Primes

Number Theory Level 2

The number of integers $n>1$ , such that $n,n+2,n+4$ are all prime numbers is

31 1 0 17 5 Infinite

1 solution

Kalpok Guha
Jun 3, 2015

$n$ is a prime so it must be odd or $2$

If $n+2,n+4$ are not prime when $n=2$

So $n$ is odd.

Then $n,n+2,n+4$ are three consecutive odd integers.

In every three consecutive odd integers,one is divisible by $3$

So there is only one triplet $3,5,7$ when three consecutive odd integers are prime.

So the answer is 3, not one.

Xi Huang - 6 years ago

Sorry but then which are the three triplets?

Kalpok Guha - 6 years ago

You are right about the triplet 3, 5, and 7. So n=3 n+2=5 and n+4=7. However the answer you put on the question is one. But it is three or one. Your answer choice is wrong.

Xi Huang - 6 years ago

@Xi Huang – First of all I asked 'how many values of $n$ are there ?',which is correct question and 69 people solved this question no one reported so I think it your problem.First read a question patiently & try to understand it.

Kalpok Guha - 6 years ago

@Kalpok Guha – Ok, now I see what you mean, Haha. I thought the question ask the value of n. It's my misunderstanding.

Xi Huang - 6 years ago

@Xi Huang – It's okay.Be careful next time :-) .You may try my other problems also

Kalpok Guha - 6 years ago

Primes

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