Cody

Problem 44403. Goldbach's marginal conjecture - Write integer as sum of three primes

Created by yurenchu in Community

Goldbach's strong conjecture states that every even integer greater than 2 can be expressed as the sum of two primes. For example: 4 = 2+2, 6 = 3+3, 8 = 3+5, 10 = 3+7 = 5+5, 12 = 5+7 etc.

As a corrollary, Goldbach's weak conjecture states that every odd integer greater than 7 can be expressed as the sum of three odd primes. For example: 9 = 3+3+3, 11 = 3+3+5, 13 = 3+3+7 = 3+5+5, 15 = 3+5+7 = 5+5+5 etc.

A third conjecture was written by Goldbach in the margin of a letter, and (in its modern version) states that

" Every integer greater than 5 can be expressed as the sum of three primes. "

Examples:

  • 6 = 2 + 2 + 2
  • 7 = 2 + 2 + 3
  • 8 = 2 + 3 + 3
  • 9 = 2 + 2 + 5 = 3 + 3 + 3
  • 10 = 2 + 3 + 5
  • 11 = 2 + 2 + 7 = 3 + 3 + 5
  • 12 = 2 + 3 + 7 = 2 + 5 + 5
  • 13 = 3 + 3 + 7 = 3 + 5 + 5
  • 14 = 2 + 5 + 7
  • 15 = 2 + 2 + 11 = 3 + 5 + 7 = 5 + 5 + 5

Your task is to write a function which takes a positive integer n as input, and which returns a 1-by-3 vector y, which contains three numbers that are primes and whose sum equals n. If there exist multiple solutions for y, then any one of those solutions will suffice. However, y must be in sorted order. You can assume that n will be an integer greater than 5.

Solution Stats

76.47% Correct | 23.53% Incorrect
Last solution submitted on Feb 11, 2019

Problem Comments

Recent Solvers11

Suggested Problems

Discover MakerZone

MATLAB and Simulink resources for Arduino, LEGO, and Raspberry Pi

Learn more

Discover what MATLAB® can do for your career.

Opportunities for recent engineering grads.

Apply Today

MATLAB Academy

New to MATLAB?

Learn MATLAB today!