Example
To find all the prime numbers less than or equal to 30, proceed as follows.
First generate a list of integers from 2 to 30:
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30First number in the list is 2; cross out every 2nd number in the list after it (by counting up in increments of 2), i.e. all the multiples of 2:
2 3Next number in the list after 2 is 3; cross out every 3rd number in the list after it (by counting up in increments of 3), i.e. all the multiples of 3:
2 3Next number not yet crossed out in the list after 3 is 5; cross out every 5th number in the list after it (by counting up in increments of 5), i.e. all the multiples of 5:
2 3Next number not yet crossed out in the list after 5 is 7; the next step would be to cross out every 7th number in the list after it, but they are all already crossed out at this point, as these numbers (14, 21, 28) are also multiples of smaller primes because 7*7 is greater than 30. The numbers left not crossed out in the list at this point are all the prime numbers below 30:
2 3 5 7 11 13 17 19 23 29Read more about this topic: Sieve Of Eratosthenes
Famous quotes containing the word example:
“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
—Marcel Proust (1871–1922)