Why is code for prime numbers not working for the number 10?

Question

I am trying to write a code in python to find all prime numbers of a number. My problem is that with this line of code it does not work to return the prime numbers of 10, the list only returns 2. Now I adapted this code from this page https://www.geeksforgeeks.org/prime-factor/ as I want to make my factors come out as a list.

The code from that website works for the number 10, however I do not understand why it does not work for number 10 when I run my own slightly modified version of it.

I have tried to +10 at the end of my range function, instead of a +1 and this does solve the problem, however I am still unsure as to why I even have a problem in the first place. Secondly, will the +10 work for all numbers with no error? In theory it should as I should only have factors unto square root of n, but I am not sure again. Lastly, if if the +10 does work, won't that make the code run slower as it will iterate through unneeded loops, how can I improve the speed?

This is my code that I used.

import math

def primefact():
    n = int(input('What is your number?:'))
    prime_factors = []
    while n % 2 == 0: # Checks if number is divisible by 2
        prime_factors.append(2) #repeats it until n is no longer divisible by 2
        n = n / 2 
    for i in range(3, int(math.sqrt(n)) + 1, 2): # Testing for odd factors
        while n % i == 0: 
            prime_factors.append(i)
            n = n / i
    print(prime_factors)
    return 

primefact()

Answer 1

Here's a piece of code that I wrote:

from numpy import mod, int0, sqrt, add, multiply, subtract, greater, equal, less, not_equal, floor_divide
class findFactors:
def __init__(self, n):
    self.primeFactorize(n)
    
def primeFactorize(self, n):
    factors = self.findFactors(n)
    self.factors = factors
    primeFactors = []
    xprimeFactors = []
    for factor in factors:
        if prime(factor).isPrime:
            primeFactors.append(factor)
    ntf = n
    nprime = 0
    while not_equal(ntf, 1):
        while equal(mod(ntf, primeFactors[nprime]), 0):
            ntf = floor_divide(ntf, primeFactors[nprime])
            xprimeFactors.append(primeFactors[nprime])
        nprime = add(nprime, 1)
    self.primeFactors = primeFactors
    self.extendedPrimeFactors = xprimeFactors

def findFactors(self, number):
    if prime(number).isPrime: return [1, number]
    factors = []
    s = int0(sqrt(float(number)))
    for v in range(1, add(s, 1)):
        if equal(mod(number, v), 0):
            factors.append(int(v))
            factors.append(int(floor_divide(number, v)))
    factors.sort()
    return factors

class prime:
def __init__(self, n):
    self.isPrime = self.verify(n)

def verify(self, n):
    if less(n, 2):
        return False
    if less(n, 4):
        return True
    if not n & 1 or equal(mod(n, 3), 0):
        return False
    s = int0(sqrt(float(n)))
    for k in range(1, add(s, 1)):
        mul = multiply(6, k)
        p = add(mul, 1)
        m = subtract(mul, 1)
        if greater(m, s):
            return True
        if equal(mod(n, p), 0) or equal(mod(n, m), 0):
            return False

Imagine func = findFactors(n)

func.factors will returns a list with all the factors of the number n,

func.extendedPrimeFactors will return a list with the prime factorization of the number,

func.primeFactors will return a list with the primes appearing only once instead of x times

also, there's a really fast prime checker down there. (Prime checker usage: prime(n).isPrime )

Answer 2

Hi you just forgot the last part of the equation

Condition if n is a prime

# number greater than 2
if n > 2:
    print n

Here Is the list of all factorial prime numbers, is not the same as prime numbers https://en.m.wikipedia.org/wiki/Table_of_prime_factors