 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
vb.net print barcode zebra 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 Decode DataMatrix In Java Using Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications. Data Matrix ECC200 Maker In Java Using Barcode encoder for Java Control to generate, create Data Matrix 2d barcode image in Java applications. definitions: DataMatrix Reader In Java Using Barcode recognizer for Java Control to read, scan read, scan image in Java applications. Make Barcode 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; Bar Code Reader In Java Using Barcode reader for Java Control to read, scan read, scan image in Java applications. DataMatrix Drawer In C# Using Barcode creation for VS .NET Control to generate, create ECC200 image in VS .NET applications. including this static initializer, which implements the Sieve of Eratosthenes: DataMatrix Printer In VS .NET Using Barcode drawer for ASP.NET Control to generate, create Data Matrix 2d barcode image in ASP.NET applications. DataMatrix Generator In VS .NET Using Barcode generation for .NET Control to generate, create Data Matrix ECC200 image in Visual Studio .NET 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); } } } } Drawing ECC200 In Visual Basic .NET Using Barcode encoder for Visual Studio .NET Control to generate, create Data Matrix 2d barcode image in VS .NET applications. Code 3/9 Encoder In Java Using Barcode creation for Java Control to generate, create ANSI/AIM Code 39 image in Java applications. 2.23 Add the following method to the Primes class and then test it: Create UCC  12 In Java Using Barcode creation for Java Control to generate, create UPC Symbol image in Java applications. Painting Barcode In Java Using Barcode printer for Java Control to generate, create barcode 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" ISSN Drawer In Java Using Barcode maker for Java Control to generate, create ISSN  10 image in Java applications. Bar Code Creation In None Using Barcode printer for Software Control to generate, create bar code image in Software 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: Encoding Code 128 Code Set B In None Using Barcode drawer for Software Control to generate, create ANSI/AIM Code 128 image in Software applications. ECC200 Maker In None Using Barcode drawer for Software Control to generate, create Data Matrix image in Software applications. 4 = 2+2 6 = 3+3 8 = 3+5
Making UPC A In .NET Framework Using Barcode creation for .NET framework Control to generate, create UPCA Supplement 5 image in Visual Studio .NET applications. DataMatrix Creation In VB.NET Using Barcode drawer for Visual Studio .NET Control to generate, create DataMatrix image in .NET framework applications. ARRAYS
Making Bar Code In ObjectiveC Using Barcode printer for iPhone Control to generate, create bar code image in iPhone applications. Code 128B Generation In VS .NET Using Barcode creator for ASP.NET Control to generate, create Code 128 image in ASP.NET applications. [CHAP. 2
10 12 14 16 18 20 22 = = = = = = = 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
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.

