ホーム - Project Euler

Problem 49¶

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?

素数数列¶

項差3330の等差数列$1487,4817,8147$は次の2つの変わった性質を持つ.

1. 3つの項はそれぞれ素数である.
2. 各項は他の項の置換で表される.

1, 2, 3桁の素数にはこのような性質を持った数列は存在しないが, 4桁の増加列にはもう1つ存在する.

それではこの数列の3つの項を連結した12桁の数を求めよ.