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Director  Joined: 07 Jun 2004
Posts: 557
Location: PA
Prime Number Formula  [#permalink]

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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
Retired Moderator Joined: 02 Sep 2010
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Re: Prime Number Formula  [#permalink]

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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.
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Retired Moderator Joined: 02 Sep 2010
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Re: Prime Number Formula  [#permalink]

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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
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GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35 Re: Prime Number Formula  [#permalink]

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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.
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Director  Joined: 07 Jun 2004
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Re: Prime Number Formula  [#permalink]

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thanks the causality direction helped
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Re: Prime Number Formula  [#permalink]

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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$problems to be solved? Well solve this one and forget about GMAT or MBA.. Relax in piece.. ! Btw, what would be the proof of 6k-1 or 6k+1, it looks like primes are of this form (trial and error), with the restriction gurpreet pointed out.. _________________ Consider kudos, they are good for health Math Expert V Joined: 02 Sep 2009 Posts: 58344 Re: Prime Number Formula [#permalink] Show Tags 1 1 mainhoon wrote: shrouded1 wrote: Some Trivia There is a long standing mathematical conjecture called the twin prime conjecture, which states that there are infinitely many twin primes (primes with a difference of 2 between them). You can't put any conditions on n for the form 6n-1 & 6n+1 to be prime (or almost all of them to be prime), because if you could, you would also end up proving the twin prime conjecture, which has been an outstanding open problem for over a 100 years Is it one of those 1M$ 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.
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Re: Prime Number Formula  [#permalink]

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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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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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_________________ Re: Prime Number Formula   [#permalink] 04 Nov 2018, 00:13
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