Questions tagged [sieve-theory]

Sieve theory deals with number theoretic sieves, and sifted sets. E.g. the Sieve of Eratosthenes, Brun sieve, and other modern sieves.

289 questions
3
votes
0 answers

Question on Brun's Work

In Brun's Pure Sieve (using standard sieve theory notation), Brun showed that $$S(A,P,z)=A-\sum_{p\leq z}A_p+\sum_{p_1
2
votes
1 answer

Selberg Sieve Question

The following question uses standard sieve theory terminology. Let $A=\vert\{a_n: a_n=n(n-2); n\in[N/2,N]\}\vert$ and let $A_d=\vert\{a_n: d\vert a_n\}\vert$. If we are looking for $S^T$ the number of $a_n$ in $A$ such that $a_n$ has no prime…
2
votes
1 answer

Connection between Brun's Sieve and the Sieve of Eratosthenes

I have read in a couple of places that the above mentioned sieves are connected in some way. In particular, Brun's Sieve builds upon that of Eratosthenes. I do not see why this is the case and hope someone could explain the connection
1
vote
0 answers

On the error term of Legendre sieve

the Legendre sieve method gives us an upper bound $S$ for the numbers that are not relatively prime to $P_{z}$ up to $x$ where $P_{z}$ is the product of prime number less than z $S=x\prod_{p
Abdo
  • 167