I prefer NumPy because of speed.
import numpy as np# Find all prime numbers using Sieve of Eratosthenesdef get_primes1(n): m = int(np.sqrt(n)) is_prime = np.ones(n, dtype=bool) is_prime[:2] = False # 0 and 1 are not primes for i in range(2, m): if is_prime[i] == False: continue is_prime[i*i::i] = False return np.nonzero(is_prime)[0]# Find all prime numbers using brute-force.def isprime(n):''' Check if integer n is a prime ''' n = abs(int(n)) # n is a positive integer if n < 2: # 0 and 1 are not primes return False if n == 2: # 2 is the only even prime number return True if not n & 1: # all other even numbers are not primes return False # Range starts with 3 and only needs to go up the square root # of n for all odd numbers for x in range(3, int(n**0.5)+1, 2): if n % x == 0: return False return True# To apply a function to a numpy array, one have to vectorize the functiondef get_primes2(n): vectorized_isprime = np.vectorize(isprime) a = np.arange(n) return a[vectorized_isprime(a)]Check the output:
n = 100print(get_primes1(n))print(get_primes2(n)) [ 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97] [ 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97]Compare the speed of Sieve of Eratosthenes and brute-force on Jupyter Notebook. Sieve of Eratosthenes in 539 times faster than brute-force for million elements.
%timeit get_primes1(1000000)%timeit get_primes2(1000000)4.79 ms ± 90.3 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)2.58 s ± 31.2 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)