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UPSC PYQPrelims 2025

Civil Services Examination · Question 27

Let both p and k be prime numbers such that (p² + k) is also a prime number less than 30. What is the number of possible values of k?

  1. 4
  2. 5
  3. 6
  4. 7
Show answer & explanation

Answer: (B) 5

Explanation

p = 2: 4 + k is prime for k = 3, 7, 13, 19. p = 3: 9 + 2 = 11 (k = 2). So k ∈ {2, 3, 7, 13, 19}: 5 values. (Answer as per the official UPSC answer key.)