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

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none of these

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Solution

The correct option is D
none of these

13986 prime numbers include 2 and 13985 odd prime numbers.
The sum of 13985 odd numbers is an odd number (x).

We know that the sum of an odd number and another odd number is odd

The sum of that odd number and 2 is another odd number (y).

y, being an odd number, is not divisible by 2 or any of its multiples.

Thus, the sum of first 13986 prime numbers is not divisible by either 4, 6 or 8.

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