Question

write a Matlab program ( solve the three questions). please use array and create your own function to check primality Question 1 : [10 points) Write a MATLAB program that will store all the first 1000 prime numbers in an array variable named arr_of_primes. Please note that a prime number is a positive integer that is bigger than or equal to 2 which is divisible only by 1 and itself. Examples of the first 8 primes are: 2, 3, 5, 7, 11, 13, 17, 19, .... Note that you cannot use the built-in functions isprime or primes from MATLAB You have to create your own functions to check for primality. Question 2: (10 points) Write a MATLAB function called: Jarr des, arr ascl-sort descending ascendingarr) that takes as an input an array of non-negative integer numbers (that is, can be positive integers or 0 values only). This function sorts the elements in the array and output the two output arrays arr des having the same elements from array arr but in and arrase having the same elements from array arr but in increasing order. Note that you cannot use any MATLAB built-in functions (if there is any) for sorting but you can use built-in functions length() or size() that return the length or size of the array, respectively. Note that there is a small difference between the two functions length) and size(). Try to find out what this difference is and use them accordingly, Question 3: (10 points) Write a MATLAB function called primprimorial(n) that will take an input which is a positive integer number and will retum an output prime which is primorial of the number n or equivalently the product of all the prime numbers from 2 to the last prime number less than or equal to the number n. Please note that a prime number is a positive integer that is bigger than or equal to 2 which is divisible only by 1 and itself. In other words: # = P.P2 ... Pk where Pu.P2, ....Pare the prime numbers upto and including n ifnis prime and is the primordial of the number n. Note that you cannot use the built-in functions isprime() or primesc from MATLAB You use your own functions created in your answer to question 1 Output: primorial(30) 2*3*5*7*11*13*17*19*23.29 whatever that number is.

Answer 1

%% question 1

% This program finds first 1000 prime numbers and store in the array
% arr_of_primes
clc
clear all

arr_of_primes = []; % Array of prime numbers
N = 2; % starting with N = 2
while length(arr_of_primes)<1000 % while no of elements in P is less than 1000
logic = ifPrime(N); % check if N is prime number
% logic = 1, if N is prime number
% logic = 0, if N is not a prime number
if(logic==1) % if N is prime number, store it in array P
arr_of_primes = [arr_of_primes, N];
end
N = N +1; % check next number
end

%% fuction file

function logic = ifPrime(N)
logic = 1; % assume N is prime number
% 2 is a prime nuber, no need to check
% if N is not 2, check if it is not a prime number
if(N~=2)
% first devide by 2, if remender is zero,it is not a prime no
% otherwise apply next check
r = mod(N,2); % remender when devide N by 2
q = floor(N/2); % quotent when devide N by 2
if(r==0) % if remender when devide by 2 is zero, it is not a prime no
logic = 0;
else if(N>3) % Else if number is greater than 2, do fuether check
% start deviding with 3
div = 3; % div is divisor variable
while div < q
r = mod(N,div);
q = floor(N/div);
if(r==0)
logic = 0;
break
else
div = div + 2;
end
end
end
end
end
end

/////////////////////////////////////////////////////////////////////////////// (2)

function [ arr_des, arr_asc ] = sort_descending_ascending( arr )
% This function arrange input array into in ascending and descending order
% Only non-negative integer should be input to this function

% assign first element of arr to variables arr_des and arr_asc
arr_des = arr(1);
arr_asc = arr(1);

% Arranging in accending and descending order one-by-one element
for k = 2:length(arr)
% descending order
if(arr(k)<=arr_des(k-1)) % if upcoming element is greater than last element in array arr_des
arr_des = [ arr_des, arr(k)];
else % otherwise, find the right postion in array arr_des and put it at right place
j = 1;
while arr_des(j)>arr(k)
j = j + 1;
end
arr_des = [arr_des(1:j-1), arr(k), arr_des(j:end)];
end
% ascending order
if(arr(k)>=arr_asc(k-1)) % if upcoming element is less than last element in array arr_asc
arr_asc = [ arr_asc, arr(k)];
else % otherwise, find the right postion in array arr_des and put it at right place
j = 1;
while arr_asc(j)<arr(k)
j = j + 1;
end
arr_asc = [arr_asc(1:j-1), arr(k), arr_asc(j:end)];
end
end
end

Command Window >> clear all >> [arr_des, arr_asc] - sort_descending_ascending([1 5 9 0 7 3 64 9 4 6 17]) arr_des - 764 17 9 9 7 6 5 4 3 1 0 arr_asc = 0 1 3 5 6 7 9 9 17 64 >>