使用 Euclid infinitude of prime proof 列出 N 以下的所有素数

Question

这里是问题：

Write a function that accepts a bound N, and finds the first N primes as determined by the classical proof of the infinitude of the set of primes. That is: begin with P = {2}; then form, m, the sum of 1 with the product over all elements of P. Place the smallest prime factor of m into P and repeat.

这是我所做的：

def get_primes(n):
    i = 2
    prime_list = []
    while i < n:
        p = prod(prime_list)+1
        r = min_symbolic(prime_divisors(p))
        prime_list.append(r)
        i = i+1
   return prime_list

当我尝试 get_primes(10) 时，它给了我一堆错误，我在这里做错了什么？我刚开始学习python，谢谢。

编辑：抱歉不清楚，这是我遇到的错误

Error in lines 1-1
Traceback (most recent call last):
File "/projects/3fe731e3-2b4d-43b9-86a0-5efb4456f029/.sagemathcloud/sage_server.py", line 881, in execute
exec compile(block+'\n', '', 'single') in namespace, locals
File "", line 1, in <module>
File "", line 6, in get_primes
File "/projects/sage/sage-6.9/local/lib/python2.7/site-packages/sage/rings/arith.py", line 2538, in prime_divisors
return [p for p,_ in factor(n)]
TypeError: 'sage.symbolic.expression.Expression' object is not iterable

Answer 1

看起来你的 prod 可能在第一个事件中实际上不是可分解的。检查 prod([])+1 会发生什么。我在火车上，否则我会亲自为您检查一下。另外，我不确定为什么你不能只使用 min，min_symbolic 实际上只适用于 min_symbolic(x,x^2) 之类的东西；你只是在寻找一些整数的最小值，所以内置 Python min 应该（？）工作正常。

Answer 2

kcrisman 是正确的，错误来自使用 min_symbolic。将其替换为 min 可消除错误，但仍需要对代码进行一些调整以提供前 n 个素数，如下所述：

def get_primes(n):
    prime_list = [2]
    i = 1
    while i < n:
        p = prod(prime_list) + 1
        r = min(prime_divisors(p))
        prime_list.append(r)
        i = i + 1
    return prime_list

使用 Euclid infinitude of prime proof 列出 N 以下的所有素数

Listing all primes below N using Euclid infinitude of prime proof

python

primes

sage