Let pp 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 1111 and 1313 are two such prime numbers, then the sum is 24.)24.)
Answer:
33
- Given, pp is a prime number such that the next larger number is a perfect square.
i.e.,p+1=n2i.e.,p+1=n2 - Rewriting p+1=n2,p+1=n2, we get
[Math Processing Error] - 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.