Question

What is the smallest perfect square that can be written as the sum of three different prime numbers?

Answer 1

Answer:

19 is the smallest prime number that is the sum of three different prime number.

Step-by-step explanation:

To find this:

   2 is the only even prime number and other prime numbers are odd

   adding any two prime number always gives even number.

   so the least numbers that are required to do is 3,5 and 7; their sum is 15

   so any prine number less than 15 is not possible for this question

   so, the next prime number is 17

   17 minus any other prime no less 17 are13,11,7.5.3,2 give the number that   4,6,10,12,14,15 which are not sum of any two different prime numbers

   

so the answer is 19=11+5+3.

Answer 2

The smallest perfect square that can be written as the sum of 3 different prime numbers is; 16.

• Prime numbers are numbers that can be divided by only themselves and 1.

• Now, we want to find the smallest perfect square that can be written as the sum of three prime numbers and so let us list the perfect squares from 1 to 30.

       They are; 4, 9, 16, 25.

• Now, for 4; sum of 3 different prime numbers cannot work here because it will give us 1 + 2 + 3 = 5.

• For 9; sum of 3 different prime numbers cannot work here because it will give us 2 + 3 + 5 = 10.

• For 16; sum of 3 different prime numbers will work here because it will give us 2 + 3 + 11 = 16

• Thus, the smallest perfect square that can be written as the sum of 3 different prime numbers is 16.

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