Which is faster pyprimesieve or Python sieve?

Which is faster pyprimesieve or Python sieve?

It can be seen here that pyprimesieve is 4.7 times faster than the fastest Python alternative using Numpy and 13.85 times faster than the fastest pure Python sieve. All benchmark scripts and algorithms are available for reproduction.

Which is the fastest sieve for many primes?

Many primes, very fast. Uses primesieve. primesieve, one of the fastest (if not the fastest) prime sieve implementaions available, is actively maintained by Kim Walisch. It uses a segmented sieve of Eratosthenes with wheel factorization for a complexity of O (nloglogn) operations.

How to implement the sieve of Eratosthenes in Python?

The Sieve of Eratosthenes is an algorithm which heavily relies on loops. Unfortunately, Python’s convenient scripty nature comes at a cost: it’s not terribly fast when it comes to loops, so it’s best to avoid them. However, this is not always possible, or one, like me in this case, is not so much into algorithms to transform them into another form.

Which is faster a ByteArray or a sieve?

Since we are storing individual flags in bytes, a bytearray should be faster: Now you can proceed with your sieve, testing only odd numbers, and marking as not prime only the odd multiples of a prime number, start with its square, up to the end of the sieve:

How does the sieve of Eratosthenes work in Python?

Here’s a version that’s a bit more memory-efficient (and: a proper sieve, not trial divisions). Basically, instead of keeping an array of all the numbers, and crossing out those that aren’t prime, this keeps an array of counters – one for each prime it’s discovered – and leap-frogging them ahead of the putative prime.

Is there a way to generate primes in Python?

I realise this isn’t really answering the question of how to generate primes quickly, but perhaps some will find this alternative interesting: because python provides lazy evaluation via generators, eratosthenes’ sieve can be implemented exactly as stated: