primes_finder_plus_optimized_v2.01

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# Filename: primes_finder_plus_optimized.py
# Version: 2.01
# Author: Jeoi Reqi

import time

"""
Primes Finder +Plus+:

This Python script identifies prime & palindromic prime numbers generated using the equation [P = y^2 - y + 41], where 'y' is a starting value provided by the user.
The script iterates through a sequence of numbers, checks if each corresponds to a prime and subsequently palindromic primes, and displays the results to the terminal.

**Requirements:**
- Python 3

**Usage:**
1. Run the script in a terminal or command prompt.
2. Enter the starting value for 'y'.
3. Specify the number of iterations to check.
4. The script will output primes & palindromic prime numbers along with their corresponding 'y' values.

**Note:**
- The equation used is [P = y^2 - y + 41].
- Prime numbers that are also palindromes will be highlighted in the output.

Example:
Enter the starting value for y: 41
Enter the number of iterations: 5000

Results:
[y=43, P=1847*]
[y=44, P=1933*]
[y=46, P=2111*]
[y=47, P=2203*]
[y=48, P=2297*]
[y=49, P=2393*]
...
[y=5034, P=25336163*]
[y=5038, P=25376447*]
[y=5040, P=25396601*]

Processing time: 0 hours, 0 minutes, 0.406290 seconds
"""

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

    i = 5
    w = 2

    while i * i <= num:
        if num % i == 0:
            return False
        i += w
        w = 6 - w

    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 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:
        list: A list of formatted strings representing the results.
    """
    results = []
    start_time = time.time()

    for y in range(start_y, start_y + iterations):
        P = y**2 - y + 41

        if is_prime(P) and is_palindrome(P):
            results.append(f"\033[31m[y={y}, pP={P}**]\033[0m")
        elif is_prime(P):
            results.append(f"[y={y}, P={P}*]")
        elif is_palindrome(P):
            results.append(f"\033[33m[y={y}, p={P}]\033[0m")

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

    hours, remainder = divmod(elapsed_time, 3600)
    minutes, seconds = divmod(remainder, 60)

    results.append(f"\nProcessing time: {int(hours)} hours, {int(minutes)} minutes, {seconds:.6f} seconds")

    return results

def main():
    """
    Main function to execute the script.
    Takes user input for 'y' and iterations, then outputs the results to the terminal.
    """
    start_y = int(input("Enter the starting value for y: "))
    iterations = int(input("Enter the number of iterations: "))
    data = generate_primes_and_palindromes(start_y, iterations)

    print("\nResults:")
    for result in data:
        print(result)

if __name__ == "__main__":
    main()