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 \[2,3,5,7\& 11\]
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 \[a\& b\] 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.