Faster Calculations Using Numpy

Question

I have this program to list prime numbers within a certain range. the problem is the larger the number the slower it becomes. how can i use numpy to imporve the speeds? if not numpy, is there any other way to speed up the calculations?

from datetime import date
import time
import numpy as np

today = date.today()

lower = int(input("Starting Number: "))
upper = int(input("Ending Number: "))

print("Prime numbers between",lower,"and",upper,"are:")
with open("primenumbers.txt","a") as file:
    file.write("\n")
    file.write("{}".format(today))
    file.write("\n")

start = time.time()

for num in range(lower,upper + 1):
   if num > 1:
       for i in range(2,num):
           if (num % i) == 0:
               break
       else:
         print(num)
         with open("primenumbers.txt","a") as file:
             file.write("\n")
             file.write("{}".format(num))
end = time.time()
print(end - start)

i want to process the data faster and please show some code.

Answer 1

Sieve method is one of the efficient way to find the prime numbers. My answer is inspired from this Answer in SO. For 1 million I got a timeit of

16 ms ± 3.68 ms per loop (mean ± std. dev. of 7 runs, 100 loops each)

​ Numpy Implementation

def first_n_prime_numbres(n):    
    s = np.arange(3, n, 2)
    for m in range(3, int(n ** 0.5)+1, 2):         
        if s[(m-3)//2]: 
            s[(m*m-3)//2::m]=0
    return np.r_[2, s[s>0]]

first_n_prime_numbres(100)

Answer 2

You are calculating the same numbers over and over again:

for num in range(lower,upper + 1):
   if num > 1:
       for i in range(2,num):

Instead you can save the results and check against them. Checkout dynamic programming.