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Prime pairs that yield primes | Matlab Examples

Posted on November 25, 2018February 20, 2019 by Yılmaz Cemalettin

Matlab Tutorials | Examples

Practice 5:

Prime pairs that yield primes

A prime number is a number that can be divided without remainder only to 1 and itself. You can find out that a number p is prime by dividing it by all numbers between

2 and p, and verifying that the remainders in all such divisions are non-zero.

Consider the pairs of successive prime numbers, such as (2, 3), (3, 5), (5, 7), (7, 11), (11, 13), (13, 17), etc. Write a program that finds the first ten successive prime pairs (p, q), such that pq+p+q is also a prime number.

While writing this program, you are expected NOT to use vectors (arrays) or any MATLAB functions that automatically give you prime numbers, such as primes(), isprime(), etc.

Solution:

Matlab
MATLAB
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%Prime pairs that yield primes
 
clc;
clear;
n=2;
b = 0;
j=0;
while(j < 10)
    result = true; %Reset boll variable for each iteration
    result2 = true;
    for i=2:n-1%Finding first prime numbers
        if (mod(n,i)==0) %Looking the divideablity
            result = false; %If it is divide mak result the false
        end
    end
    if result % if result is true in this iteration n is a prime number
        if(b>0) %Eliminition first variable
            new = (b*n)+b+n; %  pq+p+q find this value
            for i2 = 2:sqrt(new) % loking the dividablity between 2 to sqrt(new)
                if (mod(new,i2)==0)%Looking the divideablity
                    result2 = false;%If it is divide mak result2 the false
                end
            end
            if (result2)%if result2 is true in this iteration new number is a prime number
                j = j+1;%finding one of them therefore increase j
                fprintf('For (%g,%g), %gx%g+%g+%g= %g is a prime.\n',b,n,b,n,b,n,new);
            else%if result2 is false in this iteration new number is a NOT prime number
                fprintf('For (%g,%g), %gx%g+%g+%g= %g is NOT a prime.\n',b,n,b,n,b,n,new);
            end
        end
        b = n;%Storage the prime number in b for using after
    end
    n = n+1; %increase n for loop
end

 

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