Question

matlab

The Goldbach Conjecture asserts that every even integer greater than 2 can be expressed as the sum of two prime numbers. Write a program that will first generate a random even number on the interval [4, 100], and print its all possible pairs of prime numbers whose sum makes this integer. For example, if n is 50, here are 4 possible pairs: 3 and 47, 7 and 43, 13 and 37, and 19 and 31. The order of the two numbers is unimportant, so only count a pair once.

Answer 1

Please find the code below:

isPrimeNumber.m

function [ result] = isPrimeNumber( n )
%%initially set output flag to true
result = true;
%%iterate over all positive integers 2,3,...,n-1
%%if n is not divisible by any of these factors....it is prime
if (n == 1)
result = false;
elseif (n == 2)
result = true;
else
for i=2:n-1
if (mod(n,i)==0)
result = false;
break;
end
end
end

end

Script

clc
clear
%generate even random number
evenNum = 4+randi(96);
while rem(evenNum,2)==1
evenNum = 4+randi(96);
end
fprintf("Generated even number is %d\n",evenNum);

one = [];
two = [];
for num=1:evenNum
if isPrimeNumber(num)
other = evenNum-num;
if isPrimeNumber(other)
if ~ismember(num,one) && ~ismember(other,one)
one = [one num];
two = [two other];
end
end
end
end
fprintf("The prime nubers factors are as below\n");

for i=1:length(one)
fprintf("%d - %d\n",one(i),two(i));
end

output: