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