In mathematics, a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers, i.e. is it has only two factors 1 and itself. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. Note that the prime number series is: 2, 3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, ... a. Write a Java method named isPrime that takes a natural number as a parameter and returns the if the given number is prime or not using the following header: Public static boolean isPrime (int num) b. Write a Java class called PrimeNumbers that: Reads from the user a natural value n (should be less than or equal 200). Prints a list of the prime numbers from 2 to n and their number and values. o The program has to work EXACTLY as given in the following sample run. Hints: You should create a single dimension array to store the prime numbers less than or equal n. You have to check all the natural numbers less than or equal n starting from 1. 1 is not a prime number while 2 is.

In mathematics, a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers, i.e. is it has only two factors 1 and itself. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. Note that the prime number series is: 2, 3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, ... a. Write a Java method named isPrime that takes a natural number as a parameter and returns the if the given number is prime or not using the following header: Public static boolean isPrime (int num) b. Write a Java class called PrimeNumbers that: Reads from the user a natural value n (should be less than or equal 200). Prints a list of the prime numbers from 2 to n and their number and values. o The program has to work EXACTLY as given in the following sample run. Hints: You should create a single dimension array to store the prime numbers less than or equal n. You have to check all the natural numbers less than or equal n starting from 1. 1 is not a prime number while 2 is.

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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In mathematics, a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers, i.e. is it has only two factors 1 and itself. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself.Note that the prime number series is: 2, 3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, …a. Write a Java method named isPrime that takes a natural number as a parameter and returns the if the given number is prime or not using the following header: Public static boolean isPrime(int num) b. Write a Java class called PrimeNumbers that: o Reads from the user a natural value n (should be less than or equal 200). o Prints a list of the prime numbers from 2 to n and their number and values. o The program has to work EXACTLY as given in the following sample run.
A number is called a perfect number if it is equal to the sum of all of its divisors, not including the number itself. For instance, 6 is a perfect number because the divisors of 6 are 1, 2, 3, 6 and 6 = 1 + 2 + 3. As another example, 28 is a perfect number because its divisors are 1, 2, 4, 7, 14, 28 and 28 = 1 + 2 + 4 + 7+ 14. However, 15 is not a perfect number because its divisors are 1, 3, 5, 15 and 15 6= 1 + 3 + 5. Write an algorithm that asks the user to enter a positive integer n and prints all the perfect numbers that are less than n.
IN VISUAL BASIC, solve Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.
In the example below, the sum of the fourth powers of each digit that forms the 4-digit numbers gives the number itself: 1634 = 14 + 64 + 34 + 44 8208 = 84 + 24 + 04 + 84 9474 = 94 + 44 + 74 + 44 And sum of these numbers is 1634 + 8208 + 9474 = 19316. Find the sum of all numbers that can be written as the sum of the fifth forces of their numbers. (P.s.: You have to done it by C++)
In python, Problem Description:Sheldon and Leonard are physicists who are fixated on the BIG BANG theory. In order to exchange secret insights they have devised a code that encodes UPPERCASE words by shifting their letters forward. Shifting a letter by S positions means to go forward S letters in the alphabet. For example, shifting B by S = 3 positions gives E. However, sometimes this makes us go past Z, the last letter of the alphabet. Whenever this happens we wrap around, treating A as the letter that follows Z. For example, shifting Z by S = 2 positions gives B. Sheldon and Leonard’s code depends on a parameter K and also varies depending on the position of each letter in the word. For the letter at position P, they use the shift value of S = 3P + K. For example, here is how ZOOM is encoded when K = 3. The first letter Z has a shift valueof S = 3 × 1 + 3 = 6; it wraps around and becomes the letter F. The second letter, O, hasS = 3 × 2 + 3 = 9 and becomes X. The last two letters…
Blackout Math is a math puzzle in which you are given an incorrect arithmetic equation. The goal of the puzzle is to remove two of the digits and/or operators in the equation so that the resulting equation is correct. For example, given the equation 6 - 5 = 15 ^ 4/2we can remove the digit 5 and the / operator from the right-hand side in order to obtain the correct equality 6 - 5 = 1 ^ 42. Both sides of the equation now equal to 1. Observe how removing an operator between two numbers (4 and 2) causes the digits of the numbers to be concatenated (42). Here is a more complicated example: 288 / 24 x 6 = 18 x 13 x 8 We can remove digits and operators from either side of the equals sign (either both from one side, or one on each side). In this case, we can remove the 2 from the number 24 on the left-hand side and the 1 from the number 13 on the right-hand side to obtain the correct equality 288 / 4 x 6 = 18 x 3 x 8 Both sides of the equation now equal to 432. Here is another puzzle for you…
Write a program that reads a number and finds it is a prime or not. 0. A prime number is a number such that 1 and itself are the only numbers that evenly divide it. For example: 3, 5,7, 11, 13, 17. 2.
