$.

$$\text{Details and Assumptions}$$

$$\overline{xyz}$$ means the three-digit number with $$x$$ in the hundreds placem $$y$$ in the tens place, and $$z$$ in the ones place, where $$x,y,z$$ are digits.

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