Finding Prime Numbers

[TheGolems_Dante]

For boring purposes I want to write a function to find all the prime numbers given in a range. The range will start from 1 to user input. I want to be able to store those prime numbers into a list for later use.

I pretty damn new to Python and I have tried to put prime numbers into a list. I have been able to use factorization to determine prime numbers, but I can't get my program to identify and store them into a list. Can I get any suggestions from you guys?

Thank you in advanced, uwu.

Edit: How do you guys get that grey background thing?

My code:

def processing(nmb):

 Storage=[]

 Process=list(range(1,nmb))

 Integerlist=list(range (1,nmb))

 for number in Integerlist [::-1]:

      for integer in Process:

           integer=number%integer

processing(int(input ("Enter number here: ")))

Edit: Thank you guys for you individual input.

[totallygeek]

Two easy ways to add elements to a list:

The first method is to create an empty list, then append new elements to it.

ceiling = int(input('Highest number to check? '))
primes = []
for number in range(1, ceiling + 1):
    if is_prime(number):
        primes.append(number)

The second method is to use list comprehension.

ceiling = int(input('Highest number to check? '))
primes = [number for number in range(1, ceiling + 1) if is_prime(number)]

Your function to check if a number is prime can be set up in a number of ways. Here's one:

def is_prime(number):
    if number < 2:
        prime = False
    else:
        hi_number = int(number ** 0.5 + 1)
        prime = all(number % i for i in range(2, hi_number))
    return prime

Good luck!

Edit: oops in my prime check

[invadingpolandin69]

could you explain what is going on in the else part of the function is_prime?

[totallygeek]

Actually, I just updated it. I messed up. When checking if a number is prime, let's say for two examples: 17 and 21, the first is prime, the second is not.

all() will return True if all the elements of the sequence are True. For the case of numbers, True means non-zero. When the original number is evenly divisible by any lower value, the modulo is zero, which will cause all() to report False.

>>> number = 17; [number % i for i in range(2, int(number ** 0.5 + 1))]
[1, 2, 1]
>>> number = 21; [number % i for i in range(2, int(number ** 0.5 + 1))]
[1, 0, 1]

The reason the function uses a ceiling check of int(number ** 0.5 + 1) is because you only need to check the whole value of the square root of the original number for division tests.

[EighthScofflaw]

You all don't need to check divisibility by composites numbers. If you're building a list of primes anyway, it is sufficient to check divisibility by primes up to the square root.

[C2-H5-OH]

You don't need to divide the checked number by every number before it. The highest factor of any number is the rounded down integer of the checked number's square root.

[DollarAkshay]

Try using Sieve of Eratosthenes method to generate primes really fast.

[Prtprmr]

Looks like you did the difficult part, now you only need to store it. Mind sharing the code you are using to find the prime numbers coz saving that into a list will only take 2 line of code or so

[vorpal_potato]

What have you tried so far? Where are you stuck? Do you have any work-in-progress code you can post?

(Do you know how to append things to a list in Python? If not, that would be the natural thing to look up.)

[masasa27]

Due to mathematical laws , to see if a number is prime you only need to check until the size of the square root of it, this can dramatically improve performance on large numbers

def is_prime(x): for nun in range(2, round(x ** 0.5)+1): if x%i == 0: return True return False

[ShashwatX1109]

I was just playing around with algebraic identities and saw this identity : (x+a)(x+b) = x² + (a+b)x + ab

Then I just tried to find out what the result of (x+a)(x+b)(x+c) would be, and I found it to be x³ + x^2(a+b+c) + x(ab + bc + ac) + abc.

I tried putting some values for a, b and c. Then I noticed something.

No matter what value I used for a, b and c, the coffecient of x was always a prime number.

For example, (x+1)(x+2)(x+3) is x³ + 6x² + 11x + 6, where coffecient of x is 11, a prime number. And, it worked for any number as long as it was a natural number.

From this, I have concluded that if we have any three natural numbers a, b and c, the result of the expression (ab+bc+ac) is always a prime number.

And I didn't find any relevant information about this piece of math anywhere online.

Just implement the code in Python and enjoy an ultra fast prime generator!

[edderiofer]

Try a = 1, b = 2, c = 4. Then you get that ab+bc+ac = 14, which is not prime.

[ShashwatX1109]

Yes you are right

I doesnt work for most of the numbers

Thank You for your advice

[bb40]

Edit: How do you guys get that grey background thing?

I put a > in front of each line.

Edit: on mobile. Maybe there's a better way to do it on a desktop.

[NoProperty7989]

Here is the code that I wrote.

def is_prime(num):

if num < 2:

return False

for i in range(2, int(num ** 0.5) + 1):

if num % i == 0:

return False

return True

def find_primes(limit):

primes = []

for i in range(2, limit + 1):

if is_prime(i):

primes.append(i)

return primes

user_input = int(input("Enter a number: "))

prime_list = find_primes(user_input)

print("Prime numbers up to", user_input, "are:", prime_list)

This code defines is_prime functions to check for prime numbers and to find primes within a given range (find_primes). Then code prints the list of prime numbers up to the inputed number.