Reuse the smaller primes we found and only try divisions by them instead of every number. Also technically we only need to try up to sqrt(n) which is usually less than n//2 + 1.
sqrt(n)
n//2 + 1
import math def nth_prime(n: int) -> int: primes = [2] m = 3 while len(primes) < n: j = 0 sqrt_m = math.sqrt(m) is_prime = True while primes[j] <= sqrt_m: if m % primes[j] == 0: is_prime = False break j += 1 if is_prime: primes.append(m) m += 1 return primes[-1] print(nth_prime(10001))
It can save time and space complexity.
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Reuse the smaller primes we found and only try divisions by them instead of every number. Also technically we only need to try up to
sqrt(n)which is usually less thann//2 + 1.It can save time and space complexity.