在 Python 中采样大于 p 的 n 个随机素数的最快方法？

Question

I want to create a dateset of n primes greater than p ~ 2⁵⁰. I want these primes to not be consecutive but have some space in between so the difference between iᵗʰ and (i+1)ᵗʰ prime is not just a few bits.

I am using Sympy's randprime(low, hi) in a loop,

p = [start]
for i in range(n):
    curr = int(randprime(start, 2 * start + 1))
    p.append(curr)
    start = curr

This gets significantly slow for n=10,000 . Is there a better (faster) way of accomplishing the prime sampling that I want?

Answer 1

Precompute (or just download ) a list of primes once and then sample the list during the runtime.

You can generate the list for 30x smaller upper bound than 2^50 (~10^15) with this algorithm: https://primes.utm.edu/nthprime/algorithm.php

I don't know how to get further with reasonable hardware setup.