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			using System;
			using System.Collections.Generic;
			using System.Linq;
			using System.Text;
			namespace ZigBee.Common
			{
			public class BigInteger
			{
			// maximum length of the BigInteger in uint (4 bytes)
			// change this to suit the required level of precision.

			private const int maxLength = 70;

			// primes smaller than 2000 to test the generated prime number

			public static readonly int[] primesBelow2000 = {
			2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
			101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199,
			211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293,
			307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397,
			401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499,
			503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599,
			601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691,
			701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797,
			809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887,
			907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997,
			1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097,
			1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193,
			1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297,
			1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399,
			1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499,
			1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597,
			1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699,
			1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789,
			1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889,
			1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999 };


			private uint[] data = null; // stores bytes from the Big Integer
			public int dataLength; // number of actual chars used


			//***********************************************************************
			// Constructor (Default value for BigInteger is 0
			//***********************************************************************

			public BigInteger()
			{
			data = new uint[maxLength];
			dataLength = 1;
			}


			//***********************************************************************
			// Constructor (Default value provided by long)
			//***********************************************************************

			public BigInteger(long value)
			{
			data = new uint[maxLength];
			long tempVal = value;

			// copy bytes from long to BigInteger without any assumption of
			// the length of the long datatype

			dataLength = 0;
			while (value != 0 && dataLength < maxLength)
			{
			data[dataLength] = (uint)(value & 0xFFFFFFFF);
			value >>= 32;
			dataLength++;
			}

			if (tempVal > 0) // overflow check for +ve value
			{
			if (value != 0 \|\| (data[maxLength - 1] & 0x80000000) != 0)
			throw (new ArithmeticException("Positive overflow in constructor."));
			}
			else if (tempVal < 0) // underflow check for -ve value
			{
			if (value != -1 \|\| (data[dataLength - 1] & 0x80000000) == 0)
			throw (new ArithmeticException("Negative underflow in constructor."));
			}

			if (dataLength == 0)
			dataLength = 1;
			}


			//***********************************************************************
			// Constructor (Default value provided by ulong)
			//***********************************************************************

			public BigInteger(ulong value)
			{
			data = new uint[maxLength];

			// copy bytes from ulong to BigInteger without any assumption of
			// the length of the ulong datatype

			dataLength = 0;
			while (value != 0 && dataLength < maxLength)
			{
			data[dataLength] = (uint)(value & 0xFFFFFFFF);
			value >>= 32;
			dataLength++;
			}

			if (value != 0 \|\| (data[maxLength - 1] & 0x80000000) != 0)
			throw (new ArithmeticException("Positive overflow in constructor."));

			if (dataLength == 0)
			dataLength = 1;
			}

			//***********************************************************************
			// Constructor (Default value provided by BigInteger)
			//***********************************************************************

			public BigInteger(BigInteger bi)
			{
			data = new uint[maxLength];

			dataLength = bi.dataLength;

			for (int i = 0; i < dataLength; i++)
			data[i] = bi.data[i];
			}


			//***********************************************************************
			// Constructor (Default value provided by a string of digits of the
			// specified base)
			//
			// Example (base 10)
			// -----------------
			// To initialize "a" with the default value of 1234 in base 10
			// BigInteger a = new BigInteger("1234", 10)
			//
			// To initialize "a" with the default value of -1234
			// BigInteger a = new BigInteger("-1234", 10)
			//
			// Example (base 16)
			// -----------------
			// To initialize "a" with the default value of 0x1D4F in base 16
			// BigInteger a = new BigInteger("1D4F", 16)
			//
			// To initialize "a" with the default value of -0x1D4F
			// BigInteger a = new BigInteger("-1D4F", 16)
			//
			// Note that string values are specified in the <sign><magnitude>
			// format.
			//
			//***********************************************************************

			public BigInteger(string value, int radix)
			{
			BigInteger multiplier = new BigInteger(1);
			BigInteger result = new BigInteger();
			value = (value.ToUpper()).Trim();
			int limit = 0;

			if (value[0] == '-')
			limit = 1;

			for (int i = value.Length - 1; i >= limit; i--)
			{
			int posVal = (int)value[i];

			if (posVal >= '0' && posVal <= '9')
			posVal -= '0';
			else if (posVal >= 'A' && posVal <= 'Z')
			posVal = (posVal - 'A') + 10;
			else
			posVal = 9999999; // arbitrary large


			if (posVal >= radix)
			throw (new ArithmeticException("Invalid string in constructor."));
			else
			{
			if (value[0] == '-')
			posVal = -posVal;

			result = result + (multiplier * posVal);

			if ((i - 1) >= limit)
			multiplier = multiplier * radix;
			}
			}

			if (value[0] == '-') // negative values
			{
			if ((result.data[maxLength - 1] & 0x80000000) == 0)
			throw (new ArithmeticException("Negative underflow in constructor."));
			}
			else // positive values
			{
			if ((result.data[maxLength - 1] & 0x80000000) != 0)
			throw (new ArithmeticException("Positive overflow in constructor."));
			}

			data = new uint[maxLength];
			for (int i = 0; i < result.dataLength; i++)
			data[i] = result.data[i];

			dataLength = result.dataLength;
			}


			//***********************************************************************
			// Constructor (Default value provided by an array of bytes)
			//
			// The lowest index of the input byte array (i.e [0]) should contain the
			// most significant byte of the number, and the highest index should
			// contain the least significant byte.
			//
			// E.g.
			// To initialize "a" with the default value of 0x1D4F in base 16
			// byte[] temp = { 0x1D, 0x4F };
			// BigInteger a = new BigInteger(temp)
			//
			// Note that this method of initialization does not allow the
			// sign to be specified.
			//
			//***********************************************************************

			public BigInteger(byte[] inData)
			{
			dataLength = inData.Length >> 2;

			int leftOver = inData.Length & 0x3;
			if (leftOver != 0) // length not multiples of 4
			dataLength++;


			if (dataLength > maxLength)
			throw (new ArithmeticException("Byte overflow in constructor."));

			data = new uint[maxLength];

			for (int i = inData.Length - 1, j = 0; i >= 3; i -= 4, j++)
			{
			data[j] = (uint)((inData[i - 3] << 24) + (inData[i - 2] << 16) +
			(inData[i - 1] << 8) + inData[i]);
			}

			if (leftOver == 1)
			data[dataLength - 1] = (uint)inData[0];
			else if (leftOver == 2)
			data[dataLength - 1] = (uint)((inData[0] << 8) + inData[1]);
			else if (leftOver == 3)
			data[dataLength - 1] = (uint)((inData[0] << 16) + (inData[1] << 8) + inData[2]);


			while (dataLength > 1 && data[dataLength - 1] == 0)
			dataLength--;

			//Console.WriteLine("Len = " + dataLength);
			}


			//***********************************************************************
			// Constructor (Default value provided by an array of bytes of the
			// specified length.)
			//***********************************************************************

			public BigInteger(byte[] inData, int inLen)
			{
			dataLength = inLen >> 2;

			int leftOver = inLen & 0x3;
			if (leftOver != 0) // length not multiples of 4
			dataLength++;

			if (dataLength > maxLength \|\| inLen > inData.Length)
			throw (new ArithmeticException("Byte overflow in constructor."));


			data = new uint[maxLength];

			for (int i = inLen - 1, j = 0; i >= 3; i -= 4, j++)
			{
			data[j] = (uint)((inData[i - 3] << 24) + (inData[i - 2] << 16) +
			(inData[i - 1] << 8) + inData[i]);
			}

			if (leftOver == 1)
			data[dataLength - 1] = (uint)inData[0];
			else if (leftOver == 2)
			data[dataLength - 1] = (uint)((inData[0] << 8) + inData[1]);
			else if (leftOver == 3)
			data[dataLength - 1] = (uint)((inData[0] << 16) + (inData[1] << 8) + inData[2]);


			if (dataLength == 0)
			dataLength = 1;

			while (dataLength > 1 && data[dataLength - 1] == 0)
			dataLength--;

			//Console.WriteLine("Len = " + dataLength);
			}


			//***********************************************************************
			// Constructor (Default value provided by an array of unsigned integers)
			//*********************************************************************

			public BigInteger(uint[] inData)
			{
			dataLength = inData.Length;

			if (dataLength > maxLength)
			throw (new ArithmeticException("Byte overflow in constructor."));

			data = new uint[maxLength];

			for (int i = dataLength - 1, j = 0; i >= 0; i--, j++)
			data[j] = inData[i];

			while (dataLength > 1 && data[dataLength - 1] == 0)
			dataLength--;

			//Console.WriteLine("Len = " + dataLength);
			}


			//***********************************************************************
			// Overloading of the typecast operator.
			// For BigInteger bi = 10;
			//***********************************************************************

			public static implicit operator BigInteger(long value)
			{
			return (new BigInteger(value));
			}

			public static implicit operator BigInteger(ulong value)
			{
			return (new BigInteger(value));
			}

			public static implicit operator BigInteger(int value)
			{
			return (new BigInteger((long)value));
			}

			public static implicit operator BigInteger(uint value)
			{
			return (new BigInteger((ulong)value));
			}


			//***********************************************************************
			// Overloading of addition operator
			//***********************************************************************

			public static BigInteger operator +(BigInteger bi1, BigInteger bi2)
			{
			BigInteger result = new BigInteger();

			result.dataLength = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;

			long carry = 0;
			for (int i = 0; i < result.dataLength; i++)
			{
			long sum = (long)bi1.data[i] + (long)bi2.data[i] + carry;
			carry = sum >> 32;
			result.data[i] = (uint)(sum & 0xFFFFFFFF);
			}

			if (carry != 0 && result.dataLength < maxLength)
			{
			result.data[result.dataLength] = (uint)(carry);
			result.dataLength++;
			}

			while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
			result.dataLength--;


			// overflow check
			int lastPos = maxLength - 1;
			if ((bi1.data[lastPos] & 0x80000000) == (bi2.data[lastPos] & 0x80000000) &&
			(result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000))
			{
			throw (new ArithmeticException());
			}

			return result;
			}


			//***********************************************************************
			// Overloading of the unary ++ operator
			//***********************************************************************

			public static BigInteger operator ++(BigInteger bi1)
			{
			BigInteger result = new BigInteger(bi1);

			long val, carry = 1;
			int index = 0;

			while (carry != 0 && index < maxLength)
			{
			val = (long)(result.data[index]);
			val++;

			result.data[index] = (uint)(val & 0xFFFFFFFF);
			carry = val >> 32;

			index++;
			}

			if (index > result.dataLength)
			result.dataLength = index;
			else
			{
			while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
			result.dataLength--;
			}

