Question

Express $36$ as a sum of two odd primes.

Answer 1

Step 1: Explain the prime numbers.

Prime Numbers: A prime number is a positive integer that has exactly two factors.

1. If $p$ is a prime, its only factors are necessarily $1$and $p$ itself.
2. Any number that does not follow the condition is termed a composite number.
3. The numbers that are prime and odd are known as odd prime numbers.

Properties of Prime Numbers: Some of the properties of prime numbers are listed below

1. Every number greater than $1$ can be divided by at least one prime number.
2. Every even positive integer greater than $2$ which can be expressed in the form of the sum of two primes.
3. Except $2$, all other prime numbers are odd. In other words, we can say that $2$ is the only even prime number.
4. Each composite number can be factorized into prime factors and individually all of these factors are unique in nature.

Step 2: Use hit and trial to find out the two prime numbers whose sum is $36$.

Firstly, write all prime numbers between $1$ and $36$.

Prime numbers are $–3,5,7,11,13,17,1923,29,31$.

Next, we have to make the sum of two prime numbers equal to $36$.

$36–3=33$, not a prime number.

$36–5=31$, is a prime number.

So, the first pair is $(5,31)$.

$36–7=29,$ is a prime number.

So, the second pair is$(7,29)$.

$36–11=25$, not a prime number.

$36–13=23$, is a prime number.

So, the third pair is $(13,23)$.

$36–17=19$, is a prime number.

So, the fourth pair is $(17,19).$

Hence, the sum of two odd primes is $(5,31),(7,29),(13,23),(17,19).$