Given a positive integer
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
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
- Check if a number is Prime, Semi-Prime or Composite for very large numbers
- 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
- Largest number in [2, 3, .. n] which is co-prime with numbers in [2, 3, .. m]
- Express an odd number as sum of prime numbers
- 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 all the prime numbers of given number of digits
- Find a sequence of N prime numbers whose sum is a composite number
- Sum of all the prime numbers with the maximum position of set bit ≤ D
- 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
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