Prime numbers
Prime numbers
Definition: A prime number is a positive integer that has no positive integer divisors other than and itself. More concisely, a prime number is a positive integer having exactly one positive divisor other than , meaning it is a number that cannot be factored.
Positive integers other than 1 which are not prime are called composite numbers.
Example: the only divisors of are and , making a prime number, while the number has divisors , and (corresponding to the factorization ), making not a prime number.
Additional resources
- Data Pointed is the home of Stephen Von Worley's data visualization research; a journal of interesting information imagery and news from around the world; and a place where you can spend a few minutes, have a laugh or two, and discover something new. Follow this link to find a very nice visualization of prime and composite numbers: http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/
- In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. Method: 2.1. Create a list of consecutive integers from through : . 2.2. Initially, let , the smallest prime number. 2.3. Enumerate the multiples of by counting in increments of from to , and mark them in the list (these will be ; itself should not be marked). 2.4. Find the smallest number in the list greater than that is not marked. If there was no such number, stop. Otherwise, let now equal this new number (which is the next prime), and repeat from step 2.3. 2.5. When the algorithm terminates, the numbers remaining not marked in the list are all the primes below .
Formative assessment
The purpose of the applet below is to sort out prime numbers from composite numbers.
Click on the squares that contain prime numbers and then click on check.
Try it as many times as you may need.
References
Animated Factorization Diagrams – Data Pointed. Data Pointed RSS. (n.d.). http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/.
amelka12. (2019, October 14). Kopia Liczby pierwsze / Prime numbers. GeoGebra. https://www.geogebra.org/m/ntrhsppk.
Weisstein, Eric W. "Prime Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PrimeNumber.html
Vuković, A. M. (n.d.). Sieve of Eratosthenes. GeoGebra. https://www.geogebra.org/m/uGX53dy7.
Wikimedia Foundation. (2021, July 16). Sieve of Eratosthenes. Wikipedia. https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes.