Question

What is Eratothenesis Seive's method of finding Prime numbers

Answer 1

In mathematics, the sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit.

It does so by iteratively marking as composite(i.e., not prime) the multiples of each prime, starting with the first prime number, 2. The multiples of a given prime are generated as a sequence of numbers starting from that prime, with constant difference between themthat is equal to that prime.This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime.

The earliest known reference to the sieve is in Nicomachus of Gerasa's Introduction to Arithmetic, which describes it and attributes it to Eratosthenes of Cyrene, a Greek mathematician.

One of a number of prime number sieves, it is one of the most efficient ways to find all of the smaller primes. It may be used to find primes in arithmetic progressions.


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