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# If n is a positive integer, what is the maximum possible

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Current Student
Joined: 11 May 2008
Posts: 551
If n is a positive integer, what is the maximum possible [#permalink]

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31 Jul 2008, 10:47
. If n is a positive integer, what is the maximum possible number of prime numbers in the following sequences: n+1, n+2, n+3, n+4, n+5, and n+6
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

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Director
Joined: 12 Jul 2008
Posts: 512
Schools: Wharton

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31 Jul 2008, 10:55
arjtryarjtry wrote:
. If n is a positive integer, what is the maximum possible number of prime numbers in the following sequences: n+1, n+2, n+3, n+4, n+5, and n+6
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Prime numbers are closest together when they're low.

C

If n = 1:
2, 3, 4, 5, 6, 7 contains 4 prime numbers.
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Joined: 07 Nov 2007
Posts: 1738
Location: New York

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31 Jul 2008, 11:23
arjtryarjtry wrote:
. If n is a positive integer, what is the maximum possible number of prime numbers in the following sequences: n+1, n+2, n+3, n+4, n+5, and n+6
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

1,2,3,4,5,6

prime numbers....1,2,3,5

C
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Intern
Joined: 07 May 2008
Posts: 19

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31 Jul 2008, 13:29
x2suresh, careful, 1 is not a prime number. By definition, 2 is the smallest prime number.

http://en.wikipedia.org/wiki/Prime_numbers
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Joined: 07 Nov 2007
Posts: 1738
Location: New York

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31 Jul 2008, 14:05
VPRedSoxFan wrote:
x2suresh, careful, 1 is not a prime number. By definition, 2 is the smallest prime number.

http://en.wikipedia.org/wiki/Prime_numbers

thanks for pointing out..
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Joined: 24 Jun 2008
Posts: 1345

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31 Jul 2008, 15:32
I'd add that the only way to get more than two primes in the sequence is to let n be either 1 or 2.

If you take any six consecutive integers:

-three of them will be even (and therefore not prime, unless one of them is equal to 2);

-further, among the three remaining consecutive odd numbers, one of them must be divisible by 3 (and therefore not prime, unless it is equal to 3).
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Joined: 17 Jun 2008
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31 Jul 2008, 19:16
zoinnk wrote:
arjtryarjtry wrote:
. If n is a positive integer, what is the maximum possible number of prime numbers in the following sequences: n+1, n+2, n+3, n+4, n+5, and n+6
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Prime numbers are closest together when they're low.

C

If n = 1:
2, 3, 4, 5, 6, 7 contains 4 prime numbers.

I had solved the problem substituting values n=1,n=2 etc at n=1
got 4 prime numbers .I was afraid whether there are siome other numbers where 5 or more numbers possible.Hence did analysis till n=11.This wasted time like hell.

your point here is correct when low more close prime numbers
thjanks for this funda

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: prime nos.   [#permalink] 31 Jul 2008, 19:16
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# If n is a positive integer, what is the maximum possible

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