C :

#include<stdio.h>
int n;
int a[9999],b[9999],t,ans;
int main()
{
	scanf("%d",&n);
	a[1]=1;
	for(int i=2;i<=n;i++)
	if(a[i]==0)
	for(int j=2;j*i<=n;j++)
	a[i*j]=1;
	for(int i=2;i<=n;i++)
	if(a[i]==0)
	b[++t]=i;
	for(int i=1;i<=t;i++)
	for(int j=i;j<=t&&n-b[i]-b[j]>=2;j++)
	if(a[n-b[i]-b[j]]==0&&b[i]<=b[j]&&b[j]<=n-b[i]-b[j])
	ans++;
	printf("%d\n",ans);
	for(int i=1;i<=t;i++)
	for(int j=i;j<=t&&n-b[i]-b[j]>=2;j++)
	if(a[n-b[i]-b[j]]==0&&b[i]<=b[j]&&b[j]<=n-b[i]-b[j])
	printf("%d=%d+%d+%d\n",n,b[i],b[j],n-b[i]-b[j]);
	return 0;
}

C++ :

#include <bits/stdc++.h>
using namespace std;

bool sushu(int n){
	bool f = true;
	int i;
	for(i = 2;i <= sqrt(n);i++){
		if(n % i == 0){
			f = false;
			break;
		}
	}
	if(n <= 1){
		f = false;
	}
	return f;
}

int main(){
	int a[100][3];
	int n,i,j,c = 0,x;
	cin>>n;
	for(i = 2;i <= n / 3;i++){
		if(sushu(i)){
			x = n - i;
			for(j = i;j <= x / 2;j++){
				if(sushu(j) && sushu(x - j)){
					a[c][0] = i;
					a[c][1] = j;
					a[c][2] = x - j;
					c++;
				}
			}
		}
	}
	
	cout<<c<<endl;
	for(i = 0;i < c;i++){
		cout<<n<<"="<<a[i][0]<<"+"<<a[i][1]<<"+"<<a[i][2]<<endl;
	}
}