Euler conjecture

/*
https://twitter.com/pickover/status/585271919991095296

$ gcc -O3 n_nth_powers.cpp -o n_nth_powers
$ time ./n_nth_powers
27^5 + 84^5 + 110^5 + 133^5 = 144^5

real    0m0.018s
user    0m0.018s
sys 0m0.000s
*/

#include <stdio.h>
#include <stdint.h>

typedef uint64_t num;

const int MAX=7131; // 5th root of 2^64

int main()
{
  num power5[MAX+1];
  for (num i=0; i<=MAX; ++i) power5[i] = i*i*i*i*i;

  for (int n4=1; n4<=MAX; ++n4){
    num tot4 = power5[n4];
    int guess = n4;
    num guessp5 = power5[guess];
    for (int n3=1; n3<=n4; ++n3){
      num tot3 = tot4 + power5[n3];
      for (int n2=1; n2<=n3; ++n2){
        num tot2 = tot3 + power5[n2];
        for (int n1=1; n1<=n2; ++n1){
          num tot = tot2 + power5[n1];

          if (guessp5 < tot){
            do {
              guessp5 = power5[++guess];
            } while (guessp5 < tot);
          } else if (guessp5 > tot){
            do {
              guessp5 = power5[--guess];
            } while (guessp5 > tot);
          }
          if (guessp5 == tot){
            printf("%d^5 + %d^5 + %d^5 + %d^5 = %d^5\n", n1, n2, n3, n4, guess);
            return 0;
          }

        }
      }
    }
  }

  return 0;
}