Question

If 'N' is the sum of first 2,020 prime numbers, then 'N'
is always divisible by​

Answer 1

The sum , N, is not divisible by the smallest even number, 2.

However, it would be divisible by 1

Step-by-step explanation:

N is the sum of the first 2020 prime numbers.

Consider the addition of prime numbers as follows:

2 + 3 + 5 + 7……

Thus, there are 2019 odd numbers along with 2 as the even prime number.

The sum of the 2019 odd prime numbers is an odd number. When 2 is added to this odd sum, the resulting value of N would be an odd number.  

Hence, it would not be divisible by an even number.

However, it would always be divisible by 1.

Answer 2

Given:  'N' is the sum of first 2,020 prime numbers

To find: 'N'  is always divisible by​=?

Solution:

• Now we have given that sum of first 2020 prime terms is N.

• Here we can conclude that the sum is odd, because all the prime terms are odd except first term that is 2.

• So the sum of odd and even term is always odd.

• So, by this we can conclude that 'N' is an odd number.    

• Further, if we check the divisibility, we can see that it is divisible by 1 only, as it is an odd number it would not be divisible by an even number.

     

Answer:

Hence, it will always be divisible by 1.