CE book which attributes it to Eratosthenes of Cyrene, a 3rd cent. The earliest known reference to the sieve ( Ancient Greek: κόσκινον Ἐρατοσθένους, kóskinon Eratosthénous) is in Nicomachus of Gerasa's Introduction to Arithmetic, an early 2nd cent. Once all the multiples of each discovered prime have been marked as composites, the remaining unmarked numbers are primes. This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime. ![]() 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. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the first prime number, 2. In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. ![]() Sieve of Eratosthenes: algorithm steps for primes below 121 (including optimization of starting from prime's square).
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