Comments on: How would you know if 221 was a composite number? http://www.andersoncompositesquadron.org/composite/how-would-you-know-if-221-was-a-composite-number Sun, 11 Jul 2010 12:55:59 -0400 http://wordpress.org/?v=2.8.4 hourly 1 By: Not Your Average Genius http://www.andersoncompositesquadron.org/composite/how-would-you-know-if-221-was-a-composite-number/comment-page-1#comment-1172 Not Your Average Genius Fri, 22 Jan 2010 04:58:59 +0000 http://www.andersoncompositesquadron.org/composite/how-would-you-know-if-221-was-a-composite-number#comment-1172 One simple algorithm is to find the square root of the number and then consider all the primes less than or equal to that square root. Now divide the original number by each of those primes, continuing until you have either found a division with a remainder of 0 or until you've exhausted your list of prime factors. If you never get a 0 remainder, the number is prime. In your example, the square root is between 14 and 15, so you must try trial division by (at most) 2,3,5,7,11,and 13. The last such division proves that 221 is composite, as you already know. There are much more efficient algorithms for larger primes, but the mathematical machinery for implementing them is considerably more complex.<br><b>References : </b><br> One simple algorithm is to find the square root of the number and then consider all the primes less than or equal to that square root. Now divide the original number by each of those primes, continuing until you have either found a division with a remainder of 0 or until you’ve exhausted your list of prime factors. If you never get a 0 remainder, the number is prime. In your example, the square root is between 14 and 15, so you must try trial division by (at most) 2,3,5,7,11,and 13. The last such division proves that 221 is composite, as you already know. There are much more efficient algorithms for larger primes, but the mathematical machinery for implementing them is considerably more complex.
References :

]]> By: ununquadium114@ymail.com http://www.andersoncompositesquadron.org/composite/how-would-you-know-if-221-was-a-composite-number/comment-page-1#comment-1171 ununquadium114@ymail.com Fri, 22 Jan 2010 04:39:59 +0000 http://www.andersoncompositesquadron.org/composite/how-would-you-know-if-221-was-a-composite-number#comment-1171 There is a way by Eratosthenes, in which you write numbers from one to whichever number you are looking for, and then go about as follows: Cross out 1, since 1 isn't prime. Here you have 2, the first prime number; circle it but cross out all of its multiples. Find the next number that hasn't been crossed out, which will be 3, and circle it. Cross out all of the multiples of 3. Keep going like this until the number you've found is either crossed out or circled. Another way that is a lot easier is prime factorization. You factor a number into its prime factors. Since there are numbers that look like primes or that are very large, there are some helpful rules of thumb to figure out a number's factors by just looking at it. Divisibility by 2: A number ending in an even number or 0 if greater than 2 is divisible by 2. A number whose digits add up to a number divisible by 3 is divisible by 3. I won't list them all, but there is an excellent website on finding a number's divisibility: http://www.mathleague.com/help/wholenumbers/wholenumbers.htm#divisibilitytests Another way that is rather foolproof is to divide the number by the first prime number other than 2 (considering 221 isn't even); we know that it won't be divisible by 3 (example above), 5 (doesn't end in 5 or 0), 7 (we see right away that 21 divides evenly into 7 but the remainder 200 won't), etc. So we just keep going until we find a prime that divides it. If no primes divide it, the number itself might be prime. A foolproof way is to learn the first few primes above 53 by heart. Makes it easier.<br><b>References : </b><br>http://www.mathleague.com/help/wholenumbers/wholenumbers.htm#divisibilitytests There is a way by Eratosthenes, in which you write numbers from one to whichever number you are looking for, and then go about as follows:
Cross out 1, since 1 isn’t prime. Here you have 2, the first prime number; circle it but cross out all of its multiples. Find the next number that hasn’t been crossed out, which will be 3, and circle it. Cross out all of the multiples of 3. Keep going like this until the number you’ve found is either crossed out or circled.

Another way that is a lot easier is prime factorization. You factor a number into its prime factors.
Since there are numbers that look like primes or that are very large, there are some helpful rules of thumb to figure out a number’s factors by just looking at it.
Divisibility by 2: A number ending in an even number or 0 if greater than 2 is divisible by 2.
A number whose digits add up to a number divisible by 3 is divisible by 3.
I won’t list them all, but there is an excellent website on finding a number’s divisibility:

http://www.mathleague.com/help/wholenumbers/wholenumbers.htm#divisibilitytests

Another way that is rather foolproof is to divide the number by the first prime number other than 2 (considering 221 isn’t even); we know that it won’t be divisible by 3 (example above), 5 (doesn’t end in 5 or 0), 7 (we see right away that 21 divides evenly into 7 but the remainder 200 won’t), etc. So we just keep going until we find a prime that divides it. If no primes divide it, the number itself might be prime.

A foolproof way is to learn the first few primes above 53 by heart. Makes it easier.
References :
http://www.mathleague.com/help/wholenumbers/wholenumbers.htm#divisibilitytests

]]> By: ♥ Ima a Diva ♥. http://www.andersoncompositesquadron.org/composite/how-would-you-know-if-221-was-a-composite-number/comment-page-1#comment-1170 ♥ Ima a Diva ♥. Fri, 22 Jan 2010 03:57:59 +0000 http://www.andersoncompositesquadron.org/composite/how-would-you-know-if-221-was-a-composite-number#comment-1170 Because its a number that have 2 or more numbers other than itself or 1 like a prime number<br><b>References : </b><br> Because its a number that have 2 or more numbers other than itself or 1 like a prime number
References :

]]> By: Grampy 1901 http://www.andersoncompositesquadron.org/composite/how-would-you-know-if-221-was-a-composite-number/comment-page-1#comment-1169 Grampy 1901 Fri, 22 Jan 2010 03:33:59 +0000 http://www.andersoncompositesquadron.org/composite/how-would-you-know-if-221-was-a-composite-number#comment-1169 Elbow grease, he-he, that is, you have to test 'em just like Ms Dee suggested. Check against all the primes less that sqrt(221). Gets really hard to do when the numbers get to be thousands of digits long, but by jings, that's what cryptography counts on!<br><b>References : </b><br> Elbow grease, he-he, that is, you have to test ‘em just like Ms Dee suggested. Check against all the primes less that sqrt(221). Gets really hard to do when the numbers get to be thousands of digits long, but by jings, that’s what cryptography counts on!
References :

]]> By: Dee W http://www.andersoncompositesquadron.org/composite/how-would-you-know-if-221-was-a-composite-number/comment-page-1#comment-1168 Dee W Fri, 22 Jan 2010 02:43:59 +0000 http://www.andersoncompositesquadron.org/composite/how-would-you-know-if-221-was-a-composite-number#comment-1168 If it is not an obvious prime number..try division by 11, 13, 17, 19.<br><b>References : </b><br> If it is not an obvious prime number..try division by 11, 13, 17, 19.
References :

]]>