vb.net print barcode zebra implementation of the Sieve of Eratosthenes from Problem 2.21. Use these in Java

Creation Data Matrix in Java implementation of the Sieve of Eratosthenes from Problem 2.21. Use these

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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;
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including this static initializer, which implements the Sieve of Eratosthenes:
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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); } } } }
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2.23 Add the following method to the Primes class and then test it:
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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"
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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:
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4 = 2+2 6 = 3+3 8 = 3+5
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[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]
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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 2^2-1 = 3 is prime 2^3-1 = 7 is prime 2^5-1 = 31 is prime 2^7-1 = 127 is prime 2^11-1 = 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.
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