Given a positive integer . The task is to represent it as a sum of the maximum possible number of prime numbers. (N > 1)
Input : N = 5 Output : 2 3 Input : N = 6 Output : 2 2 2
At first, the problem might seem to involve some use of Goldbach’s conjecture. But the key observation here is to maximise the number of terms used, you should use as small numbers as possible. This leads to the following idea:
- If N is even, it can be represented as sum of two’s.
- Otherwise, has to be even and hence N can be represented as sum of one 3 and two’s.
This is the maximum number of primes whose sum is N.
Below is the implementation of the above approach:
Time Complexity: O(N)
- Number which has the maximum number of distinct prime factors in the range M to N
- Print the nearest prime number formed by adding prime numbers to N
- Check if a prime number can be expressed as sum of two Prime Numbers
- Find prime number K in an array such that (A[i] % K) is maximum
- Express an odd number as sum of prime numbers
- Largest number in [2, 3, .. n] which is co-prime with numbers in [2, 3, .. m]
- New Algorithm to Generate Prime Numbers from 1 to Nth Number
- Check if a number can be written as a sum of 'k' prime numbers
- Find a sequence of N prime numbers whose sum is a composite number
- Maximum no. of contiguous Prime Numbers in an array
- Minimum and Maximum prime numbers in an array
- Queries for maximum difference between prime numbers in given ranges
- Count occurrences of a prime number in the prime factorization of every element from the given range
- Minimum and Maximum Prime Numbers of a Singly Linked List
- Largest number less than N whose each digit is prime number
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.