from itertools import count, islice, takewhile
def prime_sieve2():
sieved = count(2)
prime = next(sieved)
yield prime
primes = [prime]
for x in sieved:
possible_prime_divs = takewhile(lambda p: p <= x**0.5, primes)
if any(x % prime == 0 for prime in possible_prime_divs):
continue
yield x
primes.append(x)
if __name__ == '__main__':
print("Show the 10,001st prime.\n =",
next(islice(prime_sieve2(), 10_000, 10_001)))
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Modified to test less primes:
from itertools import count, islice, takewhile def prime_sieve2(): sieved = count(2) prime = next(sieved) yield prime primes = [prime] for x in sieved: possible_prime_divs = takewhile(lambda p: p <= x**0.5, primes) if any(x % prime == 0 for prime in possible_prime_divs): continue yield x primes.append(x) if __name__ == '__main__': print("Show the 10,001st prime.\n =", next(islice(prime_sieve2(), 10_000, 10_001)))