Prime factorization of integers entered in Python ver.1

Introduction

The previously created "Program to determine whether a number entered in Python is a prime number" has a function that performs prime factorization when it is a composite number. I added it.

Program principle

Recalling the method of prime factorization that I learned when I was in elementary school, I decided to continue dividing from the smallest prime number. Specifically, create a prime number list using SymPy's primerange and continue to divide by a divisible number from that list. Then, when the division was performed to the end of the prime number list, it was finished.

Actual program

from sympy import primerange
inn = n = int(input("Enter the number you want to check if it is a prime number.>> "))
primlist = list(primerange(2,(inn+1) / 2)) #1
yaku = []

for i in primlist:
    while n % i == 0: #2
        n /= i
        yaku.append(i) #3

if not yaku: #4
    print(n, "Is a prime number.")
else:
    print(inn, "Is a composite number, and when factored into prime factors",yaku, "is.")

Rough flow

1. Create a prime number list up to (n + 1) / 2
2. Find a divisible number in the prime number list and continue to divide the integer n until it is no longer divisible.
3. Each time you divide, add the divided prime number to the list called yaku.
4. If there is nothing in yaku, it is displayed as a prime number. If anything is included, the result of prime factorization is displayed.

What you are actually doing

1. Created in # 1 using Sympy as before.
2. In # 2, by using the while syntax, it is possible to put into the operation of continuing to divide immediately without using if.
3. In # 3, add the prime i divided by yaku by doing .append (i).
4. In # 4, I noticed that if yaku contains a number, it is a composite number. Specifically, if you use the if syntax and set if ** not ** yaku, when there is nothing in yaku, the processing below if will be started.

Difficulties

When I first programmed, the range of the prime number list created by primerange () was the same as last time, "primerange (2, int (n ** (1/2)) + 1)". Then, when the input integer was "2 x prime number", only 2 was added to yaku, and there was a problem that it could not be factored accurately. Specifically, when you enter a number such as 14 (2 × 7), the result is "14 is a composite number, and when factored into prime factors, it is [2]. ] Has come out. Therefore, I set the range of the prime number list to "prime range (2, (inn + 1) / 2)". By doing this, I decided to solve the problem I mentioned earlier. At this time, by adding +1 to inn, a prime number list can be created up to a prime number even with an integer of "2 x prime number". Specifically, when 14 is entered, it becomes primerange (2, 7.5), so the content of primelist becomes [2, 3, 5, 7]. If +1 is not done, it will be primerange (2, 7), so the contents of primelist will be [2, 3, 5], and 7 will not be included in the result of prime factorization, so accurate prime factorization Will not be possible.

Reflections

If the range of prime number list creation is too wide and the integers entered are large (7 digits or more), the calculation speed will drop immediately. Therefore, I would like to improve the range setting and prime factorization method a little. Thank you for reading to the end.