Listing Prime Numbers in Python

Randomness of Prime Numbers

Prime numbers, in ascending order, are:

2, 3, 5, 7, 11, 13, 17, 19, 23, ...

Because prime numbers are so random in their progression, they are very difficult to predict as they get larger.

Hence writing a Python code to list prime numbers will involve checking every number in a range of interest and gathering those that are without factors.

Say we want to list all prime numbers between 2 and 100 inclusive, we would start from 2; check to see whether it has any factors; keep it as a prime number if it has no factors; otherwise discard it.
We would then go to 3, and repeat the same process.
Repeat same for 4, 5, 6, 7, ..., 98, 99, 100.

Code that lists Prime Numbers in Python

But we can always use a few tricks .

We will take the following steps:

Step 1:

First, we'll start our range from 9 (keeping 2, 3, 5, and 7 as prime numbers).

Step 2:

Next, we'll only check through odd numbers.

Step 3:

Next, we'll check against the factors 2, 3, and 5.

Step 4:

Lastly, we'll check with a subset of smaller prime numbers that we'll gather as our check progresses.

Create a new class file; File, New File.
Call it listPrimeNumbers.py.

Type out the adjoining Python code for listing prime numbers.

Note: You can comment out the Python code for the main class from the previous lesson if you have been following.

Python code for listPrimeNumbers Module File.

from math import sqrt, ceil

# A class
class ListPrimes:

    # Constructor: takes two arguments  -- besides its name
    # alpha and omega values for the range
    def __init__(self, alpha, omega):
        self.start = alpha
        self.stop = omega + 1
        # STEP 1:
        self.progress = 9

        self.list_of_primes = [2, 3, 5, 7]
        self.square_root = 0

    # Returns an list of the desired set of prime numbers
    def getPrimes(self):

        # STEP 2:
        for self.progress in range(self.progress, self.stop, 2):

            self.do_next_iteration = False # a flag

            # STEPS 3, 4:
            # Check through already accumulated prime numbers
            # to see if any is a factor of "progress".
            self.square_root = int(ceil(sqrt(self.progress)))

            self.index = 0
            while self.list_of_primes[self.index] <= self.square_root:
                if self.progress % self.list_of_primes[self.index] == 0:
                    self.do_next_iteration = True
                    break

                self.index += 1

            if self.do_next_iteration == True:
                continue

            # if all checks are scaled,then "progress" is our guy.
            self.list_of_primes.append(self.progress)

        return self.list_of_primes

Main class code.

#!/usr/bin/python
from PrimeNumbers import ListPrimes

# Use the prime numbers module/class
lower_boundary = 1
upper_boundary = 100
prime_list = ListPrimes(lower_boundary, upper_boundary)
answer = prime_list.getPrimes()
print("Prime numbers between", lower_boundary, "and", upper_boundary, "are:\n", answer)

print("\n\n")

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