Question

I’m trying to work through Project Euler and I’m hitting a barrier on problem 03. I have an algorithm that works for smaller numbers, but problem 3 uses a very, very large number.

Problem 03: The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143?

Here is my solution in C# and it’s been running for I think close to an hour. I’m not looking for an answer because I do actually want to solve this myself. Mainly just looking for some help.

    static void Main(string[] args) {         const long n = 600851475143;         //const long n = 13195;         long count, half, largestPrime = 0;         bool IsAPrime;          half = n / 2;          for (long i = half; i > 1 && largestPrime == 0; i--) {              if (n % i == 0) { // these are factors of n                 count = 1;                 IsAPrime = true;                 while (++count < i && IsAPrime) {                     if (i % count == 0) { // does a factor of n have a factor? (not prime)                         IsAPrime = false;                     }                 }                 if (IsAPrime) {                     largestPrime = i;                 }             }         }          Console.WriteLine('The largest prime factor is ' + largestPrime.ToString() + '.');         Console.ReadLine();     } 

Answer 1

For starters, instead of beginning your search at n / 2, start it at the square root of n. You’ll get half of the factors, the other half being their complement.

eg:

n = 27 start at floor(sqrt(27)) = 5 is 5 a factor? no is 4 a factor? no is 3 a factor? yes. 27 / 3 = 9. 9 is also a factor. is 2 a factor? no. factors are 3 and 9.