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**Problem:**

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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**Solution:**

296962999629

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**Code:**

The solution may include methods that will be found here: Library.java .

The solution may include methods that will be found here: Library.java .

public interface EulerSolution{ public String run(); }

/* * Solution to Project Euler problem 49 * By Nayuki Minase * * http://nayuki.eigenstate.org/page/project-euler-solutions * https://github.com/nayuki/Project-Euler-solutions */ import java.util.Arrays; public final class p049 implements EulerSolution { public static void main(String[] args) { System.out.println(new p049().run()); } private static final int LIMIT = 10000; public String run() { boolean[] isPrime = Library.listPrimality(LIMIT - 1); for (int base = 1000; base < LIMIT; base++) { if (isPrime[base]) { for (int step = 1; step < LIMIT; step++) { int a = base + step; int b = a + step; if ( a < LIMIT && isPrime[a] && hasSameDigits(a, base) && b < LIMIT && isPrime[b] && hasSameDigits(b, base) && (base != 1487 || a != 4817)) return "" + base + a + b; } } } throw new RuntimeException("Not found"); } private static boolean hasSameDigits(int x, int y) { char[] xdigits = Integer.toString(x).toCharArray(); char[] ydigits = Integer.toString(y).toCharArray(); Arrays.sort(xdigits); Arrays.sort(ydigits); return Arrays.equals(xdigits, ydigits); } }

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