Question

Part 1: Write a C++ function that inputs a positive integer and determines whether it is prime using trial division.

Part 2: Use the function from part 1 to make a C++ program that finds as many primes of the form n² + 1, where n is a positive integer, as you can.

Answer 1

`Hey,

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#include<iostream>

using namespace std;

//problem 1

//finding prime or not using trial division method

bool check_prime(int n)//returns true if n is prime

{

int i=2;

while(i*i < n)

{

if(n%i==0)return false;// because we have found a divisor

i++;

}

return true;

}

//problem2

//checks 2p-1 is prime or not for all primes not exceeding 100.

//problem3

//assuming n2 +1 is n^2 +1

//finding as many primes as we can

//which are of from n^2 +1

void check_primes_prob3()

{

int i=2;//taking 1 is not prime

while(i<10000)//mex this is only

{

//then checking fro n^2+1 is prime or not

if(check_prime(i*i +1))//finding and printing all such primes

{

cout<<"For "<<i<<" :"<<i<<"^"<<2<<"+1 :"<<i*i+1<<" is prime\n";

}

i++;

}

}

int main()

{

check_primes_prob3();

return 0;

}

Kindly revert for any queries

Thanks.