			// overflow check
			int lastPos = maxLength - 1;

			// overflow if initial value was +ve but ++ caused a sign
			// change to negative.

			if ((bi1.data[lastPos] & 0x80000000) == 0 &&
			(result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000))
			{
			throw (new ArithmeticException("Overflow in ++."));
			}
			return result;
			}


			//***********************************************************************
			// Overloading of subtraction operator
			//***********************************************************************

			public static BigInteger operator -(BigInteger bi1, BigInteger bi2)
			{
			BigInteger result = new BigInteger();

			result.dataLength = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;

			long carryIn = 0;
			for (int i = 0; i < result.dataLength; i++)
			{
			long diff;

			diff = (long)bi1.data[i] - (long)bi2.data[i] - carryIn;
			result.data[i] = (uint)(diff & 0xFFFFFFFF);

			if (diff < 0)
			carryIn = 1;
			else
			carryIn = 0;
			}

			// roll over to negative
			if (carryIn != 0)
			{
			for (int i = result.dataLength; i < maxLength; i++)
			result.data[i] = 0xFFFFFFFF;
			result.dataLength = maxLength;
			}

			// fixed in v1.03 to give correct datalength for a - (-b)
			while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
			result.dataLength--;

			// overflow check

			int lastPos = maxLength - 1;
			if ((bi1.data[lastPos] & 0x80000000) != (bi2.data[lastPos] & 0x80000000) &&
			(result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000))
			{
			throw (new ArithmeticException());
			}

			return result;
			}


			//***********************************************************************
			// Overloading of the unary -- operator
			//***********************************************************************

			public static BigInteger operator --(BigInteger bi1)
			{
			BigInteger result = new BigInteger(bi1);

			long val;
			bool carryIn = true;
			int index = 0;

			while (carryIn && index < maxLength)
			{
			val = (long)(result.data[index]);
			val--;

			result.data[index] = (uint)(val & 0xFFFFFFFF);

			if (val >= 0)
			carryIn = false;

			index++;
			}

			if (index > result.dataLength)
			result.dataLength = index;

			while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
			result.dataLength--;

			// overflow check
			int lastPos = maxLength - 1;

			// overflow if initial value was -ve but -- caused a sign
			// change to positive.

			if ((bi1.data[lastPos] & 0x80000000) != 0 &&
			(result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000))
			{
			throw (new ArithmeticException("Underflow in --."));
			}

			return result;
			}


			//***********************************************************************
			// Overloading of multiplication operator
			//***********************************************************************

			public static BigInteger operator *(BigInteger bi1, BigInteger bi2)
			{
			int lastPos = maxLength - 1;
			bool bi1Neg = false, bi2Neg = false;

			// take the absolute value of the inputs
			try
			{
			if ((bi1.data[lastPos] & 0x80000000) != 0) // bi1 negative
			{
			bi1Neg = true; bi1 = -bi1;
			}
			if ((bi2.data[lastPos] & 0x80000000) != 0) // bi2 negative
			{
			bi2Neg = true; bi2 = -bi2;
			}
			}
			catch (Exception) { }

			BigInteger result = new BigInteger();

			// multiply the absolute values
			try
			{
			for (int i = 0; i < bi1.dataLength; i++)
			{
			if (bi1.data[i] == 0) continue;

			ulong mcarry = 0;
			for (int j = 0, k = i; j < bi2.dataLength; j++, k++)
			{
			// k = i + j
			ulong val = ((ulong)bi1.data[i] * (ulong)bi2.data[j]) +
			(ulong)result.data[k] + mcarry;

			result.data[k] = (uint)(val & 0xFFFFFFFF);
			mcarry = (val >> 32);
			}

			if (mcarry != 0)
			result.data[i + bi2.dataLength] = (uint)mcarry;
			}
			}
			catch (Exception)
			{
			throw (new ArithmeticException("Multiplication overflow."));
			}


			result.dataLength = bi1.dataLength + bi2.dataLength;
			if (result.dataLength > maxLength)
			result.dataLength = maxLength;

			while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
			result.dataLength--;

			// overflow check (result is -ve)
			if ((result.data[lastPos] & 0x80000000) != 0)
			{
			if (bi1Neg != bi2Neg && result.data[lastPos] == 0x80000000) // different sign
			{
			// handle the special case where multiplication produces
			// a max negative number in 2's complement.

			if (result.dataLength == 1)
			return result;
			else
			{
			bool isMaxNeg = true;
			for (int i = 0; i < result.dataLength - 1 && isMaxNeg; i++)
			{
			if (result.data[i] != 0)
			isMaxNeg = false;
			}

			if (isMaxNeg)
			return result;
			}
			}

			throw (new ArithmeticException("Multiplication overflow."));
			}

			// if input has different signs, then result is -ve
			if (bi1Neg != bi2Neg)
			return -result;

			return result;
			}



			//***********************************************************************
			// Overloading of unary << operators
			//***********************************************************************

			public static BigInteger operator <<(BigInteger bi1, int shiftVal)
			{
			BigInteger result = new BigInteger(bi1);
			result.dataLength = shiftLeft(result.data, shiftVal);

			return result;
			}


			// least significant bits at lower part of buffer

			private static int shiftLeft(uint[] buffer, int shiftVal)
			{
			int shiftAmount = 32;
			int bufLen = buffer.Length;

			while (bufLen > 1 && buffer[bufLen - 1] == 0)
			bufLen--;

			for (int count = shiftVal; count > 0;)
			{
			if (count < shiftAmount)
			shiftAmount = count;

			//Console.WriteLine("shiftAmount = {0}", shiftAmount);

			ulong carry = 0;
			for (int i = 0; i < bufLen; i++)
			{
			ulong val = ((ulong)buffer[i]) << shiftAmount;
			val \|= carry;

			buffer[i] = (uint)(val & 0xFFFFFFFF);
			carry = val >> 32;
			}

			if (carry != 0)
			{
			if (bufLen + 1 <= buffer.Length)
			{
			buffer[bufLen] = (uint)carry;
			bufLen++;
			}
			}
			count -= shiftAmount;
			}
			return bufLen;
			}


			//***********************************************************************
			// Overloading of unary >> operators
			//***********************************************************************

			public static BigInteger operator >>(BigInteger bi1, int shiftVal)
			{
			BigInteger result = new BigInteger(bi1);
			result.dataLength = shiftRight(result.data, shiftVal);


			if ((bi1.data[maxLength - 1] & 0x80000000) != 0) // negative
			{
			for (int i = maxLength - 1; i >= result.dataLength; i--)
			result.data[i] = 0xFFFFFFFF;

			uint mask = 0x80000000;
			for (int i = 0; i < 32; i++)
			{
			if ((result.data[result.dataLength - 1] & mask) != 0)
			break;

			result.data[result.dataLength - 1] \|= mask;
			mask >>= 1;
			}
			result.dataLength = maxLength;
			}

			return result;
			}


			private static int shiftRight(uint[] buffer, int shiftVal)
			{
			int shiftAmount = 32;
			int invShift = 0;
			int bufLen = buffer.Length;

			while (bufLen > 1 && buffer[bufLen - 1] == 0)
			bufLen--;

			//Console.WriteLine("bufLen = " + bufLen + " buffer.Length = " + buffer.Length);

			for (int count = shiftVal; count > 0;)
			{
			if (count < shiftAmount)
			{
			shiftAmount = count;
			invShift = 32 - shiftAmount;
			}

			//Console.WriteLine("shiftAmount = {0}", shiftAmount);

			ulong carry = 0;
			for (int i = bufLen - 1; i >= 0; i--)
			{
			ulong val = ((ulong)buffer[i]) >> shiftAmount;
			val \|= carry;

			carry = ((ulong)buffer[i]) << invShift;
			buffer[i] = (uint)(val);
			}

			count -= shiftAmount;
			}

			while (bufLen > 1 && buffer[bufLen - 1] == 0)
			bufLen--;

			return bufLen;
			}


			//***********************************************************************
			// Overloading of the NOT operator (1's complement)
			//***********************************************************************

			public static BigInteger operator ~(BigInteger bi1)
			{
			BigInteger result = new BigInteger(bi1);

			for (int i = 0; i < maxLength; i++)
			result.data[i] = (uint)(~(bi1.data[i]));

			result.dataLength = maxLength;

			while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
			result.dataLength--;

			return result;
			}


			//***********************************************************************
			// Overloading of the NEGATE operator (2's complement)
			//***********************************************************************

			public static BigInteger operator -(BigInteger bi1)
			{
			// handle neg of zero separately since it'll cause an overflow
			// if we proceed.

			if (bi1.dataLength == 1 && bi1.data[0] == 0)
			return (new BigInteger());

			BigInteger result = new BigInteger(bi1);

			// 1's complement
			for (int i = 0; i < maxLength; i++)
			result.data[i] = (uint)(~(bi1.data[i]));

			// add one to result of 1's complement
			long val, carry = 1;
			int index = 0;

			while (carry != 0 && index < maxLength)
			{
			val = (long)(result.data[index]);
			val++;

			result.data[index] = (uint)(val & 0xFFFFFFFF);
			carry = val >> 32;

			index++;
			}

			if ((bi1.data[maxLength - 1] & 0x80000000) == (result.data[maxLength - 1] & 0x80000000))
			throw (new ArithmeticException("Overflow in negation.\n"));

			result.dataLength = maxLength;

			while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
			result.dataLength--;
			return result;
			}


			//***********************************************************************
			// Overloading of equality operator
			//***********************************************************************

			public static bool operator ==(BigInteger bi1, BigInteger bi2)
			{
			return bi1.Equals(bi2);
			}


			public static bool operator !=(BigInteger bi1, BigInteger bi2)
			{
			return !(bi1.Equals(bi2));
			}


			public override bool Equals(object o)
			{
			BigInteger bi = (BigInteger)o;

			if (this.dataLength != bi.dataLength)
			return false;

			for (int i = 0; i < this.dataLength; i++)
			{
			if (this.data[i] != bi.data[i])
			return false;
			}
			return true;
			}


			public override int GetHashCode()
			{
			return this.ToString().GetHashCode();
			}


			//***********************************************************************
			// Overloading of inequality operator
			//***********************************************************************

			public static bool operator >(BigInteger bi1, BigInteger bi2)
			{
			int pos = maxLength - 1;

			// bi1 is negative, bi2 is positive
			if ((bi1.data[pos] & 0x80000000) != 0 && (bi2.data[pos] & 0x80000000) == 0)
			return false;

