Prime numbers are chosen to best distribute data among hash buckets. If the distribution of inputs is random and evenly spread, then the choice of the hash code/modulus does not matter. It only has an impact when there is a certain pattern to the inputs. This is often the case when dealing with memory locations. … Read more
The basic idea of a segmented sieve is to choose the sieving primes less than the square root of n, choose a reasonably large segment size that nevertheless fits in memory, and then sieve each of the segments in turn, starting with the smallest. At the first segment, the smallest multiple of each sieving prime … Read more
This question was the first link that popped up when I googled “python prime factorization”. As pointed out by @quangpn88, this algorithm is wrong (!) for perfect squares such as n = 4, 9, 16, … However, @quangpn88’s fix does not work either, since it will yield incorrect results if the largest prime factor occurs … Read more
The fastest algorithm for general prime testing is AKS. The Wikipedia article describes it at lengths and links to the original paper. If you want to find big numbers, look into primes that have special forms like Mersenne primes. The algorithm I usually implement (easy to understand and code) is as follows (in Python): def … Read more
Here’s an example of a sieve implementation in JavaScript: function getPrimes(max) { var sieve = [], i, j, primes = []; for (i = 2; i <= max; ++i) { if (!sieve[i]) { // i has not been marked — it is prime primes.push(i); for (j = i << 1; j <= max; j += … Read more
There are some problems: Why do you print out count when it didn’t divide by x? It doesn’t mean it’s prime, it means only that this particular x doesn’t divide it continue moves to the next loop iteration – but you really want to stop it using break Here’s your code with a few fixes, … Read more
A very fast implementation of the Sieve of Atkin is Dan Bernstein’s primegen. This sieve is more efficient than the Sieve of Eratosthenes. His page has some benchmark information.
You’re not quite implementing the correct algorithm: In your first example, primes_sieve doesn’t maintain a list of primality flags to strike/unset (as in the algorithm), but instead resizes a list of integers continuously, which is very expensive: removing an item from a list requires shifting all subsequent items down by one. In the second example, … Read more
“If I have seen further…” The erat2 function from the cookbook can be further sped up (by about 20-25%): erat2a import itertools as it def erat2a( ): D = { } yield 2 for q in it.islice(it.count(3), 0, None, 2): p = D.pop(q, None) if p is None: D[q*q] = q yield q else: # … Read more
The fastest algorithm for general prime testing is AKS. The Wikipedia article describes it at lengths and links to the original paper. If you want to find big numbers, look into primes that have special forms like Mersenne primes. The algorithm I usually implement (easy to understand and code) is as follows (in Python): def … Read more