# UVa 543

## Summary

Goldbach's Conjecture is unproven, but is true for the input. (You will not have to print "Goldbach's conjecture is wrong.") Simply use the sieve, and use a naive algorithm, starting from ${\displaystyle {\frac {n}{2}}}$ going outwards, minimizing the distance between the two numbers.

## Explanation

Goldbach's Conjecture have been confirmed up to very large numbers, and this is a trivial problem, given that you know how to implement the Prime Sieve of Eratosthenes.

A C++ solution from an unknown user with IP 89.108.249.161:

#include<iostream>
#include<cmath>
using namespace std;

int primeNumbers[]={2, 3, 4, 5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41,
43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113,
121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193,
197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281,
283, 289, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 361, 367, 373,
379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463,
467, 479, 487, 491, 499, 503, 509, 521, 523, 529, 541, 547, 557, 563, 569, 571,
577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661,
673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773,
787, 797, 809, 811, 821, 823, 827, 829, 839, 841, 853, 857, 859, 863, 877, 881,
883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 961, 967, 971, 977, 983, 991,
997, 1009,1013};

bool IsPrime(int num)
{
if(num == 0)
{
return true;
}
int i=0;

{
{
return false;
}
i++;
}

return true;
}

int findPrimes(int n)
{
for(int i=2;i<n/2+1;i++)
{
if(IsPrime(i) && IsPrime(n-i))
{
cout<<n<<" = "<<i<<" + "<<n-i<<"\n";
return 0;
}
}
}

int main()
{
int m=-1;
while(m!=0)
{
cin>>m;
if(m==0) return 0;
findPrimes(m);

}
return 0;
}


## Input

8
20
42
0


## Output

8 = 3 + 5
20 = 3 + 17
42 = 5 + 37