Question

Express the following number as a sum of two odd primes, $$84$$

Answer 1

Hint: Prime numbers are the numbers which have only two factors, that is $$1$$and the number itself.
For example, the first five prime numbers are $$2,3,5,7\mathrm{\&}11$$
Odd prime numbers are the numbers which are odd numbers.
A number can be represented as a sum of two numbers like $$c=a+b$$.

Complete step by step answer:
As we know that a number can be represented as a sum of two numbers,
i.e. $$c=a+b$$
In this case we have $$c=84$$ and $$a\mathrm{\&}b$$ has to be of prime numbers.
An odd prime number that is nearest to the number $$84$$ is $$83$$ but there is no other odd prime number which will give $$84$$ by adding it to $$83$$. So, we cannot use $$83$$.
For instance, let us take the least odd prime number $$3$$,
$$83+3=86$$, which is not equal to $$84$$
Let us consider another odd prime number $$79$$ which is nearest to $$83$$.
Now consider the least odd prime number 3.
$$79+3=82$$ which is not equal to $$84$$.
Let us take the next least odd prime number $$5$$,
$$79+3=82$$,
Now we got the results.
Thus $$84$$ can be represented as a sum of two odd prime numbers that is $$79$$and $$5$$.

Note: The numbers other than prime numbers are called composite numbers. $$1$$ is neither a prime number nor a composite number because by the definition of prime number it should have two factors but $$1$$ does not have any other factor other than itself so $$1$$ is not a prime number and by the definition of composite number it should have more than two factors again $$1$$ has no other factor other than itself so, $$1$$ is not a composite number.