The word ladder game was invented by Lewis Carroll in 1877. The idea is to begin with a start word and then change one letter at a time until you arrive at an end word. Each word along the way must be an English word. For example, starting from FISH, you can arrive at MAST through the following word ladder:FISH, WISH, WASH, MASH, MAST Write a program that uses recursion to find the word ladder given a start word and an end word, or that determines no word ladder exists. Use the file words.txt that is available online with the source code for the book as your dictionary of valid words. This file contains 87,314 words. Your program does not need to find the shortest word ladder between words; any word ladder will do if one exists. list aalii aardvark aardvarks aardwolf aba abaca abaci abacist aback abacus abacuses abaft abalone abalones abamp abampere abandon abandoned abandonee abandoner abandoners
1.Given a positive integer, N, the ’3N+1’ sequence starting from N is defined as follows:If N is an even number, then divide N by two to get a new value for NIf N is an odd number, then multiply N by 3 and add 1 to get a new value for N.Continue to generate numbers in this way until N becomes equal to 1For example, starting from N = 3 the complete ’3N+1’ sequence would be:3, 10, 5, 16, 8, 4, 2, 1Write c++ code to ask the user to enter a positive integer (N) in the main() function. Write a function sequence()that receives the integer value N and display the ‘3N+1’ sequence starting from the integer value that wasreceived (entered by the user). The function must also count and return the numbers that the sequenceconsists of. The returned value must be displayed from the main() function.
A number is called pandigital if it uses all of the digits from 1 to n exactly once, where n is the number of digits in the number. So, for example, the five-digit number 15432 is pandigital, but the five-digit number 11132 is not. Again, the four-digit number 4123 is pandigital, but the four-digit number 8312 is not. Finally, the one-digit number 1 is pandigital, but the one-digit number 3 is not. You should use list comprehension in your solution. Fill out the function is_pandigital. Hint: Using the range function list out all the numbers that should be in a pandigital number of a given length and then check if each of those numbers appears in the number you're checking >>> is_pandigital(1) True >>> is_pandigital(2) False >>> is_pandigital(12) True >>> is_pandigital(15432) True >>> is_pandigital(11123) False def is_pandigital(num): Note: Python Programming
A popular word game involves finding words from a grid of randomly generatedletters. Words must be at least three letters long and formed from adjoining letters.Letters may not be reused and it is valid to move across diagonals. As an example,consider the following 4 * 4 grid of letters: A B C DE F G HI J K LM N O P The word “FAB” is valid (letters in the upper left corner) and the word “KNIFE”is valid. The word “BABE” is not valid because the “B” may not be reused. Theword “MINE” is not valid because the “E” is not adjacent to the “N”. Write a program that uses a 4 * 4 two-dimensional array to represent the gameboard. The program should randomly select letters for the board. You may wishto select vowels with a higher probability than consonants. You may also wish toalways place a “U” next to a “Q” or to treat “QU” as a single letter. The programshould read the words from the text file words.txt (included on the website withthis book) and then use a recursive algorithm to…
When we say arithmetic expression, we mean a kind of expression you can type in a very basic desk calculator. That is, neither variables nor brackets are allowed. It contains only numbers and four arithmetic operators, +, -, *, and /. The following are some examples of arithmetic expression: Any number string with or without signs - e.g. 3, -1, +10, 3.14, -0.70 and 099. Number strings mixed with arithmetic operators - e.g. 3+5, -1+2*3, 7/10-0.7, and -1.4-+8.2. An example of FA diagram for recognising a non-negative integer is given below. You may use it as a start point. You need to add a few more states and transitions to handle numbers with decimal point and signs (e.g. -5, +2, 0.21, -32.6, +99.05, but not the form 1.0E-3). Most importantly, you also need to add a few more things to deal with the arithmetic operators +, -, *, /.