Question

Express each of the following number as the sum of three odd primes
$a)21$
$b)31$
$c)53$
$d)61$

Answer 1

Hint: First, we need to know what the prime numbers are.
Prime numbers are known as the number that will divide by itself and one, which means it will need not divide any other number except one and itself (given number) So, we use this concept and find out all the prime numbers which are less than or equal to the given numbers. Finally, after finding the prime numbers we just need to find which the number is while the sum of the prime numbers equals the given number.

Complete step by step answer:
$a)21$
First, we will find the prime numbers for the number less than or equals to the $21$
Since $21$its not the prime number as it will be divided by the number three or seven, so find the prime number less than $21$are given as $2,3,5,7,9,11,13,17,19$(which are all the prime numbers less than or equal to the given number)
Now we need to check the sum of the prime number yields $21$
There is only possible that the sum of the numbers is $3,7,11$(no other terms will involve, if involved then we don’t get them $21$)
Hence, we get the odd primes number to the sum is $21 = 3 + 7 + 11$(the three prime numbers are odd)
$b)31$
Second, we will find the prime numbers for the number less than or equals to the $31$
Since $31$is the prime number itself, so find the prime number less than and also $31$are given as $2,3,5,7,9,11,13,17,19,23,29,31$(which are all the prime numbers less than or equal the given number)
Now we need to check the sum of the prime number yields $31$
There is the only possibility that the sum of the numbers is $3,11,17$(no other terms will involve, if involved then we don’t get them $31$)
Hence, we get the odd primes number to the sum is $31 = 3 + 11 + 17$(the three prime numbers are odd)
$c)53$
Now, we will find the prime numbers for the number less than or equals to the $53$
Since $53$is the prime number itself, so find the prime number less than and also $53$are given as $2,3,5,7,9,11,13,17,19,23,29,31,42,43,47,53$(which are all the prime numbers less than or equal the given number)
Now we need to check the sum of the prime number yields $53$
There is the only possibility that the sum of the numbers is $13,17,23$(no other terms will involve, if involved then we don’t get them $53$)
Hence, we get the odd primes number to the sum is $53 = 13 + 17 + 23$(the three prime numbers are odd)
$d)61$
Finally, we will find the prime numbers for the number less than or equals to the $61$
Since $61$is the prime number itself, so find the prime number less than and also $61$are given as $2,3,5,7,9,11,13,17,19,23,29,31,42,43,47,53,59,61$(which are all the prime numbers less than or equal the given number)
Now we need to check the sum of the prime number yields $61$
There is only possible that the sum of the numbers is $11,19,31$and $11,13,37$(no other terms will involve, if involved then we don’t get them $53$)
Hence, we get the odd primes number to the sum is $61 = 11 + 13 + 37,61 = 11 + 19 + 31$(the three prime numbers are odd)

Note:
Since two is the only prime number in the whole numbers, here the given terms are is odd so there is no possibility of getting the number two as a prime number.
Be careful while remembering the concept of the prime number, which needs to divide by one and itself only.
Composite numbers are known as the non-prime numbers (the numbers which are not the prime numbers)