			// bi1 is positive, bi2 is negative
			else if ((bi1.data[pos] & 0x80000000) == 0 && (bi2.data[pos] & 0x80000000) != 0)
			return true;

			// same sign
			int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;
			for (pos = len - 1; pos >= 0 && bi1.data[pos] == bi2.data[pos]; pos--) ;

			if (pos >= 0)
			{
			if (bi1.data[pos] > bi2.data[pos])
			return true;
			return false;
			}
			return false;
			}


			public static bool operator <(BigInteger bi1, BigInteger bi2)
			{
			int pos = maxLength - 1;

			// bi1 is negative, bi2 is positive
			if ((bi1.data[pos] & 0x80000000) != 0 && (bi2.data[pos] & 0x80000000) == 0)
			return true;

			// bi1 is positive, bi2 is negative
			else if ((bi1.data[pos] & 0x80000000) == 0 && (bi2.data[pos] & 0x80000000) != 0)
			return false;

			// same sign
			int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;
			for (pos = len - 1; pos >= 0 && bi1.data[pos] == bi2.data[pos]; pos--) ;

			if (pos >= 0)
			{
			if (bi1.data[pos] < bi2.data[pos])
			return true;
			return false;
			}
			return false;
			}


			public static bool operator >=(BigInteger bi1, BigInteger bi2)
			{
			return (bi1 == bi2 \|\| bi1 > bi2);
			}


			public static bool operator <=(BigInteger bi1, BigInteger bi2)
			{
			return (bi1 == bi2 \|\| bi1 < bi2);
			}


			//***********************************************************************
			// Private function that supports the division of two numbers with
			// a divisor that has more than 1 digit.
			//
			// Algorithm taken from [1]
			//***********************************************************************

			private static void multiByteDivide(BigInteger bi1, BigInteger bi2,
			BigInteger outQuotient, BigInteger outRemainder)
			{
			uint[] result = new uint[maxLength];

			int remainderLen = bi1.dataLength + 1;
			uint[] remainder = new uint[remainderLen];

			uint mask = 0x80000000;
			uint val = bi2.data[bi2.dataLength - 1];
			int shift = 0, resultPos = 0;

			while (mask != 0 && (val & mask) == 0)
			{
			shift++; mask >>= 1;
			}

			//Console.WriteLine("shift = {0}", shift);
			//Console.WriteLine("Before bi1 Len = {0}, bi2 Len = {1}", bi1.dataLength, bi2.dataLength);

			for (int i = 0; i < bi1.dataLength; i++)
			remainder[i] = bi1.data[i];
			shiftLeft(remainder, shift);
			bi2 = bi2 << shift;

			/*
			Console.WriteLine("bi1 Len = {0}, bi2 Len = {1}", bi1.dataLength, bi2.dataLength);
			Console.WriteLine("dividend = " + bi1 + "\ndivisor = " + bi2);
			for(int q = remainderLen - 1; q >= 0; q--)
			Console.Write("{0:x2}", remainder[q]);
			Console.WriteLine();
			*/

			int j = remainderLen - bi2.dataLength;
			int pos = remainderLen - 1;

			ulong firstDivisorByte = bi2.data[bi2.dataLength - 1];
			ulong secondDivisorByte = bi2.data[bi2.dataLength - 2];

			int divisorLen = bi2.dataLength + 1;
			uint[] dividendPart = new uint[divisorLen];

			while (j > 0)
			{
			ulong dividend = ((ulong)remainder[pos] << 32) + (ulong)remainder[pos - 1];
			//Console.WriteLine("dividend = {0}", dividend);

			ulong q_hat = dividend / firstDivisorByte;
			ulong r_hat = dividend % firstDivisorByte;

			//Console.WriteLine("q_hat = {0:X}, r_hat = {1:X}", q_hat, r_hat);

			bool done = false;
			while (!done)
			{
			done = true;

			if (q_hat == 0x100000000 \|\|
			(q_hat * secondDivisorByte) > ((r_hat << 32) + remainder[pos - 2]))
			{
			q_hat--;
			r_hat += firstDivisorByte;

			if (r_hat < 0x100000000)
			done = false;
			}
			}

			for (int h = 0; h < divisorLen; h++)
			dividendPart[h] = remainder[pos - h];

			BigInteger kk = new BigInteger(dividendPart);
			BigInteger ss = bi2 * (long)q_hat;

			//Console.WriteLine("ss before = " + ss);
			while (ss > kk)
			{
			q_hat--;
			ss -= bi2;
			//Console.WriteLine(ss);
			}
			BigInteger yy = kk - ss;

			//Console.WriteLine("ss = " + ss);
			//Console.WriteLine("kk = " + kk);
			//Console.WriteLine("yy = " + yy);

			for (int h = 0; h < divisorLen; h++)
			remainder[pos - h] = yy.data[bi2.dataLength - h];

			/*
			Console.WriteLine("dividend = ");
			for(int q = remainderLen - 1; q >= 0; q--)
			Console.Write("{0:x2}", remainder[q]);
			Console.WriteLine("\n************ q_hat = {0:X}\n", q_hat);
			*/

			result[resultPos++] = (uint)q_hat;

			pos--;
			j--;
			}

			outQuotient.dataLength = resultPos;
			int y = 0;
			for (int x = outQuotient.dataLength - 1; x >= 0; x--, y++)
			outQuotient.data[y] = result[x];
			for (; y < maxLength; y++)
			outQuotient.data[y] = 0;

			while (outQuotient.dataLength > 1 && outQuotient.data[outQuotient.dataLength - 1] == 0)
			outQuotient.dataLength--;

			if (outQuotient.dataLength == 0)
			outQuotient.dataLength = 1;

			outRemainder.dataLength = shiftRight(remainder, shift);

			for (y = 0; y < outRemainder.dataLength; y++)
			outRemainder.data[y] = remainder[y];
			for (; y < maxLength; y++)
			outRemainder.data[y] = 0;
			}


			//***********************************************************************
			// Private function that supports the division of two numbers with
			// a divisor that has only 1 digit.
			//***********************************************************************

			private static void singleByteDivide(BigInteger bi1, BigInteger bi2,
			BigInteger outQuotient, BigInteger outRemainder)
			{
			uint[] result = new uint[maxLength];
			int resultPos = 0;

			// copy dividend to reminder
			for (int i = 0; i < maxLength; i++)
			outRemainder.data[i] = bi1.data[i];
			outRemainder.dataLength = bi1.dataLength;

			while (outRemainder.dataLength > 1 && outRemainder.data[outRemainder.dataLength - 1] == 0)
			outRemainder.dataLength--;

			ulong divisor = (ulong)bi2.data[0];
			int pos = outRemainder.dataLength - 1;
			ulong dividend = (ulong)outRemainder.data[pos];

			//Console.WriteLine("divisor = " + divisor + " dividend = " + dividend);
			//Console.WriteLine("divisor = " + bi2 + "\ndividend = " + bi1);

			if (dividend >= divisor)
			{
			ulong quotient = dividend / divisor;
			result[resultPos++] = (uint)quotient;

			outRemainder.data[pos] = (uint)(dividend % divisor);
			}
			pos--;

			while (pos >= 0)
			{
			//Console.WriteLine(pos);

			dividend = ((ulong)outRemainder.data[pos + 1] << 32) + (ulong)outRemainder.data[pos];
			ulong quotient = dividend / divisor;
			result[resultPos++] = (uint)quotient;

			outRemainder.data[pos + 1] = 0;
			outRemainder.data[pos--] = (uint)(dividend % divisor);
			//Console.WriteLine(">>>> " + bi1);
			}

			outQuotient.dataLength = resultPos;
			int j = 0;
			for (int i = outQuotient.dataLength - 1; i >= 0; i--, j++)
			outQuotient.data[j] = result[i];
			for (; j < maxLength; j++)
			outQuotient.data[j] = 0;

			while (outQuotient.dataLength > 1 && outQuotient.data[outQuotient.dataLength - 1] == 0)
			outQuotient.dataLength--;

			if (outQuotient.dataLength == 0)
			outQuotient.dataLength = 1;

			while (outRemainder.dataLength > 1 && outRemainder.data[outRemainder.dataLength - 1] == 0)
			outRemainder.dataLength--;
			}


			//***********************************************************************
			// Overloading of division operator
			//***********************************************************************

			public static BigInteger operator /(BigInteger bi1, BigInteger bi2)
			{
			BigInteger quotient = new BigInteger();
			BigInteger remainder = new BigInteger();

			int lastPos = maxLength - 1;
			bool divisorNeg = false, dividendNeg = false;

			if ((bi1.data[lastPos] & 0x80000000) != 0) // bi1 negative
			{
			bi1 = -bi1;
			dividendNeg = true;
			}
			if ((bi2.data[lastPos] & 0x80000000) != 0) // bi2 negative
			{
			bi2 = -bi2;
			divisorNeg = true;
			}

			if (bi1 < bi2)
			{
			return quotient;
			}

			else
			{
			if (bi2.dataLength == 1)
			singleByteDivide(bi1, bi2, quotient, remainder);
			else
			multiByteDivide(bi1, bi2, quotient, remainder);

			if (dividendNeg != divisorNeg)
			return -quotient;

			return quotient;
			}
			}


			//***********************************************************************
			// Overloading of modulus operator
			//***********************************************************************

			public static BigInteger operator %(BigInteger bi1, BigInteger bi2)
			{
			BigInteger quotient = new BigInteger();
			BigInteger remainder = new BigInteger(bi1);

			int lastPos = maxLength - 1;
			bool dividendNeg = false;

			if ((bi1.data[lastPos] & 0x80000000) != 0) // bi1 negative
			{
			bi1 = -bi1;
			dividendNeg = true;
			}
			if ((bi2.data[lastPos] & 0x80000000) != 0) // bi2 negative
			bi2 = -bi2;

			if (bi1 < bi2)
			{
			return remainder;
			}

			else
			{
			if (bi2.dataLength == 1)
			singleByteDivide(bi1, bi2, quotient, remainder);
			else
			multiByteDivide(bi1, bi2, quotient, remainder);

			if (dividendNeg)
			return -remainder;

			return remainder;
			}
			}


			//***********************************************************************
			// Overloading of bitwise AND operator
			//***********************************************************************

			public static BigInteger operator &(BigInteger bi1, BigInteger bi2)
			{
			BigInteger result = new BigInteger();

			int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;

			for (int i = 0; i < len; i++)
			{
			uint sum = (uint)(bi1.data[i] & bi2.data[i]);
			result.data[i] = sum;
			}

			result.dataLength = maxLength;

			while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
			result.dataLength--;

			return result;
			}


			//***********************************************************************
			// Overloading of bitwise OR operator
			//***********************************************************************

			public static BigInteger operator \|(BigInteger bi1, BigInteger bi2)
			{
			BigInteger result = new BigInteger();

			int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;

			for (int i = 0; i < len; i++)
			{
			uint sum = (uint)(bi1.data[i] \| bi2.data[i]);
			result.data[i] = sum;
			}

			result.dataLength = maxLength;

			while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
			result.dataLength--;

			return result;
			}


			//***********************************************************************
			// Overloading of bitwise XOR operator
			//***********************************************************************

			public static BigInteger operator ^(BigInteger bi1, BigInteger bi2)
			{
			BigInteger result = new BigInteger();

			int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;

			for (int i = 0; i < len; i++)
			{
			uint sum = (uint)(bi1.data[i] ^ bi2.data[i]);
			result.data[i] = sum;
			}

			result.dataLength = maxLength;

			while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
			result.dataLength--;

			return result;
			}


			//***********************************************************************
			// Returns max(this, bi)
			//***********************************************************************

			public BigInteger max(BigInteger bi)
			{
			if (this > bi)
			return (new BigInteger(this));
			else
			return (new BigInteger(bi));
			}


