Let us start with the definition of a Prime Number.
Do you remember?
A natural number that can be divided by only 2 numbers – 1 and the number itself is called a prime number.
The first prime number that comes to our mind is “1” but if you had paid attention to your Math teacher, then you will know that: 1 is neither primer nor composite. The reason behind this conclusion is a topic for another post. Let us look at identifying prime numbers.
6 – Prime or Composite?
Steps to identify prime numbers
1) Divide the number into factors
2) If the number of factors is more than two then it is composite.
Ex: 6 has three factors 2, 3, 1. So 6 is not prime
6 = 2 x 3 x 1
Before going into shortcuts to find large prime number, here are a few properties of Prime Numbers
1) The lowest even prime number is 2
2) The lowest odd prime number is 3
3) All prime numbers above 3 can be represented by the formula 6n + 1 and 6n -1 for n>=1
Prove It!
Take 5 = 6 x 1 -1
Take 7 = 6 x 1 + 1
Take 47 = 6 x 8 – 1
4) There are 25 prime number between 1 and 100
List Them: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
P.S: Learn the series for GMAT.
5) All prime numbers except 2 and 5 ends in 1, 3, 7 or 9 (noticed it?)
How to find whether a large number is prime or not
Let us take a number 2,329
Step 1: If the number ends in 0,2,4,6,8 then it is not prime
Step 2: Add the digits of your number; if the sum is divisible by 3 then it is not a prime number
2329 = 2 + 3 + 2 + 9 = 16
Still would be a prime number!
Step 3: If Steps 1 and 2 are not true then find the square root of the number
48.25
Step 4: Divide the number by all prime numbers less than 48.25 (exclude 2, 3, 5)
Prime Numbers less than 48: 7,11,13,17,19,23,29,31,37,41,43,47
Still would be a prime number!!!!!
Dammit!!!
2329 = 17 x 137 (Divisible by 17)
2329 is not a prime number.
Now try a large prime number and let us know whether the method works! We at F1GMAT have been contacted by computer programmers about this method. Trying multiple large numbers is the only test that you can perform before creating a foolproof algorithm.
This technique applies to Quant questions in Computer Adaptive tests.
About the Author
I am Atul Jose, Founding Consultant of F1GMAT, an MBA admissions consultancy that has worked with applicants since 2009.
For the past 15 years I have edited the application files of admits to the M7 programs: Harvard Business School, Stanford Graduate School of Business, the Wharton School, MIT Sloan, Chicago Booth, Kellogg School of Management, and Columbia Business School, together with admits to Berkeley Haas, Yale School of Management, NYU Stern, Michigan Ross, Duke Fuqua, Darden, Tuck, IMD, London Business School, INSEAD, SDA Bocconi, IESE Business School, HEC Paris, McCombs, and Tepper, plus other programs inside the global top 30.
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