prime_sieve's Introduction

Prime Sieve

An understandable prime sieve implementation in numpy or pure python. The focus is providing a sieve that is easy to understand rather than the absolute fastest implementation. Though the numpy implementation is reasonably quick, being able to compute the first 100 million primes in 30 seconds on my mid-tier laptop.

This library implements a version of the segmented sieve of Eratosthenes.

First take a look at the pure python implementation in prime_sieve/list.py. Then see the numpy implementation in prime_sieve/array.py. Sieve operations that are independent of the actual computation of primes, such as looking up the nth-prime number, are found in prime_sieve/base.py.

Free software: MIT license
Documentation: https://prime-sieve.readthedocs.io.

Usage

# Use a numpy or pure python implementation
from prime_sieve.array import PrimeArraySieve
# from prime_sieve.list import PrimeListSieve

sieve = PrimeArraySieve()
# sieve = PrimeListSieve()

print(sieve.nth_prime(0)) # 2
print(sieve[4]) # 7
print(sieve.index_of(7)) # 4

print(sieve[:100]) # [2, 3, ..., 541]
print(sieve[1:6]) # [3, 5, 7, 11, 13]

print(86*97 in sieve) # False
print(sieve.is_prime(2 ** 13 - 1)) # True

# ranges are like python ranges, inclusive start, exclusive stop
print(sieve.primes_in_range(10, 20)) # [11, 13, 17, 19]
print(sieve.primes_in_range(10, 19)) # [11, 13, 17]

print(sieve.count_primes_in_range(3, 7)) # 2
print(sieve.count_primes_in_range(3, 8)) # 3

print(sieve.next_prime_greater_than(100)) # 101
print(sieve.next_prime_greater_than(101)) # 103

print(sieve.prev_prime_less_than(8)) # 7
print(sieve.prev_prime_less_than(7)) # 5

print(sieve.count_primes_less_or_equal(10 ** 7)) # 664579

for p in sieve.iter_all_primes(): # infinite loop
    print(p)

# see sieve internals
print(len(sieve)) # how many primes have currently been computed
print(sieve.primes) # read-only view of already computed primes