			//***********************************************************************
			// Returns min(this, bi)
			//***********************************************************************

			public BigInteger min(BigInteger bi)
			{
			if (this < bi)
			return (new BigInteger(this));
			else
			return (new BigInteger(bi));

			}


			//***********************************************************************
			// Returns the absolute value
			//***********************************************************************

			public BigInteger abs()
			{
			if ((this.data[maxLength - 1] & 0x80000000) != 0)
			return (-this);
			else
			return (new BigInteger(this));
			}


			//***********************************************************************
			// Returns a string representing the BigInteger in base 10.
			//***********************************************************************

			public override string ToString()
			{
			return ToString(10);
			}


			//***********************************************************************
			// Returns a string representing the BigInteger in sign-and-magnitude
			// format in the specified radix.
			//
			// Example
			// -------
			// If the value of BigInteger is -255 in base 10, then
			// ToString(16) returns "-FF"
			//
			//***********************************************************************

			public string ToString(int radix)
			{
			if (radix < 2 \|\| radix > 36)
			throw (new ArgumentException("Radix must be >= 2 and <= 36"));

			string charSet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
			string result = "";

			BigInteger a = this;

			bool negative = false;
			if ((a.data[maxLength - 1] & 0x80000000) != 0)
			{
			negative = true;
			try
			{
			a = -a;
			}
			catch (Exception) { }
			}

			BigInteger quotient = new BigInteger();
			BigInteger remainder = new BigInteger();
			BigInteger biRadix = new BigInteger(radix);

			if (a.dataLength == 1 && a.data[0] == 0)
			result = "0";
			else
			{
			while (a.dataLength > 1 \|\| (a.dataLength == 1 && a.data[0] != 0))
			{
			singleByteDivide(a, biRadix, quotient, remainder);

			if (remainder.data[0] < 10)
			result = remainder.data[0] + result;
			else
			result = charSet[(int)remainder.data[0] - 10] + result;

			a = quotient;
			}
			if (negative)
			result = "-" + result;
			}

			return result;
			}


			//***********************************************************************
			// Returns a hex string showing the contains of the BigInteger
			//
			// Examples
			// -------
			// 1) If the value of BigInteger is 255 in base 10, then
			// ToHexString() returns "FF"
			//
			// 2) If the value of BigInteger is -255 in base 10, then
			// ToHexString() returns ".....FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF01",
			// which is the 2's complement representation of -255.
			//
			//***********************************************************************

			public string ToHexString()
			{
			string result = data[dataLength - 1].ToString("X");

			for (int i = dataLength - 2; i >= 0; i--)
			{
			result += data[i].ToString("X8");
			}

			return result;
			}



			//***********************************************************************
			// Modulo Exponentiation
			//***********************************************************************

			public BigInteger modPow(BigInteger exp, BigInteger n)
			{
			if ((exp.data[maxLength - 1] & 0x80000000) != 0)
			throw (new ArithmeticException("Positive exponents only."));

			BigInteger resultNum = 1;
			BigInteger tempNum;
			bool thisNegative = false;

			if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative this
			{
			tempNum = -this % n;
			thisNegative = true;
			}
			else
			tempNum = this % n; // ensures (tempNum * tempNum) < b^(2k)

			if ((n.data[maxLength - 1] & 0x80000000) != 0) // negative n
			n = -n;

			// calculate constant = b^(2k) / m
			BigInteger constant = new BigInteger();

			int i = n.dataLength << 1;
			constant.data[i] = 0x00000001;
			constant.dataLength = i + 1;

			constant = constant / n;
			int totalBits = exp.bitCount();
			int count = 0;

			// perform squaring and multiply exponentiation
			for (int pos = 0; pos < exp.dataLength; pos++)
			{
			uint mask = 0x01;
			//Console.WriteLine("pos = " + pos);

			for (int index = 0; index < 32; index++)
			{
			if ((exp.data[pos] & mask) != 0)
			resultNum = BarrettReduction(resultNum * tempNum, n, constant);

			mask <<= 1;

			tempNum = BarrettReduction(tempNum * tempNum, n, constant);


			if (tempNum.dataLength == 1 && tempNum.data[0] == 1)
			{
			if (thisNegative && (exp.data[0] & 0x1) != 0) //odd exp
			return -resultNum;
			return resultNum;
			}
			count++;
			if (count == totalBits)
			break;
			}
			}

			if (thisNegative && (exp.data[0] & 0x1) != 0) //odd exp
			return -resultNum;

			return resultNum;
			}



			//***********************************************************************
			// Fast calculation of modular reduction using Barrett's reduction.
			// Requires x < b^(2k), where b is the base. In this case, base is
			// 2^32 (uint).
			//
			// Reference [4]
			//***********************************************************************

			private BigInteger BarrettReduction(BigInteger x, BigInteger n, BigInteger constant)
			{
			int k = n.dataLength,
			kPlusOne = k + 1,
			kMinusOne = k - 1;

			BigInteger q1 = new BigInteger();

			// q1 = x / b^(k-1)
			for (int i = kMinusOne, j = 0; i < x.dataLength; i++, j++)
			q1.data[j] = x.data[i];
			q1.dataLength = x.dataLength - kMinusOne;
			if (q1.dataLength <= 0)
			q1.dataLength = 1;


			BigInteger q2 = q1 * constant;
			BigInteger q3 = new BigInteger();

			// q3 = q2 / b^(k+1)
			for (int i = kPlusOne, j = 0; i < q2.dataLength; i++, j++)
			q3.data[j] = q2.data[i];
			q3.dataLength = q2.dataLength - kPlusOne;
			if (q3.dataLength <= 0)
			q3.dataLength = 1;


			// r1 = x mod b^(k+1)
			// i.e. keep the lowest (k+1) words
			BigInteger r1 = new BigInteger();
			int lengthToCopy = (x.dataLength > kPlusOne) ? kPlusOne : x.dataLength;
			for (int i = 0; i < lengthToCopy; i++)
			r1.data[i] = x.data[i];
			r1.dataLength = lengthToCopy;


			// r2 = (q3 * n) mod b^(k+1)
			// partial multiplication of q3 and n

			BigInteger r2 = new BigInteger();
			for (int i = 0; i < q3.dataLength; i++)
			{
			if (q3.data[i] == 0) continue;

			ulong mcarry = 0;
			int t = i;
			for (int j = 0; j < n.dataLength && t < kPlusOne; j++, t++)
			{
			// t = i + j
			ulong val = ((ulong)q3.data[i] * (ulong)n.data[j]) +
			(ulong)r2.data[t] + mcarry;

			r2.data[t] = (uint)(val & 0xFFFFFFFF);
			mcarry = (val >> 32);
			}

			if (t < kPlusOne)
			r2.data[t] = (uint)mcarry;
			}
			r2.dataLength = kPlusOne;
			while (r2.dataLength > 1 && r2.data[r2.dataLength - 1] == 0)
			r2.dataLength--;

			r1 -= r2;
			if ((r1.data[maxLength - 1] & 0x80000000) != 0) // negative
			{
			BigInteger val = new BigInteger();
			val.data[kPlusOne] = 0x00000001;
			val.dataLength = kPlusOne + 1;
			r1 += val;
			}

			while (r1 >= n)
			r1 -= n;

			return r1;
			}


			//***********************************************************************
			// Returns gcd(this, bi)
			//***********************************************************************

			public BigInteger gcd(BigInteger bi)
			{
			BigInteger x;
			BigInteger y;

			if ((data[maxLength - 1] & 0x80000000) != 0) // negative
			x = -this;
			else
			x = this;

			if ((bi.data[maxLength - 1] & 0x80000000) != 0) // negative
			y = -bi;
			else
			y = bi;

