ERATOSTHENES SIEVE

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Eratothenes´sieve.
Steps to find prime numbers from 1 to 100.

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ERATOSTHENES SIEVE

  1. 1. The Eratosthenes&apos; Sieve<br />Back in 200 BC <br /> a Greek mathematician <br /> named Eratosthenes <br /> developed a simple step-by-step method <br /> for determining which numbers are prime. <br />This method is called &quot;Eratosthenes&apos; Sieve&quot;. <br />
  2. 2. A sieve<br />is a strainer<br /> that allows <br /> small particles <br /> to pass through <br /> while catching the larger particles. <br />
  3. 3. In the case of Eratosthenes&apos; Sieve, <br />the small particles that pass through <br />are all the non-prime numbers <br />and the large particles that remain <br />are the Prime Numbers. <br />
  4. 4. Eratosthenes<br />
  5. 5. He was born in Cirene <br />(actually Shahhat, Libia,<br /> which is in Africa)<br />He studied in Alexandria<br />Arquimedes was his friend<br />He died at the age of 80.<br />
  6. 6. He was a great mathematician, <br /> philosopher, <br /> poet and astronomer.<br />People knew him as the second Plato or<br /> because he was always second in <br /> every subject he studied.<br />
  7. 7. His method to <br /> find out <br /> the prime numbers <br /> can be divided into 5 simple steps.<br />
  8. 8. But wait a minute, folks!<br />
  9. 9. What are Prime Numbers?<br />Numbers Divisible Only by Themselves and 1<br />Any number that has only two factors, itself and 1.<br />
  10. 10. Is the number 1 a prime number?<br />No, it isn´t. <br />The number 1 is NOT considered Prime <br />Why?<br />Because it only has one factor , itself.<br />
  11. 11. What is a sieve?<br />What can we do with Eratosthenes´ sieve?<br />We can find out which of the numbers from 1 to 100 are prime<br />Let´s do it!<br />
  12. 12. The Eratosthenes&apos; Sieve - Step 1<br />Make a table of the numbers 1 to 100 <br /> organized into 10 rows<br />
  13. 13. The Eratosthenes&apos; Sieve - Step 2<br /> Cross out the number 1<br /> because by definition it is NOT Prime number<br />
  14. 14. The Eratosthenes&apos; Sieve - Step 3<br />Circle the number 2 and <br /> cross out all the multiples of 2 <br /> (or all the even numbers)<br />
  15. 15. The Eratosthenes&apos; Sieve - Step 4<br /> Look for the following number that is not crossed out. <br />Circle the number and cross out all the multiples of that number.<br />
  16. 16. The Eratosthenes&apos; Sieve - Step 5<br /> Repeat step 4 <br /> until you get to the number 7.<br />
  17. 17. Finished?<br />All of the circled numbers <br /> are PRIME NUMBERS!<br />
  18. 18. Now you can watch a simulation of the sieve...Pay attention!<br />

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