Large pseudo random numbers

**JosAH** · Apr 20 '07, 08:19 AM

Originally posted by shana07

I hope I can get some pointers about multiple precision integers in here.
My lecturer has given us a task about using java big integer class.

I use calculator to calculate 2 to the power of 128 and result is this:
3.4028236692093 846346337460743 177e+38
What does this 'e+38' mean?

How multiple precision numbers are being processed in a program?

Kindly please share some info about this subject with me
....Thank You.

The 'e+38' notation means 'times ten raised to the power 38'. Your floating
point number approximates 2**128 (** being my notation for 'raise to the power).

You can use BigInteger numbers for this which can calculate, well, very big
integer numbers; read all about the BigInteger class API docs and pay special
attention to the pow method.

kind regards,

Jos

**shana07** · Apr 20 '07, 09:38 AM

Originally posted by JosAH

The 'e+38' notation means 'times ten raised to the power 38'. Your floating
point number approximates 2**128 (** being my notation for 'raise to the power).

You can use BigInteger numbers for this which can calculate, well, very big
integer numbers; read all about the BigInteger class API docs and pay special
attention to the pow method.

kind regards,

Jos

Thank you Jos. Appreciate your effort to reply my question.
As I have found one website just now, it is also called decimal exponent notation.

Can I clarify with you that using scien. calc it can only display until 32 decimal digits only, isn't?

One more question regarding this subject and random number generators.
Could you please take a look at the below source code, why it produces numbers only differs at the last 4 digits?

Is it possible for me to get min range of random number =0 from this code,
it is like from: 0 - 2**49 random numbers?

I provide 49 numDigits from command prompt ......
Thank you

Prime 1 = 772932660120059 030808394745599 610734462482434 1311
Prime 2 = 772932660120059 030808394745599 610734462482434 1503
Prime 3 = 772932660120059 030808394745599 610734462482434 1643
Prime 4 = 772932660120059 030808394745599 610734462482434 1653
Prime 5 = 772932660120059 030808394745599 610734462482434 1721
Prime 6 = 772932660120059 030808394745599 610734462482434 1823
Prime 7 = 772932660120059 030808394745599 610734462482434 1989
Prime 8 = 772932660120059 030808394745599 610734462482434 2009
Prime 9 = 772932660120059 030808394745599 610734462482434 2049

Code:

import java.math.BigInteger;

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");
  
   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()));
  }

  /** Simple command-line program to test. Enter number
   *  of digits, and it picks a random number of that
   *  length and then prints the first 50 prime numbers
   *  above that.
   */
  
  public static void main(String[] args) 
  {
    int numDigits;
    if (args.length > 0)
      numDigits = Integer.parseInt(args[0]);
    else
      numDigits = 150;
    BigInteger start = random(numDigits);
    for(int i=0; i<10; i++) 
    {
      start = nextPrime(start);
      System.out.println("Prime " + i + " = " + start);
    }
  }
}

**prometheuzz** · Apr 20 '07, 10:18 AM

Originally posted by shana07

One more question regarding this subject and random number generators.
Could you please take a look at the below source code, why it produces numbers only differs at the last 4 digits?

Because you create a starting number in your main method and then call the method nextPrime(...) ten times on that starting number getting the next prime after that number. That way you get ten increasing number of (probable) primes, which (if large enough) only differ in their last digits.

Originally posted by shana07

Is it possible for me to get min range of random number =0 from this code, it is like from: 0 - 2**49 random numbers?

If you want a (pseudo) random BigInteger between 0 and 2**49, you could just do this in your main method:

Code:

BigInteger start = random(numDigits);
final BigInteger _2pow49 = new BigInteger("562949953421312"); // == 2**49
start = start.mod(_2pow49); // start is now between 0 (inclusive) and 2**49 (exclusive)

The mod(...) method is short for modulo. Details about it can be found here:

Modulo - Wikipedia

http://en.wikipedia.org/wiki/Modulo_operation

Good luck.

