public bool IsPrime(PrimeType N, int accuracy)
{
var NMinus1 = N - 1;
if ((NMinus1 % 6 != 0) && ((N + 1) % 6 != 0))
{
return(false);
}
var factors = Power2Factorizer.Factorize(NMinus1);
var witnesses = WitnessProvider.GetRandomWitnesses(N, accuracy);
for (var i = 0; i < accuracy; i++)
{
var a = witnesses[i];
var x = BigInteger.ModPow(a, factors.d, N);
if (x == 1 || x == NMinus1)
{
continue;
}
for (var r = 1; r < factors.s; r++)
{
x = BigInteger.ModPow(x, 2, N);
if (x == NMinus1)
{
break;
}
}
if (x != NMinus1)
{
return(false);
}
}
return(true);
}
public static int[] GetWitnesses(PrimeType N)
{
foreach (var aSet in witnesses)
{
if (N < aSet.Key)
{
return(aSet.Value);
}
}
throw new ArgumentOutOfRangeException(nameof(N));
}
public static Factorization Factorize(PrimeType evenNumber)
{
int s = 0;
var d = evenNumber;
do
{
s++;
d >>= 1; //d /= 2;
} while ((d & 1) == 0); //(d % 2 == 0);
return(new Factorization(s, d));
}
public static int[] GetRandomWitnesses(PrimeType N, int k)
{
var rand = new Random();
var max = N - 1 > int.MaxValue ? int.MaxValue : (int)(N - 1);
var a = new int[k];
for (var i = 0; i < k; i++)
{
a[i] = rand.Next(2, max);
}
return(a);
}
public List <int> EratosthenesList(int size)
{
List <int> result = new List <int>();
PrimeType[] types = Eratosthenes(size);
for (int i = 0, l = types.Length; i < l; i++)
{
PrimeType type = types[i];
if (PrimeType.Prim == type)
{
result.Add(i + 1);
}
}
return(result);
}
public bool IsPrime(PrimeType N)
{
var factors = Power2Factorizer.Factorize(N - 1);
var witnesses = WitnessProvider.GetWitnesses(N);
foreach (var a in witnesses)
{
var rSet = Enumerable.Range(0, factors.s).ToList();
if (rSet.All(r =>
BigInteger.ModPow(a, ((PrimeType)Math.Pow(2, r)) * factors.d, N) != N - 1 &&
BigInteger.ModPow(a, factors.d, N) != 1))
{
return(false);
}
}
return(true);
}
private static void PrintResult(PrimeType[] types)
{
for (int i = 0, l = types.Length; i < l; i++)
{
PrimeType type = types[i];
int num = i + 1;
if (0 < i && i % 10 == 0) {
Console.Write("\r\n");
}
if (PrimeType.NotPrim == type)
{
Console.Write("_ ");
}
else
{
Console.Write(num.ToString() + " ");
}
}
}
public PrimeType[] Eratosthenes(int size)
{
PrimeType[] result = new PrimeType[size];
for (int i = 1; i < size; i++)
{
int number = i + 1;
if (number * number <= size)
{
for (int j = i + 1; j < size; j++)
{
int nextNumber = j + 1;
if (nextNumber % number == 0)
{
result[j] = PrimeType.NotPrim;
}
}
}
}
return(result);
}
private static void PrintResult(PrimeType[] types)
{
for (int i = 0, l = types.Length; i < l; i++)
{
PrimeType type = types[i];
int num = i + 1;
if (0 < i && i % 10 == 0)
{
Console.Write("\r\n");
}
if (PrimeType.NotPrim == type)
{
Console.Write("_ ");
}
else
{
Console.Write(num.ToString() + " ");
}
}
}
public PrimeType[] Eratosthenes(int size)
{
PrimeType[] result = new PrimeType[size];
for (int i = 1; i < size; i++)
{
int number = i + 1;
if (number * number <= size)
{
for (int j = i + 1; j < size; j++)
{
int nextNumber = j + 1;
if (nextNumber % number == 0)
{
result[j] = PrimeType.NotPrim;
}
}
}
}
return result;
}
public Factorization(int s, PrimeType d)
{
this.s = s;
this.d = d;
}
