A palindromic prime (palprime) is a prime number that is also palindromic. So out of curiosity I wrote a simple program a few days ago that can find the palindromic numbers within a given range. Here is the code in C++:

```#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
#include <math.h>
#include <iostream>

using namespace std;

bool IsPrime(unsigned long long n) {
bool r = true;

for (unsigned long long i = 3; i < sqrt((double) n) + 1; i+= 2)
{
if (n % i ==0) {
r = false;
break;
}
}

return r;
}

bool IsPalindrome(unsigned long long n) {
bool r = true;
char s;
int l = sprintf(s, "%llu", n);

if (l == 1 && n != 1) {
r = true;
} else	{
for (int i = 0; i < l/2; i++) {
if (s[i] != s[l-i-1]) {
r = false;
break;
}
}
}

return r;
}

/*
* usage: palprime [lbound] [ubound]
*/
int main(int argc, char** argv) {
unsigned long long beginNum = 3;
unsigned long long endNum = 3;

if (argc == 2) { // lbound default to 3
#ifdef _WIN32
endNum = _strtoui64(argv, NULL, 10);
#else
endNum = strtoull(argv, NULL, 10);
#endif

} else if (argc == 3) {
#ifdef _WIN32
beginNum = _strtoui64(argv, NULL, 10);
endNum = _strtoui64(argv, NULL, 10);
#else
beginNum = strtoull(argv, NULL, 10);
endNum = strtoull(argv, NULL, 10);
#endif
}

unsigned long long i = beginNum;

while (i < endNum) {
char s;
int l = sprintf(s, "%llu", i);

//length cannot be even as even length palindrome numbers
//can be divided by 11.
if (l % 2 == 0) {
i = ((unsigned long long) (i / 10)) * 100 + 1;
continue;
}

if (IsPalindrome(i)) {
if (IsPrime(i)) {
cout << i << endl;
}
}

i+=2;

if (s % 2 == 0) {
i+=pow(10, l-1);

if (((int) (s - '0')) + 1 == 5) {
i += 2 * pow(10, l-1);
}
}
}
return (EXIT_SUCCESS);
}
```

At first, I was trying to find all the palprimes that can be represented by 64 bit integers. But soon I realized that it would take months to do so using the code above with a quad-core PC (using 4 processes with different ranges). Anyway, here’s the last few palindromic primes less than 10,000,000,000,000:

9999899989999
9999901099999
9999907099999
9999913199999
9999919199999
9999938399999
9999961699999
9999970799999
9999980899999
9999987899999

And here are a few interesting ones:

11357975311
1112345432111
1300000000031
1700000000071
1900000000091
7900000000097
9200000000029
1357900097531