Extra safe Prime Number

A safe prime is a prime number of the form (2 * p) + 1 where p is also a prime.

5 = 2 * 2 + 1

7 = 2 * 3 + 1

11 = 2 * 5 + 1

You can check more about safe prime number in the below link:

https://en.wikipedia.org/wiki/Safe_prime

MATLAB CODE to check a number is safe prime or not:

clc

clear all

close all

x=input('Enter the number');

y=[];

qam=0;

for re=2:(x-1)

    if(rem(x,re)==0)

        qam=qam+1;

    end

end

if(qam==0)

for i=2:(x-1)

    m=i;

    c=0;

    for j=2:m-1

        if(rem(m,j)==0)

            c=c+1;

        end

    end

    if(c==0)

        y=[y i];

    end

end

d=0;

for i=1:length(y)

    if(2*y(i)+1==x)

        d=d+1;

    end

end

if(d==1)

    disp("Yes");

else

    disp("No");

end

else

    disp('Not a prime number');

end

Explanation:

Sample Output:

MATLAB CODE to print all safe prime numbers less than or equal to the input number:

clc

clear all

close all

uo=[];

g=input('Enter the number');

for x=1:g

y=[];

qam=0;

for re=2:(x-1)

    if(rem(x,re)==0)

        qam=qam+1;

    end

end

if(qam==0)

for i=2:(x-1)

    m=i;

    c=0;

    for j=2:m-1

        if(rem(m,j)==0)

            c=c+1;

        end

    end

    if(c==0)

        y=[y i];

    end

end

d=0;

for i=1:length(y)

    if(2*y(i)+1==x)

        d=d+1;

    end

end

if(d==1)

    uo=[uo x];

end

end

end

You can check the safe prime numbers list in the below link:

https://prime-numbers.info/list/safe-primes

Sample Output:

    

MATLAB CODE to check an input prime number is extra safe or not:

clc

clear all

close all

x=input('Enter the number');

y=[];

qam=0;

for re=2:(x-1)

    if(rem(x,re)==0)

        qam=qam+1;

    end

end

if(qam==0)

for i=2:(x-1)

    m=i;

    c=0;

    for j=2:m-1

        if(rem(m,j)==0)

            c=c+1;

        end

    end

    if(c==0)

        y=[y i];

    end

end

d=0;

for i=1:length(y)

    if(2*y(i)+1==x)

        d=y(i);

    end

end

x=d;

y=[];

qam=0;

for re=2:(x-1)

    if(rem(x,re)==0)

        qam=qam+1;

    end

end

if(qam==0)

for i=2:(x-1)

    m=i;

    c=0;

    for j=2:m-1

        if(rem(m,j)==0)

            c=c+1;

        end

    end

    if(c==0)

        y=[y i];

    end

end

d=0;

for i=1:length(y)

    if(2*y(i)+1==x)

        d=d+1;

    end

end

if(d==1)

    disp('true');

else

    disp('false');

end

else

    disp('false');

end

else

    disp('false');

end

Sample Output:

(because 23=2*11+1 and 11 is also a safe prime (11=2*5+1))

Function implementation:

function tf = isextrasafe(x)

y=[];

qam=0;

for re=2:(x-1)

if(rem(x,re)==0)

qam=qam+1;

end

end

if(qam==0)

for i=2:(x-1)

m=i;

c=0;

for j=2:m-1

if(rem(m,j)==0)

c=c+1;

end

end

if(c==0)

y=[y i];

end

end

d=0;

for i=1:length(y)

if(2*y(i)+1==x)

d=y(i);

end

end

x=d;

y=[];

qam=0;

for re=2:(x-1)

if(rem(x,re)==0)

qam=qam+1;

end

end

if(qam==0)

for i=2:(x-1)

m=i;

c=0;

for j=2:m-1

if(rem(m,j)==0)

c=c+1;

end

end

if(c==0)

y=[y i];

end

end

d=0;

for i=1:length(y)

if(2*y(i)+1==x)

d=d+1;

end

end

if(d==1)

tf=true;

else

tf=false;

end

else

tf=true;

end

else

tf=false;

end

end