Question

Express the following as the sum of two odd primes: 44

Answer 1

Hint: We solve this problem by assuming that there are 2 odd primes $a,b$ such that their sum is equal to the given number. We know that the prime numbers are odd numbers except ‘2’. So, we assume one of the values of $a,b$ as one odd prime number so that we can find the other number and check whether it is an odd prime or not. Then we can represent the given number as the sum of two odd primes.

Complete step by step solution:
We are asked to represent the number 44 as the sum of two odd primes.
Let us assume that there are two odd primes $x,y$ less than 44 such that their sum is 44.
Now, by representing the above statement in mathematical equation then we get,
$\Rightarrow x+y=44$
We know that all prime numbers starting from 3 are odd numbers only.
Let us assume that $y=3$ then we get the value of $'x'$ as,
$\begin{align}
  & \Rightarrow x+3=44 \\
 & \Rightarrow x=41 \\
\end{align}$
Here, we can see that the number 41 is a prime number and also is an odd number.
Therefore, we can conclude that the given number 44 can be represented as the sum of two odd primes which are 3 and 41.
$\therefore 44=3+41$

Where, $3,41$ are odd prime numbers.

Note: Here, we can see that we got one pair of odd primes whose sum will be 44. But we know that there might be some other pair of odd primes also whose sum is 44.
Here, we can see that the question is asked to represent the given number as the sum of two odd primes but did not ask about all possible pairs. So, mentioning one pair of odd primes whose sum is 44 is enough for this question. Checking for all possibilities is just a waste of time for this type of problem.