Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 22 May 2015, 01:12

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Prime Number

Author Message
TAGS:
Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 661
Followers: 37

Kudos [?]: 363 [0], given: 39

Prime Number [#permalink]  22 Feb 2011, 03:22
all prime numbers above 3 are of the form 6n-1or 6n+1, because all other numbers are divisible by 2 or 3.

Please make clear the meaning of the sentence with example.
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Math Expert
Joined: 02 Sep 2009
Posts: 27457
Followers: 4303

Kudos [?]: 42074 [3] , given: 5945

Re: Prime Number [#permalink]  22 Feb 2011, 04:46
3
KUDOS
Expert's post
Baten80 wrote:
all prime numbers above 3 are of the form 6n-1or 6n+1, because all other numbers are divisible by 2 or 3.

Please make clear the meaning of the sentence with example.

Any prime number $$p>3$$ when divided by 6 can only give remainder of 1 or 5 (remainder can not be 2 or 4 as in this case $$p$$ would be even and remainder can not be 3 as in this case $$p$$ would be divisible by 3).

So any prime number $$p>3$$ could be expressed as $$p=6n+1$$ or $$p=6n+5$$ ($$p=6n-1$$), where n is an integer >0.

For example: 5=prime=6-1, 7=prime=6+1, 11=prime=6*2-1, 13=prime=6*2+1, 17=prime=6*3-1, ...

But:
Not all number which yield a remainder of 1 or 5 upon division by 6 are prime, so vise-versa of above property is not correct. For example 25 yields a remainder of 1 upon division be 6 and it's not a prime number.
_________________
Director
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 926
Followers: 13

Kudos [?]: 222 [0], given: 123

Re: Prime Number [#permalink]  28 Feb 2011, 19:51
Thanks Bunuel ! Amazing explanation.
Director
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 926
Followers: 13

Kudos [?]: 222 [0], given: 123

Re: Prime Number [#permalink]  28 Feb 2011, 20:20
Bunuel
Any OG question using this property?

Thanks

Bunuel wrote:
Baten80 wrote:
all prime numbers above 3 are of the form 6n-1or 6n+1, because all other numbers are divisible by 2 or 3.

Please make clear the meaning of the sentence with example.

Any prime number $$p>3$$ when divided by 6 can only give remainder of 1 or 5 (remainder can not be 2 or 4 as in this case $$p$$ would be even and remainder can not be 3 as in this case $$p$$ would be divisible by 3).

So any prime number $$p>3$$ could be expressed as $$p=6n+1$$ or $$p=6n+5$$ ($$p=6n-1$$), where n is an integer >0.

For example: 5=prime=6-1, 7=prime=6+1, 11=prime=6*2-1, 13=prime=6*2+1, 17=prime=6*3-1, ...

But:
Not all number which yield a remainder of 1 or 5 upon division by 6 are prime, so vise-versa of above property is not correct. For example 25 yields a remainder of 1 upon division be 6 and it's not a prime number.
Re: Prime Number   [#permalink] 28 Feb 2011, 20:20
Similar topics Replies Last post
Similar
Topics:
4 If N is a positive integer, is 9 a factor of N? 8 24 May 2010, 21:58
1 Prime Numbers 3 08 Feb 2010, 10:23
prime numbers........... 4 06 Apr 2009, 00:57
prime numbers 5 05 Oct 2008, 11:15
Prime number 5 03 Jan 2007, 22:32
Display posts from previous: Sort by