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If N is the sum of first 13986 prime numbers, then N is always divisible by:

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None of these

answer is D.

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Detailed Solution

Concept- We have given that

is the sum of first

prime numbers . and we need to find that by which number the

will get divisible.
So, we know we need to find the

and then the number which is divisible by

.
Let’s see the conditions:

If we add an odd number with an odd number 3 times we will get an odd number as a result.
E.g. :

as a result we got an odd number.
And in the given question we have prime number in that we have

which are even and remain odd .
And hence remaining are odd we will get the results as an odd number .
That means it cannot be divisible by an even number. And

are the even number then it cannot be divisible by any of these .
Hence, the correct option is 4.

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