//
// On an HP Z600, It takes about 38 seconds to generate
// the first 150 million primes (about 4 million primes per second)
//
public static UInt32[] GeneratePrimes(UInt32 max, out UInt32 outPrimeCount)
{
if (max == UInt32.MaxValue)
{
throw new ArgumentOutOfRangeException("max", "max cannot be UInt32.MaxValue");
}
UInt32[] primes = new UInt32[PrimeCount.UpperBound(max)];
UInt32 primeCount;
UInt32 maxSquareRoot = (UInt32)Math.Sqrt(max);
BetterBitArray isComposite = new BetterBitArray((max + 1) >> 1);
primes[0] = 2;
primes[1] = 3;
primeCount = 2;
UInt32 candidatePrime;
UInt32 incrementAmount = 0;
for (candidatePrime = 5; candidatePrime <= maxSquareRoot; candidatePrime += incrementAmount)
{
if (!isComposite.Get(candidatePrime >> 1))
{
//
// Mark all multiples of this prime as composites
//
UInt32 candidatePrimeDoubled = 2 * candidatePrime;
for (UInt32 j = candidatePrime * candidatePrime; j <= max; j += candidatePrimeDoubled)
{
isComposite.Assert(j >> 1);
}
//
// Add to the primes
//
primes[primeCount++] = candidatePrime;
}
incrementAmount = (incrementAmount == 2) ? 4U : 2U;
}
// Add the rest of the primes
for (; candidatePrime <= max; candidatePrime += incrementAmount)
{
if (!isComposite.Get(candidatePrime >> 1))
{
primes[primeCount++] = candidatePrime;
}
incrementAmount = (incrementAmount == 2) ? 4U : 2U;
}
outPrimeCount = primeCount;
return(primes);
}
public static UInt32[] GeneratePrimes(UInt32 max, out UInt32 outPrimeCount)
{
if (max < 5)
{
throw new ArgumentOutOfRangeException("max", "max can't be too small");
}
if (max == UInt32.MaxValue)
{
throw new ArgumentOutOfRangeException("max", "max cannot be UInt32.MaxValue");
}
UInt32[] primes = new UInt32[PrimeCount.UpperBound(max)];
UInt32 primeCount;
UInt32 maxSquareRoot = (UInt32)Math.Sqrt(max);
BetterBitArray isPrime = new BetterBitArray(max + 1);
// put in candidate primes
for (UInt32 i = 1; i <= maxSquareRoot; i++)
{
for (UInt32 j = 1; j <= maxSquareRoot; j++)
{
UInt32 n;
n = 4 * i + j;
//if (n > max) throw new InvalidOperationException();
if (n <= max) // Should always be true for large enough max (maybe take this out0
{
UInt32 nMod12 = n % 12;
if (nMod12 == 1 || nMod12 == 5)
{
isPrime.Flip(n);
}
}
n = 3 * i + j;
//if (n > max) throw new InvalidOperationException();
if (n <= max) // Should always be true for large enough max (maybe take this out0
{
UInt32 nMod12 = n % 12;
if (nMod12 == 7)
{
isPrime.Flip(n);
}
}
if (i > j)
{
n = 3 * i - j;
//if (n > max) throw new InvalidOperationException();
if (n <= max) // Should always be true for large enough max (maybe take this out0
{
UInt32 nMod12 = n % 12;
if (nMod12 == 11)
{
isPrime.Flip(n);
}
}
}
}
}
primes[0] = 2;
primes[1] = 3;
primeCount = 2;
UInt32 candidatePrime;
for (candidatePrime = 5; candidatePrime <= maxSquareRoot; candidatePrime += 2)
{
if (isPrime.Get(candidatePrime))
{
//
// Mark all multiples of its square as composite
//
//
UInt32 candidatePrimeSquared = candidatePrime * candidatePrime;
//UInt32 candidatePrimeSquaredThenDoubled = iSquared * 2;
for (UInt32 j = candidatePrimeSquared; j <= max; j += candidatePrimeSquared)
{
isPrime.Deassert(j);
}
//
// Add to the primes
//
primes[primeCount++] = candidatePrime;
}
}
// Add the rest of the primes
for (; candidatePrime <= max; candidatePrime += 2)
{
if (isPrime.Get(candidatePrime))
{
primes[primeCount++] = candidatePrime;
}
}
outPrimeCount = primeCount;
return(primes);
}