Given a positive integer N, check if it can be expressed as a sum of two semi-primes or not.
Semi-primes A number is said to be a semi-prime if it can be expressed as product of two primes number ( not necessarily distinct ).
Semi-primes in the range 1 -100 are:
4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95.
Input : N = 30 Output: YES Explanation: 30 can be expressed as '15 + 15' 15 is semi-primes as 15 is a product of two primes 3 and 5. Input : N = 45 Output : YES Explanation: 45 can be expressed as '35 + 10' 35 and 10 are also semi-primes as it can a be expressed as product of two primes: 35 = 5 * 7 10 = 2 * 5
A Simple Solution is to traverse form i=1 to and check if i and N-i are semi-primes or not. If yes, print i and n-i.
An Efficient Solution is to pre-compute semi-primes in an array up to the given range and then traverse the semi-prime array and check if n-arr[i] is semi-prime or not. As, arr[i] is already a semi-prime if n-arr[i] is also a semi-prime, then n can be expressed as sum of two semi-primes.
Below is the implementation of above approach:
- Elements of Array which can be expressed as power of some integer to given exponent K
- Find ways an Integer can be expressed as sum of n-th power of unique natural numbers
- Check if a number can be expressed as a^b | Set 2
- Check if a number can be expressed as 2^x + 2^y
- Check if a number can be expressed as power | Set 2 (Using Log)
- Check if N can be expressed as product of 3 distinct numbers
- Check if a number can be expressed as a sum of consecutive numbers
- Check if a number can be expressed as sum two abundant numbers
- Check if a number can be expressed as x^y (x raised to power y)
- Check if a number can be expressed as a product of exactly K prime divisors
- Square free semiprimes in a given range using C++ STL
- Check whether a number can be expressed as a product of single digit numbers
- Check if a prime number can be expressed as sum of two Prime Numbers
- Check if two Integer are anagrams of each other
- Check if the given array contains all the divisors of some integer
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