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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