package hall;

import java.math.BigInteger;

/** A few utilities to generate a large random BigInteger,
 *  and find the next prime number above a given BigInteger.
 *  <P>
 *  Part of tutorial on servlets and JSP that appears at
 *  http://www.apl.jhu.edu/~hall/java/Servlet-Tutorial/
 *  1999 Marty Hall; may be freely used or adapted.
 */

public class Primes {
  // Note that BigInteger.ZERO was new in JDK 1.2, and 1.1
  // code is being used to support the most servlet engines.
  private static final BigInteger ZERO = new BigInteger("0");
  private static final BigInteger ONE = new BigInteger("1");
  private static final BigInteger TWO = new BigInteger("2");
  
  // Likelihood of false prime is less than 1/2^ERR_VAL
  // Assumedly BigInteger uses the Miller-Rabin test or
  // equivalent, and thus is NOT fooled by Carmichael numbers.
  // See section 33.8 of Cormen et al's Introduction to Algorithms
  // for details.
  private static final int ERR_VAL = 100;
  
  public static BigInteger nextPrime(BigInteger start) {
    if (isEven(start))
      start = start.add(ONE);
    else
      start = start.add(TWO);
    if (start.isProbablePrime(ERR_VAL))
      return(start);
    else
      return(nextPrime(start));
  }

  private static boolean isEven(BigInteger n) {
    return(n.mod(TWO).equals(ZERO));
  }

  private static StringBuffer[] digits =
    { new StringBuffer("0"), new StringBuffer("1"),
      new StringBuffer("2"), new StringBuffer("3"),
      new StringBuffer("4"), new StringBuffer("5"),
      new StringBuffer("6"), new StringBuffer("7"),
      new StringBuffer("8"), new StringBuffer("9") };

  private static StringBuffer randomDigit() {
    int index = (int)Math.floor(Math.random() * 10);
    return(digits[index]);
  }
  
  public static BigInteger random(int numDigits) {
    StringBuffer s = new StringBuffer("");
    for(int i=0; i<numDigits; i++) {
      s.append(randomDigit());
    }
    return(new BigInteger(s.toString()));
  }

  public static void main(String[] args) {
    int numDigits;
    if (args.length > 0)
      numDigits = Integer.parseInt(args[0]);
    else
      numDigits = 150;
    BigInteger start = random(150);
    for(int i=0; i<50; i++) {
      start = nextPrime(start);
      System.out.println("Prime " + i + " = " + start);
    }
  }
}