**shana07** · Apr 20 '07, 10:59 AM

Originally posted by prometheuzz

Because you create a starting number in your main method and then call the method nextPrime(...) ten times on that starting number getting the next prime after that number. That way you get ten increasing number of (probable) primes, which (if large enough) only differ in their last digits.

If you want a (pseudo) random BigInteger between 0 and 2**49, you could just do this in your main method:

Code:

BigInteger start = random(numDigits);
final BigInteger _2pow49 = new BigInteger("562949953421312"); // == 2**49
start = start.mod(_2pow49); // start is now between 0 (inclusive) and 2**49 (exclusive)

The mod(...) method is short for modulo. Details about it can be found here:

Modulo - Wikipedia

http://en.wikipedia.org/wiki/Modulo_operation

Good luck.

Thank you. I have replace my main method as what you've suggested. It works but I think it still without start from min: 0. This is the sample result (excerpt) for 1000 random numbers:
Prime 0 = 140164539147929
Prime 1 = 140164539147959
Prime 2 = 140164539148019
Prime 3 = 140164539148061
Prime 4 = 140164539148069
Prime 5 = 140164539148087
Prime 6 = 140164539148091
Prime 7 = 140164539148097
Prime 8 = 140164539148111
Prime 9 = 140164539148121
Prime 10 = 140164539148189
Kindly please advise me ....

**JosAH** · Apr 20 '07, 11:21 AM

[QUOTE=shana07]Thank you. I have replace my main method as what you've suggested. It works but I think it still without start from min: 0.

I don't understand your remark; it doesn't make sense when I read the comments
just above your main method:

Code:

/** Simple command-line program to test. Enter number
   *  of digits, and it picks a random number of that
   *  length and then prints the first 50 prime numbers
   *  above that.
   */

The program/class does exactly what your comments state (except for the 50
numbers: you print just 10 of them).

kind regards,

Jos

**shana07** · Apr 20 '07, 11:37 AM

[QUOTE=JosAH]

Originally posted by shana07

Thank you. I have replace my main method as what you've suggested. It works but I think it still without start from min: 0.

I don't understand your remark; it doesn't make sense when I read the comments
just above your main method:

Code:

/** Simple command-line program to test. Enter number
   *  of digits, and it picks a random number of that
   *  length and then prints the first 50 prime numbers
   *  above that.
   */

The program/class does exactly what your comments state (except for the 50
numbers: you print just 10 of them).

kind regards,

Jos

Erm so sorry I still don't get it ...as if I provide 'java Primes 5 > check.txt' to prompt, why it printed this: (I just paste for 10 random numbers)
Prime 0 = 62851
Prime 1 = 62861
Prime 2 = 62869
Prime 3 = 62873
Prime 4 = 62897
Prime 5 = 62903
Prime 6 = 62921
Prime 7 = 62927
Prime 8 = 62929
Prime 9 = 62939
From my understanding, it prints 5 decimal digit numbers. Correct me if i'm wrong. learning...than k you

**JosAH** · Apr 20 '07, 11:45 AM

[QUOTE=shana07]

Originally posted by JosAH

Erm so sorry I still don't get it ...as if I provide 'java Primes 5 > check.txt' to prompt, why it printed this: (I just paste for 10 random numbers)
Prime 0 = 62851
Prime 1 = 62861
Prime 2 = 62869
Prime 3 = 62873
Prime 4 = 62897
Prime 5 = 62903
Prime 6 = 62921
Prime 7 = 62927
Prime 8 = 62929
Prime 9 = 62939
From my understanding, it prints 5 decimal digit numbers. Correct me if i'm wrong. learning...than k you

Well the series 62851 ... are five digit numbers aren't they? The first one is a
pseudo random number. Exactly as your comment said so. You even created
some methods for that: a random number with 'n' digits. Did you change your
mind and do you want to start at, e.g. the number 5 now?

