Project Euler Problem 51

Problem 51

29 August 2003

By replacing the 1^st digit of *3, it turns out that six of the nine possible values: 13, 23, 43, 53, 73, and 83, are all prime.

By replacing the 3^rd and 4^th digits of 56**3 with the same digit, this 5-digit number is the first example having seven primes among the ten generated numbers, yielding the family: 56003, 56113, 56333, 56443, 56663, 56773, and 56993. Consequently 56003, being the first member of this family, is the smallest prime with this property.

Find the smallest prime which, by replacing part of the number (not necessarily adjacent digits) with the same digit, is part of an eight prime value family.

Answer: 121313

 

C#

 

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Numerics;

namespace Euler {
    static class Program {
        /// <summary>
        /// Returns primes under limit using sieve.
        /// </summary>
        /// <param name="limit">An integer to limit.</param>
        /// <returns>Primes under limit.</returns>
        static HashSet<int> primesUnder(int limit) {
            var p = new bool[limit];
            if (limit >= 3) p[2] = true;
            for (int i = 3; i < limit; i += 2) p[i] = true;
            for (int i = 3; i * i < limit; i += 2) {
                if (!p[i]) continue;
                for (int j = i + i; j < limit; j += i)
                    p[j] = false;
            }
            var r = new HashSet<int>();
            for (int i = 2; i < limit; i++)
                if (p[i]) r.Add(i);
            return r;
        }

        static void Main(string[] args) {
            var primes = primesUnder(10000000);
            foreach (var p in primes) {                
                var lMax = p.ToString().Length - 2;
                for (var i = 0; i <= lMax; i++) {
                    for (var i2 = i + 1; i2 <= lMax; i2++) {
                        for (var i3 = i2 + 1; i3 <= lMax; i3++) {
                            var numPrimes = 0;
                            var strTemp = new StringBuilder(p.ToString()); ;
                            var firstPrime = "";
                            for (var d = '0'; d <= '9'; d++) {
                                if (i == 0 && d == '0') continue;
                                strTemp[i] = d;
                                strTemp[i2] = d;
                                strTemp[i3] = d;                                
                                if (primes.Contains(Convert.ToInt32(strTemp.ToString()))) {
                                    if (firstPrime.ToString() == "") firstPrime = strTemp.ToString();
                                    numPrimes++;
                                    //Console.Write(strTemp + " ");
                                }
                            }
                            //Console.WriteLine();
                            if (numPrimes == 8) {
                                Console.WriteLine("{0} {1} {2} {3}", i, i2, i3, firstPrime);
                                goto End;
                            }
                        }
                    }
                }
            }
        End:
            Console.WriteLine("Press");
            Console.ReadKey();
        }
    }
}