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Problem 60


Problem 60


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.


素数对的集合

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,我们得到7109和1097均为素数。这四个素数的和是792,这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。