(Prime Numbers) An integer is said to be prime if it's divisible by only 1 and itself. For ex_
ample, 2. 3, 5 and 7 are prime, but 4, 6, 8 and 9 are not.
a) Wright a function that determines whether a number is prime.
b) Use this function in a program that determines and prints all the prime numbers between 2 and 10.000. How many these numbers do you really have to test before being sure that you've found all the primes?
c)Initially, you might think that is the upper limit for which you must test to sec whether a number is prime. but you need only go as high as the square root of n. Why? Rewrite the program. and run it both ways. Estimate the performance improvement.
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Chapter 6 Solutions
C++ How to Program (10th Edition)
- Functions & Loops : Case Studies Prompt the user to input two positive integers. Variables: firstNum and secondNum (firstNum must be less than secondNum) (use while loop); create a user-defined function called validateUserInput() to validate the user's input. Use Call-by-Value. validateUserInput() is a value returning function. Output all odd numbers between firstNum and secondNum. (use while loop); create a user-defined function called oddNumbers(). Use Call-by-Value. oddNumbers() is a void function. Output the sum of all even numbers between firstNum and secondNum. (use while loop); create a user-defined function called sumEvenNumbers(). Use Call-by-Value. Declare a variable called sumEven in the main() for the sumEvenNumbers(). sumEvenNumbers() is a value returning function. Use sumEven to hold a returned value. Output the numbers and their squares between 1 and 10. (use while loop): create a user-defined function called displaySquareNumbers(). Call-by-Value.…arrow_forwardQuestions: Computer-Assisted Instruction) The use of computers in education is referred to as computer- assisted instruction (CAI). Write a program that will help an elementary school student learn multiplication. Use the rand function to produce two positive one-digit integers. The program should then prompt the user with a question, such as How much is 6 times 7? The student then inputs the answer. Next, the program checks the student’s answer. If it’s correct, display the message "Very good!" and ask another multiplication question. If the answer is wrong, display the message "No. Please try again." and let the student try the same question repeatedly until the student finally gets it right. A separate function should be used to generate each new question. This function should be called once when the application begins execution and each time the user answers the question correctly. PLEASE IN C++ LANGUAGEarrow_forward1. A prime number is a number that is only evenly divisible by itself and 1. For example, the number 5 is prime because it can only be evenly divided by 1 and 5. The number 6, however, is not prime because it can be divided evenly by 1, 2, 3, and 6.Write a Boolean function named is_prime which takes an integer as an argument and returns true if the argument is a prime number, or false otherwise. Use the function in a program that prompts the user to enter a number then displays a message indicating whether the number is prime.Tip:Recall that the % operator divides one number by another and returns the remainder of the division. In an expression such as num1 % num2, the % operator will return 0 if num1 is evenly divisible by num2.arrow_forward
- % WRITE CODE BELOW: % Step 1: Write a function called "collatz" below where you take an input % n, and if n is odd, return 3*n+1. If n is even, return n/2. (You need to % compute mod (n, 2) to test for even/odd. If mod(n,2)==1, n is odd, % otherwise n is even) Matlab codearrow_forward*You need to use at least one user define function Write a program to find the first n numbers of the Fibonacci series. You have to take a positive number from input and show all the Fibonacci numbers belongs to that range. If the number is not valid then notify the user and ask to input positive number again. If valid, then print the series. Input: Key in a number: 10 Output: Fibonacci Series: 0 1 1 2 3 5 8 13 21 34 Do you want to continue (y/n)? n Good bye!! Language:(C programming)arrow_forward(Quality Points for Student’s Grades) Write a function toQualityPoints that inputs a student’s average and returns 4 it’s 90–100, 3 if it’s 80–89, 2 if it’s 70–79, 1 if it’s 60–69, and 0 if theaverage is lower than 60arrow_forward
- Alert dont submit AI generated answer. (Central city) Given a set of cities, the central city is the city that has the shortest total distance to all other cities. Write a program that prompts the user to enter the number of the cities and the locations of the cities (coordinates), and finds the central city and its total distance to all other cities. Sample Run Enter the number of cities: 5 Enter the coordinates of the cities: 2.5 5 5.1 3 1 9 5.4 54 5.5 2.1 The central city is at (2.5, 5.0) The total distance to all other cities is 60.81 Class Name: Exercise08_21arrow_forward#5.Incorrect gurantee downvote. Euler's totient function, also known as phi-function ϕ(n),counts the number of integers between 1 and n inclusive,which are coprime to n.(Two numbers are coprime if their greatest common divisor (GCD) equals 1)."""def euler_totient(n): """Euler's totient function or Phi function. Time Complexity: O(sqrt(n)).""" result = n for i in range(2, int(n ** 0.5) + 1): if n % i == 0: while n % i == 0: n //= i.arrow_forward: Write a function that adds two numbers. You should not use+ or any arithmeticoperators.arrow_forward
- Complete the function that calculates the sum of the first n+1 terms of the geometric series a, ar, ar² ar³, arª ….. arn Note that the series begins with a and the last term is ar", in total there are n+1 terms. 1: # complete the function given the #variables a,r,n and return the value as series_sum. def sum geometric_series(a,r,n): # YOUR CODE HERE return series_sum print (sum_geometric_series (4.0, 5, 10))arrow_forwardA(n) statement is a statement that returns a value to the statement that called the function. Select one: a.value b.exit C.return d.replacearrow_forwardA variable x is assigned a NULL value. The return value from the function is.null(x) will be a. TRUE b. "Number" c. NULL d. "Character"arrow_forward
- C++ Programming: From Problem Analysis to Program...Computer ScienceISBN:9781337102087Author:D. S. MalikPublisher:Cengage Learning