Sieve of Eratosthenes
Now let’s flip issues round a bit and take a look at how coding helps us deal with and perceive one of many traditional issues of math: discovering primeness. An historical algorithm was described by Eratosthenes, working within the third century BC. The algorithm, now referred to as the Sieve of Eratosthenes, offers a set of steps for locating all of the primes for a given quantity.
The fundamental thought behind the algorithm is to take a quantity, n, and thru a sequence of passes, get rid of the non-prime numbers. What stays whenever you’re executed is the set of primes you might be after. There are a lot of potential methods to refine this course of, however the primary fashionable model of the sieve begins by taking 2 and noting it as prime, then discovering all of the even numbers as much as n, noting them as not prime. Then, we transfer to three and carry out the identical factor for multiples of three. Persevering with on, we do the identical for all of the numbers as much as n, solely skipping these numbers we’ve got already famous as non-prime.
This can be a very historical instance of an algorithm, and a programmer’s potential to place it into an executable format is a superpower, for positive. Here’s a model in JavaScript (from Wikipedia):
