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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # Prime Number Formula  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Director Joined: 07 Jun 2004 Posts: 600 Location: PA Prime Number Formula [#permalink] ### Show Tags 20 Sep 2010, 06:45 1 hi we have this 6n + 1 or 6n -1 that represents a prime number is this true for all 'n' ? for eg : n =111 here 665 and 667 are not prime numbers what is the criterion for n ? thanks _________________ If the Q jogged your mind do Kudos me : ) Retired Moderator Joined: 02 Sep 2010 Posts: 769 Location: London Re: Prime Number Formula [#permalink] ### Show Tags 20 Sep 2010, 07:02 rxs0005 wrote: hi we have this 6n + 1 or 6n -1 that represents a prime number is this true for all 'n' ? for eg : n =111 here 665 and 667 are not prime numbers what is the criterion for n ? thanks There is no known formula for prime numbers. _________________ Retired Moderator Joined: 02 Sep 2010 Posts: 769 Location: London Re: Prime Number Formula [#permalink] ### Show Tags 20 Sep 2010, 07:09 Some Trivia There is a long standing mathematical conjecture called the twin prime conjecture, which states that there are infinitely many twin primes (primes with a difference of 2 between them). You can't put any conditions on n for the form 6n-1 & 6n+1 to be prime (or almost all of them to be prime), because if you could, you would also end up proving the twin prime conjecture, which has been an outstanding open problem for over a 100 years _________________ CEO Status: Nothing comes easy: neither do I want. Joined: 12 Oct 2009 Posts: 2601 Location: Malaysia Concentration: Technology, Entrepreneurship Schools: ISB '15 (M) GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35 Re: Prime Number Formula [#permalink] ### Show Tags 20 Sep 2010, 07:23 1 I think if a number is a prime, then it is always of the form 6k+1 and 6k-1. But a non prime number could also be of the form 6k+1 and 6k-1. So the causality is one way only. _________________ Fight for your dreams :For all those who fear from Verbal- lets give it a fight Money Saved is the Money Earned Jo Bole So Nihaal , Sat Shri Akaal Support GMAT Club by putting a GMAT Club badge on your blog/Facebook GMAT Club Premium Membership - big benefits and savings Gmat test review : http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html Director Joined: 07 Jun 2004 Posts: 600 Location: PA Re: Prime Number Formula [#permalink] ### Show Tags 20 Sep 2010, 07:57 thanks the causality direction helped _________________ If the Q jogged your mind do Kudos me : ) Director Status: Apply - Last Chance Affiliations: IIT, Purdue, PhD, TauBetaPi Joined: 17 Jul 2010 Posts: 628 Schools: Wharton, Sloan, Chicago, Haas WE 1: 8 years in Oil&Gas Re: Prime Number Formula [#permalink] ### Show Tags 22 Sep 2010, 21:03 shrouded1 wrote: Some Trivia There is a long standing mathematical conjecture called the twin prime conjecture, which states that there are infinitely many twin primes (primes with a difference of 2 between them). You can't put any conditions on n for the form 6n-1 & 6n+1 to be prime (or almost all of them to be prime), because if you could, you would also end up proving the twin prime conjecture, which has been an outstanding open problem for over a 100 years Is it one of those 1M$ problems to be solved? Well solve this one and forget about GMAT or MBA.. Relax in piece.. !

Btw, what would be the proof of 6k-1 or 6k+1, it looks like primes are of this form (trial and error), with the restriction gurpreet pointed out..
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Re: Prime Number Formula  [#permalink]

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22 Sep 2010, 22:46
mainhoon wrote:
shrouded1 wrote:
Some Trivia

There is a long standing mathematical conjecture called the twin prime conjecture, which states that there are infinitely many twin primes (primes with a difference of 2 between them).

You can't put any conditions on n for the form 6n-1 & 6n+1 to be prime (or almost all of them to be prime), because if you could, you would also end up proving the twin prime conjecture, which has been an outstanding open problem for over a 100 years

Is it one of those 1M$problems to be solved? Well solve this one and forget about GMAT or MBA.. Relax in piece.. ! Btw, what would be the proof of 6k-1 or 6k+1, it looks like primes are of this form (trial and error), with the restriction gurpreet pointed out.. 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$$p=6n+5$$ or $$p=6n-1$$, where n is an integer >1. Hope it helps. _________________ Retired Moderator Joined: 02 Sep 2010 Posts: 769 Location: London Re: Prime Number Formula [#permalink] ### Show Tags 23 Sep 2010, 00:21 mainhoon wrote: Is it one of those 1M$ problems to be solved? Well solve this one and forget about GMAT or MBA.. Relax in piece.. !

Nope, its not. Those \$1M ones aren't that straight forward to understand generally

Mathematicians are strange. A couple of years ago, a Russian guy solved one of these problems and refused to take the prize money.
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Re: Prime Number Formula  [#permalink]

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29 May 2017, 21:16
1
1
While we are talking about prime numbers, there is another general rule for identifying whether a positive integer 'N' is prime or not:

Take square root of N, and if its not an integer, round it down to nearest integer. Let that integer be M. Now divide N by all the prime numbers between 1 and M exclusive, and if its NOT divisible by either of those, then N must be prime.

Eg, lets see if 199 and 299 are prime or not. Lets start with 199.
Square root of 199 when rounded down to nearest integer = 14 (14^2 = 196).
Now we should check if 199 is divisible by any prime number between 1 and 14.. these prime numbers are 2, 3, 5, 7, 11, 13.
199 is NOT divisible by any of these - hence 199 is prime.

Lets now look at 299. Square root of 299 rounded down to nearest integer = 17 (17^2 = 289).
Now we should check if 299 is divisible by any prime number between 1 and 17.. these prime numbers are 2, 3, 5, 7, 11, 13.
But 299 is Divisible by 13. (13*23).. we found a factor - hence 299 is NOT prime
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Re: Prime Number Formula  [#permalink]

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03 Nov 2018, 23:13
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Prime Number Formula &nbs [#permalink] 03 Nov 2018, 23:13
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# Prime Number Formula

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