public bool Fermat(Int64 n, Int64 accuracy = 100)
{
if (n < 1)
{
throw new ArgumentException("The number must be natural");
}
if (n == 1 || n == 2)
{
return(true);
}
Random rnd = new Random();
bool isPrime = true;
for (Int64 i = 0; i < accuracy; ++i)
{
Int64 a = rnd.Next(2, (int)n);
if ((BinaryMath.Gcd(n, a) != 1 && !(BinaryMath.Gcd(n, a) == n)) ||
BinaryMath.PowByModulo(a, n - 1, n) != 1)
{
isPrime = false;
break;
}
}
return(isPrime);
}
public bool SolovayStrassen(Int64 n, Int64 accuracy = 1)
{
if (n < 1)
{
throw new ArgumentException("The number must be natural");
}
if (n == 1 || n == 2)
{
return(true);
}
Random rnd = new Random();
bool isPrime = true;
for (Int64 i = 1; i <= accuracy; ++i)
{
Int64 a = rnd.Next(2, (int)n + 1);
long lez = SymbolLegendre.Calculate(a, n);
if (lez == -1)
{
lez += n;
}
if (BinaryMath.Gcd(a, n) > 1 || BinaryMath.PowByModulo(a, (n - 1) / 2, n) % n != lez)
{
isPrime = false;
break;
}
}
return(isPrime);
}
public bool MillerRabin(Int64 n, Int64 accuracy = 100)
{
if (n < 1)
{
throw new ArgumentException("The number must be natural");
}
if (n == 1 || n == 2)
{
return(true);
}
if (n % 2 == 0)
{
return(false);
}
Tuple <Int64, Int64> tAnds = FindT(n);
Random rnd = new Random();
for (Int64 i = 1; i <= accuracy; ++i)
{
Int64 a = rnd.Next(2, (int)n - 2);
Int64 x = BinaryMath.PowByModulo(a, tAnds.Item1, n);
if (x == 1 || x == n - 1)
{
continue;
}
bool isCont = false;
for (Int64 j = 0; j < tAnds.Item2 - 1; ++j)
{
x = (x * x) % n;
if (x == 1)
{
return(false);
}
if (x == n - 1)
{
isCont = true;
}
}
if (isCont)
{
continue;
}
return(false);
}
return(true);
}
