palindromic_primes_finder_v3.03

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# Filename: palindromic_primes_finder_v3.03.py
# Author: Jeoi Reqi

"""
Palindromic Primes Finder:

This Python script exclusively focuses on identifying prime numbers that are palindromes.
It utilizes the equation [P = y^2 - y + 41], where 'y' is provided by the user.
The script iterates through a sequence of numbers, checking for palindromic primes using a custom primality test, and displays the results.

**Requirements:**
- Python 3

**Usage:**
1. Run the script in a terminal or command prompt.
2. Enter the starting value for 'y' (or press [ENTER] to exit).
3. Specify the number of iterations to check.
4. The script will output prime numbers that are also palindromes along with their corresponding 'y' values.

**Note:**
- The equation used is [P = y^2 - y + 41].
- Only prime numbers that are palindromes will be displayed in the output.
- The script uses a custom primality test for checking prime numbers.

Example:
Enter the starting value for y (or press [ENTER] to exit): 41
Enter the number of iterations: 10000000

Results:
[y=131, p=17071]
[y=1814, p=3288823]
[y=2738, p=7493947]
[y=2813, p=7910197]
[y=12176, p=148242841]
[y=13951, p=194616491]
[y=17692, p=312989213]
[y=281233, p=79091719097]
[y=1372760, p=1884468644881]
[y=1956282, p=3827037307283]

Processing time: 0 hours, 0 minutes, 7.526364 seconds
"""

import time

def is_prime(num):
    """
    Checks if a given number is prime.

    Args:
        num (int): The number to check for primality.

    Returns:
        bool: True if the number is prime, False otherwise.
    """
    if num < 2:
        return False
    if num == 2 or num == 3:
        return True
    if num % 2 == 0 or num % 3 == 0:
        return False

    for i in range(5, int(num**0.5) + 1, 6):
        if num % i == 0 or num % (i + 2) == 0:
            return False

    return True

def is_palindrome(num):
    """
    Checks if a given number is a palindrome.

    Args:
        num (int): The number to check for palindrome.

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

def check_palindrome_prime(y):
    """
    Checks if a given 'y' produces a palindromic prime.

    Args:
        y (int): The 'y' value.

    Returns:
        tuple: A tuple (y, P) if 'y' produces a palindromic prime, None otherwise.
    """
    P = y**2 - y + 41
    return (y, P) if is_palindrome(P) else None

def generate_primes_and_palindromes(start_y, iterations):
    """
    Generates and identifies prime and palindromic prime numbers.

    Args:
        start_y (int): The starting value for 'y'.
        iterations (int): The number of iterations to check.

    Returns:
        None
    """
    results = []
    start_time = time.time()

    for y in range(start_y, start_y + iterations):
        result = check_palindrome_prime(y)
        if result:
            results.append(result)

    print("\nResults:")
    if not results:
        print("No Palindromic Primes found.")
    else:
        for result in results:
            print(f"[y={result[0]}, p={result[1]}]")

    end_time = time.time()
    elapsed_time = end_time - start_time

    hours, remainder = divmod(elapsed_time, 3600)
    minutes, seconds = divmod(remainder, 60)
    print(f"\nProcessing time: {int(hours)} hours, {int(minutes)} minutes, {seconds:.6f} seconds\n")

if __name__ == "__main__":
    while True:
        start_y_input = input("Enter the starting value for y (or press [ENTER] to exit): ")
        if start_y_input == "":
            print("Exiting...")
            break
        try:
            start_y = int(start_y_input)
            iterations = int(input("Enter the number of iterations: "))
            generate_primes_and_palindromes(start_y, iterations)
        except ValueError:
            print("Invalid input. Please try again.")