C#-Code

using static System.Console;
using System.Collections.Generic;

int n = (int)1e+9;
WriteLine($"Palindromische Primzahlen bis {n.ToString("n0")}:");

bool[] b = Primes_Until(n);
int counter = 0;
for (var i = 2; i < b.Length; i++)
    if (!b[i] && !b[InversInt(i)])
            WriteLine($"{(++counter).ToString("n0"), 10}: {i.ToString("n0"), 12}");
WriteLine($"fertig: insgesamt {counter.ToString("n0")} Palindromische Primzahlen bis {n.ToString("n0")}");
ReadKey();

#region methods
static bool[] Primes_Until(int n)  {
    bool[] b = new bool[n + 1];
    for (var i = 4; i <= n; i += 2)
        b[i] = true;
    for (var i = 3; i <= n; i += 2)
        if (!b[i])
            for (var j = i + i; j <= n; j += i)
                b[j] = true;
    return b;
}

static int InversInt(int i)  {
    List<int> digits = new();
    while (i > 0)  {
        digits.Add(i % 10);
        i /= 10;
    }
    int pot = 1, result = 0;
    for (var j = digits.Count - 1; j >= 0; j--)  {
        result += pot * digits[j];
        pot *= 10;
    }
    return result;
}
#endregion