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for (int n = 2; 2*n < SIZE; n++) { if ((isPrime.get(n))) { for (int m = n; m*n < SIZE; m++) { isPrime.set(m*n, false); } } } } private static void printSieve() int n=0; for (int i = 0; i < SIZE; i++) if (isPrime.get(i)) { System.out.printf("%5d%s", } } System.out.printf("%n%d primes } } { { i, ++n%16==0 "\n":"");
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[CHAP. 2
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less than %d%n", n, SIZE);
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public class TestSieve { private static final int SIZE=1000; private static BitSet isPrime = new BitSet(SIZE); public static void main(String[] args) { initializeSieve(); ch02.pr20.TestSieve.printSieve(); } private static void initializeSieve() { for (int i = 2; i < SIZE; i++) { isPrime.set(i); } for (int n = 2; 2*n < SIZE; n++) { if (isPrime.get(n)) { for (int m = n; m*n <SIZE; m++) { isPrime.clear(m*n); } } } } private static void printSieve() int n=0; for (int i = 0; i < SIZE; i++) if (isPrime.get(i)) { System.out.printf("%5d%s", } } System.out.printf("%n%d primes } } { { i, ++n%16==0 "\n":"");
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less than %d%n", n, SIZE);
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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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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); } } } } public static void setLast(int n) { last = n; } public static void setLast() { last = 1; } public static void setSize(int n) { size = n; } public static void setSize() { size = 1000; } public static boolean isPrime(int n) { return sieve.get(n); } public static int next() { while (++last<size) { if (sieve.get(last)) { return last; } } return -1; } public static void printPrimes() { int n=0; for (int i=0; i<SIZE; i++) { if (sieve.get(i)) { System.out.print((n++%10==0 "\n":"\t")+i); } } System.out.println("\n" + n + " primes less than " + SIZE); } }
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public static String factor(int n) { public static String factor(int n) { String primes=""; int p = next(); while (n > 1) { if (n%p==0) { primes += (primes.length()==0 "":"*") + p; n /= p; } else p = next(); if (p == -1) { primes += " OVERFLOW"; break; }
} setLast(); return primes; }
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[CHAP. 2
public class TestGoldbach { public static void main(String[] args) { Primes.setSize(1000); System.out.println("4 = 2+2"); for (int n = 6; n < 100; n += 2) { System.out.print(n); for (int p = 3; p <= n/2; p += 2) { if (Primes.isPrime(p) && Primes.isPrime(n-p)) { System.out.print(" = "+p+"+"+(n-p)); } } System.out.println(); } } } public class TestFermat { public static void main(String[] args) { Primes.setSize(1000); for (int p = 0; p < 5; p++) { int n = (int)Math.pow(2,Math.pow(2,p)) + 1; if (Primes.isPrime(n)) { System.out.println("p = "+p+", n = 2^2^p = "+n); } } } } public class TestBabbage { public static void main(String[] args) { Primes.setSize(1000); for (int x = 0; x < 50; x++) { System.out.print(x); int n = x*x + x + 41; if (Primes.isPrime(n)) { System.out.println("\t"+n+" is prime"); } else { System.out.println(); } } } } public class TestTwinPrimes { public static void main(String[] args) { Primes.setSize(1000); int n = Primes.next(); while (n < 0.9*N) { if (Primes.isPrime(n+2)) { System.out.println(n + "\t" + (n+2)); } n = primes.next(); } } }
CHAP. 2]
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public class TestSquares { public static void main(String[] args) { Primes.setSize(1000); for (int n = 1; n < 100; n++) { for (int i = n*n+1; i < (n+1)*(n+1); i++) { if (Primes.isPrime(i)) { System.out.printf("%d < %d < %d%n", n*n, i, (n+1)*(n+1)); break; } } } } } public class TestMersenne { public static void main(String[] args) { Primes.setSize(1000); for (int p = Primes.next(); p < 30; p = Primes.next()) { int n = (int)Math.round(Math.pow(2,p)) - 1; System.out.printf("%d\t2^%d-1%d", p, p, n); if (Primes.isPrime(n)) { System.out.println(" is prime "); } else { System.out.println(" is not prime "); } } } } boolean isPalindromic(int n) { if (n < 0) { return false; } int p10=1; // make p10 is the greatest power of 10 that is < n while (p10 < n) { p10 *= 10; } p10 /= 10; while (n > 9) { if (n/p10 != n%10) { return false; } n /= 10; // remove rightmost digit from n p10 /= 10; n %= p10; // remove leftmost digit from n } return true; // single digit integers are palindromic } }
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