public static bool Fermat(long n)
{
if (n <= 1 || n == 4)
{
return(false);
}
if (n <= 3)
{
return(true);
}
var random = new Random();
for (int i = 0; i < FermatIterationCount; i++)
{
var m = random.Next(2, n - 2);
if (GCD.EuclidNaive(n, m) != 1)
{
return(false);
}
if (Exponentiation.Pow(m, n - 1, n) != 1)
{
return(false);
}
}
return(true);
}
/// <summary>
/// Karatsuba is a fast multiplication algorithm
/// </summary>
public static long Karatsuba(long x, long y)
{
if (x < KaratsubaMinValue || y < KaratsubaMinValue)
{
return(x * y);
}
var n = Math.Max(GetSize(x), GetSize(y));
var m = (n / 2) + (n % 2);
var k = Exponentiation.BinExp(10, m);
var a = (x / k);
var b = (x % k);
var c = (y / k);
var d = (y % k);
var z0 = Karatsuba(a, c);
var z1 = Karatsuba(b, d);
var z2 = Karatsuba(a + b, c + d);
return((Exponentiation.BinExp(10, m * 2) * z0) + z1 + ((z2 - z1 - z0) * k));
}