Question

How many prime numbers are there that are less than 30 and can be represented both as a sum and a difference of two primes?

• A. 4
• B. 1
• C. 10
• D. 0

Answer 1

The Correct Option is B

Prime Number Identification 

- We need to identify prime numbers less than 30 that can be written both as a sum and a difference of two primes.

- The prime numbers less than 30 are:

\[ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 \]

Step 1: Checking for primes that can be written as the sum of two primes

• 5 = 2 + 3 (✔ Valid - both are primes)
• 7 = 3 + 4 (❌ Not valid as 4 is not prime)
• 11 = 5 + 6 (❌ Not valid as 6 is not prime)
• 13 = 3 + 10 (❌ Not valid as 10 is not prime)
• 17 = 2 + 15 (❌ Not valid as 15 is not prime)
• 19 = 2 + 17 (✔ Valid - both are primes)

Step 2: Checking for primes that can be written as the difference of two primes

• 5 = 7 − 2 (✔ Valid - both are primes)
• 19 = 23 − 4 (❌ Not valid as 4 is not prime)

- Hence, only 5 can be represented both as a sum and a difference of two primes.

Conclusion: The correct answer is 1.