Count distinct prime triplets up to N such that sum of two primes is equal to the third prime
Given an integer N, the task is to count the number of distinct prime triplets (a, b, c) from the range [1, N] such that a < b < c ≤ N and a + b = c.
Note: Two prime tuples are distinct if at least one of the primes present in them are different.
Input: N = 6
Explanation: Among numbers in the range [1, 6], the only prime triplet is (2, 3, 5) (Since 2 + 3 = 5).
Input: N = 10
Explanation: The distinct prime triplets satisfying the condition are (2, 3, 5), (2, 5, 7).
Approach: The problem can be solved based on the observation stated below:
For every prime number p from 1 to N, it is a part of a triplet if and only if it can be represented as a sum of two prime numbers.
Since a prime number is an odd number, it must be equal to the sum of an even number and an odd number.
Hence the only even prime is 2. Therefore, for a prime number p to constitute a unique tuple (2, p-2, p), the number p – 2 must be a prime number.
Follow the steps below to solve the problem:
- Initialize a variable, say count = 0, to store the number of prime triplets.
- Iterate from 1 to N and for each number p, check if this number p and p – 2 are prime or not.
- If they are prime, then increment count by 1.
- Print the value of count.
Below is the implementation of the above approach:
Time Complexity: O(N3/2)
Auxiliary Space: O(1)
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