Python prime numbers list

How to Generate a List of Prime Numbers (Primes) in Python

This is frequently used as a programming challenge. There are a few ways to do this, but here is one especially interesting way that I’ve found. For this guide, we’ll assume we want a list of all primes under 50.

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First, generate a list of non-primes

Generating a list of non-primes is much simpler than generating a list of primes. To begin, we need to think about what a prime number is. A prime number is one that is only divisible by 1 and itself. Therefore, if we want to generate a list of non-primes under 50 we can do so by generating multiples.

noprimes = set(j for i in range(2, 8) for j in range(i*2, 50, i))

We are using a set in this case because we only want to include each multiple once. The function range(2, 8) will generate the numbers 2-7. In this example we are using set comprehension to iterate through the numbers 2 through 7. During each iteration we will use the number to iterate through the range 2i through 50 with an interval of i.

Hopefully that isn’t too complicated! As an example, the first time we iterate through the outer loop, we generate the number 2. Then we iterate through the inner loop using 2 to produce this range: range(4, 50, 2). This produces: 4, 6, 8, 10, etc until we hit 50. Each of these numbers will be added to our noprimes set.

The next time through we generate the number 3. Then in our inner loop we will produce range(6, 50, 3) which will add 6, 9, 12, 15, etc to our noprimes set.

As you can see, this simply generates multiples. Once we calculate all the multiples through 7 we can be sure that we’ve generated all of the multiples. Anything 8 or higher will simply duplicate the work we’ve already done.

Now generate primes

The second part is easy. Now that we have a list of non-primes, we can use list comprehension to loop through all numbers less than 50. Then we will check to see if each number exists in our noprimes set. If it doesn’t exist, we can be sure that it is a prime number.

primes = [x for x in range(2, 50) if x not in noprimes]

This will generate our list of prime numbers less than 50!

[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]

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Using Python to Create List of Prime Numbers

In Python, we can create a list of prime numbers easily – all we need is a custom function to check if a number is prime or not.

To generate a list of the first N prime numbers in Python, you can create your own function and loop until you have N prime numbers.

def isPrime(n): if (n % 2 == 0): return False for i in range(3, int(n**0.5 + 1), 2): if (n % i == 0): return False return True def getFirstPrimes(n): primes = [2] num = 3 while (len(primes) < n): if(isPrime(num)): primes.append(num) num = num + 2 return primes print(getFirstPrimes(10)) #Output: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]

If you want to create a list of prime numbers in a certain range, you can create your own function and loop over that range to find prime numbers.

def isPrime(n): if (n % 2 == 0): return False for i in range(3, int(n**0.5 + 1), 2): if (n % i == 0): return False return True def getPrimesRange(a, b): primes = [] if a > 1 and b > 1: count = 0 if a > b: t = a a = b b = t if a == 2: count = 1 a = 3 if a % 2 == 0: a = a + 1 while (a < b): if(isPrime(a)): primes.append(a) a = a + 2 return primes else: return "Not a valid range." print(getPrimesRange(200,300)) #Output: [211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293]

When working with numbers in Python, the ability to create collections of specific numbers can be useful.

One such example is if you are working with prime numbers and want to create a list of prime numbers.

With Python, we can check if a number is prime or not with a simple user-defined Python isprime() function.

def isPrime(n): if (n % 2 == 0): return False for i in range(3, int(n**0.5 + 1), 2): if (n % i == 0): return False return True

Then, depending on the list you want to make, you can create a loop which will gather the primes in a list for you.

The rest of this article shows you two methods you can use to create prime number lists using Python.

Creating Prime Number List of First N Prime Numbers Using Python

One example of creating a list of primes is to create a list which has the first N prime numbers.

To generate a list of the first N prime numbers in Python, you can create your own function and loop until you have N prime numbers.

Below is an example of how you can get the first 10 prime numbers using Python.

def isPrime(n): if (n % 2 == 0): return False for i in range(3, int(n**0.5 + 1), 2): if (n % i == 0): return False return True def getFirstPrimes(n): primes = [2] num = 3 while (len(primes) < n): if(isPrime(num)): primes.append(num) num = num + 2 return primes print(getFirstPrimes(10)) #Output: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]

Creating Prime Number List of Prime Numbers in Range Using Python

Another example where you might want to create a list of prime numbers is if you want only the prime numbers in a specific range.

If you want to create a list of prime numbers in a certain range, you can create your own function and loop over that range to find prime numbers.

