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

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31 Jul 2008, 10:47

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. 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

. 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.

. 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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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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. 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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