**Part 1.****Problem 1.** Write a C++ function that inputs a positive integer and determines whether it is prime using trial division.*Use your function from Problem 1 to write a C++ program for solving each of the following computational problems. For each problem, find the running time function of the algorithm you are using to write the corresponding program.***Problem 2.** Determine whether \(2^p - 1\) is prime for each of the primes not exceeding 100.**Problem 3.** Find as many primes of the form \(n^2 + 1\), where \(n\) is a positive integer, as you can.*Note:* Problems 2 and 3 are not related to each other. You need to develop a separate program for each problem. Your programs should invoke your function from Problem 1.*For Part 1, submit your C++ programs, test results, and make a conclusion.*

Time complexity to check whether n is prime or not is O(sqrt(n)) logic:- iterate from i=2 to i<sqrt(n) and check if n%i==0 if it is , then it is non prime . If remainder is not zero for any of number between 2 and sqrt(n) then it is prime. End. #include <iostream>#include<math.h>using namespace std;void check(){ int n,f=0; cout<<"enter a number: "; cin>>n; for(int i=2;i<(sqrt(n));i++) { if(n%i==0) { f=1; break; } } if(f==1) { cout<<"number is not prime"; } else { cout<<"number is prime"; }}int main(){ check(); return 0;}Thanks.