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How to identify a large prime number

Identify Large Prime NumbersLet 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 is an integer then it is not prime

Step 2: If the number ends in 0,2,4,6,8 then it is not prime


Step 3: 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 4: If Steps 1,2 and 3 are not true then find the square root of the number

48.25

Step 5: 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.


Top 31 MBA Programs + Analysis of 24 Industries (United States)


We analyze the MBA Curriculum, Class Profile, Total Cost and Post-MBA Salary of Top 31 MBA programs in the US.

+ Industry Trends

+ Future of Aerospace, Agriculture, Artificial Intelligence (AI), Automobile, Clean Tech, Education, Energy, Fashion, Financial Services, Insurance, FinTech, Government, Healthcare, Life Sciences, Military, Manufacturing, Maritime, Media/Advertising, Technology, Tourism, Trade, Transportation and Logistics, Virtual Reality (VR), and Augmented Reality (AR).


Pages: 327

Reviews

"I have not reviewed many books for MBA Admission consulting companies but doing it now to give all applicants a brief idea on what the book covers. The book includes 31 top MBA programs - almost all the top schools you have heard or considering for your MBA application. Each chapter is categorized by US States where there is at least one top MBA program. So you have California and Massachusetts with the most number of MBA programs and several states with one top program (Washington, Minnesota, Washington D.C., Connecticut, Virginia, and Maryland) and other states with two to three MBA programs. The book focuses on four aspects of an MBA program - curriculum, cost, class profile and post-MBA salary. For me, the breakdown of the cost and post-MBA industry was useful to make my decision on selecting the top 5 programs for 2017-18. It is a fascinating read in an industry where consultants overprice for their expertise. I recently bought a 30-page guide for $49. Compared to the obvious observation in that book, the 300+ page, MBA in US - the Ultimate guide is a goldmine of information and analysis." - Verified Purchase (21st June 2017)

"I bought the ultimate guide after a friend recommended it for me. The guide covers a lot of ground on the history of each prominent US states and goes into the reasons why a certain industry emerged from each state. In addition to the analysis of the economy, trends and expected changes in the next 5 years, the book features top MBA programs in each state with an extensive study of its curriculum. Ultimate guide is an essential reference book for MBA Applicants if they want to shortlist MBA programs based on value and cost, and not just ranking. " - Verified Purchase (14th June 2017)

"Should be a required reading before applying for an MBA. School events and MBA Tours are PR events disguised as a Q&A. On the contrary, the book is an unbiased analysis of each Top MBA program in the US supported by a large dataset and historical context on each industry. The guide builds a case for indstries that are likely to emerge as favourite for MBA graduates. Thorough and a valuable book." - Verified Purchase (15th June 2017)

"What I liked: The breadth of the information. Some of my favorite nonfiction books have taken the same approach as the ultimate guide have - cover background information in-depth. In the book, the author uses parallel threads to demonstrate the history of the state and the rise of industries. Will make you think how schools thrive based on the policy set by the state. California's obsession with Technology has revolutionized how we do Business and changed post-MBA trends. Many MBA applicants will be consulting or doing marketing for a Technology company. That is one key finding from the book. The latest development in AI, FinTech, and Automation is an additional context that I found valuable in the book.

Very informative. I would recommend that you read the book at least once in chronological order before using Table of Contents." - Verified Purchase (2nd July 2017)

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