How can I find all prime numbers in a given range?

问题

def all primes(start,end):
    list_primes = []
    for i in range(start,end):
        for a in range(2,i):
            if i % a == 0:
                list_primes.append(i)

    return list_primes

For some reason it returns everything but the primes. Its probably some silly mistake. Can anyone help?

回答1:

Try this (uses Sieve of Eratosthenes):

    def all_primes(start, end):
        return list(sorted(set(range(start,end+1)).difference(set((p * f) for p in range(2, int(end ** 0.5) + 2) for f in range(2, (end/p) + 1)))))

回答2:

For getting prime numbers, try to implement Sieve of Eratosthenes algorithm https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

In Python 3 for seeking in 1 million numbers, it takes about 0.5 secs for me

def get_primes(start, stop):
    dct = {x: True for x in list(range(start, stop+1))}
    x = start

    while x ** 2 <= stop:
        if dct[x]:
            y = x ** 2
            while y <= stop:
                dct[y] = False
                y += x
        x += 1

    lst = []
    for x, y in dct.items():
        if y:
            lst.append(x)

    return lst

res = get_primes(2, 1000000)
print(res)

回答3:

I wanted to share that the fastest way I've found to generate primes in a range is to use the SymPy symbolic mathematics library:

import sympy 

def all_primes(start, end):
    return list(sympy.sieve.primerange(start, end))

The sympy.sieve.primerange() function returns a generator, so we need list() to convert it to a list.

Here's an example of the performance difference between this, and the already-very-optimized answer that is currently most upvoted in this thread:

import sympy

def get_primes_python(start, stop):
    dct = {x: True for x in list(range(start, stop+1))}
    x = start

    while x ** 2 <= stop:
        if dct[x]:
            y = x ** 2
            while y <= stop:
                dct[y] = False
                y += x
        x += 1

    lst = []
    for x, y in dct.items():
        if y:
            lst.append(x)

    return lst

def get_primes_sympy(start, stop):
    return list(sympy.sieve.primerange(start, stop))

In [2]: %timeit test.get_primes_python(1, 10**7)
1 loop, best of 3: 4.21 s per loop

In [3]: %timeit test.get_primes_sympy(1, 10**7)
10 loops, best of 3: 138 ms per loop

回答4:

Change your inner loop to:

for a in range(2,i):
    if i % a == 0:
        break
else:
    list_primes.append(i)

Copy pasted from here:-)
Incidentally, they used same code for example :)

回答5:

you can try this function

def generate_primes(lower_limit,upper_limit):
    if not isprime(lower_limit):
        return False
    candidate = lower_limit
    r = []
    while(candidate <= upper_limit):
        trial_divisor = 2
        prime = 1 # assume it's prime
        while(trial_divisor**2 <= candidate and prime):
            if(candidate%trial_divisor == 0):
                prime = 0 # it isn't prime
            trial_divisor+=1
        if(prime):
            r += [candidate]
        candidate += 2
    return r

def isprime(n):
    '''check if integer n is a prime'''
    # make sure n is a positive integer
    n = abs(int(n))
    # 0 and 1 are not primes
    if n < 2:
        return False
    # 2 is the only even prime number
    if n == 2: 
        return True    
    # all other even numbers are not primes
    if not n & 1: 
        return False
    # range starts with 3 and only needs to go up the squareroot 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

I am modified it from this page http://dunningrb.wordpress.com/2009/02/12/prime-numbers-and-a-simple-python-code/

回答6:

Try this:

def isprime (x):
    isprime=True
    if x!=2:
        for i in range (2,x):
            if x%2==0:
                isprime=False
            break
        return isprime
x=int(input("enter a number"))
z=isprime(x)
print(z)

来源：https://stackoverflow.com/questions/13427890/how-can-i-find-all-prime-numbers-in-a-given-range