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Problem 60

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Prime pair sets

The primes $3$, $7$, $109$, and $673$, are quite remarkable. By taking any two primes and concatenating them in any order the result will always be prime. For example, taking $7$ and $109$, both $7109$ and $1097$ are prime. The sum of these four primes, $792$, represents the lowest sum for a set of four primes with this property.

Find the lowest sum for a set of five primes for which any two primes concatenate to produce another prime.

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素数对集合

$3$、$7$、$109$和$673$是非常特别的一组素数。任取其中的两个并且以任意顺序连接起来，其结果仍然是个素数。例如，选择$7$和$109$，得到$7109$和$1097$均为素数。这四个素数的和是$792$，而且是满足这个性质的一组四个素数的最小和。

若有一组五个素数，任取其中的两个并且以任意顺序连接起来，其结果仍然是个素数，求这样一组素数的最小和。

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