Let p be a prime number such that the next larger number is a perfect square. Find the sum of all such prime numbers. (For example, if you think 11 and 13 are two such prime numbers, then the sum is 24.)


Answer:

3

Step by Step Explanation:
  1. Given, p is a prime number such that the next larger number is a perfect square.
    i.e.,p+1=n2
  2. Rewriting p+1=n2, we get
    p=n21p=(n1)(n+1)
  3. Since p is a prime number, therefore n1 needs to be equal to 1.
    n=2
    Therefore, p=3 is unique.
    Hence, the required sum is 3.

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