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Which of the following is a prime triplet?
  • a)
    (2, 3, 5)
  • b)
    (3, 5, 7)
  • c)
    (5, 7, 11)
  • d)
    (7, 9, 11)
Correct answer is option 'B'. Can you explain this answer?

Saikat Pillai answered
Understanding Prime Triplets
A prime triplet consists of three prime numbers that are closely related in value. To determine which of the given options is a prime triplet, we need to identify the prime numbers in each option.
Definition of Prime Numbers
- A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Analyzing Each Option
- Option A: (2, 3, 5)
- All three numbers are prime.
- However, they are not consecutive primes, as there is a gap between 2 and 3; thus, it does not form a triplet.
- Option B: (3, 5, 7)
- All three numbers are prime.
- They are consecutive prime numbers and differ by 2, making this a valid prime triplet.
- Option C: (5, 7, 11)
- While all are prime, they are not consecutive. There is a gap (9) between 7 and 11, disqualifying them as a triplet.
- Option D: (7, 9, 11)
- The number 9 is not a prime number (it has divisors: 1, 3, 9).
- Thus, this option cannot be a prime triplet.
Conclusion
The only valid prime triplet among the options is Option B: (3, 5, 7). It consists of three consecutive prime numbers, making it the correct answer.

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