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# Prime Number

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Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 615

Kudos [?]: 1133 [0], given: 39

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22 Feb 2011, 04:22
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.
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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

Kudos [?]: 1133 [0], given: 39

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128837 [3], given: 12183

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22 Feb 2011, 05:46
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.
_________________

Kudos [?]: 128837 [3], given: 12183

Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 871

Kudos [?]: 396 [0], given: 123

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28 Feb 2011, 20:51
Thanks Bunuel ! Amazing explanation.

Kudos [?]: 396 [0], given: 123

Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 871

Kudos [?]: 396 [0], given: 123

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28 Feb 2011, 21:20
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.

Kudos [?]: 396 [0], given: 123

Re: Prime Number   [#permalink] 28 Feb 2011, 21:20
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