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vb.net code to generate barcode implementation of the Sieve of Eratosthenes from Problem 2.21. Use these in Java
implementation of the Sieve of Eratosthenes from Problem 2.21. Use these Decoding GS1  13 In Java Using Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications. Print UPC  13 In Java Using Barcode printer for Java Control to generate, create EAN / UCC  13 image in Java applications. definitions: Decode EAN / UCC  13 In Java Using Barcode recognizer for Java Control to read, scan read, scan image in Java applications. Bar Code Printer In Java Using Barcode printer for Java Control to generate, create barcode image in Java applications. public class Primes { private static final int SIZE = 1000; private static int size = SIZE; private static BitSet sieve = new BitSet(size); private static int last = 1; Decode Bar Code In Java Using Barcode scanner for Java Control to read, scan read, scan image in Java applications. UPC  13 Drawer In C#.NET Using Barcode generator for .NET Control to generate, create EAN 13 image in .NET applications. including this static initializer, which implements the Sieve of Eratosthenes: Paint EAN13 In .NET Framework Using Barcode generator for ASP.NET Control to generate, create UPC  13 image in ASP.NET applications. Encode EAN13 Supplement 5 In .NET Using Barcode printer for VS .NET Control to generate, create GS1  13 image in .NET framework applications. static { for (int i = 2; i < SIZE; i++) { sieve.set(i); } for (int n = 2; 2*n < SIZE; n++) { if (sieve.get(n)) { for (int m=n; m*n<SIZE; m++) { sieve.clear(m*n); } } } } Making EAN 13 In VB.NET Using Barcode creation for VS .NET Control to generate, create EAN13 image in VS .NET applications. Code 128C Drawer In Java Using Barcode generator for Java Control to generate, create Code128 image in Java applications. 2.23 Add the following method to the Primes class and then test it: ANSI/AIM Code 39 Printer In Java Using Barcode printer for Java Control to generate, create Code 39 Extended image in Java applications. Encode EAN 128 In Java Using Barcode generator for Java Control to generate, create GTIN  128 image in Java applications. public static String factor(int n) // precondition: n > 1 // returns the prime factorization of n; // example: factor(4840) returns "2*2*2*5*11*11" Print Leitcode In Java Using Barcode generation for Java Control to generate, create Leitcode image in Java applications. Making EAN / UCC  13 In None Using Barcode creation for Word Control to generate, create UCC.EAN  128 image in Office Word applications. 2.24 Christian Goldbach (1690 1764) conjectured in 1742 that every even number greater than 2 is the sum of two primes. Write a program that tests the Goldbach conjecture for all even numbers less than 100. Use the Primes class from Problem 2.22. Your first 10 lines of output should look like this: Encode Code 128 Code Set C In None Using Barcode encoder for Software Control to generate, create Code 128 Code Set C image in Software applications. Code 128C Drawer In .NET Using Barcode generation for .NET framework Control to generate, create Code 128 image in Visual Studio .NET applications. 4 = 2+2 6 = 3+3 8 = 3+5
Paint European Article Number 13 In Java Using Barcode maker for Android Control to generate, create EAN / UCC  13 image in Android applications. Encoding ECC200 In None Using Barcode creation for Office Word Control to generate, create DataMatrix image in Word applications. 10 12 14 16 18 20 22 = = = = = = = EAN13 Generator In Java Using Barcode printer for BIRT reports Control to generate, create EAN13 Supplement 5 image in BIRT applications. Encoding Data Matrix In .NET Framework Using Barcode maker for VS .NET Control to generate, create Data Matrix image in VS .NET applications. ARRAYS
3+7 = 5+5 5+7 3+11 = 7+7 3+13 = 5+11 5+13 = 7+11 3+17 = 7+13 3+19 = 5+17 = 11+11
[CHAP. 2
2.25 Pierre de Fermat (1601 1665) conjectured that there are infinitely many prime numbers of p 2 the form n = 2 +1 for some integer p. These numbers are called Fermat primes. For exam1 2 ple, 5 is a Fermat prime because it is a prime number and it has the form 2 +1. Write a program that finds all the Fermat primes that are in the range of the int type. Use the Primes class from Problem 2.22 and the Math.pow() method. Your first 5 lines of output should look like this: 2^2^0 2^2^1 2^2^2 2^2^3 2^2^4 + + + + + 1 1 1 1 1 = = = = = 3 5 17 257 65537
2.26 Charles Babbage (1792 1871) obtained the first government grant in history when in 1823 he persuaded the British government to provide 1000 to build his difference engine. In his grant proposal, Babbage gave the formula x 2 + x + 41 as an example of a function that his computer would tabulate. This particular function was of interest to mathematicians because it produces an unusual number of prime numbers.Primes that have this form n = x 2 + x + 41 for some integer x could be called Babbage primes. Write a program that finds all the Babbage primes that are less than 10,000. Use the Primes class from Problem 2.22. Your first five lines of output should look like this: 0 1 2 3 4 41 43 47 53 61 is is is is is prime prime prime prime prime
2.27 Two consecutive odd integers that are both prime are called twin primes. The twin primes conjecture is that there are infinitely many twin primes. Write a program that finds all the twin primes that are less than 1000. Use the Primes class from Problem 2.22. Your first five lines of output should look like this: 3 5 11 17 29 5 7 13 19 31 2.28 Test the conjecture that there is at least one prime between each pair of consecutive square numbers. (The square numbers are 1, 4, 9, 16, 25, . . .). Use the Primes class from Problem 2.22. Your first five lines of output should look like this: 1 < 2 < 4 4 < 5 < 9 9 < 11 < 16 16 < 17 < 25 25 < 29 < 36
2.29 The Minimite friar Marin Mersenne (1588 1648) undertook in 1644 the study of numbers of the form n = 2 p 1, where p is a prime. He believed that most of these n are also primes, now CHAP. 2] ARRAYS
called Mersenne primes.Write a program that finds all the Mersenne primes for p < 30. Use the Primes class from Problem 2.22. Your first five lines of output should look like this: 2 3 5 7 11 2^21 = 3 is prime 2^31 = 7 is prime 2^51 = 31 is prime 2^71 = 127 is prime 2^111 = 2047 is not prime 2.30 A number is said to be palindromic if it is invariant under reversion; that is, the number is the same if its digits are reversed. For example, 3456543 is palindromic. Write a program that checks each of the first 10,000 prime numbers and prints those that are palindromic. Use the Primes class from Problem 2.22.

