public static bool Lucas(ulong n)
{
var random = new System.Random();
var factorisation = Factorise.Optimised(n - 1);
for (ulong a = 2; a < n;)
{
c:
if (GCD.Standard(a, n) > 1)
{
return(false);
}
if (Power.BinaryMod(a, n - 1, n) == 1)
{
foreach (uint prime in factorisation)
{
if (Power.BinaryMod(a, (n - 1) / prime, n) == 1)
{
a++;
goto c;
}
}
return(true);
}
else
{
return(false);
}
}
return(false);
}
/// <summary>
///
/// </summary>
/// <param name="n"></param>
/// <param name="iterations"></param>
/// <returns>true if n is prime, false if n is possibly composite</returns>
public static bool Lucas(ulong n, ulong iterations)
{
ulong[] factorisation = Factorise.Optimised(n - 1);
for (ulong i = 0; i < iterations; i++)
{
c:
ulong a = (ulong)random.Next(2, (int)n);
if (GCD.Standard(a, n) > 1)
{
return(false);
}
if (Power.BinaryMod(a, n - 1, n) == 1)
{
foreach (uint prime in factorisation)
{
if (Power.BinaryMod(a, (n - 1) / prime, n) == 1)
{
goto c;
}
}
return(true);
}
else
{
return(false);
}
}
return(false);
}
public static bool Pocklington(ulong n)
{
ulong[] primes = Sieve.Standard((ulong)System.Math.Log(n - 1)).Cast <ulong>().ToArray();
ulong f = n - 1, sqrt = (ulong)System.Math.Sqrt(n);
foreach (ulong prime in primes)
{
if (f / prime < sqrt)
{
goto g;
}
while (f % prime == 0)
{
if (f / prime < sqrt)
{
goto g;
}
f /= prime;
}
}
g:
var factors = Factorise.Standard(f, (z) => (ulong)Factoring.Special.TrialDivision((int)z));
for (uint i = 2; i < n; i++)
{
if (Power.BinaryMod(i, n - 1, n) == 1)
{
bool isPrime = true;
foreach (uint factor in factors)
{
if (GCD.Standard((uint)Power.Binary(i, (n - 1) / factor) - 1, n) != 1)
{
isPrime = false;
break;
}
}
if (isPrime)
{
return(true);
}
}
}
return(false);
}