Question

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

• A. 6
• B. 4
• C. 8
• D. none of these

Answer 1

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).
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.