			BigInteger g = y;

			while (x.dataLength > 1 \|\| (x.dataLength == 1 && x.data[0] != 0))
			{
			g = x;
			x = y % x;
			y = g;
			}

			return g;
			}


			//***********************************************************************
			// Populates "this" with the specified amount of random bits
			//***********************************************************************

			public void genRandomBits(int bits, Random rand)
			{
			int dwords = bits >> 5;
			int remBits = bits & 0x1F;

			if (remBits != 0)
			dwords++;

			if (dwords > maxLength)
			throw (new ArithmeticException("Number of required bits > maxLength."));

			for (int i = 0; i < dwords; i++)
			data[i] = (uint)(rand.NextDouble() * 0x100000000);

			for (int i = dwords; i < maxLength; i++)
			data[i] = 0;

			if (remBits != 0)
			{
			uint mask = (uint)(0x01 << (remBits - 1));
			data[dwords - 1] \|= mask;

			mask = (uint)(0xFFFFFFFF >> (32 - remBits));
			data[dwords - 1] &= mask;
			}
			else
			data[dwords - 1] \|= 0x80000000;

			dataLength = dwords;

			if (dataLength == 0)
			dataLength = 1;
			}


			//***********************************************************************
			// Returns the position of the most significant bit in the BigInteger.
			//
			// Eg. The result is 0, if the value of BigInteger is 0...0000 0000
			// The result is 1, if the value of BigInteger is 0...0000 0001
			// The result is 2, if the value of BigInteger is 0...0000 0010
			// The result is 2, if the value of BigInteger is 0...0000 0011
			//
			//***********************************************************************

			public int bitCount()
			{
			while (dataLength > 1 && data[dataLength - 1] == 0)
			dataLength--;

			uint value = data[dataLength - 1];
			uint mask = 0x80000000;
			int bits = 32;

			while (bits > 0 && (value & mask) == 0)
			{
			bits--;
			mask >>= 1;
			}
			bits += ((dataLength - 1) << 5);

			return bits;
			}


			//***********************************************************************
			// Probabilistic prime test based on Fermat's little theorem
			//
			// for any a < p (p does not divide a) if
			// a^(p-1) mod p != 1 then p is not prime.
			//
			// Otherwise, p is probably prime (pseudoprime to the chosen base).
			//
			// Returns
			// -------
			// True if "this" is a pseudoprime to randomly chosen
			// bases. The number of chosen bases is given by the "confidence"
			// parameter.
			//
			// False if "this" is definitely NOT prime.
			//
			// Note - this method is fast but fails for Carmichael numbers except
			// when the randomly chosen base is a factor of the number.
			//
			//***********************************************************************

			public bool FermatLittleTest(int confidence)
			{
			BigInteger thisVal;
			if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative
			thisVal = -this;
			else
			thisVal = this;

			if (thisVal.dataLength == 1)
			{
			// test small numbers
			if (thisVal.data[0] == 0 \|\| thisVal.data[0] == 1)
			return false;
			else if (thisVal.data[0] == 2 \|\| thisVal.data[0] == 3)
			return true;
			}

			if ((thisVal.data[0] & 0x1) == 0) // even numbers
			return false;

			int bits = thisVal.bitCount();
			BigInteger a = new BigInteger();
			BigInteger p_sub1 = thisVal - (new BigInteger(1));
			Random rand = new Random();

			for (int round = 0; round < confidence; round++)
			{
			bool done = false;

			while (!done) // generate a < n
			{
			int testBits = 0;

			// make sure "a" has at least 2 bits
			while (testBits < 2)
			testBits = (int)(rand.NextDouble() * bits);

			a.genRandomBits(testBits, rand);

			int byteLen = a.dataLength;

			// make sure "a" is not 0
			if (byteLen > 1 \|\| (byteLen == 1 && a.data[0] != 1))
			done = true;
			}

			// check whether a factor exists (fix for version 1.03)
			BigInteger gcdTest = a.gcd(thisVal);
			if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1)
			return false;

			// calculate a^(p-1) mod p
			BigInteger expResult = a.modPow(p_sub1, thisVal);

			int resultLen = expResult.dataLength;

			// is NOT prime is a^(p-1) mod p != 1

			if (resultLen > 1 \|\| (resultLen == 1 && expResult.data[0] != 1))
			{
			//Console.WriteLine("a = " + a.ToString());
			return false;
			}
			}

			return true;
			}


			//***********************************************************************
			// Probabilistic prime test based on Rabin-Miller's
			//
			// for any p > 0 with p - 1 = 2^s * t
			//
			// p is probably prime (strong pseudoprime) if for any a < p,
			// 1) a^t mod p = 1 or
			// 2) a^((2^j)*t) mod p = p-1 for some 0 <= j <= s-1
			//
			// Otherwise, p is composite.
			//
			// Returns
			// -------
			// True if "this" is a strong pseudoprime to randomly chosen
			// bases. The number of chosen bases is given by the "confidence"
			// parameter.
			//
			// False if "this" is definitely NOT prime.
			//
			//***********************************************************************

			public bool RabinMillerTest(int confidence)
			{
			BigInteger thisVal;
			if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative
			thisVal = -this;
			else
			thisVal = this;

			if (thisVal.dataLength == 1)
			{
			// test small numbers
			if (thisVal.data[0] == 0 \|\| thisVal.data[0] == 1)
			return false;
			else if (thisVal.data[0] == 2 \|\| thisVal.data[0] == 3)
			return true;
			}

			if ((thisVal.data[0] & 0x1) == 0) // even numbers
			return false;


			// calculate values of s and t
			BigInteger p_sub1 = thisVal - (new BigInteger(1));
			int s = 0;

			for (int index = 0; index < p_sub1.dataLength; index++)
			{
			uint mask = 0x01;

			for (int i = 0; i < 32; i++)
			{
			if ((p_sub1.data[index] & mask) != 0)
			{
			index = p_sub1.dataLength; // to break the outer loop
			break;
			}
			mask <<= 1;
			s++;
			}
			}

			BigInteger t = p_sub1 >> s;

			int bits = thisVal.bitCount();
			BigInteger a = new BigInteger();
			Random rand = new Random();

			for (int round = 0; round < confidence; round++)
			{
			bool done = false;

			while (!done) // generate a < n
			{
			int testBits = 0;

			// make sure "a" has at least 2 bits
			while (testBits < 2)
			testBits = (int)(rand.NextDouble() * bits);

			a.genRandomBits(testBits, rand);

			int byteLen = a.dataLength;

			// make sure "a" is not 0
			if (byteLen > 1 \|\| (byteLen == 1 && a.data[0] != 1))
			done = true;
			}

			// check whether a factor exists (fix for version 1.03)
			BigInteger gcdTest = a.gcd(thisVal);
			if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1)
			return false;

			BigInteger b = a.modPow(t, thisVal);

			/*
			Console.WriteLine("a = " + a.ToString(10));
			Console.WriteLine("b = " + b.ToString(10));
			Console.WriteLine("t = " + t.ToString(10));
			Console.WriteLine("s = " + s);
			*/

			bool result = false;

			if (b.dataLength == 1 && b.data[0] == 1) // a^t mod p = 1
			result = true;

			for (int j = 0; result == false && j < s; j++)
			{
			if (b == p_sub1) // a^((2^j)*t) mod p = p-1 for some 0 <= j <= s-1
			{
			result = true;
			break;
			}

			b = (b * b) % thisVal;
			}

			if (result == false)
			return false;
			}
			return true;
			}


			//***********************************************************************
			// Probabilistic prime test based on Solovay-Strassen (Euler Criterion)
			//
			// p is probably prime if for any a < p (a is not multiple of p),
			// a^((p-1)/2) mod p = J(a, p)
			//
			// where J is the Jacobi symbol.
			//
			// Otherwise, p is composite.
			//
			// Returns
			// -------
			// True if "this" is a Euler pseudoprime to randomly chosen
			// bases. The number of chosen bases is given by the "confidence"
			// parameter.
			//
			// False if "this" is definitely NOT prime.
			//
			//***********************************************************************

			public bool SolovayStrassenTest(int confidence)
			{
			BigInteger thisVal;
			if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative
			thisVal = -this;
			else
			thisVal = this;

			if (thisVal.dataLength == 1)
			{
			// test small numbers
			if (thisVal.data[0] == 0 \|\| thisVal.data[0] == 1)
			return false;
			else if (thisVal.data[0] == 2 \|\| thisVal.data[0] == 3)
			return true;
			}

			if ((thisVal.data[0] & 0x1) == 0) // even numbers
			return false;


			int bits = thisVal.bitCount();
			BigInteger a = new BigInteger();
			BigInteger p_sub1 = thisVal - 1;
			BigInteger p_sub1_shift = p_sub1 >> 1;

			Random rand = new Random();

			for (int round = 0; round < confidence; round++)
			{
			bool done = false;

			while (!done) // generate a < n
			{
			int testBits = 0;

			// make sure "a" has at least 2 bits
			while (testBits < 2)
			testBits = (int)(rand.NextDouble() * bits);

			a.genRandomBits(testBits, rand);

			int byteLen = a.dataLength;

			// make sure "a" is not 0
			if (byteLen > 1 \|\| (byteLen == 1 && a.data[0] != 1))
			done = true;
			}

			// check whether a factor exists (fix for version 1.03)
			BigInteger gcdTest = a.gcd(thisVal);
			if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1)
			return false;

			// calculate a^((p-1)/2) mod p

			BigInteger expResult = a.modPow(p_sub1_shift, thisVal);
			if (expResult == p_sub1)
			expResult = -1;

			// calculate Jacobi symbol
			BigInteger jacob = Jacobi(a, thisVal);

			//Console.WriteLine("a = " + a.ToString(10) + " b = " + thisVal.ToString(10));
			//Console.WriteLine("expResult = " + expResult.ToString(10) + " Jacob = " + jacob.ToString(10));

			// if they are different then it is not prime
			if (expResult != jacob)
			return false;
			}

			return true;
			}


			//***********************************************************************
			// Implementation of the Lucas Strong Pseudo Prime test.
			//
			// Let n be an odd number with gcd(n,D) = 1, and n - J(D, n) = 2^s * d
			// with d odd and s >= 0.
			//
			// If Ud mod n = 0 or V2^r*d mod n = 0 for some 0 <= r < s, then n
			// is a strong Lucas pseudoprime with parameters (P, Q). We select
			// P and Q based on Selfridge.
			//
			// Returns True if number is a strong Lucus pseudo prime.
			// Otherwise, returns False indicating that number is composite.
			//***********************************************************************

			public bool LucasStrongTest()
			{
			BigInteger thisVal;
			if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative
			thisVal = -this;
			else
			thisVal = this;

			if (thisVal.dataLength == 1)
			{
			// test small numbers
			if (thisVal.data[0] == 0 \|\| thisVal.data[0] == 1)
			return false;
			else if (thisVal.data[0] == 2 \|\| thisVal.data[0] == 3)
			return true;
			}

			if ((thisVal.data[0] & 0x1) == 0) // even numbers
			return false;

			return LucasStrongTestHelper(thisVal);
			}


			private bool LucasStrongTestHelper(BigInteger thisVal)
			{
			// Do the test (selects D based on Selfridge)
			// Let D be the first element of the sequence
			// 5, -7, 9, -11, 13, ... for which J(D,n) = -1
			// Let P = 1, Q = (1-D) / 4

			long D = 5, sign = -1, dCount = 0;
			bool done = false;

			while (!done)
			{
			int Jresult = BigInteger.Jacobi(D, thisVal);

			if (Jresult == -1)
			done = true; // J(D, this) = 1
			else
			{
			if (Jresult == 0 && Math.Abs(D) < thisVal) // divisor found
			return false;

			if (dCount == 20)
			{
			// check for square
			BigInteger root = thisVal.sqrt();
			if (root * root == thisVal)
			return false;
			}

			//Console.WriteLine(D);
			D = (Math.Abs(D) + 2) * sign;
			sign = -sign;
			}
			dCount++;
			}

			long Q = (1 - D) >> 2;

