pp_in_range_11_to_1t

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# Filename: pp_in_range_11_to_1t.py
# Author: Jeoi Reqi

"""
Find and save Prime Palindromes within the range from 11 to 1 trillion.

Requirements:
- Python 3.x

Usage:
1. Ensure you have Python 3.x installed on your system.
2. Run the script.

Important Notes:
- The script finds Prime Palindromes within the range from 11 to 1 trillion.
- It skips values less than 11 since the first palindromic prime is 11.
- Prime Palindromes found within each million-range are saved to separate text files.
- The script may take some time to execute, especially for larger ranges.
- Make sure you have sufficient disk space to save the output files.
"""

def is_prime(n):
    """
    Check if a number is prime.

    Parameters:
    - n (int): The number to check.

    Returns:
    - bool: True if the number is prime, False otherwise.
    """
    if n <= 1:
        return False
    if n <= 3:
        return True
    if n % 2 == 0 or n % 3 == 0:
        return False
    i = 5
    while i * i <= n:
        if n % i == 0 or n % (i + 2) == 0:
            return False
        i += 6
    return True

def is_palindrome(n):
    """
    Check if a number is a palindrome.

    Parameters:
    - n (int): The number to check.

    Returns:
    - bool: True if the number is a palindrome, False otherwise.
    """
    return str(n) == str(n)[::-1]

def find_prime_palindromes(start, end):
    """
    Find prime palindromes within a given range.

    Parameters:
    - start (int): The starting number of the range.
    - end (int): The ending number of the range.

    Returns:
    - list: A list of prime palindromes found within the range.
    """
    primes = []
    for num in range(max(11, start), end):
        if is_prime(num) and is_palindrome(num):
            primes.append(num)
    return primes


def save_prime_palindromes(primes, range_start, range_end, max_end):
    """
    Save prime palindromes to a file.

    Parameters:
    - primes (list): List of Prime Palindromes to save.
    - range_start (int): The starting number of the range.
    - range_end (int): The ending number of the range.
    - max_end (int): The maximum value of the range.

    Returns:
    - None
    """
    if primes:
        num_zeros = len(str(max_end))
        padded_range_start = str(range_start).zfill(num_zeros)
        padded_range_end = str(range_end).zfill(num_zeros)
        file_name = f"prime_palindromes_{padded_range_start}_{padded_range_end}.txt"
        with open(file_name, "w") as file:
            for prime in primes:
                file.write(str(prime) + "\n")
        print(f"\nSaved Prime Palindromes in range {padded_range_start}-{padded_range_end} to {file_name}")
    else:
        print(f"\nNo palindromic Primes found in range {range_start}-{range_end}")

def should_skip_range(range_start):
    """
    Check if a range should be skipped based on its starting number.

    Parameters:
    - range_start (int): The starting number of the range.

    Returns:
    - bool: True if the range should be skipped, False otherwise.
    """
    return str(range_start)[0] in {'2', '3', '4', '5', '6', '8'}

if __name__ == "__main__":  # Minimum range_start=11 (Max determined by system capacity)
    start_range = 11
    end_range = 1000000000000

    print("\nFinding and saving prime palindromes...")
    max_end = end_range
    for i in range(start_range, end_range, 1000000):
        if should_skip_range(i):
            continue
        primes_in_range = find_prime_palindromes(i, i + 1000000)
        save_prime_palindromes(primes_in_range, i, i + 999999, max_end)

    print("\nAll Prime Palindromes have been saved to files.\tGoodbye!")