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Mathematical Algorithms

Mathematical algorithms

Euclidean algorithm | sieve of Eratosthenes

Statements

The Euclidean algorithm is an algorithm for finding the greatest common divisor of two numbers.

The sieve of Eratosthenes is a simple algorithm for finding all prime numbers up to a specified integer. To apply the algorithm, sequentially write down the integers from 2 to the highest number n to be included in the table. Cross out all numbers greater than 2 which are divisible by 2, i.e., every second number. Find the smallest remaining number greater than 2, which is 3. Therefore, cross out all numbers greater than 3 which are divisible by 3, i.e., every third number. Find the smallest remaining number greater than 3. It is 5. Therefore, cross out all numbers greater than 5 which are divisible by 5, i.e., every fifth number. Continue until you have crossed out all numbers divisible by ⌊sqrt(n)⌋. Then the numbers remaining are prime.

History

| Euclidean algorithm | sieve of Eratosthenes formulation date | 300 BC (2324 years ago) | 250 BC (2274 years ago) formulators | Euclid | Eratosthenes status | proved | proved additional people involved | Gabriel Lamé | Nicomachus

Common classes

mathematical algorithms | solved mathematics problems

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