Question

if N is the sum of first 13986 prime numbers then N is always divisible by



a) 6


b ) 4



c) 8




d) non of these



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Answer 1

HERE IS YOUR ANSWER :

The correct option is (d) None of these

EXPLANATION : All the prime no.s are odd except one i. e. 2. So when we'll multiply all 13985 odd prime no.s with an even odd no. 2 then the no. that we'll obtain will be divisible by odd no.


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Answer 2

$\huge\underline\mathfrak\green{Explanation}$

In my opinion ,

13986 prime number

= 2 + 3 + 5 + 7 + 11 +13 +......

We see 2 is even and except this all prime are odd

Therefore there will be 13985 odd numbers which on addition will give odd and +2 will make it odd . So it will not be divisible by 2.

And also we cannot say about the about any pattern followed by prime number except the (6n ±1) which here makes no sense.

Had the number been 13985 then , there must be 13984 odd numbers which make even and we add the first bomber 2 ,even, which ultimately results in even number.

So divisible by 2

Therefore,

$\large{\boxed{\tt{d).None-of-these}}}$

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