问题
I'm currently trying to use an implementation of the sieve of erasthonese, but it still takes a very long time to find a long list of prime numbers.
def sieve(n=1000000):
not_prime = []
prime = []
for i in range(2, n+1):
if i not in not_prime:
prime.append(i)
for j in range(i*i, n+1, i):
not_prime.append(j)
return prime[10002]
I tried to hard code to what value the sieve should run to, and hopefully, it's long enough so that I can find the 10002nd element. Runtime is a big problem at the moment, so any tips or advice on cutting runtime down or anything else is appreciated.
回答1:
If you are interested in improving this code in particular, then the first thing you could do is use a set to store the non primes.
def sieve_set(n=1000000):
not_prime = set()
primes = []
for i in range(2, n+1):
if i not in not_prime:
primes.append(i)
for j in range(i*i, n+1, i):
not_prime.add(j)
return primes
This prevents repetition of numbers within the list, and makes searches within the list fast. This will vastly improve your run time.
In [1]: %timeit -n 1 -r 1 sieve(10000)
1 loops, best of 1: 775 ms per loop
In [2]: %timeit -n 1 -r 1 sieve_set(10000)
1 loops, best of 1: 5.85 ms per loop
Now finding the 10,001 prime is achievable:
In [3]: %timeit sieve_set(105000)
10 loops, best of 3: 26.6 ms per loop
In [4]: sieve_set(105000)[10000]
Out[4]: 104743
来源：https://stackoverflow.com/questions/37312540/finding-the-10001st-prime-number-in-python