Question

State true or false.
Odd numbers cannot be written as the sum of primes.
A) True
B) False

Answer 1

Hint: Here we will take some prime numbers and will add them and will check if the result is an odd number or even number. Before that we must know about odd numbers, even numbers and prime numbers.

Complete step-by-step answer:
Odd numbers are those numbers which cannot be divided by 2.
Even numbers are those numbers which can be divided by 2.
Prime numbers are those numbers which can be divided by 1 and itself. (Number 1 is exceptionally not a prime number.
Let’s take some prime numbers such as 2, 3, 5, 7, 11 and so on.
Case 1- Adding two prime numbers 2 and 3 we get,
$2 + 3 = 5$
And 5 is an odd number.
Case 2- Adding two prime numbers 5 and 7 we get,
$5 + 7 = 12$
And 12 is an even number.
Case 3- Adding three other prime numbers 2, 3 and 11 we get,
$2 + 3 + 11 = 16$
And 16 is also an even number.
Case 4- Adding three other prime numbers 3, 5 and 7 we get,
$3 + 5 + 7 = 15$
And 15 is also an odd number.
From all above the cases we concluded that odd numbers can be written as the sum of prime numbers.
Hence, the statement is false. Option (B) is correct.

Note: Prime numbers are those numbers which can be divided by 1 and itself such as 2, 3, 5, 7, 11, 13…..etc.
The smallest prime number is 2.
1 is not a prime number. It is because it itself and 1 are not two distinct factors.
The question might be mistaken as the sum of two prime numbers. But there is not mentioned anywhere to add only two prime numbers.
2 is the only even prime number.
You can also prove this by taking bigger prime numbers.
Odd numbers are those numbers which cannot be divided by 2. Examples- 1, 3, 5, 7, 9, 11, 13….etc.
Even numbers are those numbers which can be divided by 2. Examples- 2, 4, 6, 8, 10, 12……etc.