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Problem 49

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Prime Permutations

The arithmetic sequence, $1487$, $4817$, $8147$, in which each of the terms increases by $3330$, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the $4$-digit numbers are permutations of one another.

There are no arithmetic sequences made up of three $1$-, $2$-, or $3$-digit primes, exhibiting this property, but there is one other $4$-digit increasing sequence.

What $12$-digit number do you form by concatenating the three terms in this sequence?

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素数重排

公差为$3330$的三项等差数列$1487$、$4817$、$8147$在两个方面非常特别：其一，每一项都是素数；其二，两两都是重新排列的关系。

不存在由一位、两位或三位素数构成的三项等差数列同时满足上述性质，但存在另一个由四位素数构成的此类递增等差数列。

将这个数列的三项连接起来得到的$12$位数是多少？

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