# Prime number question.

There exist at least one prime number between n and 9n/8. What is the minimum value of n???

To cont your assumption

For a=3 the number are 24, 25, 26 & 27 and none of them are prime.

So its wrong.

I am not going to prove it but this is one of the great works of Joseph Bertrand and according to him

**if n is an integer greater than 3, then there is at least one prime between n and 2n-2**

**Few other important points are**

- If n is at least 48, then there is at least one prime between n and 9n/8.
- If n is greater than 6, then there is at least one prime of theform 4k+1 and at least one of the form 4k+3 between n and 2n.
- If n is greater than or equal to 118, then the interval n to 4n/3 inclusive contains a prime of each of the forms 4n+1, 4n-1, 6n+1, and 6n-1.
- If n is greater than 15, then there is at least one number between n and 2n that is the product of three different primes.

n/a

y cant d answer be 10???

n and 9n/8 means between 10 and 11.25, right...

11 is a prime number....

so 10 can b d answer, right???

Simply because 11.25 is not an integer

does the question specify dat it shud be an integer?

The answer is very simple.It is clear that n/8 should be an integer.Taking n/8=1,I get no prime number between 8 & 9.Then assuming n/8=2,I get a prime number 17 between 16 & 18,i.e.,between n & 9n/8.So, the correct answer is "n=2".

The answer is very simple.It is clear that n/8 should be an integer.Taking n/8=1,I get no prime number between 8 & 9.Then assuming n/8=2,I get a prime number 17 between 16 & 18,i.e.,between n & 9n/8.So, the correct answer is "n=2".

The answer should be guessed first that it is an integer or not,so what are the options anyway???

9 has no factor of 2 so N must be divisible by 8

Let it be 8a where a ≥ 1

Now as per the question there shd be one prime number between 8a and 9a

For a =1, there is no number

a=2 , we have 17 a prime number

So the answer is 16.