Primal_Rage

#!/usr/bin/env python

import time                           # ONLY used for speed testing.
import math                           # For use of modulus 'mod' and square root 'sqrt'.

""" A mildly convoluted, jumbled mess to check if the value of 'p' is both
a Prime Number and a Palindromic Number. Time included for speed tests. """

n = 0                #   <---         <--- Main int. Increase +1 per cycle
# z = 41                              <--- Constant Variable
# p = n**2 - n + z                    <--- Main Equation
"""  ^^^ Moved above Maths to 'is_prime'  ^^^ """

def is_prime(p):
  """ Return 'True' if 'p' IS a prime number and False if 'p' is NOT prime. """
  if p == 1:
    return False                      # 1 is NOT a prime number!
          # Check if EVEN and NOT 2, (3, 5 and 11 as exceptions) '1' is NOT prime.
  if p == 2:
    return True
  if p > 2 and p % 2 == 0 or p % 3 == 0 or p % 5 == 0 or p % 11 == 0:
    return False
          # Check if EVEN (p > 2) can it be divided by 3, 5 or 11?
  max_div = math.floor(math.sqrt(p))  #<--- Python uses mod from the floor
  for d in range(3, 1 + max_div, 2):  #<--- Skip ALL EVEN numbers
    if p % d == 0:
      return False
  return True

def is_pal():
                                      # Test: IS 'p' Prime & Palindromic?
                                      # Yes == True | No == False
  for n in range(0, 10000):
    z = 41                            # Constant Variable
    p = n**2 - n + z                  # Equation Variable
    is_prime(p)                       # Check if 'p' is prime
    if (is_prime(p) == True):         #<--- Test if Prime
      if (str(p) == str(p)[::-1]):    #<--- Test if Palindrome
        print("\n","(",n,")","P =",p)

""" ========= TEST: Time Function ========= """
def test_time():
  t0 = time.time()                    #<--- time 0
  for p in range(1,10000):          # Check if prime up to 'Some Number'
    is_prime(p)                       # Initialize is_prime Test for 'p'.
  t1 = time.time()                    #<--- time 1
  print("Time Required:", t1 - t0)    # Output Time (Compare Time 0 & Time 1).

def run():
  is_pal()
  test_time()                         # Test Time Required to complete task.

run()                                 # Initialize the script.

""" ========= RESULTS ========= """
# OUTPUT:
#Python 3.6.1 (default, Dec 2015, 13:05:11)
#[GCC 4.8.2] on linux
# ...
# ( 10 ) P = 131
#
# ( 11 ) P = 151
#
# ( 17 ) P = 313
#
# ( 19 ) P = 383
#
# ( 28 ) P = 797
#
# ( 1814 ) P = 3288823
#
# ( 2738 ) P = 7493947
""" ========= Time Required ========= """
#
# Range:  n @ 10000 p @ 10000           <--- 10K!
# 0.007488250732421875 ~ 0.008120298385620117
#
# Range:  n @ 10000 p @ 100000          <--- 100K!
# 0.2168869972229004 ~ 0.21737384796142578
#
# Range:  n @ 10000 p @ 1000000         <--- 1 Million!
# 5.324736595153809 ~ 5.35823392868042
#
# Range:  n @ 10000 p @ 10000000        <--- 10 Million!
# 188.01961374282837 ~ 207.1309757232666
#
# Range:  n @ 10000 p @ 100000000       <--- 100 Million!
# HAHAHA! ~ HAHAHA!
#
# ...
""" ================================== """

#END