09/09/2014, 01:10 AM

Consider all the primes between 1 and 100.

Call them p_i.

If we want to count the primes between 100 and 10000 then we sieve that interval with 0 mod p_i.

But what happens if say we sieve 7 mod p_i ?

( 7 mod 2 => 1 mod 2 , 7 mod 3 => 1 mod 3 , 7 mod 5 => 2 mod 5 , 7 mod 7 => 0 mod 7 , 7 mod 11 , ... )

In general what happens if we sieve a_i mod p_i with 0 < a_i < p_i ?

How do we choose the a_i such that we sieve as many numbers as possible ?

Or how do we choose the a_i such that there are as many numbers left as possible ?

regards

tommy1729

Call them p_i.

If we want to count the primes between 100 and 10000 then we sieve that interval with 0 mod p_i.

But what happens if say we sieve 7 mod p_i ?

( 7 mod 2 => 1 mod 2 , 7 mod 3 => 1 mod 3 , 7 mod 5 => 2 mod 5 , 7 mod 7 => 0 mod 7 , 7 mod 11 , ... )

In general what happens if we sieve a_i mod p_i with 0 < a_i < p_i ?

How do we choose the a_i such that we sieve as many numbers as possible ?

Or how do we choose the a_i such that there are as many numbers left as possible ?

regards

tommy1729