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Problem 49

1. Problem

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?

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?

2. Solution