Question

Express 56 as the sum of twin primes

Answer 1

Answer:

Hint: In this question, we need to determine the sum of the twin primes of the given numbers. For this, we will evaluate the prime factors of the given numbers and then, add them. In the second part and the third part of the question we will determine all the prime numbers between the given ranges.

Complete step-by-step answer:

Sum of twin primes

a.36

Let x be the number which is the half of the given number, so we can write

⇒x=362=18⇒x=362=18

Now 18 is the half of the given number, now to find the twin prime number which show have a difference of 2 or more, we can write the sum of twin primes as

(19−1)(17+1)=36(19−1)(17+1)=36

{For the difference of 2}

Hence by further solving this equation we get

⇒19+17+1−1=36⇒19+17=36⇒19+17+1−1=36⇒19+17=36

 Hence the twin prime of 36 is 19 and 17

So, the correct answer is “19 and 17”.

b.84

Let x be the number which is the half of the given

number

⇒x=842=42⇒x=842=42

Following the same method as above, we can write the sum of twin primes as

(43−1)+(41+1)=84(43−1)+(41+1)=84

{For the difference of 2}

Hence by further solving this equation we get

⇒43+41+1−1=84⇒43+41=84⇒43+41+1−1=84⇒43+41=84

 Hence the twin prime of 84 is 43 and 41

So, the correct answer is “43 and 41”.

c.120

Let x be the number which is the half of the given number

⇒x=1202=60⇒x=1202=60

Following the same method as above, we can write the sum of twin primes as

(61−1)+(59+1)=120