## Prime Number Computation and Prime Twin Pairs### (a) Computing Prime Numbers Less Than 200**Task:** Write a Java program that computes and prints out all prime numbers less than 200. Print these prime numbers 8 in a row. **Definition:** A prime number is a positive integer greater than 1, with 1 and itself as its only two divisors. For example, 2, 3, 5, 7, 11, 13, 17, 19 are the first 8 prime integers. To compute prime numbers, you may use the `%` (modulo) operator.### (b) Computing Prime Numbers Less Than 1000**Task:** Enhance your Java program to compute the total number of prime numbers less than 1000. You do not have to print out the prime numbers 8 in a row; just print how many there are. **Clarification:** If asked to compute and print prime numbers less than 100, you’ll print `2 3 5 7 11 13 17 19` in the first row, `23 29 31 37 41 43 47 53` in the second row, etc.; but if asked to compute the total number of prime numbers less than 100, the total is 25, since there are 25 prime numbers from 2, 3 up to 89, 97, which are less than 100.### (c) Computing Prime Twin Pairs Less Than 300**Definition:** A prime twin pair is a pair of two odd prime numbers \( p \) and \( p + 2 \). For example, \(\{3, 5\}\) and \(\{5, 7\}\) are both prime twins, while \(\{7, 9\}\) and \(\{53, 59\}\) are not prime twins, since 9 is not a prime and 53 and 59 differ by more than 2.**Task:** Enhance your Java program to compute and print all the prime twin pairs less than 300, and print the twin pairs in sets of 4 in a row.---By implementing these enhancements, the user will be able to compute and understand the distribution of prime numbers and prime twin pairs within specified ranges using Java programming.

Java: Java is a high level object oriented programming language. It was developed by James Gosling…

(a) Write a Java program that computes and prints out all prime numbers <200. Print these prime numbers 8 in a row. A prime number is a positive integer > 1 with 1 and itself as the only two divisors. So, 2, 3, 5, 7, 11, 13, 17, 19 are the first 8 prime integers. To compute prime numbers, you may use the % (modulo) operator.

(a) Write a Java program that computes and prints out all prime numbers <200. Print these prime numbers 8 in a row. A prime number is a positive integer > 1 with 1 and itself as the only two divisors. So, 2, 3, 5, 7, 11, 13, 17, 19 are the first 8 prime integers. To compute prime numbers, you may use the % (modulo) operator.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

## Prime Number Computation and Prime Twin Pairs

### (a) Computing Prime Numbers Less Than 200

**Task:** Write a Java program that computes and prints out all prime numbers less than 200. Print these prime numbers 8 in a row.

**Definition:** A prime number is a positive integer greater than 1, with 1 and itself as its only two divisors. For example, 2, 3, 5, 7, 11, 13, 17, 19 are the first 8 prime integers. To compute prime numbers, you may use the `%` (modulo) operator.

### (b) Computing Prime Numbers Less Than 1000

**Task:** Enhance your Java program to compute the total number of prime numbers less than 1000. You do not have to print out the prime numbers 8 in a row; just print how many there are.

**Clarification:** If asked to compute and print prime numbers less than 100, you’ll print `2 3 5 7 11 13 17 19` in the first row, `23 29 31 37 41 43 47 53` in the second row, etc.; but if asked to compute the total number of prime numbers less than 100, the total is 25, since there are 25 prime numbers from 2, 3 up to 89, 97, which are less than 100.

### (c) Computing Prime Twin Pairs Less Than 300

**Definition:** A prime twin pair is a pair of two odd prime numbers \( p \) and \( p + 2 \). For example, \(\{3, 5\}\) and \(\{5, 7\}\) are both prime twins, while \(\{7, 9\}\) and \(\{53, 59\}\) are not prime twins, since 9 is not a prime and 53 and 59 differ by more than 2.

**Task:** Enhance your Java program to compute and print all the prime twin pairs less than 300, and print the twin pairs in sets of 4 in a row.

---

By implementing these enhancements, the user will be able to compute and understand the distribution of prime numbers and prime twin pairs within specified ranges using Java programming.

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