Given a positive integer n, count distinct number of pairs (x, y) that satisfy following conditions :
- (x + y) is a prime number.
- (x + y) < n
- x != y
- 1 <= x, y
Input : n = 6 Output : 3 prime pairs whose sum is less than 6 are: (1,2), (1,4), (2,3) Input : 12 Output : 11 prime pairs whose sum is less than 12 are: (1,2), (1,4), (2,3), (1,6), (2,5), (3,4), (1,10), (2,9), (3,8), (4,7), (5,6)
1) Find all prime numbers less than n using Sieve of Sundaram 2) For each prime number p, count distinct pairs that sum up to p. For any odd number n, number of distinct pairs that add upto n are n/2 Since, a prime number is a odd number, the same applies for it too.
For prime number p = 7
distinct pairs that add upto p: p/2 = 7/2 = 3
The three pairs are (1,6), (2,5), (3,4)
For prime number p = 23
distinct pairs that add upto p: p/2 = 23/2 = 11
Number of prime pairs: 11
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