C # Sieve method to find all prime numbers in the range

Popular Science article: Sieve method is a simple method of verifying prime numbers. It is said that the ancient Greek Eratosthenes (Eratosthenes, about 274-194 BC) invented, also known as Eratosthenes sieve method (Sieve of Eratosthenes).

To tell the truth, before I was in the case of the prime is to verify whether a number is a prime, with the definition of the easy to come to the conclusion, the code is as follows:

:Public static BOOLIsPrime (intN) by : {//Determine if n is a prime number :     if(n < 2)return False; Note:      for(inti = n-1; i > 1; i--)    To : {//n divided by each of the natural numbers smaller than n 1 large :         if(n% i = = 0): {//If it is divisible, it is not a prime number :             return False; : } Ten: }//Otherwise it is prime       number one:return True; : }

But in this way, if you require all prime numbers between two numbers x and y, you need to use a loop to determine:

 1:  for   ( int  i = x; i < y; i++)  { 3:   if   (IsPrime (i))  { 5:   console  6: }
7: }  

Today's book of books by chance saw that the Sieve method may be more appropriate to deal with such problems--to find all prime numbers within a certain limit:

:private static List<int> Genprime (intj) by : {:     List<int> Ints=NewList<int> (); Note:      BitArraybts=NewBitArray(j+1); To :      for(intx = 2; x < BTS. LENGTH/2; x + +): {:          for(inty = x + 1; y < BTS. Length; y++): {:             if(bts[y] = =false&& y% x = = 0)            Ten: {One: bts[y] =true; : } : } : } :      for(intx = 2; x < BTS. Length; x + +): {:         if(bts[x] = =false): {: ints. ADD (x); : } : } :     returnints; : }

However, if a range of prime numbers is required, a difference of two ranges is required:

1:   List < int > Listresult = Genprime (x). Except (Genprime (y)). ToList ();

Then in another master's blog found a linear sieve algorithm, I changed it to C # code:

:private staticList<int> GenPrime1 (intx) by : {:     intnum_prime = 0; Note:     List<int> ints =NewList<int> (); To :     BitArrayIsnotprime =NewBitArray(x); :      for(inti = 2; i < x; i++)    : {:         if(!isnotprime[i]): {: ints. ADD (i); One : num_prime++;       : } :          for(intj = 0; J < num_prime && I * ints[j] < X; j + +)        : {: isnotprime[i * ints[j]] =true; :             if(!Convert. ToBoolean (i% ints[j])) :                  Break; : } : } :     returnints; : }

Transfer to original post: General Sieve method for prime number + fast linear sieve method

PS. The first time to write a blog, if there is insufficient place please tell me, I must change!

C # Sieve method to find all prime numbers in the range