C :

#include<stdio.h>
int prime(int a)
{
	if(a<=1) return 0;
	for(int i=2;i<a;i++){
		if(a%i==0) return 0;
	}
	return 1;
}
int main()
{
	int i,j;
	for(i=10;i<100;i++){
		for(j=10;j<100;j++){
			if(i+j<100&&prime(i+j)&&((i+j)%10+(i+j)/10)==13&&i-13==j)
			printf("%d %d",i,j);
		}
	}
	return 0;
}

C++ :

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

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

int sum(int n){
    int s = 0;
    while(n != 0){
        s = s + n % 10;
        n = n / 10;
    }
    return s;
}

int main(){
	int j;
	//甲的年龄 
	for(int i = 1;i <= 100;i++){
		j = i - 13;//乙的年龄
		if((i+j)>=10 && (i+j)<99 && sushu(i+j) && sum(i+j)==13){
			cout<<i<<" "<<j<<endl;
		} 
	}
}

Java :

import java.util.*;
public class Main{
	public static boolean isPrime(int n){
		if(n<2)
			return false;
		for(int i = 2; i<=Math.sqrt(n);i++){
			if(n%i==0)
				return false;
		}
		return true;		
	}


	public static void main(String args[]){
		int i,z;//乙的年龄 ，总年龄
		for(i=1;i<99;i++){
			z=i*2+13;
			if(isPrime(z)&&z>=10&&z<=99&&z%10+z/10==13)
				System.out.println(i+13+" "+i);
		}
	}
}

Python :

import math
def zhiShu(n):
    f = True
    for i in range (2, int(math.sqrt(n))+1):
        if n % i == 0:
            f = False; 
    return f and n != 1
 
for n in range (10,100):
        for i in range (4, 10):
                if i * 10 == n - (13 - i) and zhiShu(n):
                        print (int(n-13)//2 + 13,int(n-13)//2)