			/*
			Console.WriteLine("D = " + D);
			Console.WriteLine("Q = " + Q);
			Console.WriteLine("(n,D) = " + thisVal.gcd(D));
			Console.WriteLine("(n,Q) = " + thisVal.gcd(Q));
			Console.WriteLine("J(D\|n) = " + BigInteger.Jacobi(D, thisVal));
			*/

			BigInteger p_add1 = thisVal + 1;
			int s = 0;

			for (int index = 0; index < p_add1.dataLength; index++)
			{
			uint mask = 0x01;

			for (int i = 0; i < 32; i++)
			{
			if ((p_add1.data[index] & mask) != 0)
			{
			index = p_add1.dataLength; // to break the outer loop
			break;
			}
			mask <<= 1;
			s++;
			}
			}

			BigInteger t = p_add1 >> s;

			// calculate constant = b^(2k) / m
			// for Barrett Reduction
			BigInteger constant = new BigInteger();

			int nLen = thisVal.dataLength << 1;
			constant.data[nLen] = 0x00000001;
			constant.dataLength = nLen + 1;

			constant = constant / thisVal;

			BigInteger[] lucas = LucasSequenceHelper(1, Q, t, thisVal, constant, 0);
			bool isPrime = false;

			if ((lucas[0].dataLength == 1 && lucas[0].data[0] == 0) \|\|
			(lucas[1].dataLength == 1 && lucas[1].data[0] == 0))
			{
			// u(t) = 0 or V(t) = 0
			isPrime = true;
			}

			for (int i = 1; i < s; i++)
			{
			if (!isPrime)
			{
			// doubling of index
			lucas[1] = thisVal.BarrettReduction(lucas[1] * lucas[1], thisVal, constant);
			lucas[1] = (lucas[1] - (lucas[2] << 1)) % thisVal;

			//lucas[1] = ((lucas[1] * lucas[1]) - (lucas[2] << 1)) % thisVal;

			if ((lucas[1].dataLength == 1 && lucas[1].data[0] == 0))
			isPrime = true;
			}

			lucas[2] = thisVal.BarrettReduction(lucas[2] * lucas[2], thisVal, constant); //Q^k
			}


			if (isPrime) // additional checks for composite numbers
			{
			// If n is prime and gcd(n, Q) == 1, then
			// Q^((n+1)/2) = Q * Q^((n-1)/2) is congruent to (Q * J(Q, n)) mod n

			BigInteger g = thisVal.gcd(Q);
			if (g.dataLength == 1 && g.data[0] == 1) // gcd(this, Q) == 1
			{
			if ((lucas[2].data[maxLength - 1] & 0x80000000) != 0)
			lucas[2] += thisVal;

			BigInteger temp = (Q * BigInteger.Jacobi(Q, thisVal)) % thisVal;
			if ((temp.data[maxLength - 1] & 0x80000000) != 0)
			temp += thisVal;

			if (lucas[2] != temp)
			isPrime = false;
			}
			}

			return isPrime;
			}


			//***********************************************************************
			// Determines whether a number is probably prime, using the Rabin-Miller's
			// test. Before applying the test, the number is tested for divisibility
			// by primes < 2000
			//
			// Returns true if number is probably prime.
			//***********************************************************************

			public bool isProbablePrime(int confidence)
			{
			BigInteger thisVal;
			if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative
			thisVal = -this;
			else
			thisVal = this;


			// test for divisibility by primes < 2000
			for (int p = 0; p < primesBelow2000.Length; p++)
			{
			BigInteger divisor = primesBelow2000[p];

			if (divisor >= thisVal)
			break;

			BigInteger resultNum = thisVal % divisor;
			if (resultNum.IntValue() == 0)
			{
			/*
			Console.WriteLine("Not prime! Divisible by {0}\n",
			primesBelow2000[p]);
			*/
			return false;
			}
			}

			if (thisVal.RabinMillerTest(confidence))
			return true;
			else
			{
			//Console.WriteLine("Not prime! Failed primality test\n");
			return false;
			}
			}


			//***********************************************************************
			// Determines whether this BigInteger is probably prime using a
			// combination of base 2 strong pseudoprime test and Lucas strong
			// pseudoprime test.
			//
			// The sequence of the primality test is as follows,
			//
			// 1) Trial divisions are carried out using prime numbers below 2000.
			// if any of the primes divides this BigInteger, then it is not prime.
			//
			// 2) Perform base 2 strong pseudoprime test. If this BigInteger is a
			// base 2 strong pseudoprime, proceed on to the next step.
			//
			// 3) Perform strong Lucas pseudoprime test.
			//
			// Returns True if this BigInteger is both a base 2 strong pseudoprime
			// and a strong Lucas pseudoprime.
			//
			// For a detailed discussion of this primality test, see [6].
			//
			//***********************************************************************

			public bool isProbablePrime()
			{
			BigInteger thisVal;
			if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative
			thisVal = -this;
			else
			thisVal = this;

			if (thisVal.dataLength == 1)
			{
			// test small numbers
			if (thisVal.data[0] == 0 \|\| thisVal.data[0] == 1)
			return false;
			else if (thisVal.data[0] == 2 \|\| thisVal.data[0] == 3)
			return true;
			}

			if ((thisVal.data[0] & 0x1) == 0) // even numbers
			return false;


			// test for divisibility by primes < 2000
			for (int p = 0; p < primesBelow2000.Length; p++)
			{
			BigInteger divisor = primesBelow2000[p];

			if (divisor >= thisVal)
			break;

			BigInteger resultNum = thisVal % divisor;
			if (resultNum.IntValue() == 0)
			{
			//Console.WriteLine("Not prime! Divisible by {0}\n",
			// primesBelow2000[p]);

			return false;
			}
			}

			// Perform BASE 2 Rabin-Miller Test

			// calculate values of s and t
			BigInteger p_sub1 = thisVal - (new BigInteger(1));
			int s = 0;

			for (int index = 0; index < p_sub1.dataLength; index++)
			{
			uint mask = 0x01;

			for (int i = 0; i < 32; i++)
			{
			if ((p_sub1.data[index] & mask) != 0)
			{
			index = p_sub1.dataLength; // to break the outer loop
			break;
			}
			mask <<= 1;
			s++;
			}
			}

			BigInteger t = p_sub1 >> s;

			int bits = thisVal.bitCount();
			BigInteger a = 2;

			// b = a^t mod p
			BigInteger b = a.modPow(t, thisVal);
			bool result = false;

			if (b.dataLength == 1 && b.data[0] == 1) // a^t mod p = 1
			result = true;

			for (int j = 0; result == false && j < s; j++)
			{
			if (b == p_sub1) // a^((2^j)*t) mod p = p-1 for some 0 <= j <= s-1
			{
			result = true;
			break;
			}

			b = (b * b) % thisVal;
			}

			// if number is strong pseudoprime to base 2, then do a strong lucas test
			if (result)
			result = LucasStrongTestHelper(thisVal);

			return result;
			}



			//***********************************************************************
			// Returns the lowest 4 bytes of the BigInteger as an int.
			//***********************************************************************

			public int IntValue()
			{
			return (int)data[0];
			}


			//***********************************************************************
			// Returns the lowest 8 bytes of the BigInteger as a long.
			//***********************************************************************

			public long LongValue()
			{
			long val = 0;

			val = (long)data[0];
			try
			{ // exception if maxLength = 1
			val \|= (long)data[1] << 32;
			}
			catch (Exception)
			{
			if ((data[0] & 0x80000000) != 0) // negative
			val = (int)data[0];
			}

			return val;
			}


			//***********************************************************************
			// Computes the Jacobi Symbol for a and b.
			// Algorithm adapted from [3] and [4] with some optimizations
			//***********************************************************************

			public static int Jacobi(BigInteger a, BigInteger b)
			{
			// Jacobi defined only for odd integers
			if ((b.data[0] & 0x1) == 0)
			throw (new ArgumentException("Jacobi defined only for odd integers."));

			if (a >= b) a %= b;
			if (a.dataLength == 1 && a.data[0] == 0) return 0; // a == 0
			if (a.dataLength == 1 && a.data[0] == 1) return 1; // a == 1

			if (a < 0)
			{
			if ((((b - 1).data[0]) & 0x2) == 0) //if( (((b-1) >> 1).data[0] & 0x1) == 0)
			return Jacobi(-a, b);
			else
			return -Jacobi(-a, b);
			}

			int e = 0;
			for (int index = 0; index < a.dataLength; index++)
			{
			uint mask = 0x01;

			for (int i = 0; i < 32; i++)
			{
			if ((a.data[index] & mask) != 0)
			{
			index = a.dataLength; // to break the outer loop
			break;
			}
			mask <<= 1;
			e++;
			}
			}

			BigInteger a1 = a >> e;

			int s = 1;
			if ((e & 0x1) != 0 && ((b.data[0] & 0x7) == 3 \|\| (b.data[0] & 0x7) == 5))
			s = -1;

			if ((b.data[0] & 0x3) == 3 && (a1.data[0] & 0x3) == 3)
			s = -s;

			if (a1.dataLength == 1 && a1.data[0] == 1)
			return s;
			else
			return (s * Jacobi(b % a1, a1));
			}



			//***********************************************************************
			// Generates a positive BigInteger that is probably prime.
			//***********************************************************************

			public static BigInteger genPseudoPrime(int bits, int confidence, Random rand)
			{
			BigInteger result = new BigInteger();
			bool done = false;

			while (!done)
			{
			result.genRandomBits(bits, rand);
			result.data[0] \|= 0x01; // make it odd

			// prime test
			done = result.isProbablePrime(confidence);
			}
			return result;
			}


			//***********************************************************************
			// Generates a random number with the specified number of bits such
			// that gcd(number, this) = 1
			//***********************************************************************

			public BigInteger genCoPrime(int bits, Random rand)
			{
			bool done = false;
			BigInteger result = new BigInteger();

			while (!done)
			{
			result.genRandomBits(bits, rand);
			//Console.WriteLine(result.ToString(16));

			// gcd test
			BigInteger g = result.gcd(this);
			if (g.dataLength == 1 && g.data[0] == 1)
			done = true;
			}

			return result;
			}


			//***********************************************************************
			// Returns the modulo inverse of this. Throws ArithmeticException if
			// the inverse does not exist. (i.e. gcd(this, modulus) != 1)
			//***********************************************************************

			public BigInteger modInverse(BigInteger modulus)
			{
			BigInteger[] p = { 0, 1 };
			BigInteger[] q = new BigInteger[2]; // quotients
			BigInteger[] r = { 0, 0 }; // remainders

			int step = 0;

