#LIST OF PRIME NUMBERS UP TO 50 PDF#

However, we also found numbers in those columns that are composites (not prime) thus, that location is not a sufficient condition for a number to be prime. This means that it is necessary for the number to be located in one of those two columns if it is prime and greater than 3. We have shown that every prime greater than 3 is located in either the fourth or sixth columns of our grid. The previous activities illustrate the difference between a necessary and a sufficient condition. In This Part:В Necessary and Sufficient Conditions You can find this segment on the session video approximately 10 minutes and 56 seconds after the Annenberg Media logo. Watch how Professor Findell and the participants worked on Problems B1-B3 in this video segment.ДЄre you convinced that the conjecture about locating prime numbers is true? Try extending the table by a few more rows to see if the rule still applies. Where on the extended grid should you look to find prime numbers greater than 3? Continue in a similar manner until all the numbers on the grid are either circled or crossed out.Д®xamine the grid and imagine that it extends to infinity. Notice that these multiples are not all located in particular columns, so crossing them out is not as easy as before.

(Of course, the fifth column is already gone because it contains multiples of 2!)Д«.В Could multiples of 3 be located in any other column?ДЄgain, circle the smallest remaining prime number (i.e., 5) and cross out all the multiples of 5, as they are not prime. Present a convincing argument for the fact that all the numbers in the second and fifth columns are multiples of 3 and would thus be crossed out. Cross out all the multiples of 3, as they are not prime.ДЄ.В Again imagine that the grid goes on forever. Next, circle the smallest remaining prime number (i.e., 3). Present a convincing argument for the fact that all the numbers in the first, third, and fifth columns are multiples of 2 and would thus be crossed out.Д«.В Could multiples of 2 be located in any other column? Next, cross out all the multiples of 2, as they are not prime numbers.ДЄ.В Imagine that the grid goes on forever.

#LIST OF PRIME NUMBERS UP TO 50 PDF#

As you will see, such positioning of numbers will make the patterns more noticeable and consequently will be more helpful in answering the question of where the prime numbers are located.Д¬opy the grid above or print a PDF version.Д¬ircle the 2, which is a prime number.

This grid has only six columns, starting with the numbers 2 through 7. In the following activity, we will use a different grid to locate the prime numbers. If you try looking for prime numbers in this grid, you will discover that itвЂ™s not so easy to locate them in a systematic way: This grid does locate the prime numbers, but it does not help us understand where to look for them. In this part, weвЂ™ll continue a mathematics tradition begun by Eratosthenes of Cyrene (276-194 B.C.E.) - the same person whoвЂ™s known for accurately estimating the diameter of the Earth based on the shadow cast by the SunвЂ™s light.Д®ratosthenes worked out a method, now called the вЂњSieve of Eratosthenes,вЂќ to collect all the prime numbers and allow all composites (multiples of prime numbers) to вЂњdrain through.вЂќ He used a grid that looked like what we now call the 100 board - the first row is 1-10, the second row 11-20, etc.

List of prime numbers up to 50