public IEnumerable <BigInteger> PrimeFactorsByRationalSieve(BigInteger value, BigInteger bound)
{
if (IsPrimeByMillerRabin(value, 10))
{
return new[] { value }
}
;
var primes = PrimesByAtkin(bound);
var suitablePrimes = primes.Where(m => value % m == 0);
if (suitablePrimes.Any())
{
var product = suitablePrimes.Aggregate(BigInteger.One, (accumulator, current) => accumulator * current);
return(suitablePrimes.Union(this.PrimeFactorsByRationalSieve(value / product, bound)));
}
var zValues = new Dictionary <BigInteger, List <List <int> > >();
for (int i = 1; i < value && zValues.Count < (primes.Count + 3); i++)
{
if (!IsBSmooth(i, bound) || !IsBSmooth(i + value, bound))
{
continue;
}
var leftList = new List <int>(primes.Count);
var rightList = new List <int>(primes.Count);
foreach (var prime in primes)
{
var exponent = 1;
while (i % BigInteger.Pow(prime, exponent) == 0)
{
exponent += 1;
}
leftList.Add(exponent - 1);
exponent = 1;
while ((i + value) % BigInteger.Pow(prime, exponent) == 0)
{
exponent += 1;
}
rightList.Add(exponent - 1);
}
zValues.Add(i, new List <List <int> > {
leftList, rightList
});
}
if (zValues.Any() == false)
{
return(suitablePrimes);
}
var allEvens = zValues.Values.FirstOrDefault(m => m[0].All(n => n % 2 == 0) && m[1].All(n => n % 2 == 0));
if (allEvens == null)
{
for (int i = 0; i < zValues.Count && allEvens == null; i++)
{
for (int n = i + 1; n < zValues.Count && allEvens == null; n++)
{
var leftList = new List <int>(primes.Count);
var rightList = new List <int>(primes.Count);
for (int j = 0; j < primes.Count; j++)
{
var leftAddition = zValues.ElementAt(i).Value[0][j] + zValues.ElementAt(n).Value[0][j];
var rightAddition = zValues.ElementAt(i).Value[1][j] + zValues.ElementAt(n).Value[1][j];
if (leftAddition == rightAddition)
{
leftList.Add(0);
rightList.Add(0);
}
else
{
leftList.Add(leftAddition);
rightList.Add(rightAddition);
}
}
if (leftList.All(m => m % 2 == 0) && rightList.All(m => m % 2 == 0))
{
allEvens = new List <List <int> > {
leftList, rightList
}
}
;
}
}
}
var leftProduct = BigInteger.One;
var rightProduct = BigInteger.One;
for (int i = 0; i < primes.Count; i++)
{
leftProduct *= BigInteger.Pow(primes.ElementAt(i), allEvens[0][i]);
rightProduct *= BigInteger.Pow(primes.ElementAt(i), allEvens[1][i]);
}
var leftSquare = MathHelpers.Sqrt(leftProduct);
var rightSquare = MathHelpers.Sqrt(rightProduct);
return(suitablePrimes.Union(new[] { GreatestCommonFactor(Math.Abs((int)leftSquare - (int)rightSquare), value), GreatestCommonFactor((int)leftSquare + (int)rightSquare, value) }));
}
/// <summary>
/// Calculates the sum of the digits of the number 2^1000
/// </summary>
static void P016()
{
Console.WriteLine((from i in (BigInteger.Pow(2, 1000)).ToString() select(int) Char.GetNumericValue(i)).Sum());
}
/// <summary>
/// Calculates the number of n-digit positive integers which are also an nth power
/// </summary>
static void P063()
{
Console.WriteLine((from i in Enumerable.Range(1, 9)
select(from j in Enumerable.Range(1, 25)
where BigInteger.Pow(i, j).ToString().Length == j select 1).Count()).Sum());
}