			BigInteger a = modulus;
			BigInteger b = this;

			while (b.dataLength > 1 \|\| (b.dataLength == 1 && b.data[0] != 0))
			{
			BigInteger quotient = new BigInteger();
			BigInteger remainder = new BigInteger();

			if (step > 1)
			{
			BigInteger pval = (p[0] - (p[1] * q[0])) % modulus;
			p[0] = p[1];
			p[1] = pval;
			}

			if (b.dataLength == 1)
			singleByteDivide(a, b, quotient, remainder);
			else
			multiByteDivide(a, b, quotient, remainder);

			/*
			Console.WriteLine(quotient.dataLength);
			Console.WriteLine("{0} = {1}({2}) + {3} p = {4}", a.ToString(10),
			b.ToString(10), quotient.ToString(10), remainder.ToString(10),
			p[1].ToString(10));
			*/

			q[0] = q[1];
			r[0] = r[1];
			q[1] = quotient; r[1] = remainder;

			a = b;
			b = remainder;

			step++;
			}

			if (r[0].dataLength > 1 \|\| (r[0].dataLength == 1 && r[0].data[0] != 1))
			throw (new ArithmeticException("No inverse!"));

			BigInteger result = ((p[0] - (p[1] * q[0])) % modulus);

			if ((result.data[maxLength - 1] & 0x80000000) != 0)
			result += modulus; // get the least positive modulus

			return result;
			}


			//***********************************************************************
			// Returns the value of the BigInteger as a byte array. The lowest
			// index contains the MSB.
			//***********************************************************************

			public byte[] getBytes()
			{
			int numBits = bitCount();

			int numBytes = numBits >> 3;
			if ((numBits & 0x7) != 0)
			numBytes++;

			byte[] result = new byte[numBytes];

			//Console.WriteLine(result.Length);

			int pos = 0;
			uint tempVal, val = data[dataLength - 1];

			if ((tempVal = (val >> 24 & 0xFF)) != 0)
			result[pos++] = (byte)tempVal;
			if ((tempVal = (val >> 16 & 0xFF)) != 0)
			result[pos++] = (byte)tempVal;
			if ((tempVal = (val >> 8 & 0xFF)) != 0)
			result[pos++] = (byte)tempVal;
			if ((tempVal = (val & 0xFF)) != 0)
			result[pos++] = (byte)tempVal;

			for (int i = dataLength - 2; i >= 0; i--, pos += 4)
			{
			val = data[i];
			result[pos + 3] = (byte)(val & 0xFF);
			val >>= 8;
			result[pos + 2] = (byte)(val & 0xFF);
			val >>= 8;
			result[pos + 1] = (byte)(val & 0xFF);
			val >>= 8;
			result[pos] = (byte)(val & 0xFF);
			}

			return result;
			}


			//***********************************************************************
			// Sets the value of the specified bit to 1
			// The Least Significant Bit position is 0.
			//***********************************************************************

			public void setBit(uint bitNum)
			{
			uint bytePos = bitNum >> 5; // divide by 32
			byte bitPos = (byte)(bitNum & 0x1F); // get the lowest 5 bits

			uint mask = (uint)1 << bitPos;
			this.data[bytePos] \|= mask;

			if (bytePos >= this.dataLength)
			this.dataLength = (int)bytePos + 1;
			}


			//***********************************************************************
			// Sets the value of the specified bit to 0
			// The Least Significant Bit position is 0.
			//***********************************************************************

			public void unsetBit(uint bitNum)
			{
			uint bytePos = bitNum >> 5;

			if (bytePos < this.dataLength)
			{
			byte bitPos = (byte)(bitNum & 0x1F);

			uint mask = (uint)1 << bitPos;
			uint mask2 = 0xFFFFFFFF ^ mask;

			this.data[bytePos] &= mask2;

			if (this.dataLength > 1 && this.data[this.dataLength - 1] == 0)
			this.dataLength--;
			}
			}


			//***********************************************************************
			// Returns a value that is equivalent to the integer square root
			// of the BigInteger.
			//
			// The integer square root of "this" is defined as the largest integer n
			// such that (n * n) <= this
			//
			//***********************************************************************

			public BigInteger sqrt()
			{
			uint numBits = (uint)this.bitCount();

			if ((numBits & 0x1) != 0) // odd number of bits
			numBits = (numBits >> 1) + 1;
			else
			numBits = (numBits >> 1);

			uint bytePos = numBits >> 5;
			byte bitPos = (byte)(numBits & 0x1F);

			uint mask;

			BigInteger result = new BigInteger();
			if (bitPos == 0)
			mask = 0x80000000;
			else
			{
			mask = (uint)1 << bitPos;
			bytePos++;
			}
			result.dataLength = (int)bytePos;

			for (int i = (int)bytePos - 1; i >= 0; i--)
			{
			while (mask != 0)
			{
			// guess
			result.data[i] ^= mask;

			// undo the guess if its square is larger than this
			if ((result * result) > this)
			result.data[i] ^= mask;

			mask >>= 1;
			}
			mask = 0x80000000;
			}
			return result;
			}


			//***********************************************************************
			// Returns the k_th number in the Lucas Sequence reduced modulo n.
			//
			// Uses index doubling to speed up the process. For example, to calculate V(k),
			// we maintain two numbers in the sequence V(n) and V(n+1).
			//
			// To obtain V(2n), we use the identity
			// V(2n) = (V(n) * V(n)) - (2 * Q^n)
			// To obtain V(2n+1), we first write it as
			// V(2n+1) = V((n+1) + n)
			// and use the identity
			// V(m+n) = V(m) * V(n) - Q * V(m-n)
			// Hence,
			// V((n+1) + n) = V(n+1) * V(n) - Q^n * V((n+1) - n)
			// = V(n+1) * V(n) - Q^n * V(1)
			// = V(n+1) * V(n) - Q^n * P
			//
			// We use k in its binary expansion and perform index doubling for each
			// bit position. For each bit position that is set, we perform an
			// index doubling followed by an index addition. This means that for V(n),
			// we need to update it to V(2n+1). For V(n+1), we need to update it to
			// V((2n+1)+1) = V(2*(n+1))
			//
			// This function returns
			// [0] = U(k)
			// [1] = V(k)
			// [2] = Q^n
			//
			// Where U(0) = 0 % n, U(1) = 1 % n
			// V(0) = 2 % n, V(1) = P % n
			//***********************************************************************

			public static BigInteger[] LucasSequence(BigInteger P, BigInteger Q,
			BigInteger k, BigInteger n)
			{
			if (k.dataLength == 1 && k.data[0] == 0)
			{
			BigInteger[] result = new BigInteger[3];

			result[0] = 0; result[1] = 2 % n; result[2] = 1 % n;
			return result;
			}

			// calculate constant = b^(2k) / m
			// for Barrett Reduction
			BigInteger constant = new BigInteger();

			int nLen = n.dataLength << 1;
			constant.data[nLen] = 0x00000001;
			constant.dataLength = nLen + 1;

			constant = constant / n;

			// calculate values of s and t
			int s = 0;

			for (int index = 0; index < k.dataLength; index++)
			{
			uint mask = 0x01;

			for (int i = 0; i < 32; i++)
			{
			if ((k.data[index] & mask) != 0)
			{
			index = k.dataLength; // to break the outer loop
			break;
			}
			mask <<= 1;
			s++;
			}
			}

			BigInteger t = k >> s;

			//Console.WriteLine("s = " + s + " t = " + t);
			return LucasSequenceHelper(P, Q, t, n, constant, s);
			}


			//***********************************************************************
			// Performs the calculation of the kth term in the Lucas Sequence.
			// For details of the algorithm, see reference [9].
			//
			// k must be odd. i.e LSB == 1
			//***********************************************************************

			private static BigInteger[] LucasSequenceHelper(BigInteger P, BigInteger Q,
			BigInteger k, BigInteger n,
			BigInteger constant, int s)
			{
			BigInteger[] result = new BigInteger[3];

			if ((k.data[0] & 0x00000001) == 0)
			throw (new ArgumentException("Argument k must be odd."));

			int numbits = k.bitCount();
			uint mask = (uint)0x1 << ((numbits & 0x1F) - 1);

			// v = v0, v1 = v1, u1 = u1, Q_k = Q^0

			BigInteger v = 2 % n, Q_k = 1 % n,
			v1 = P % n, u1 = Q_k;
			bool flag = true;

			for (int i = k.dataLength - 1; i >= 0; i--) // iterate on the binary expansion of k
			{
			//Console.WriteLine("round");
			while (mask != 0)
			{
			if (i == 0 && mask == 0x00000001) // last bit
			break;

			if ((k.data[i] & mask) != 0) // bit is set
			{
			// index doubling with addition

			u1 = (u1 * v1) % n;

			v = ((v * v1) - (P * Q_k)) % n;
			v1 = n.BarrettReduction(v1 * v1, n, constant);
			v1 = (v1 - ((Q_k * Q) << 1)) % n;

			if (flag)
			flag = false;
			else
			Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);

			Q_k = (Q_k * Q) % n;
			}
			else
			{
			// index doubling
			u1 = ((u1 * v) - Q_k) % n;

			v1 = ((v * v1) - (P * Q_k)) % n;
			v = n.BarrettReduction(v * v, n, constant);
			v = (v - (Q_k << 1)) % n;

			if (flag)
			{
			Q_k = Q % n;
			flag = false;
			}
			else
			Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
			}

			mask >>= 1;
			}
			mask = 0x80000000;
			}

			// at this point u1 = u(n+1) and v = v(n)
			// since the last bit always 1, we need to transform u1 to u(2n+1) and v to v(2n+1)

			u1 = ((u1 * v) - Q_k) % n;
			v = ((v * v1) - (P * Q_k)) % n;
			if (flag)
			flag = false;
			else
			Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);

			Q_k = (Q_k * Q) % n;


			for (int i = 0; i < s; i++)
			{
			// index doubling
			u1 = (u1 * v) % n;
			v = ((v * v) - (Q_k << 1)) % n;

			if (flag)
			{
			Q_k = Q % n;
			flag = false;
			}
			else
			Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
			}

			result[0] = u1;
			result[1] = v;
			result[2] = Q_k;

			return result;
			}


			//***********************************************************************
			// Tests the correct implementation of the /, %, * and + operators
			//***********************************************************************

			public static void MulDivTest(int rounds)
			{
			Random rand = new Random();
			byte[] val = new byte[64];
			byte[] val2 = new byte[64];

			for (int count = 0; count < rounds; count++)
			{
			// generate 2 numbers of random length
			int t1 = 0;
			while (t1 == 0)
			t1 = (int)(rand.NextDouble() * 65);

			int t2 = 0;
			while (t2 == 0)
			t2 = (int)(rand.NextDouble() * 65);

			bool done = false;
			while (!done)
			{
			for (int i = 0; i < 64; i++)
			{
			if (i < t1)
			val[i] = (byte)(rand.NextDouble() * 256);
			else
			val[i] = 0;

			if (val[i] != 0)
			done = true;
			}
			}

			done = false;
			while (!done)
			{
			for (int i = 0; i < 64; i++)
			{
			if (i < t2)
			val2[i] = (byte)(rand.NextDouble() * 256);
			else
			val2[i] = 0;

			if (val2[i] != 0)
			done = true;
			}
			}

			while (val[0] == 0)
			val[0] = (byte)(rand.NextDouble() * 256);
			while (val2[0] == 0)
			val2[0] = (byte)(rand.NextDouble() * 256);

			Console.WriteLine(count);
			BigInteger bn1 = new BigInteger(val, t1);
			BigInteger bn2 = new BigInteger(val2, t2);


			// Determine the quotient and remainder by dividing
			// the first number by the second.

