//Uses a strong probable prime test with base two
public static bool IsBaseTwoStrongProbablePrime(long n)
{
long s = 0;
long d = n;
for (long testS = 0; testS < Math.Log(n, 2); testS++) //O(log(n))
{
for (long testD = 1; testD < n; testD += 2) //O(n) (check to see what limit must be here)
{
if (n - 1 == Math.Pow(2, testS) * testD) //n = d*2^s + 1
{
s = testS;
d = testD;
}
}
}
if (PrimeCalculatorUtilities.PowerModulo(2, d, n) == PrimeCalculatorUtilities.PowerModulo(1, 1, n)) //O(log n)
{
return(true);
}
for (long r = 0; r < s; r++) //O(s - 1) == O(log(n))
{
long power = d * (long)Math.Pow(2, r);
if (PrimeCalculatorUtilities.PowerModulo(2, power, n) == PrimeCalculatorUtilities.PowerModulo(-1, 1, n))
{
return(true);
}
}
return(false);
}
public static long CalculateJacobiSymbol(long a, long b)
{
if (b <= 0 || (PrimeCalculatorUtilities.Modulo(b, 2)) == 0)
{
return(0);
}
long j = 1;
if (a < 0)
{
a = -a;
if (PrimeCalculatorUtilities.Modulo(b, 4) == 3)
{
j = -j;
}
}
while (a != 0)
{
while ((PrimeCalculatorUtilities.Modulo(a, 2) == 0))
{
a = a / 2;
if ((PrimeCalculatorUtilities.Modulo(b, 8)) == 3 || (PrimeCalculatorUtilities.Modulo(b, 8)) == 5)
{
j = -j;
}
}
long temp = a;
a = b;
b = temp;
if ((PrimeCalculatorUtilities.Modulo(a, 4)) == 3 && (PrimeCalculatorUtilities.Modulo(b, 4)) == 3)
{
j = -j;
}
a = PrimeCalculatorUtilities.Modulo(a, b);
}
if (b == 1)
{
return(j);
}
else
{
return(0);
}
}