kind regards,

Jos

**shana07** · Apr 20 '07, 12:03 PM

[QUOTE=JosAH]

Originally posted by shana07

Well the series 62851 ... are five digit numbers aren't they? The first one is a
pseudo random number. Exactly as your comment said so. You even created
some methods for that: a random number with 'n' digits. Did you change your
mind and do you want to start at, e.g. the number 5 now?

kind regards,

Jos

Yes, I have tried replace the main method as what has been suggested:(beca use my aim is to get 50 random numbers between 0 ~ 2**49).....

Code:

 BigInteger start = random(numDigits);         
    final BigInteger _2pow49 = new BigInteger("562949953421312"); // == 2**49
    start = start.mod(_2pow49); // start is now between 0 (inclusive) and 2**49 (exclusive)*/

What else missing in the codes ......

**shana07** · Apr 20 '07, 12:10 PM

Ok. I should mention that I need to print out 50 random digits between 0 ~ 2**49 - not prime random number. I downloaded this program and trying to adjust to suite with my aims.....kindly please advise me.Thanks

**JosAH** · Apr 20 '07, 12:12 PM

[QUOTE=shana07]

Originally posted by JosAH

Yes, I have tried replace the main method as what has been suggested:(beca use my aim is to get 50 random numbers between 0 ~ 2**49).....

Code:

 BigInteger start = random(numDigits);         
    final BigInteger _2pow49 = new BigInteger("562949953421312"); // == 2**49
    start = start.mod(_2pow49); // start is now between 0 (inclusive) and 2**49 (exclusive)*/

What else missing in the codes ......

But you got 50 numbers (well 10 actually but that's not the problem) in that range.
All you said was that these (prime) numbers should be at least 5 digits long.

Think over your requirements and try to write them down in a clear and concise
way because this thread is going nowhere as it goes now, i.e. you keep on
changing your requirements, at least that's what it looks like now and this way
none of your questions can be answered properly.

kind regards,

Jos

**shana07** · Apr 20 '07, 01:17 PM

[QUOTE=JosAH]

Originally posted by shana07

But you got 50 numbers (well 10 actually but that's not the problem) in that range.
All you said was that these (prime) numbers should be at least 5 digits long.

Think over your requirements and try to write them down in a clear and concise
way because this thread is going nowhere as it goes now, i.e. you keep on
changing your requirements, at least that's what it looks like now and this way
none of your questions can be answered properly.

kind regards,

Jos

Thank Jos.
Ok. I should mention that I need to print out 50 random digits between 0 ~ 2**49 - not only primes..it should be totally any random numbers.
I downloaded this program and trying to adjust to suite with my aims - that involves with Big Integers.....ki ndly please advise me again...

**JosAH** · Apr 20 '07, 01:21 PM

[QUOTE=shana07]

Originally posted by JosAH

Thank Jos.
Ok. I should mention that I need to print out 50 random digits between 0 ~ 2**49 - not only primes..it should be totally any random numbers.
I downloaded this program and trying to adjust to suite with my aims - that involves with Big Integers.....ki ndly please advise me again...

It doesn't involve BigIntegers at all. Ordinary longs can handle numbers up to
2**64. Read the API docs for the Random class and pay special attention to
the nextLong() method.

kind regards,

Jos

**JosAH** · Apr 20 '07, 01:23 PM

ps. I changed the thread title.

kind regards,

Jos

**shana07** · Apr 20 '07, 01:35 PM

[QUOTE=JosAH]

Originally posted by shana07

It doesn't involve BigIntegers at all. Ordinary longs can handle numbers up to
2**64. Read the API docs for the Random class and pay special attention to
the nextLong() method.

kind regards,

Jos

How about 2**160? It does involve with BigIntegers right. So I need to use nextLong() method....thank u again

Large pseudo random numbers

Large pseudo random numbers

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