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Eratosthenes proposed a simple algorithm for finding prime numbers. This algorithm is known in mathematics as the Sieve of Eratosthenes . In mathematics, the sieve of Eratosthenes (Greek: κόσκινον Ἐρατοσθένους), one of a number of prime number sieves , is a simple, ancient algorithm for finding all prime numbers up to any ...
The sieve of Eratosthenes is a popular way to benchmark computer performance. [14] The time complexity of calculating all primes below n in the random access machine model is O ( n log log n ) operations, a direct consequence of the fact that the prime harmonic series asymptotically approaches log log n .
Eratosthenes of Athens (Ancient Greek: Ἐρατοσθένης) was one of the Thirty Tyrants elected to rule the city of Athens after the Peloponnesian War (431–404 BC). Having lost the war to the Spartans , the citizens of Athens elected thirty men as oligarchs .
In this example the fact that the Legendre identity is derived from the Sieve of Eratosthenes is clear: the first term is the number of integers below X, the second term removes the multiples of all primes, the third term adds back the multiples of two primes (which were miscounted by being "crossed out twice") but also adds back the multiples ...
Eratosthenes calculated the Earth's circumference with great precision. [14] Since the distance from the Atlantic to India was roughly known, this raised the important question of what was in the vast region east of Asia and to the west of Europe. Crates of Mallus proposed that there were in fact four inhabitable land masses, two in each ...
Furthermore, the fact that Eratosthenes's measure corresponds precisely to 252,000 stadia might be intentional, since it is a number that can be divided by all natural numbers from 1 to 10: some historians believe that Eratosthenes changed from the 250,000 value written by Cleomedes to this new value to simplify calculations; [27] other ...
The commented-out line is all that is necessary to convert the Sieve of Sundaram to the Odds-Only Sieve of Eratosthenes; this clarifies that the only difference between these two algorithms is that the Sieve of Sundaram culls composite numbers using all odd numbers as the base values, whereas the Odds-Only Sieve of Eratosthenes uses only the ...
The Eratosthenian period in the lunar geologic timescale runs from 3,200 million years ago to 1,100 million years ago. It is named after the crater Eratosthenes, which displays characteristics typical of craters of this age, including a surface that is not significantly eroded by subsequent impacts, but which also does not possess a ray system.