Below is a function which you can use which will get the prime numbers in a range using Python.

def isPrime(n): if (n % 2 == 0): return False for i in range(3, int(n**0.5 + 1), 2): if (n % i == 0): return False return True def getPrimesRange(a, b): primes = [] if a > 1 and b > 1: count = 0 if a > b: t = a a = b b = t if a == 2: count = 1 a = 3 if a % 2 == 0: a = a + 1 while (a < b): if(isPrime(a)): primes.append(a) a = a + 2 return primes else: return "Not a valid range." print(getPrimesRange(200,300)) #Output: [211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293]

Hopefully this article has been useful for you to learn how to get a list of prime numbers with Python.

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Create and Print a List of Prime Numbers in Python

Prime numbers mean the numbers which can be divided only by 1 or the number itself(e.g 2, 3, 5, 7, 11, etc). Today, we will learn how to create and print a list of prime numbers in Python. We will create a list of prime numbers which are under 50 using a function. We will store the returned prime numbers in a list and will print that list simply.

Code to Create and Print a List of Prime Numbers in Python

1. With Function

def prime_numbers(n): primes = [] for i in range(2, n + 1): for j in range(2, int(i ** 0.5) + 1): if i%j == 0: break else: primes.append(i) return primes prime_list = prime_numbers(50) print(prime_list)

Output:

2. One-Liner

print([i for i in range(2, 50) if 0 not in [i%n for n in range(2, i)]])

Output:

[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]

Conclusion

We have learned how can we create and print a list of prime numbers in Python. The logic behind creating a list of prime numbers is simple, we need to check all the numbers whether they are prime or not before we append them to the list.

We hope you find this article on Create and Print a List of Prime Numbers in Python helpful for you.

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Python Prime Numbers: Find a Value or a Range of Values

In this tutorial, you’ll learn how to use Python to find prime numbers, either by checking if a single value is a prime number or finding all prime numbers in a range of values. Prime numbers are numbers that have no factors other than 1 and the number itself. Being able to work with prime numbers is a common task in occupations such as computer and cyber security.

By the end of this tutorial, you’ll have learned:

• What prime numbers are
• Different ways of finding prime numbers in Python
• Optimizing our algorithms for finding prime numbers in Python
• Finding all prime numbers between a range of values in Python

What are Prime Numbers

Prime numbers are a positive integer that’s greater than 1 that also have no other factors except for 1 and the number itself. For example, the number 5 is a prime number, while the number 6 isn’t (since 2 x 3 is equal to 6).

The first few prime numbers are: 3, 7, 11, 13, etc.

Finding Prime Numbers in Python (Optimized Code)

Let’s take a look at how we can use Python to determine if a number is a prime number. The most naive and straightforward implementation is to loop over the range of numbers from 2 to the number and see if the modulo of the number and the range is equal to 0. If that occurs, then the number has a divisor other than 1 and the number itself and the number isn’t a prime number.

Let’s take a look at how we can implement this first code:

# Writing a Simple Function to Check if a Number is a Prime Number def is_prime(number): if number > 1: for num in range(2, number): if number % num == 0: return False return True return False print(is_prime(4)) # Returns: False

Let’s break down what we did here:

1. We defined a function is_prime that takes a single argument, a number
2. If the number is not greater than 1, then the function returns False as prime numbers need to be larger than 1
3. It then loops over the range from 2 through to the number (but not including)
4. If the modulo of the number and the iteration is equal to zero (meaning the number is divided cleanly), then the function returns False
5. Otherwise, the function returns True

This function works well! However, it’s not the most efficient function. We can divide the number by 2 since any composite number (a non-prime number) will also have a factor of its half.

This means that the number of iterations that our code has to complete is reduced by roughly half! Let’s see how we can write this function:

# Improving our function def is_prime(number): if number > 1: for num in range(2, number // 2 + 1): if number % num == 0: return False return True return False print(is_prime(941))

In the function above, we’e made the following improvement:

Now let’s take a look at one more improvement we can make. We can actually take the square root of the number that we’re checking. This can have significant improvement on the number of checks the function needs to make.

# The Final Function to Check for Prime Numbers def is_prime(number): if number > 1: for num in range(2, int(number**0.5) + 1): if number % num == 0: return False return True return False print(is_prime(2011)) # Returns: True

In the next section, you’ll learn how to find all the prime numbers in a range of numbers.

Comparing Performance of Prime Number Functions

Now that we’ve developed three functions, we can easily compare the performance of these functions to see the performance gains that we’ll get from them.

In order to test these, let’s use a large prime number, 433,494,437. Since we know this number is a prime number, the function will need to run through all iterations.

The table below breaks down the performance between these three functions:

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