How can I generate a random BigInteger within a certain range?

Question

Consider this method that works well:

public static bool mightBePrime(int N) {
    BigInteger a = rGen.Next (1, N-1);
    return modExp (a, N - 1, N) == 1;
}
         


        

Answer 1

Here's an alternate way to generate numbers within range without throwing away values and allowing BigIntegers for min and max.

public BigInteger RandomBigInteger(BigInteger min, BigInteger max)
    {
        Random rnd = new Random();
        string numeratorString, denominatorString;
        double fraction = rnd.NextDouble();
        BigInteger inRange;

        //Maintain all 17 digits of precision, 
        //but remove the leading zero and the decimal point;
        numeratorString = fraction.ToString("G17").Remove(0, 2);  

        //Use the length instead of 17 in case the random
        //fraction ends with one or more zeros
        denominatorString = string.Format("1E{0}", numeratorString.Length); 

        inRange = (max - min) * BigInteger.Parse(numeratorString) /
           BigInteger.Parse(denominatorString, 
           System.Globalization.NumberStyles.AllowExponent) 
           + min;
        return inRange;
    }

For generality you may want to specify precision as well. This seems to work.

    public BigInteger RandomBigIntegerInRange(BigInteger min, BigInteger max, int precision)
    {
        Random rnd = new Random();
        string numeratorString, denominatorString;
        double fraction = rnd.NextDouble();
        BigInteger inRange;

        numeratorString = GenerateNumeratorWithSpecifiedPrecision(precision);
        denominatorString = string.Format("1E{0}", numeratorString.Length); 

        inRange = (max - min) * BigInteger.Parse(numeratorString) / BigInteger.Parse(denominatorString, System.Globalization.NumberStyles.AllowExponent) + min;
        return inRange;
    }

    private string GenerateNumeratorWithSpecifiedPrecision(int precision)
    {
        Random rnd = new Random();
        string answer = string.Empty;

        while(answer.Length < precision)
        {
            answer += rnd.NextDouble().ToString("G17").Remove(0, 2);                
        }
        if (answer.Length > precision) //Most likely
        {
            answer = answer.Substring(0, precision);
        }
        return answer;
    }