Sieve of Eratosthenes PDF

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Sieve of Eratosthenes...

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Sieve of Eratosthenes The Sieve of Eratosthenes is an ancient method for finding all primes numbers up to a specified number. It was created by Eratosthenes (275-194 B.C., Greece), an ancient Greek mathematician. Just as a sieve is a strainer for draining spaghetti, Eratosthenes's sieve drains out composite numbers and leaves prime numbers behind. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the first prime number. The multiples of a given prime are generated as a sequence of numbers starting from that prime, with constant difference between them that 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 (Ancient Greek: κόσκινον Ἐρατοσθένους, kóskinon Eratosthénous) 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. Sieve of Eratosthenes is a basic and antiquated calculation used to locate the prime numbers up to any random limit. It is one of the most efficient ways to find small prime numbers. For a given maximum limit (n) the calculation works by iteratively denoting the products of primes as composite, beginning from 2. When all products of 2 have been checked composite, the multiples of next prime, ie 3 are marked composite. This procedure proceeds until ( p...