			BigInteger bn3 = bn1 / bn2;
			BigInteger bn4 = bn1 % bn2;

			// Recalculate the number
			BigInteger bn5 = (bn3 * bn2) + bn4;

			// Make sure they're the same
			if (bn5 != bn1)
			{
			Console.WriteLine("Error at " + count);
			Console.WriteLine(bn1 + "\n");
			Console.WriteLine(bn2 + "\n");
			Console.WriteLine(bn3 + "\n");
			Console.WriteLine(bn4 + "\n");
			Console.WriteLine(bn5 + "\n");
			return;
			}
			}
			}


			//***********************************************************************
			// Tests the correct implementation of the modulo exponential function
			// using RSA encryption and decryption (using pre-computed encryption and
			// decryption keys).
			//***********************************************************************

			public static void RSATest(int rounds)
			{
			Random rand = new Random(1);
			byte[] val = new byte[64];

			// private and public key
			BigInteger bi_e = new BigInteger("a932b948feed4fb2b692609bd22164fc9edb59fae7880cc1eaff7b3c9626b7e5b241c27a974833b2622ebe09beb451917663d47232488f23a117fc97720f1e7", 16);
			BigInteger bi_d = new BigInteger("4adf2f7a89da93248509347d2ae506d683dd3a16357e859a980c4f77a4e2f7a01fae289f13a851df6e9db5adaa60bfd2b162bbbe31f7c8f828261a6839311929d2cef4f864dde65e556ce43c89bbbf9f1ac5511315847ce9cc8dc92470a747b8792d6a83b0092d2e5ebaf852c85cacf34278efa99160f2f8aa7ee7214de07b7", 16);
			BigInteger bi_n = new BigInteger("e8e77781f36a7b3188d711c2190b560f205a52391b3479cdb99fa010745cbeba5f2adc08e1de6bf38398a0487c4a73610d94ec36f17f3f46ad75e17bc1adfec99839589f45f95ccc94cb2a5c500b477eb3323d8cfab0c8458c96f0147a45d27e45a4d11d54d77684f65d48f15fafcc1ba208e71e921b9bd9017c16a5231af7f", 16);

			Console.WriteLine("e =\n" + bi_e.ToString(10));
			Console.WriteLine("\nd =\n" + bi_d.ToString(10));
			Console.WriteLine("\nn =\n" + bi_n.ToString(10) + "\n");

			for (int count = 0; count < rounds; count++)
			{
			// generate data of random length
			int t1 = 0;
			while (t1 == 0)
			t1 = (int)(rand.NextDouble() * 65);

			bool done = false;
			while (!done)
			{
			for (int i = 0; i < 64; i++)
			{
			if (i < t1)
			val[i] = (byte)(rand.NextDouble() * 256);
			else
			val[i] = 0;

			if (val[i] != 0)
			done = true;
			}
			}

			while (val[0] == 0)
			val[0] = (byte)(rand.NextDouble() * 256);

			Console.Write("Round = " + count);

			// encrypt and decrypt data
			BigInteger bi_data = new BigInteger(val, t1);
			BigInteger bi_encrypted = bi_data.modPow(bi_e, bi_n);
			BigInteger bi_decrypted = bi_encrypted.modPow(bi_d, bi_n);

			// compare
			if (bi_decrypted != bi_data)
			{
			Console.WriteLine("\nError at round " + count);
			Console.WriteLine(bi_data + "\n");
			return;
			}
			Console.WriteLine(" <PASSED>.");
			}

			}


			//***********************************************************************
			// Tests the correct implementation of the modulo exponential and
			// inverse modulo functions using RSA encryption and decryption. The two
			// pseudoprimes p and q are fixed, but the two RSA keys are generated
			// for each round of testing.
			//***********************************************************************

			public static void RSATest2(int rounds)
			{
			Random rand = new Random();
			byte[] val = new byte[64];

			byte[] pseudoPrime1 = {
			(byte)0x85, (byte)0x84, (byte)0x64, (byte)0xFD, (byte)0x70, (byte)0x6A,
			(byte)0x9F, (byte)0xF0, (byte)0x94, (byte)0x0C, (byte)0x3E, (byte)0x2C,
			(byte)0x74, (byte)0x34, (byte)0x05, (byte)0xC9, (byte)0x55, (byte)0xB3,
			(byte)0x85, (byte)0x32, (byte)0x98, (byte)0x71, (byte)0xF9, (byte)0x41,
			(byte)0x21, (byte)0x5F, (byte)0x02, (byte)0x9E, (byte)0xEA, (byte)0x56,
			(byte)0x8D, (byte)0x8C, (byte)0x44, (byte)0xCC, (byte)0xEE, (byte)0xEE,
			(byte)0x3D, (byte)0x2C, (byte)0x9D, (byte)0x2C, (byte)0x12, (byte)0x41,
			(byte)0x1E, (byte)0xF1, (byte)0xC5, (byte)0x32, (byte)0xC3, (byte)0xAA,
			(byte)0x31, (byte)0x4A, (byte)0x52, (byte)0xD8, (byte)0xE8, (byte)0xAF,
			(byte)0x42, (byte)0xF4, (byte)0x72, (byte)0xA1, (byte)0x2A, (byte)0x0D,
			(byte)0x97, (byte)0xB1, (byte)0x31, (byte)0xB3,
			};

			byte[] pseudoPrime2 = {
			(byte)0x99, (byte)0x98, (byte)0xCA, (byte)0xB8, (byte)0x5E, (byte)0xD7,
			(byte)0xE5, (byte)0xDC, (byte)0x28, (byte)0x5C, (byte)0x6F, (byte)0x0E,
			(byte)0x15, (byte)0x09, (byte)0x59, (byte)0x6E, (byte)0x84, (byte)0xF3,
			(byte)0x81, (byte)0xCD, (byte)0xDE, (byte)0x42, (byte)0xDC, (byte)0x93,
			(byte)0xC2, (byte)0x7A, (byte)0x62, (byte)0xAC, (byte)0x6C, (byte)0xAF,
			(byte)0xDE, (byte)0x74, (byte)0xE3, (byte)0xCB, (byte)0x60, (byte)0x20,
			(byte)0x38, (byte)0x9C, (byte)0x21, (byte)0xC3, (byte)0xDC, (byte)0xC8,
			(byte)0xA2, (byte)0x4D, (byte)0xC6, (byte)0x2A, (byte)0x35, (byte)0x7F,
			(byte)0xF3, (byte)0xA9, (byte)0xE8, (byte)0x1D, (byte)0x7B, (byte)0x2C,
			(byte)0x78, (byte)0xFA, (byte)0xB8, (byte)0x02, (byte)0x55, (byte)0x80,
			(byte)0x9B, (byte)0xC2, (byte)0xA5, (byte)0xCB,
			};


			BigInteger bi_p = new BigInteger(pseudoPrime1);
			BigInteger bi_q = new BigInteger(pseudoPrime2);
			BigInteger bi_pq = (bi_p - 1) * (bi_q - 1);
			BigInteger bi_n = bi_p * bi_q;

			for (int count = 0; count < rounds; count++)
			{
			// generate private and public key
			BigInteger bi_e = bi_pq.genCoPrime(512, rand);
			BigInteger bi_d = bi_e.modInverse(bi_pq);

			Console.WriteLine("\ne =\n" + bi_e.ToString(10));
			Console.WriteLine("\nd =\n" + bi_d.ToString(10));
			Console.WriteLine("\nn =\n" + bi_n.ToString(10) + "\n");

			// generate data of random length
			int t1 = 0;
			while (t1 == 0)
			t1 = (int)(rand.NextDouble() * 65);

			bool done = false;
			while (!done)
			{
			for (int i = 0; i < 64; i++)
			{
			if (i < t1)
			val[i] = (byte)(rand.NextDouble() * 256);
			else
			val[i] = 0;

			if (val[i] != 0)
			done = true;
			}
			}

			while (val[0] == 0)
			val[0] = (byte)(rand.NextDouble() * 256);

			Console.Write("Round = " + count);

			// encrypt and decrypt data
			BigInteger bi_data = new BigInteger(val, t1);
			BigInteger bi_encrypted = bi_data.modPow(bi_e, bi_n);
			BigInteger bi_decrypted = bi_encrypted.modPow(bi_d, bi_n);

			// compare
			if (bi_decrypted != bi_data)
			{
			Console.WriteLine("\nError at round " + count);
			Console.WriteLine(bi_data + "\n");
			return;
			}
			Console.WriteLine(" <PASSED>.");
			}

			}


			//***********************************************************************
			// Tests the correct implementation of sqrt() method.
			//***********************************************************************

			public static void SqrtTest(int rounds)
			{
			Random rand = new Random();
			for (int count = 0; count < rounds; count++)
			{
			// generate data of random length
			int t1 = 0;
			while (t1 == 0)
			t1 = (int)(rand.NextDouble() * 1024);

			Console.Write("Round = " + count);

			BigInteger a = new BigInteger();
			a.genRandomBits(t1, rand);

			BigInteger b = a.sqrt();
			BigInteger c = (b + 1) * (b + 1);

			// check that b is the largest integer such that b*b <= a
			if (c <= a)
			{
			Console.WriteLine("\nError at round " + count);
			Console.WriteLine(a + "\n");
			return;
			}
			Console.WriteLine(" <PASSED>.");
			}
			}
			}
			}